Add the most common matrix decompositions.

CHANGELOG.md

@@ -4,20 +4,89 @@ documented here.
 
 This project adheres to [Semantic Versioning](http://semver.org/).
 
-## [0.13.0] - WIP
+
+## [0.13.0]
+
+### Modified
+  * The trait `Axpy` takes one additional parameter for the type of `x`.
+  * The alias `MatrixNM` is now deprecated. Use `MatrixMN` instead (we
+    reordered M and N to be in alphabetical order).
+
 ### Added
+  * `alga::general::Real` is now re-exported by nalgebra.
+  * `.trace()` that computes the trace of a matrix (the sum of its diagonal
+    elements.)
+  * `::zeros(...)` that creates a matrix filled with zeroes.
+  * `::from_partial_diagonal(...)` that creates a matrix from diagonal elements.
+    The matrix can be rectangular. If not enough elements are provided, the rest
+    of the diagonal is set to 0.
+  * `.conjugate_transpose()` computes the transposed conjugate of a
+    complex matrix.
+  * `.conjugate_transpose_to(...)` computes the transposed conjugate of a
+    complex matrix. The result written into a user-provided matrix.
+  * `.transpose_to(...)` is the same as `.transpose()` but stores the result in
+    the provided matrix.
+  * `.conjugate_transpose_to(...)` is the same as `.conjugate_transpose()` but
+    stores the result in the provided matrix.
+  * Implements `IntoIterator` for `&Matrix`, `&mut Matrix` and `Matrix`.
+  * `.mul_to(...)` multiplies two matrices and stores the result to the given buffer.
+  * `.tr_mul_to(...)` left-multiplies `self.transpose()` to another matrix and stores the result to the given buffer.
+  * `.rows_range(...)` that retrieves a reference to a range of rows.
+  * `.rows_range_mut(...)` that retrieves a mutable reference to a range of rows.
+  * `.columns_range(...)` that retrieves a reference to a range of columns.
+  * `.columns_range_mut(...)` that retrieves a mutable reference to a range of columns.
+  * `.add_scalar(...)` that adds a scalar to each component of a matrix.
+  * `.add_scalar_mut(...)` that adds in-place a scalar to each component of a matrix.
   * `.kronecker(a, b)` computes the kronecker product (i.e. matrix tensor
     product) of two matrices.
-  * `.set_row(i, row)` sets the i-th row of the matrix.
-  * `.set_column(j, column)` sets the i-th column of the matrix.
 
+Matrix decompositions:
+  * Cholesky, SVD, LU, QR, Hessenberg, Schur, Symmetric eigendecompositions,
+    Bidiagonal, Symmetric tridiagonal
+  * Computation of householder reflectors and givens rotations.
+
+Matrix edition:
+  * `.upper_triangle()` extracts the upper triangle of a matrix, including the diagonal.
+  * `.lower_triangle()` extracts the lower triangle of a matrix, including the diagonal.
+  * `.fill(...)` fills the matrix with a single value.
+  * `.fill_with_identity(...)` fills the matrix with the identity.
+  * `.fill_diagonal(...)` fills the matrix diagonal with a single value.
+  * `.fill_row(...)` fills a selected matrix row with a single value.
+  * `.fill_column(...)` fills a selected matrix column with a single value.
+  * `.set_diagonal(...)` sets the matrix diagonal.
+  * `.set_row(...)` sets a selected row.
+  * `.set_column(...)` sets a selected column.
+  * `.fill_lower_triangle(...)` fills some sub-diagonals bellow the main diagonal with a value.
+  * `.fill_upper_triangle(...)` fills some sub-diagonals above the main diagonal with a value.
+  * `.swap_rows(...)` swaps two rows.
+  * `.swap_columns(...)` swaps two columns.
+
+Column removal:
+  * `.remove_column(...)` removes one column.
+  * `.remove_fixed_columns<D>(...)` removes `D` columns.
+  * `.remove_columns(...)` removes a number of columns known at run-time.
+
+Row removal:
+  * `.remove_row(...)` removes one row.
+  * `.remove_fixed_rows<D>(...)` removes `D` rows.
+  * `.remove_rows(...)` removes a number of rows known at run-time.
+
+Column insertion:
+  * `.insert_column(...)` adds one column at the given position.
+  * `.insert_fixed_columns<D>(...)` adds `D` columns at the given position.
+  * `.insert_columns(...)` adds at the given position a number of columns known at run-time.
+
+Row insertion:
+  * `.insert_row(...)` adds one row at the given position.
+  * `.insert_fixed_rows<D>(...)` adds `D` rows at the given position.
+  * `.insert_rows(...)` adds at the given position a number of rows known at run-time.
 
 ## [0.12.0]
 The main change of this release is the update of the dependency serde to 1.0.
 
 ### Added
- * `.trace()` that computes the trace of a matrix (i.e., the sum of its
-   diagonal elements.)
+ * `.trace()` that computes the trace of a matrix (the sum of its diagonal
+   elements.)
 
 ## [0.11.0]
 The [website](http://nalgebra.org) has been fully rewritten and gives a good

Cargo.toml

@@ -18,18 +18,19 @@ path = "src/lib.rs"
 [features]
 arbitrary       = [ "quickcheck" ]
 serde-serialize = [ "serde", "serde_derive", "num-complex/serde" ]
+debug = [ ]
 
 [dependencies]
-typenum         = "1.4"
+typenum        = "1.7"
 generic-array  = "0.8"
 rand           = "0.3"
 num-traits     = "0.1"
 num-complex    = "0.1"
 approx         = "0.1"
 alga           = "0.5"
+matrixmultiply = "0.1"
 serde          = { version = "1.0", optional = true }
 serde_derive   = { version = "1.0", optional = true }
-# clippy = "*"
 
 [dependencies.quickcheck]
 optional = true
@@ -37,3 +38,6 @@ version  = "0.4"
 
 [dev-dependencies]
 serde_json = "1.0"
+
+[workspace]
+members = [ "nalgebra-lapack" ]

Makefile

@@ -1,11 +1,11 @@
 all:
-	CARGO_INCREMENTAL=1 cargo build --features "arbitrary serde-serialize"
+	cargo check --features "debug arbitrary serde-serialize"
 
 doc:
-	CARGO_INCREMENTAL=1 cargo doc --no-deps --features "arbitrary serde-serialize"
+	cargo doc --no-deps --features "debug arbitrary serde-serialize"
 
 bench:
 	cargo bench
 
 test:
-	cargo test --features "arbitrary serde-serialize"
+	cargo test --features "debug arbitrary serde-serialize"

benches/common/macros.rs

@@ -4,20 +4,12 @@ macro_rules! bench_binop(
     ($name: ident, $t1: ty, $t2: ty, $binop: ident) => {
         #[bench]
         fn $name(bh: &mut Bencher) {
-            const LEN: usize = 1 << 13;
-
             let mut rng = IsaacRng::new_unseeded();
-
-            let elems1: Vec<$t1> = (0usize .. LEN).map(|_| rng.gen::<$t1>()).collect();
-            let elems2: Vec<$t2> = (0usize .. LEN).map(|_| rng.gen::<$t2>()).collect();
-            let mut i = 0;
+            let a = rng.gen::<$t1>();
+            let b = rng.gen::<$t2>();
 
             bh.iter(|| {
-                i = (i + 1) & (LEN - 1);
-
-                unsafe {
-                    test::black_box(elems1.get_unchecked(i).$binop(*elems2.get_unchecked(i)))
-                }
+                a.$binop(b)
             })
         }
     }
@@ -27,43 +19,27 @@ macro_rules! bench_binop_ref(
     ($name: ident, $t1: ty, $t2: ty, $binop: ident) => {
         #[bench]
         fn $name(bh: &mut Bencher) {
-            const LEN: usize = 1 << 13;
-
             let mut rng = IsaacRng::new_unseeded();
-
-            let elems1: Vec<$t1> = (0usize .. LEN).map(|_| rng.gen::<$t1>()).collect();
-            let elems2: Vec<$t2> = (0usize .. LEN).map(|_| rng.gen::<$t2>()).collect();
-            let mut i = 0;
+            let a = rng.gen::<$t1>();
+            let b = rng.gen::<$t2>();
 
             bh.iter(|| {
-                i = (i + 1) & (LEN - 1);
-
-                unsafe {
-                    test::black_box(elems1.get_unchecked(i).$binop(elems2.get_unchecked(i)))
-                }
+                a.$binop(&b)
             })
         }
     }
 );
 
-macro_rules! bench_binop_na(
-    ($name: ident, $t1: ty, $t2: ty, $binop: ident) => {
+macro_rules! bench_binop_fn(
+    ($name: ident, $t1: ty, $t2: ty, $binop: path) => {
         #[bench]
         fn $name(bh: &mut Bencher) {
-            const LEN: usize = 1 << 13;
-
             let mut rng = IsaacRng::new_unseeded();
-
-            let elems1: Vec<$t1> = (0usize .. LEN).map(|_| rng.gen::<$t1>()).collect();
-            let elems2: Vec<$t2> = (0usize .. LEN).map(|_| rng.gen::<$t2>()).collect();
-            let mut i = 0;
+            let a = rng.gen::<$t1>();
+            let b = rng.gen::<$t2>();
 
             bh.iter(|| {
-                i = (i + 1) & (LEN - 1);
-
-                unsafe {
-                    test::black_box(na::$binop(elems1.get_unchecked(i), elems2.get_unchecked(i)))
-                }
+                $binop(&a, &b)
             })
         }
     }

benches/core/matrix.rs

@@ -0,0 +1,192 @@
+use rand::{IsaacRng, Rng};
+use test::{self, Bencher};
+use na::{Vector2, Vector3, Vector4, Matrix2, Matrix3, Matrix4,
+         MatrixN, U10,
+         DMatrix, DVector};
+use std::ops::{Add, Sub, Mul, Div};
+
+#[path="../common/macros.rs"]
+mod macros;
+
+bench_binop!(mat2_mul_m, Matrix2<f32>, Matrix2<f32>, mul);
+bench_binop!(mat3_mul_m, Matrix3<f32>, Matrix3<f32>, mul);
+bench_binop!(mat4_mul_m, Matrix4<f32>, Matrix4<f32>, mul);
+
+bench_binop_ref!(mat2_tr_mul_m, Matrix2<f32>, Matrix2<f32>, tr_mul);
+bench_binop_ref!(mat3_tr_mul_m, Matrix3<f32>, Matrix3<f32>, tr_mul);
+bench_binop_ref!(mat4_tr_mul_m, Matrix4<f32>, Matrix4<f32>, tr_mul);
+
+bench_binop!(mat2_add_m, Matrix2<f32>, Matrix2<f32>, add);
+bench_binop!(mat3_add_m, Matrix3<f32>, Matrix3<f32>, add);
+bench_binop!(mat4_add_m, Matrix4<f32>, Matrix4<f32>, add);
+
+bench_binop!(mat2_sub_m, Matrix2<f32>, Matrix2<f32>, sub);
+bench_binop!(mat3_sub_m, Matrix3<f32>, Matrix3<f32>, sub);
+bench_binop!(mat4_sub_m, Matrix4<f32>, Matrix4<f32>, sub);
+
+bench_binop!(mat2_mul_v, Matrix2<f32>, Vector2<f32>, mul);
+bench_binop!(mat3_mul_v, Matrix3<f32>, Vector3<f32>, mul);
+bench_binop!(mat4_mul_v, Matrix4<f32>, Vector4<f32>, mul);
+
+bench_binop_ref!(mat2_tr_mul_v, Matrix2<f32>, Vector2<f32>, tr_mul);
+bench_binop_ref!(mat3_tr_mul_v, Matrix3<f32>, Vector3<f32>, tr_mul);
+bench_binop_ref!(mat4_tr_mul_v, Matrix4<f32>, Vector4<f32>, tr_mul);
+
+bench_binop!(mat2_mul_s, Matrix2<f32>, f32, mul);
+bench_binop!(mat3_mul_s, Matrix3<f32>, f32, mul);
+bench_binop!(mat4_mul_s, Matrix4<f32>, f32, mul);
+
+bench_binop!(mat2_div_s, Matrix2<f32>, f32, div);
+bench_binop!(mat3_div_s, Matrix3<f32>, f32, div);
+bench_binop!(mat4_div_s, Matrix4<f32>, f32, div);
+
+bench_unop!(mat2_inv, Matrix2<f32>, try_inverse);
+bench_unop!(mat3_inv, Matrix3<f32>, try_inverse);
+bench_unop!(mat4_inv, Matrix4<f32>, try_inverse);
+
+bench_unop!(mat2_transpose, Matrix2<f32>, transpose);
+bench_unop!(mat3_transpose, Matrix3<f32>, transpose);
+bench_unop!(mat4_transpose, Matrix4<f32>, transpose);
+
+#[bench]
+fn mat_div_scalar(b: &mut Bencher) {
+    let a = DMatrix::from_row_slice(1000, 1000, &vec![2.0;1000000]);
+    let n = 42.0;
+
+    b.iter(|| {
+        let mut aa = a.clone();
+        let mut b = aa.slice_mut((0, 0), (1000, 1000));
+        b /= n
+    })
+}
+
+#[bench]
+fn mat100_add_mat100(bench: &mut Bencher) {
+    let a = DMatrix::<f64>::new_random(100, 100);
+    let b = DMatrix::<f64>::new_random(100, 100);
+
+    bench.iter(|| { &a + &b })
+}
+
+#[bench]
+fn mat4_mul_mat4(bench: &mut Bencher) {
+    let a = DMatrix::<f64>::new_random(4, 4);
+    let b = DMatrix::<f64>::new_random(4, 4);
+
+    bench.iter(|| { &a * &b })
+}
+
+#[bench]
+fn mat5_mul_mat5(bench: &mut Bencher) {
+    let a = DMatrix::<f64>::new_random(5, 5);
+    let b = DMatrix::<f64>::new_random(5, 5);
+
+    bench.iter(|| { &a * &b })
+}
+
+#[bench]
+fn mat6_mul_mat6(bench: &mut Bencher) {
+    let a = DMatrix::<f64>::new_random(6, 6);
+    let b = DMatrix::<f64>::new_random(6, 6);
+
+    bench.iter(|| { &a * &b })
+}
+
+#[bench]
+fn mat7_mul_mat7(bench: &mut Bencher) {
+    let a = DMatrix::<f64>::new_random(7, 7);
+    let b = DMatrix::<f64>::new_random(7, 7);
+
+    bench.iter(|| { &a * &b })
+}
+
+#[bench]
+fn mat8_mul_mat8(bench: &mut Bencher) {
+    let a = DMatrix::<f64>::new_random(8, 8);
+    let b = DMatrix::<f64>::new_random(8, 8);
+
+    bench.iter(|| { &a * &b })
+}
+
+#[bench]
+fn mat9_mul_mat9(bench: &mut Bencher) {
+    let a = DMatrix::<f64>::new_random(9, 9);
+    let b = DMatrix::<f64>::new_random(9, 9);
+
+    bench.iter(|| { &a * &b })
+}
+
+#[bench]
+fn mat10_mul_mat10(bench: &mut Bencher) {
+    let a = DMatrix::<f64>::new_random(10, 10);
+    let b = DMatrix::<f64>::new_random(10, 10);
+
+    bench.iter(|| { &a * &b })
+}
+
+#[bench]
+fn mat10_mul_mat10_static(bench: &mut Bencher) {
+    let a = MatrixN::<f64, U10>::new_random();
+    let b = MatrixN::<f64, U10>::new_random();
+
+    bench.iter(|| { &a * &b })
+}
+
+#[bench]
+fn mat100_mul_mat100(bench: &mut Bencher) {
+    let a = DMatrix::<f64>::new_random(100, 100);
+    let b = DMatrix::<f64>::new_random(100, 100);
+
+    bench.iter(|| { &a * &b })
+}
+
+#[bench]
+fn mat500_mul_mat500(bench: &mut Bencher) {
+    let a = DMatrix::<f64>::from_element(500, 500, 5f64);
+    let b = DMatrix::<f64>::from_element(500, 500, 6f64);
+
+    bench.iter(|| { &a * &b })
+}
+
+#[bench]
+fn copy_from(bench: &mut Bencher) {
+    let a = DMatrix::<f64>::new_random(1000, 1000);
+    let mut b = DMatrix::<f64>::new_random(1000, 1000);
+
+    bench.iter(|| {
+        b.copy_from(&a);
+    })
+}
+
+#[bench]
+fn axpy(bench: &mut Bencher) {
+    let x = DVector::<f64>::from_element(100000, 2.0);
+    let mut y = DVector::<f64>::from_element(100000, 3.0);
+    let a = 42.0;
+
+    bench.iter(|| {
+        y.axpy(a, &x, 1.0);
+    })
+}
+
+#[bench]
+fn tr_mul_to(bench: &mut Bencher) {
+    let a = DMatrix::<f64>::new_random(1000, 1000);
+    let b = DVector::<f64>::new_random(1000);
+    let mut c = DVector::from_element(1000, 0.0);
+
+    bench.iter(|| {
+        a.tr_mul_to(&b, &mut c)
+    })
+}
+
+#[bench]
+fn mat_mul_mat(bench: &mut Bencher) {
+    let a = DMatrix::<f64>::new_random(100, 100);
+    let b = DMatrix::<f64>::new_random(100, 100);
+    let mut ab = DMatrix::<f64>::from_element(100, 100, 0.0);
+
+    bench.iter(|| {
+        test::black_box(a.mul_to(&b, &mut ab));
+    })
+}

benches/core/mod.rs

@@ -0,0 +1,2 @@
+mod matrix;
+mod vector;

benches/core/vector.rs

@@ -0,0 +1,128 @@
+use rand::{IsaacRng, Rng};
+use test::{self, Bencher};
+use typenum::U10000;
+use na::{Vector2, Vector3, Vector4, VectorN, DVector};
+use std::ops::{Add, Sub, Mul, Div};
+
+#[path="../common/macros.rs"]
+mod macros;
+
+bench_binop!(vec2_add_v_f32, Vector2<f32>, Vector2<f32>, add);
+bench_binop!(vec3_add_v_f32, Vector3<f32>, Vector3<f32>, add);
+bench_binop!(vec4_add_v_f32, Vector4<f32>, Vector4<f32>, add);
+
+bench_binop!(vec2_add_v_f64, Vector2<f64>, Vector2<f64>, add);
+bench_binop!(vec3_add_v_f64, Vector3<f64>, Vector3<f64>, add);
+bench_binop!(vec4_add_v_f64, Vector4<f64>, Vector4<f64>, add);
+
+bench_binop!(vec2_sub_v, Vector2<f32>, Vector2<f32>, sub);
+bench_binop!(vec3_sub_v, Vector3<f32>, Vector3<f32>, sub);
+bench_binop!(vec4_sub_v, Vector4<f32>, Vector4<f32>, sub);
+
+bench_binop!(vec2_mul_s, Vector2<f32>, f32, mul);
+bench_binop!(vec3_mul_s, Vector3<f32>, f32, mul);
+bench_binop!(vec4_mul_s, Vector4<f32>, f32, mul);
+
+bench_binop!(vec2_div_s, Vector2<f32>, f32, div);
+bench_binop!(vec3_div_s, Vector3<f32>, f32, div);
+bench_binop!(vec4_div_s, Vector4<f32>, f32, div);
+
+bench_binop_ref!(vec2_dot_f32, Vector2<f32>, Vector2<f32>, dot);
+bench_binop_ref!(vec3_dot_f32, Vector3<f32>, Vector3<f32>, dot);
+bench_binop_ref!(vec4_dot_f32, Vector4<f32>, Vector4<f32>, dot);
+
+bench_binop_ref!(vec2_dot_f64, Vector2<f64>, Vector2<f64>, dot);
+bench_binop_ref!(vec3_dot_f64, Vector3<f64>, Vector3<f64>, dot);
+bench_binop_ref!(vec4_dot_f64, Vector4<f64>, Vector4<f64>, dot);
+
+bench_binop_ref!(vec3_cross, Vector3<f32>, Vector3<f32>, cross);
+
+bench_unop!(vec2_norm, Vector2<f32>, norm);
+bench_unop!(vec3_norm, Vector3<f32>, norm);
+bench_unop!(vec4_norm, Vector4<f32>, norm);
+
+bench_unop!(vec2_normalize, Vector2<f32>, normalize);
+bench_unop!(vec3_normalize, Vector3<f32>, normalize);
+bench_unop!(vec4_normalize, Vector4<f32>, normalize);
+
+bench_binop_ref!(vec10000_dot_f64, VectorN<f64, U10000>, VectorN<f64, U10000>, dot);
+bench_binop_ref!(vec10000_dot_f32, VectorN<f32, U10000>, VectorN<f32, U10000>, dot);
+
+#[bench]
+fn vec10000_axpy_f64(bh: &mut Bencher) {
+    let mut rng = IsaacRng::new_unseeded();
+    let mut a = DVector::new_random(10000);
+    let b = DVector::new_random(10000);
+    let n = rng.gen::<f64>();
+
+    bh.iter(|| {
+        a.axpy(n, &b, 1.0)
+    })
+}
+
+#[bench]
+fn vec10000_axpy_beta_f64(bh: &mut Bencher) {
+    let mut rng = IsaacRng::new_unseeded();
+    let mut a = DVector::new_random(10000);
+    let b = DVector::new_random(10000);
+    let n = rng.gen::<f64>();
+    let beta = rng.gen::<f64>();
+
+    bh.iter(|| {
+        a.axpy(n, &b, beta)
+    })
+}
+
+#[bench]
+fn vec10000_axpy_f64_slice(bh: &mut Bencher) {
+    let mut rng = IsaacRng::new_unseeded();
+    let mut a = DVector::new_random(10000);
+    let b = DVector::new_random(10000);
+    let n = rng.gen::<f64>();
+
+    bh.iter(|| {
+        let mut a = a.fixed_rows_mut::<U10000>(0);
+        let b = b.fixed_rows::<U10000>(0);
+
+        a.axpy(n, &b, 1.0)
+    })
+}
+
+#[bench]
+fn vec10000_axpy_f64_static(bh: &mut Bencher) {
+    let mut rng = IsaacRng::new_unseeded();
+    let mut a = VectorN::<f64, U10000>::new_random();
+    let b = VectorN::<f64, U10000>::new_random();
+    let n = rng.gen::<f64>();
+
+    // NOTE: for some reasons, it is much faster if the arument are boxed (Box::new(VectorN...)).
+    bh.iter(|| {
+        a.axpy(n, &b, 1.0)
+    })
+}
+
+
+#[bench]
+fn vec10000_axpy_f32(bh: &mut Bencher) {
+    let mut rng = IsaacRng::new_unseeded();
+    let mut a = DVector::new_random(10000);
+    let b = DVector::new_random(10000);
+    let n = rng.gen::<f32>();
+
+    bh.iter(|| {
+        a.axpy(n, &b, 1.0)
+    })
+}
+
+#[bench]
+fn vec10000_axpy_beta_f32(bh: &mut Bencher) {
+    let mut rng = IsaacRng::new_unseeded();
+    let mut a = DVector::new_random(10000);
+    let b = DVector::new_random(10000);
+    let n = rng.gen::<f32>();
+    let beta = rng.gen::<f32>();
+
+    bh.iter(|| {
+        a.axpy(n, &b, beta)
+    })
+}

benches/geometry/mod.rs

@@ -0,0 +1 @@
+mod quaternion;

benches/geometry/quaternion.rs

@@ -0,0 +1,22 @@
+use rand::{IsaacRng, Rng};
+use test::{self, Bencher};
+use na::{Quaternion, UnitQuaternion, Vector3};
+use std::ops::{Add, Sub, Mul, Div};
+
+#[path="../common/macros.rs"]
+mod macros;
+
+bench_binop!(quaternion_add_q, Quaternion<f32>, Quaternion<f32>, add);
+bench_binop!(quaternion_sub_q, Quaternion<f32>, Quaternion<f32>, sub);
+bench_binop!(quaternion_mul_q, Quaternion<f32>, Quaternion<f32>, mul);
+
+bench_binop!(unit_quaternion_mul_v, UnitQuaternion<f32>, Vector3<f32>, mul);
+
+bench_binop!(quaternion_mul_s, Quaternion<f32>, f32, mul);
+bench_binop!(quaternion_div_s, Quaternion<f32>, f32, div);
+
+bench_unop!(quaternion_inv, Quaternion<f32>, try_inverse);
+bench_unop!(unit_quaternion_inv, UnitQuaternion<f32>, inverse);
+
+// bench_unop_self!(quaternion_conjugate, Quaternion<f32>, conjugate);
+// bench_unop!(quaternion_normalize, Quaternion<f32>, normalize);

benches/lib.rs

@@ -0,0 +1,20 @@
+#![feature(test)]
+
+extern crate test;
+extern crate rand;
+extern crate typenum;
+extern crate nalgebra as na;
+
+
+use rand::{Rng, IsaacRng};
+use na::DMatrix;
+
+
+mod core;
+mod linalg;
+mod geometry;
+
+fn reproductible_dmatrix(nrows: usize, ncols: usize) -> DMatrix<f64> {
+    let mut rng = IsaacRng::new_unseeded();
+    DMatrix::<f64>::from_fn(nrows, ncols, |_, _| rng.gen())
+}

benches/linalg/bidiagonal.rs

@@ -0,0 +1,75 @@
+use test::{self, Bencher};
+use na::{Matrix4, DMatrix, Bidiagonal};
+
+#[path="../common/macros.rs"]
+mod macros;
+
+// Without unpack.
+#[bench]
+fn bidiagonalize_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    bh.iter(|| test::black_box(Bidiagonal::new(m.clone())))
+}
+
+#[bench]
+fn bidiagonalize_100x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 500);
+    bh.iter(|| test::black_box(Bidiagonal::new(m.clone())))
+}
+
+#[bench]
+fn bidiagonalize_4x4(bh: &mut Bencher) {
+    let m = Matrix4::<f64>::new_random();
+    bh.iter(|| test::black_box(Bidiagonal::new(m.clone())))
+}
+
+#[bench]
+fn bidiagonalize_500x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 100);
+    bh.iter(|| test::black_box(Bidiagonal::new(m.clone())))
+}
+
+#[bench]
+fn bidiagonalize_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+    bh.iter(|| test::black_box(Bidiagonal::new(m.clone())))
+}
+
+
+// With unpack.
+#[bench]
+fn bidiagonalize_unpack_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    bh.iter(|| {
+        let bidiag = Bidiagonal::new(m.clone());
+        let _ = bidiag.unpack();
+    })
+}
+
+#[bench]
+fn bidiagonalize_unpack_100x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 500);
+    bh.iter(|| {
+        let bidiag = Bidiagonal::new(m.clone());
+        let _ = bidiag.unpack();
+    })
+}
+
+#[bench]
+fn bidiagonalize_unpack_500x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 100);
+    bh.iter(|| {
+        let bidiag = Bidiagonal::new(m.clone());
+        let _ = bidiag.unpack();
+    })
+}
+
+#[bench]
+fn bidiagonalize_unpack_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+    bh.iter(|| {
+        let bidiag = Bidiagonal::new(m.clone());
+        let _ = bidiag.unpack();
+    })
+}
+

benches/linalg/cholesky.rs

@@ -0,0 +1,109 @@
+use test::{self, Bencher};
+use na::{DMatrix, DVector, Cholesky};
+
+#[bench]
+fn cholesky_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    let m = &m * m.transpose();
+
+    bh.iter(|| test::black_box(Cholesky::new(m.clone())))
+}
+
+#[bench]
+fn cholesky_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+    let m = &m * m.transpose();
+
+    bh.iter(|| test::black_box(Cholesky::new(m.clone())))
+}
+
+// With unpack.
+#[bench]
+fn cholesky_decompose_unpack_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    let m = &m * m.transpose();
+
+    bh.iter(|| {
+        let chol = Cholesky::new(m.clone()).unwrap();
+        let _ = chol.unpack();
+    })
+}
+#[bench]
+fn cholesky_decompose_unpack_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+    let m = &m * m.transpose();
+
+    bh.iter(|| {
+        let chol = Cholesky::new(m.clone()).unwrap();
+        let _ = chol.unpack();
+    })
+}
+
+#[bench]
+fn cholesky_solve_10x10(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(10, 10);
+    let m = &m * m.transpose();
+    let v = DVector::<f64>::new_random(10);
+    let chol = Cholesky::new(m.clone()).unwrap();
+
+    bh.iter(|| {
+        let _ = chol.solve(&v);
+    })
+}
+
+#[bench]
+fn cholesky_solve_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    let m = &m * m.transpose();
+    let v = DVector::<f64>::new_random(100);
+    let chol = Cholesky::new(m.clone()).unwrap();
+
+    bh.iter(|| {
+        let _ = chol.solve(&v);
+    })
+}
+
+#[bench]
+fn cholesky_solve_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+    let m = &m * m.transpose();
+    let v = DVector::<f64>::new_random(500);
+    let chol = Cholesky::new(m.clone()).unwrap();
+
+    bh.iter(|| {
+        let _ = chol.solve(&v);
+    })
+}
+
+#[bench]
+fn cholesky_inverse_10x10(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(10, 10);
+    let m = &m * m.transpose();
+    let chol = Cholesky::new(m.clone()).unwrap();
+
+    bh.iter(|| {
+        let _ = chol.inverse();
+    })
+}
+
+#[bench]
+fn cholesky_inverse_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    let m = &m * m.transpose();
+    let chol = Cholesky::new(m.clone()).unwrap();
+
+    bh.iter(|| {
+        let _ = chol.inverse();
+    })
+}
+
+#[bench]
+fn cholesky_inverse_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+    let m = &m * m.transpose();
+    let chol = Cholesky::new(m.clone()).unwrap();
+
+    bh.iter(|| {
+        let _ = chol.inverse();
+    })
+}

benches/linalg/eigen.rs

@@ -0,0 +1,30 @@
+use test::Bencher;
+use na::{DMatrix, Eigen};
+
+#[bench]
+fn eigen_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+
+    bh.iter(|| Eigen::new(m.clone(), 1.0e-7, 0))
+}
+
+#[bench]
+fn eigen_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+
+    bh.iter(|| Eigen::new(m.clone(), 1.0e-7, 0))
+}
+
+#[bench]
+fn eigenvalues_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+
+    bh.iter(|| m.clone().eigenvalues(1.0e-7, 0))
+}
+
+#[bench]
+fn eigenvalues_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+
+    bh.iter(|| m.clone().eigenvalues(1.0e-7, 0))
+}

benches/linalg/full_piv_lu.rs

@@ -0,0 +1,114 @@
+use test::{self, Bencher};
+use na::{DMatrix, DVector, FullPivLU};
+
+// Without unpack.
+#[bench]
+fn full_piv_lu_decompose_10x10(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(10, 10);
+    bh.iter(|| test::black_box(FullPivLU::new(m.clone())))
+}
+
+#[bench]
+fn full_piv_lu_decompose_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    bh.iter(|| test::black_box(FullPivLU::new(m.clone())))
+}
+
+#[bench]
+fn full_piv_lu_decompose_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+    bh.iter(|| test::black_box(FullPivLU::new(m.clone())))
+}
+
+#[bench]
+fn full_piv_lu_solve_10x10(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(10, 10);
+    let lu = FullPivLU::new(m.clone());
+
+    bh.iter(|| {
+        let mut b = DVector::<f64>::from_element(10, 1.0);
+        lu.solve(&mut b);
+    })
+}
+
+#[bench]
+fn full_piv_lu_solve_100x100(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(100, 100);
+    let lu = FullPivLU::new(m.clone());
+
+    bh.iter(|| {
+        let mut b = DVector::<f64>::from_element(100, 1.0);
+        lu.solve(&mut b);
+    })
+}
+
+#[bench]
+fn full_piv_lu_solve_500x500(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(500, 500);
+    let lu = FullPivLU::new(m.clone());
+
+    bh.iter(|| {
+        let mut b = DVector::<f64>::from_element(500, 1.0);
+        lu.solve(&mut b);
+    })
+}
+
+#[bench]
+fn full_piv_lu_inverse_10x10(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(10, 10);
+    let lu = FullPivLU::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(lu.try_inverse())
+    })
+}
+
+#[bench]
+fn full_piv_lu_inverse_100x100(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(100, 100);
+    let lu = FullPivLU::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(lu.try_inverse())
+    })
+}
+
+#[bench]
+fn full_piv_lu_inverse_500x500(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(500, 500);
+    let lu = FullPivLU::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(lu.try_inverse())
+    })
+}
+
+#[bench]
+fn full_piv_lu_determinant_10x10(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(10, 10);
+    let lu = FullPivLU::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(lu.determinant())
+    })
+}
+
+#[bench]
+fn full_piv_lu_determinant_100x100(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(100, 100);
+    let lu = FullPivLU::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(lu.determinant())
+    })
+}
+
+#[bench]
+fn full_piv_lu_determinant_500x500(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(500, 500);
+    let lu = FullPivLU::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(lu.determinant())
+    })
+}

benches/linalg/hessenberg.rs

@@ -0,0 +1,60 @@
+use test::{self, Bencher};
+use na::{Matrix4, DMatrix, Hessenberg};
+
+#[path="../common/macros.rs"]
+mod macros;
+
+// Without unpack.
+#[bench]
+fn hessenberg_decompose_4x4(bh: &mut Bencher) {
+    let m = Matrix4::<f64>::new_random();
+    bh.iter(|| test::black_box(Hessenberg::new(m.clone())))
+}
+
+#[bench]
+fn hessenberg_decompose_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    bh.iter(|| test::black_box(Hessenberg::new(m.clone())))
+}
+
+#[bench]
+fn hessenberg_decompose_200x200(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(200, 200);
+    bh.iter(|| test::black_box(Hessenberg::new(m.clone())))
+}
+
+
+#[bench]
+fn hessenberg_decompose_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+    bh.iter(|| test::black_box(Hessenberg::new(m.clone())))
+}
+
+
+// With unpack.
+#[bench]
+fn hessenberg_decompose_unpack_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    bh.iter(|| {
+        let hess = Hessenberg::new(m.clone());
+        let _ = hess.unpack();
+    })
+}
+
+#[bench]
+fn hessenberg_decompose_unpack_200x200(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(200, 200);
+    bh.iter(|| {
+        let hess = Hessenberg::new(m.clone());
+        let _ = hess.unpack();
+    })
+}
+
+#[bench]
+fn hessenberg_decompose_unpack_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+    bh.iter(|| {
+        let hess = Hessenberg::new(m.clone());
+        let _ = hess.unpack();
+    })
+}

benches/linalg/lu.rs

@@ -0,0 +1,114 @@
+use test::{self, Bencher};
+use na::{DMatrix, DVector, LU};
+
+// Without unpack.
+#[bench]
+fn lu_decompose_10x10(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(10, 10);
+    bh.iter(|| test::black_box(LU::new(m.clone())))
+}
+
+#[bench]
+fn lu_decompose_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    bh.iter(|| test::black_box(LU::new(m.clone())))
+}
+
+#[bench]
+fn lu_decompose_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+    bh.iter(|| test::black_box(LU::new(m.clone())))
+}
+
+#[bench]
+fn lu_solve_10x10(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(10, 10);
+    let lu = LU::new(m.clone());
+
+    bh.iter(|| {
+        let mut b = DVector::<f64>::from_element(10, 1.0);
+        lu.solve(&mut b);
+    })
+}
+
+#[bench]
+fn lu_solve_100x100(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(100, 100);
+    let lu = LU::new(m.clone());
+
+    bh.iter(|| {
+        let mut b = DVector::<f64>::from_element(100, 1.0);
+        lu.solve(&mut b);
+    })
+}
+
+#[bench]
+fn lu_solve_500x500(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(500, 500);
+    let lu = LU::new(m.clone());
+
+    bh.iter(|| {
+        let mut b = DVector::<f64>::from_element(500, 1.0);
+        lu.solve(&mut b);
+    })
+}
+
+#[bench]
+fn lu_inverse_10x10(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(10, 10);
+    let lu = LU::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(lu.try_inverse())
+    })
+}
+
+#[bench]
+fn lu_inverse_100x100(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(100, 100);
+    let lu = LU::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(lu.try_inverse())
+    })
+}
+
+#[bench]
+fn lu_inverse_500x500(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(500, 500);
+    let lu = LU::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(lu.try_inverse())
+    })
+}
+
+#[bench]
+fn lu_determinant_10x10(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(10, 10);
+    let lu = LU::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(lu.determinant())
+    })
+}
+
+#[bench]
+fn lu_determinant_100x100(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(100, 100);
+    let lu = LU::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(lu.determinant())
+    })
+}
+
+#[bench]
+fn lu_determinant_500x500(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(500, 500);
+    let lu = LU::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(lu.determinant())
+    })
+}

benches/linalg/mod.rs

@@ -0,0 +1,11 @@
+mod solve;
+mod cholesky;
+mod qr;
+mod hessenberg;
+mod bidiagonal;
+mod lu;
+mod full_piv_lu;
+mod svd;
+mod schur;
+mod symmetric_eigen;
+// mod eigen;

benches/linalg/qr.rs

@@ -0,0 +1,137 @@
+use test::{self, Bencher};
+use na::{Matrix4, DMatrix, DVector, QR};
+
+#[path="../common/macros.rs"]
+mod macros;
+
+// Without unpack.
+#[bench]
+fn qr_decompose_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    bh.iter(|| test::black_box(QR::new(m.clone())))
+}
+
+#[bench]
+fn qr_decompose_100x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 500);
+    bh.iter(|| test::black_box(QR::new(m.clone())))
+}
+
+#[bench]
+fn qr_decompose_4x4(bh: &mut Bencher) {
+    let m = Matrix4::<f64>::new_random();
+    bh.iter(|| test::black_box(QR::new(m.clone())))
+}
+
+#[bench]
+fn qr_decompose_500x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 100);
+    bh.iter(|| test::black_box(QR::new(m.clone())))
+}
+
+#[bench]
+fn qr_decompose_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+    bh.iter(|| test::black_box(QR::new(m.clone())))
+}
+
+
+// With unpack.
+#[bench]
+fn qr_decompose_unpack_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    bh.iter(|| {
+        let qr = QR::new(m.clone());
+        let _ = qr.unpack();
+    })
+}
+
+#[bench]
+fn qr_decompose_unpack_100x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 500);
+    bh.iter(|| {
+        let qr = QR::new(m.clone());
+        let _ = qr.unpack();
+    })
+}
+
+#[bench]
+fn qr_decompose_unpack_500x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 100);
+    bh.iter(|| {
+        let qr = QR::new(m.clone());
+        let _ = qr.unpack();
+    })
+}
+
+#[bench]
+fn qr_decompose_unpack_500x500(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(500, 500);
+    bh.iter(|| {
+        let qr = QR::new(m.clone());
+        let _ = qr.unpack();
+    })
+}
+
+#[bench]
+fn qr_solve_10x10(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(10, 10);
+    let qr = QR::new(m.clone());
+
+    bh.iter(|| {
+        let mut b = DVector::<f64>::from_element(10, 1.0);
+        qr.solve(&mut b);
+    })
+}
+
+#[bench]
+fn qr_solve_100x100(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(100, 100);
+    let qr = QR::new(m.clone());
+
+    bh.iter(|| {
+        let mut b = DVector::<f64>::from_element(100, 1.0);
+        qr.solve(&mut b);
+    })
+}
+
+#[bench]
+fn qr_solve_500x500(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(500, 500);
+    let qr = QR::new(m.clone());
+
+    bh.iter(|| {
+        let mut b = DVector::<f64>::from_element(500, 1.0);
+        qr.solve(&mut b);
+    })
+}
+
+#[bench]
+fn qr_inverse_10x10(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(10, 10);
+    let qr = QR::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(qr.try_inverse())
+    })
+}
+
+#[bench]
+fn qr_inverse_100x100(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(100, 100);
+    let qr = QR::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(qr.try_inverse())
+    })
+}
+
+#[bench]
+fn qr_inverse_500x500(bh: &mut Bencher) {
+    let m  = DMatrix::<f64>::new_random(500, 500);
+    let qr = QR::new(m.clone());
+
+    bh.iter(|| {
+        test::black_box(qr.try_inverse())
+    })
+}

benches/linalg/schur.rs

@@ -0,0 +1,51 @@
+use test::{self, Bencher};
+use na::{Matrix4, RealSchur};
+
+#[bench]
+fn schur_decompose_4x4(bh: &mut Bencher) {
+    let m = Matrix4::<f64>::new_random();
+    bh.iter(|| test::black_box(RealSchur::new(m.clone())))
+}
+
+#[bench]
+fn schur_decompose_10x10(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(10, 10);
+    bh.iter(|| test::black_box(RealSchur::new(m.clone())))
+}
+
+
+#[bench]
+fn schur_decompose_100x100(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(100, 100);
+    bh.iter(|| test::black_box(RealSchur::new(m.clone())))
+}
+
+#[bench]
+fn schur_decompose_200x200(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(200, 200);
+    bh.iter(|| test::black_box(RealSchur::new(m.clone())))
+}
+
+#[bench]
+fn eigenvalues_4x4(bh: &mut Bencher) {
+    let m = Matrix4::<f64>::new_random();
+    bh.iter(|| test::black_box(m.complex_eigenvalues()))
+}
+
+#[bench]
+fn eigenvalues_10x10(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(10, 10);
+    bh.iter(|| test::black_box(m.complex_eigenvalues()))
+}
+
+#[bench]
+fn eigenvalues_100x100(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(100, 100);
+    bh.iter(|| test::black_box(m.complex_eigenvalues()))
+}
+
+#[bench]
+fn eigenvalues_200x200(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(200, 200);
+    bh.iter(|| test::black_box(m.complex_eigenvalues()))
+}

benches/linalg/solve.rs

@@ -0,0 +1,82 @@
+use test::Bencher;
+use na::{DMatrix, DVector};
+
+#[bench]
+fn solve_l_triangular_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    let v = DVector::<f64>::new_random(100);
+
+    bh.iter(|| {
+        let _ = m.solve_lower_triangular(&v);
+    })
+}
+
+#[bench]
+fn solve_l_triangular_1000x1000(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(1000, 1000);
+    let v = DVector::<f64>::new_random(1000);
+
+    bh.iter(|| {
+        let _ = m.solve_lower_triangular(&v);
+    })
+}
+
+#[bench]
+fn tr_solve_l_triangular_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    let v = DVector::<f64>::new_random(100);
+
+    bh.iter(|| {
+        let _ = m.tr_solve_lower_triangular(&v);
+    })
+}
+
+#[bench]
+fn tr_solve_l_triangular_1000x1000(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(1000, 1000);
+    let v = DVector::<f64>::new_random(1000);
+
+    bh.iter(|| {
+        let _ = m.tr_solve_lower_triangular(&v);
+    })
+}
+
+#[bench]
+fn solve_u_triangular_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    let v = DVector::<f64>::new_random(100);
+
+    bh.iter(|| {
+        let _ = m.solve_upper_triangular(&v);
+    })
+}
+
+#[bench]
+fn solve_u_triangular_1000x1000(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(1000, 1000);
+    let v = DVector::<f64>::new_random(1000);
+
+    bh.iter(|| {
+        let _ = m.solve_upper_triangular(&v);
+    })
+}
+
+#[bench]
+fn tr_solve_u_triangular_100x100(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(100, 100);
+    let v = DVector::<f64>::new_random(100);
+
+    bh.iter(|| {
+        let _ = m.tr_solve_upper_triangular(&v);
+    })
+}
+
+#[bench]
+fn tr_solve_u_triangular_1000x1000(bh: &mut Bencher) {
+    let m = DMatrix::<f64>::new_random(1000, 1000);
+    let v = DVector::<f64>::new_random(1000);
+
+    bh.iter(|| {
+        let _ = m.tr_solve_upper_triangular(&v);
+    })
+}

benches/linalg/svd.rs

@@ -0,0 +1,99 @@
+use test::{self, Bencher};
+use na::{Matrix4, SVD};
+
+#[bench]
+fn svd_decompose_4x4(bh: &mut Bencher) {
+    let m = Matrix4::<f64>::new_random();
+    bh.iter(|| test::black_box(SVD::new(m.clone(), true, true)))
+}
+
+#[bench]
+fn svd_decompose_10x10(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(10, 10);
+    bh.iter(|| test::black_box(SVD::new(m.clone(), true, true)))
+}
+
+#[bench]
+fn svd_decompose_100x100(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(100, 100);
+    bh.iter(|| test::black_box(SVD::new(m.clone(), true, true)))
+}
+
+#[bench]
+fn svd_decompose_200x200(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(200, 200);
+    bh.iter(|| test::black_box(SVD::new(m.clone(), true, true)))
+}
+
+#[bench]
+fn rank_4x4(bh: &mut Bencher) {
+    let m = Matrix4::<f64>::new_random();
+    bh.iter(|| test::black_box(m.rank(1.0e-10)))
+}
+
+#[bench]
+fn rank_10x10(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(10, 10);
+    bh.iter(|| test::black_box(m.rank(1.0e-10)))
+}
+
+#[bench]
+fn rank_100x100(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(100, 100);
+    bh.iter(|| test::black_box(m.rank(1.0e-10)))
+}
+
+#[bench]
+fn rank_200x200(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(200, 200);
+    bh.iter(|| test::black_box(m.rank(1.0e-10)))
+}
+
+#[bench]
+fn singular_values_4x4(bh: &mut Bencher) {
+    let m = Matrix4::<f64>::new_random();
+    bh.iter(|| test::black_box(m.singular_values()))
+}
+
+#[bench]
+fn singular_values_10x10(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(10, 10);
+    bh.iter(|| test::black_box(m.singular_values()))
+}
+
+#[bench]
+fn singular_values_100x100(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(100, 100);
+    bh.iter(|| test::black_box(m.singular_values()))
+}
+
+#[bench]
+fn singular_values_200x200(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(200, 200);
+    bh.iter(|| test::black_box(m.singular_values()))
+}
+
+
+#[bench]
+fn pseudo_inverse_4x4(bh: &mut Bencher) {
+    let m = Matrix4::<f64>::new_random();
+    bh.iter(|| test::black_box(m.clone().pseudo_inverse(1.0e-10)))
+}
+
+#[bench]
+fn pseudo_inverse_10x10(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(10, 10);
+    bh.iter(|| test::black_box(m.clone().pseudo_inverse(1.0e-10)))
+}
+
+#[bench]
+fn pseudo_inverse_100x100(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(100, 100);
+    bh.iter(|| test::black_box(m.clone().pseudo_inverse(1.0e-10)))
+}
+
+#[bench]
+fn pseudo_inverse_200x200(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(200, 200);
+    bh.iter(|| test::black_box(m.clone().pseudo_inverse(1.0e-10)))
+}

benches/linalg/symmetric_eigen.rs

@@ -0,0 +1,27 @@
+use test::{self, Bencher};
+use na::{Matrix4, SymmetricEigen};
+
+#[bench]
+fn symmetric_eigen_decompose_4x4(bh: &mut Bencher) {
+    let m = Matrix4::<f64>::new_random();
+    bh.iter(|| test::black_box(SymmetricEigen::new(m.clone())))
+}
+
+#[bench]
+fn symmetric_eigen_decompose_10x10(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(10, 10);
+    bh.iter(|| test::black_box(SymmetricEigen::new(m.clone())))
+}
+
+
+#[bench]
+fn symmetric_eigen_decompose_100x100(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(100, 100);
+    bh.iter(|| test::black_box(SymmetricEigen::new(m.clone())))
+}
+
+#[bench]
+fn symmetric_eigen_decompose_200x200(bh: &mut Bencher) {
+    let m = ::reproductible_dmatrix(200, 200);
+    bh.iter(|| test::black_box(SymmetricEigen::new(m.clone())))
+}

benches/matrix.rs

@@ -1,53 +0,0 @@
-#![feature(test)]
-
-extern crate test;
-extern crate rand;
-extern crate nalgebra as na;
-
-use rand::{IsaacRng, Rng};
-use test::Bencher;
-use na::{Vector2, Vector3, Vector4, Matrix2, Matrix3, Matrix4};
-use std::ops::{Add, Sub, Mul, Div};
-
-#[path="common/macros.rs"]
-mod macros;
-
-bench_binop!(_bench_mat2_mul_m, Matrix2<f32>, Matrix2<f32>, mul);
-bench_binop!(_bench_mat3_mul_m, Matrix3<f32>, Matrix3<f32>, mul);
-bench_binop!(_bench_mat4_mul_m, Matrix4<f32>, Matrix4<f32>, mul);
-
-bench_binop_ref!(_bench_mat2_tr_mul_m, Matrix2<f32>, Matrix2<f32>, tr_mul);
-bench_binop_ref!(_bench_mat3_tr_mul_m, Matrix3<f32>, Matrix3<f32>, tr_mul);
-bench_binop_ref!(_bench_mat4_tr_mul_m, Matrix4<f32>, Matrix4<f32>, tr_mul);
-
-bench_binop!(_bench_mat2_add_m, Matrix2<f32>, Matrix2<f32>, add);
-bench_binop!(_bench_mat3_add_m, Matrix3<f32>, Matrix3<f32>, add);
-bench_binop!(_bench_mat4_add_m, Matrix4<f32>, Matrix4<f32>, add);
-
-bench_binop!(_bench_mat2_sub_m, Matrix2<f32>, Matrix2<f32>, sub);
-bench_binop!(_bench_mat3_sub_m, Matrix3<f32>, Matrix3<f32>, sub);
-bench_binop!(_bench_mat4_sub_m, Matrix4<f32>, Matrix4<f32>, sub);
-
-bench_binop!(_bench_mat2_mul_v, Matrix2<f32>, Vector2<f32>, mul);
-bench_binop!(_bench_mat3_mul_v, Matrix3<f32>, Vector3<f32>, mul);
-bench_binop!(_bench_mat4_mul_v, Matrix4<f32>, Vector4<f32>, mul);
-
-bench_binop_ref!(_bench_mat2_tr_mul_v, Matrix2<f32>, Vector2<f32>, tr_mul);
-bench_binop_ref!(_bench_mat3_tr_mul_v, Matrix3<f32>, Vector3<f32>, tr_mul);
-bench_binop_ref!(_bench_mat4_tr_mul_v, Matrix4<f32>, Vector4<f32>, tr_mul);
-
-bench_binop!(_bench_mat2_mul_s, Matrix2<f32>, f32, mul);
-bench_binop!(_bench_mat3_mul_s, Matrix3<f32>, f32, mul);
-bench_binop!(_bench_mat4_mul_s, Matrix4<f32>, f32, mul);
-
-bench_binop!(_bench_mat2_div_s, Matrix2<f32>, f32, div);
-bench_binop!(_bench_mat3_div_s, Matrix3<f32>, f32, div);
-bench_binop!(_bench_mat4_div_s, Matrix4<f32>, f32, div);
-
-bench_unop!(_bench_mat2_inv, Matrix2<f32>, try_inverse);
-bench_unop!(_bench_mat3_inv, Matrix3<f32>, try_inverse);
-bench_unop!(_bench_mat4_inv, Matrix4<f32>, try_inverse);
-
-bench_unop!(_bench_mat2_transpose, Matrix2<f32>, transpose);
-bench_unop!(_bench_mat3_transpose, Matrix3<f32>, transpose);
-bench_unop!(_bench_mat4_transpose, Matrix4<f32>, transpose);

benches/quaternion.rs

@@ -1,28 +0,0 @@
-#![feature(test)]
-
-extern crate test;
-extern crate rand;
-extern crate nalgebra as na;
-
-use rand::{IsaacRng, Rng};
-use test::Bencher;
-use na::{Quaternion, UnitQuaternion, Vector3};
-use std::ops::{Add, Sub, Mul, Div};
-
-#[path="common/macros.rs"]
-mod macros;
-
-bench_binop!(_bench_quaternion_add_q, Quaternion<f32>, Quaternion<f32>, add);
-bench_binop!(_bench_quaternion_sub_q, Quaternion<f32>, Quaternion<f32>, sub);
-bench_binop!(_bench_quaternion_mul_q, Quaternion<f32>, Quaternion<f32>, mul);
-
-bench_binop!(_bench_unit_quaternion_mul_v, UnitQuaternion<f32>, Vector3<f32>, mul);
-
-bench_binop!(_bench_quaternion_mul_s, Quaternion<f32>, f32, mul);
-bench_binop!(_bench_quaternion_div_s, Quaternion<f32>, f32, div);
-
-bench_unop!(_bench_quaternion_inv, Quaternion<f32>, try_inverse);
-bench_unop!(_bench_unit_quaternion_inv, UnitQuaternion<f32>, inverse);
-
-// bench_unop_self!(_bench_quaternion_conjugate, Quaternion<f32>, conjugate);
-// bench_unop!(_bench_quaternion_normalize, Quaternion<f32>, normalize);

benches/vector.rs

@@ -1,43 +0,0 @@
-#![feature(test)]
-
-extern crate test;
-extern crate rand;
-extern crate nalgebra as na;
-
-use rand::{IsaacRng, Rng};
-use test::Bencher;
-use na::{Vector2, Vector3, Vector4};
-use std::ops::{Add, Sub, Mul, Div};
-
-#[path="common/macros.rs"]
-mod macros;
-
-bench_binop!(_bench_vec2_add_v, Vector2<f32>, Vector2<f32>, add);
-bench_binop!(_bench_vec3_add_v, Vector3<f32>, Vector3<f32>, add);
-bench_binop!(_bench_vec4_add_v, Vector4<f32>, Vector4<f32>, add);
-
-bench_binop!(_bench_vec2_sub_v, Vector2<f32>, Vector2<f32>, sub);
-bench_binop!(_bench_vec3_sub_v, Vector3<f32>, Vector3<f32>, sub);
-bench_binop!(_bench_vec4_sub_v, Vector4<f32>, Vector4<f32>, sub);
-
-bench_binop!(_bench_vec2_mul_s, Vector2<f32>, f32, mul);
-bench_binop!(_bench_vec3_mul_s, Vector3<f32>, f32, mul);
-bench_binop!(_bench_vec4_mul_s, Vector4<f32>, f32, mul);
-
-bench_binop!(_bench_vec2_div_s, Vector2<f32>, f32, div);
-bench_binop!(_bench_vec3_div_s, Vector3<f32>, f32, div);
-bench_binop!(_bench_vec4_div_s, Vector4<f32>, f32, div);
-
-bench_binop_ref!(_bench_vec2_dot, Vector2<f32>, Vector2<f32>, dot);
-bench_binop_ref!(_bench_vec3_dot, Vector3<f32>, Vector3<f32>, dot);
-bench_binop_ref!(_bench_vec4_dot, Vector4<f32>, Vector4<f32>, dot);
-
-bench_binop_ref!(_bench_vec3_cross, Vector3<f32>, Vector3<f32>, cross);
-
-bench_unop!(_bench_vec2_norm, Vector2<f32>, norm);
-bench_unop!(_bench_vec3_norm, Vector3<f32>, norm);
-bench_unop!(_bench_vec4_norm, Vector4<f32>, norm);
-
-bench_unop!(_bench_vec2_normalize, Vector2<f32>, normalize);
-bench_unop!(_bench_vec3_normalize, Vector3<f32>, normalize);
-bench_unop!(_bench_vec4_normalize, Vector4<f32>, normalize);

examples/dimensional_genericity.rs

@@ -1,11 +1,10 @@
 extern crate alga;
 extern crate nalgebra as na;
 
-use alga::general::Real;
 use alga::linear::FiniteDimInnerSpace;
-use na::{Unit, ColumnVector, OwnedColumnVector, Vector2, Vector3};
-use na::storage::Storage;
-use na::dimension::{DimName, U1};
+use na::{Real, DefaultAllocator, Unit, VectorN, Vector2, Vector3};
+use na::allocator::Allocator;
+use na::dimension::Dim;
 
 /// Reflects a vector wrt. the hyperplane with normal `plane_normal`.
 fn reflect_wrt_hyperplane_with_algebraic_genericity<V>(plane_normal: &Unit<V>, vector: &V) -> V
@@ -16,12 +15,12 @@ fn reflect_wrt_hyperplane_with_algebraic_genericity<V>(plane_normal: &Unit<V>, v
 
 
 /// Reflects a vector wrt. the hyperplane with normal `plane_normal`.
-fn reflect_wrt_hyperplane_with_structural_genericity<N, D, S>(plane_normal: &Unit<ColumnVector<N, D, S>>,
-                                                               vector:       &ColumnVector<N, D, S>)
-                                                               -> OwnedColumnVector<N, D, S::Alloc>
+fn reflect_wrt_hyperplane_with_dimensional_genericity<N: Real, D: Dim>(plane_normal: &Unit<VectorN<N, D>>,
+                                                                       vector:       &VectorN<N, D>)
+                                                                       -> VectorN<N, D>
     where N: Real,
-          D: DimName,
-          S: Storage<N, D, U1> {
+          D: Dim,
+          DefaultAllocator: Allocator<N, D> {
     let n = plane_normal.as_ref(); // Get the underlying V.
     vector - n * (n.dot(vector) * na::convert(2.0))
 }
@@ -57,8 +56,8 @@ fn main() {
     assert_eq!(reflect_wrt_hyperplane_with_algebraic_genericity(&plane2, &v2).y, -2.0);
     assert_eq!(reflect_wrt_hyperplane_with_algebraic_genericity(&plane3, &v3).y, -2.0);
 
-    assert_eq!(reflect_wrt_hyperplane_with_structural_genericity(&plane2, &v2).y, -2.0);
-    assert_eq!(reflect_wrt_hyperplane_with_structural_genericity(&plane3, &v3).y, -2.0);
+    assert_eq!(reflect_wrt_hyperplane_with_dimensional_genericity(&plane2, &v2).y, -2.0);
+    assert_eq!(reflect_wrt_hyperplane_with_dimensional_genericity(&plane3, &v3).y, -2.0);
 
     // Call each specific implementation depending on the dimension.
     assert_eq!(reflect_wrt_hyperplane2(&plane2, &v2).y, -2.0);

src/core/alias.rs

@@ -1,7 +1,7 @@
 use core::Matrix;
 use core::dimension::{Dynamic, U1, U2, U3, U4, U5, U6};
-use core::matrix_array::MatrixArray;
 use core::matrix_vec::MatrixVec;
+use core::storage::Owned;
 
 /*
  *
@@ -10,14 +10,18 @@ use core::matrix_vec::MatrixVec;
  *
  *
  */
-/// A dynamically sized column-major matrix.
-pub type DMatrix<N> = Matrix<N, Dynamic, Dynamic, MatrixVec<N, Dynamic, Dynamic>>;
+/// A staticaly sized column-major matrix with `R` rows and `C` columns.
+#[deprecated(note = "This matrix name contains a typo. Use MatrixMN instead.")]
+pub type MatrixNM<N, R, C> = Matrix<N, R, C, Owned<N, R, C>>;
 
 /// A staticaly sized column-major matrix with `R` rows and `C` columns.
-pub type MatrixNM<N, R, C> = Matrix<N, R, C, MatrixArray<N, R, C>>;
+pub type MatrixMN<N, R, C> = Matrix<N, R, C, Owned<N, R, C>>;
 
 /// A staticaly sized column-major square matrix with `D` rows and columns.
-pub type MatrixN<N, D> = MatrixNM<N, D, D>;
+pub type MatrixN<N, D> = MatrixMN<N, D, D>;
+
+/// A dynamically sized column-major matrix.
+pub type DMatrix<N> = MatrixN<N, Dynamic>;
 
 /// A stack-allocated, column-major, 1x1 square matrix.
 pub type Matrix1<N> = MatrixN<N, U1>;
@@ -33,75 +37,75 @@ pub type Matrix5<N> = MatrixN<N, U5>;
 pub type Matrix6<N> = MatrixN<N, U6>;
 
 /// A stack-allocated, column-major, 1x2 square matrix.
-pub type Matrix1x2<N> = MatrixNM<N, U1, U2>;
+pub type Matrix1x2<N> = MatrixMN<N, U1, U2>;
 /// A stack-allocated, column-major, 1x3 square matrix.
-pub type Matrix1x3<N> = MatrixNM<N, U1, U3>;
+pub type Matrix1x3<N> = MatrixMN<N, U1, U3>;
 /// A stack-allocated, column-major, 1x4 square matrix.
-pub type Matrix1x4<N> = MatrixNM<N, U1, U4>;
+pub type Matrix1x4<N> = MatrixMN<N, U1, U4>;
 /// A stack-allocated, column-major, 1x5 square matrix.
-pub type Matrix1x5<N> = MatrixNM<N, U1, U5>;
+pub type Matrix1x5<N> = MatrixMN<N, U1, U5>;
 /// A stack-allocated, column-major, 1x6 square matrix.
-pub type Matrix1x6<N> = MatrixNM<N, U1, U6>;
+pub type Matrix1x6<N> = MatrixMN<N, U1, U6>;
 
 /// A stack-allocated, column-major, 2x3 square matrix.
-pub type Matrix2x3<N> = MatrixNM<N, U2, U3>;
+pub type Matrix2x3<N> = MatrixMN<N, U2, U3>;
 /// A stack-allocated, column-major, 2x4 square matrix.
-pub type Matrix2x4<N> = MatrixNM<N, U2, U4>;
+pub type Matrix2x4<N> = MatrixMN<N, U2, U4>;
 /// A stack-allocated, column-major, 2x5 square matrix.
-pub type Matrix2x5<N> = MatrixNM<N, U2, U5>;
+pub type Matrix2x5<N> = MatrixMN<N, U2, U5>;
 /// A stack-allocated, column-major, 2x6 square matrix.
-pub type Matrix2x6<N> = MatrixNM<N, U2, U6>;
+pub type Matrix2x6<N> = MatrixMN<N, U2, U6>;
 
 /// A stack-allocated, column-major, 3x4 square matrix.
-pub type Matrix3x4<N> = MatrixNM<N, U3, U4>;
+pub type Matrix3x4<N> = MatrixMN<N, U3, U4>;
 /// A stack-allocated, column-major, 3x5 square matrix.
-pub type Matrix3x5<N> = MatrixNM<N, U3, U5>;
+pub type Matrix3x5<N> = MatrixMN<N, U3, U5>;
 /// A stack-allocated, column-major, 3x6 square matrix.
-pub type Matrix3x6<N> = MatrixNM<N, U3, U6>;
+pub type Matrix3x6<N> = MatrixMN<N, U3, U6>;
 
 /// A stack-allocated, column-major, 4x5 square matrix.
-pub type Matrix4x5<N> = MatrixNM<N, U4, U5>;
+pub type Matrix4x5<N> = MatrixMN<N, U4, U5>;
 /// A stack-allocated, column-major, 4x6 square matrix.
-pub type Matrix4x6<N> = MatrixNM<N, U4, U6>;
+pub type Matrix4x6<N> = MatrixMN<N, U4, U6>;
 
 /// A stack-allocated, column-major, 5x6 square matrix.
-pub type Matrix5x6<N> = MatrixNM<N, U5, U6>;
+pub type Matrix5x6<N> = MatrixMN<N, U5, U6>;
 
 
 /// A stack-allocated, column-major, 2x1 square matrix.
-pub type Matrix2x1<N> = MatrixNM<N, U2, U1>;
+pub type Matrix2x1<N> = MatrixMN<N, U2, U1>;
 /// A stack-allocated, column-major, 3x1 square matrix.
-pub type Matrix3x1<N> = MatrixNM<N, U3, U1>;
+pub type Matrix3x1<N> = MatrixMN<N, U3, U1>;
 /// A stack-allocated, column-major, 4x1 square matrix.
-pub type Matrix4x1<N> = MatrixNM<N, U4, U1>;
+pub type Matrix4x1<N> = MatrixMN<N, U4, U1>;
 /// A stack-allocated, column-major, 5x1 square matrix.
-pub type Matrix5x1<N> = MatrixNM<N, U5, U1>;
+pub type Matrix5x1<N> = MatrixMN<N, U5, U1>;
 /// A stack-allocated, column-major, 6x1 square matrix.
-pub type Matrix6x1<N> = MatrixNM<N, U6, U1>;
+pub type Matrix6x1<N> = MatrixMN<N, U6, U1>;
 
 /// A stack-allocated, column-major, 3x2 square matrix.
-pub type Matrix3x2<N> = MatrixNM<N, U3, U2>;
+pub type Matrix3x2<N> = MatrixMN<N, U3, U2>;
 /// A stack-allocated, column-major, 4x2 square matrix.
-pub type Matrix4x2<N> = MatrixNM<N, U4, U2>;
+pub type Matrix4x2<N> = MatrixMN<N, U4, U2>;
 /// A stack-allocated, column-major, 5x2 square matrix.
-pub type Matrix5x2<N> = MatrixNM<N, U5, U2>;
+pub type Matrix5x2<N> = MatrixMN<N, U5, U2>;
 /// A stack-allocated, column-major, 6x2 square matrix.
-pub type Matrix6x2<N> = MatrixNM<N, U6, U2>;
+pub type Matrix6x2<N> = MatrixMN<N, U6, U2>;
 
 /// A stack-allocated, column-major, 4x3 square matrix.
-pub type Matrix4x3<N> = MatrixNM<N, U4, U3>;
+pub type Matrix4x3<N> = MatrixMN<N, U4, U3>;
 /// A stack-allocated, column-major, 5x3 square matrix.
-pub type Matrix5x3<N> = MatrixNM<N, U5, U3>;
+pub type Matrix5x3<N> = MatrixMN<N, U5, U3>;
 /// A stack-allocated, column-major, 6x3 square matrix.
-pub type Matrix6x3<N> = MatrixNM<N, U6, U3>;
+pub type Matrix6x3<N> = MatrixMN<N, U6, U3>;
 
 /// A stack-allocated, column-major, 5x4 square matrix.
-pub type Matrix5x4<N> = MatrixNM<N, U5, U4>;
+pub type Matrix5x4<N> = MatrixMN<N, U5, U4>;
 /// A stack-allocated, column-major, 6x4 square matrix.
-pub type Matrix6x4<N> = MatrixNM<N, U6, U4>;
+pub type Matrix6x4<N> = MatrixMN<N, U6, U4>;
 
 /// A stack-allocated, column-major, 6x5 square matrix.
-pub type Matrix6x5<N> = MatrixNM<N, U6, U5>;
+pub type Matrix6x5<N> = MatrixMN<N, U6, U5>;
 
 
 /*
@@ -115,7 +119,7 @@ pub type Matrix6x5<N> = MatrixNM<N, U6, U5>;
 pub type DVector<N> = Matrix<N, Dynamic, U1, MatrixVec<N, Dynamic, U1>>;
 
 /// A statically sized D-dimensional column vector.
-pub type VectorN<N, D> = MatrixNM<N, D, U1>;
+pub type VectorN<N, D> = MatrixMN<N, D, U1>;
 
 /// A stack-allocated, 1-dimensional column vector.
 pub type Vector1<N> = VectorN<N, U1>;
@@ -142,7 +146,7 @@ pub type Vector6<N> = VectorN<N, U6>;
 pub type RowDVector<N> = Matrix<N, U1, Dynamic, MatrixVec<N, U1, Dynamic>>;
 
 /// A statically sized D-dimensional row vector.
-pub type RowVectorN<N, D> = MatrixNM<N, U1, D>;
+pub type RowVectorN<N, D> = MatrixMN<N, U1, D>;
 
 /// A stack-allocated, 1-dimensional row vector.
 pub type RowVector1<N> = RowVectorN<N, U1>;

src/core/allocator.rs

@@ -2,10 +2,10 @@
 
 use std::any::Any;
 
-use core::Scalar;
+use core::{DefaultAllocator, Scalar};
 use core::constraint::{SameNumberOfRows, SameNumberOfColumns, ShapeConstraint};
 use core::dimension::{Dim, U1};
-use core::storage::{Storage, OwnedStorage};
+use core::storage::ContiguousStorageMut;
 
 /// A matrix allocator of a memory buffer that may contain `R::to_usize() * C::to_usize()`
 /// elements of type `N`.
@@ -16,9 +16,9 @@ use core::storage::{Storage, OwnedStorage};
 ///
 /// Every allocator must be both static and dynamic. Though not all implementations may share the
 /// same `Buffer` type.
-pub trait Allocator<N: Scalar, R: Dim, C: Dim>: Any + Sized {
+pub trait Allocator<N: Scalar, R: Dim, C: Dim = U1>: Any + Sized {
     /// The type of buffer this allocator can instanciate.
-    type Buffer: OwnedStorage<N, R, C, Alloc = Self>;
+    type Buffer: ContiguousStorageMut<N, R, C> + Clone;
 
     /// Allocates a buffer with the given number of rows and columns without initializing its content.
     unsafe fn allocate_uninitialized(nrows: R, ncols: C) -> Self::Buffer;
@@ -27,15 +27,20 @@ pub trait Allocator<N: Scalar, R: Dim, C: Dim>: Any + Sized {
     fn allocate_from_iterator<I: IntoIterator<Item = N>>(nrows: R, ncols: C, iter: I) -> Self::Buffer;
 }
 
-/// A matrix data allocator dedicated to the given owned matrix storage.
-pub trait OwnedAllocator<N: Scalar, R: Dim, C: Dim, S: OwnedStorage<N, R, C, Alloc = Self>>:
-    Allocator<N, R, C, Buffer = S> {
-}
-
-impl<N, R, C, T, S> OwnedAllocator<N, R, C, S> for T
-    where N: Scalar, R: Dim, C: Dim,
-          T: Allocator<N, R, C, Buffer = S>,
-          S: OwnedStorage<N, R, C, Alloc = T> {
+/// A matrix reallocator. Changes the size of the memory buffer that initially contains (RFrom ×
+/// CFrom) elements to a smaller or larger size (RTo, CTo).
+pub trait Reallocator<N: Scalar, RFrom: Dim, CFrom: Dim, RTo: Dim, CTo: Dim>:
+    Allocator<N, RFrom, CFrom> + Allocator<N, RTo, CTo> {
+    /// Reallocates a buffer of shape `(RTo, CTo)`, possibly reusing a previously allocated buffer
+    /// `buf`. Data stored by `buf` are linearly copied to the output:
+    ///
+    /// * The copy is performed as if both were just arrays (without a matrix structure).
+    /// * If `buf` is larger than the output size, then extra elements of `buf` are truncated.
+    /// * If `buf` is smaller than the output size, then extra elements of the output are left
+    /// uninitialized.
+    unsafe fn reallocate_copy(nrows: RTo, ncols: CTo,
+                              buf: <Self as Allocator<N, RFrom, CFrom>>::Buffer)
+                              -> <Self as Allocator<N, RTo, CTo>>::Buffer;
 }
 
 /// The number of rows of the result of a componentwise operation on two matrices.
@@ -45,45 +50,36 @@ pub type SameShapeR<R1, R2> = <ShapeConstraint as SameNumberOfRows<R1, R2>>::Rep
 pub type SameShapeC<C1, C2> = <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative;
 
 // FIXME: Bad name.
-/// Restricts the given number of rows and columns to be respectively the same. Can only be used
-/// when `Self = SA::Alloc`.
-pub trait SameShapeAllocator<N, R1, C1, R2, C2, SA>:
+/// Restricts the given number of rows and columns to be respectively the same.
+pub trait SameShapeAllocator<N, R1, C1, R2, C2>:
         Allocator<N, R1, C1> +
         Allocator<N, SameShapeR<R1, R2>, SameShapeC<C1, C2>>
     where R1: Dim, R2: Dim, C1: Dim, C2: Dim,
           N: Scalar,
-          SA: Storage<N, R1, C1, Alloc = Self>,
           ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
 }
 
-impl<N, R1, R2, C1, C2, SA> SameShapeAllocator<N, R1, C1, R2, C2, SA> for SA::Alloc
+impl<N, R1, R2, C1, C2> SameShapeAllocator<N, R1, C1, R2, C2> for DefaultAllocator
     where R1: Dim, R2: Dim, C1: Dim, C2: Dim,
           N: Scalar,
-          SA: Storage<N, R1, C1>,
-          SA::Alloc:
-            Allocator<N, R1, C1> +
-            Allocator<N, SameShapeR<R1, R2>, SameShapeC<C1, C2>>,
+          DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, SameShapeR<R1, R2>, SameShapeC<C1, C2>>,
           ShapeConstraint:  SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
 }
 
 // XXX: Bad name.
-/// Restricts the given number of rows to be equal. Can only be used when `Self = SA::Alloc`.
-pub trait SameShapeColumnVectorAllocator<N, R1, R2, SA>:
-        Allocator<N, R1, U1> +
-        Allocator<N, SameShapeR<R1, R2>, U1> +
-        SameShapeAllocator<N, R1, U1, R2, U1, SA>
+/// Restricts the given number of rows to be equal.
+pub trait SameShapeVectorAllocator<N, R1, R2>:
+        Allocator<N, R1> +
+        Allocator<N, SameShapeR<R1, R2>> +
+        SameShapeAllocator<N, R1, U1, R2, U1>
     where R1: Dim, R2: Dim,
           N: Scalar,
-          SA: Storage<N, R1, U1, Alloc = Self>,
           ShapeConstraint: SameNumberOfRows<R1, R2> {
 }
 
-impl<N, R1, R2, SA> SameShapeColumnVectorAllocator<N, R1, R2, SA> for SA::Alloc
+impl<N, R1, R2> SameShapeVectorAllocator<N, R1, R2> for DefaultAllocator
     where R1: Dim, R2: Dim,
           N: Scalar,
-          SA: Storage<N, R1, U1>,
-          SA::Alloc:
-            Allocator<N, R1, U1> +
-            Allocator<N, SameShapeR<R1, R2>, U1>,
+          DefaultAllocator: Allocator<N, R1, U1> + Allocator<N, SameShapeR<R1, R2>>,
           ShapeConstraint:  SameNumberOfRows<R1, R2> {
 }

src/core/blas.rs

@@ -0,0 +1,458 @@
+use std::mem;
+use num::{Zero, One, Signed};
+use matrixmultiply;
+use alga::general::{ClosedMul, ClosedAdd};
+
+use core::{Scalar, Matrix, Vector};
+use core::dimension::{Dim, U1, U2, U3, U4, Dynamic};
+use core::constraint::{ShapeConstraint, SameNumberOfRows, SameNumberOfColumns, AreMultipliable, DimEq};
+use core::storage::{Storage, StorageMut};
+
+
+
+impl<N: Scalar + PartialOrd + Signed, D: Dim, S: Storage<N, D>> Vector<N, D, S> {
+    /// Computes the index of the vector component with the largest absolute value.
+    #[inline]
+    pub fn iamax(&self) -> usize {
+        assert!(!self.is_empty(), "The input vector must not be empty.");
+
+        let mut the_max = unsafe { self.vget_unchecked(0).abs() };
+        let mut the_i   = 0;
+
+        for i in 1 .. self.nrows() {
+            let val = unsafe { self.vget_unchecked(i).abs() };
+
+            if val > the_max {
+                the_max = val;
+                the_i   = i;
+            }
+        }
+
+        the_i
+    }
+}
+
+impl<N: Scalar + PartialOrd + Signed, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
+    /// Computes the index of the matrix component with the largest absolute value.
+    #[inline]
+    pub fn iamax_full(&self) -> (usize, usize) {
+        assert!(!self.is_empty(), "The input matrix must not be empty.");
+
+        let mut the_max = unsafe { self.get_unchecked(0, 0).abs() };
+        let mut the_ij  = (0, 0);
+
+        for j in 0 .. self.ncols() {
+            for i in 0 .. self.nrows() {
+                let val = unsafe { self.get_unchecked(i, j).abs() };
+
+                if val > the_max {
+                    the_max = val;
+                    the_ij  = (i, j);
+                }
+            }
+        }
+
+        the_ij
+    }
+}
+
+impl<N, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S>
+    where N: Scalar + Zero + ClosedAdd + ClosedMul {
+    /// The dot product between two matrices (seen as vectors).
+    ///
+    /// Note that this is **not** the matrix multiplication as in, e.g., numpy. For matrix
+    /// multiplication, use one of: `.gemm`, `mul_to`, `.mul`, `*`.
+    #[inline]
+    pub fn dot<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<N, R2, C2, SB>) -> N
+        where SB: Storage<N, R2, C2>,
+              ShapeConstraint: DimEq<R, R2> + DimEq<C, C2> {
+        assert!(self.nrows() == rhs.nrows(), "Dot product dimensions mismatch.");
+
+
+        // So we do some special cases for common fixed-size vectors of dimension lower than 8
+        // because the `for` loop bellow won't be very efficient on those.
+        if (R::is::<U2>() || R2::is::<U2>()) &&
+           (C::is::<U1>() || C2::is::<U1>()) {
+            unsafe {
+                let a = *self.get_unchecked(0, 0) * *rhs.get_unchecked(0, 0);
+                let b = *self.get_unchecked(1, 0) * *rhs.get_unchecked(1, 0);
+
+                return a + b;
+            }
+        }
+        if (R::is::<U3>() || R2::is::<U3>()) &&
+           (C::is::<U1>() || C2::is::<U1>()) {
+            unsafe {
+                let a = *self.get_unchecked(0, 0) * *rhs.get_unchecked(0, 0);
+                let b = *self.get_unchecked(1, 0) * *rhs.get_unchecked(1, 0);
+                let c = *self.get_unchecked(2, 0) * *rhs.get_unchecked(2, 0);
+
+                return a + b + c;
+            }
+        }
+        if (R::is::<U4>() || R2::is::<U4>()) &&
+           (C::is::<U1>() || C2::is::<U1>()) {
+            unsafe {
+                let mut a = *self.get_unchecked(0, 0) * *rhs.get_unchecked(0, 0);
+                let mut b = *self.get_unchecked(1, 0) * *rhs.get_unchecked(1, 0);
+                let c = *self.get_unchecked(2, 0) * *rhs.get_unchecked(2, 0);
+                let d = *self.get_unchecked(3, 0) * *rhs.get_unchecked(3, 0);
+
+                a += c;
+                b += d;
+
+                return a + b;
+            }
+        }
+
+
+        // All this is inspired from the "unrolled version" discussed in:
+        // http://blog.theincredibleholk.org/blog/2012/12/10/optimizing-dot-product/
+        //
+        // And this comment from bluss:
+        // https://users.rust-lang.org/t/how-to-zip-two-slices-efficiently/2048/12
+        let mut res = N::zero();
+
+        // We have to define them outside of the loop (and not inside at first assignment)
+        // otherwize vectorization won't kick in for some reason.
+        let mut acc0;
+        let mut acc1;
+        let mut acc2;
+        let mut acc3;
+        let mut acc4;
+        let mut acc5;
+        let mut acc6;
+        let mut acc7;
+
+        for j in 0 .. self.ncols() {
+            let mut i = 0;
+
+            acc0 = N::zero();
+            acc1 = N::zero();
+            acc2 = N::zero();
+            acc3 = N::zero();
+            acc4 = N::zero();
+            acc5 = N::zero();
+            acc6 = N::zero();
+            acc7 = N::zero();
+
+            while self.nrows() - i >= 8 {
+                acc0 += unsafe { *self.get_unchecked(i + 0, j) * *rhs.get_unchecked(i + 0, j) };
+                acc1 += unsafe { *self.get_unchecked(i + 1, j) * *rhs.get_unchecked(i + 1, j) };
+                acc2 += unsafe { *self.get_unchecked(i + 2, j) * *rhs.get_unchecked(i + 2, j) };
+                acc3 += unsafe { *self.get_unchecked(i + 3, j) * *rhs.get_unchecked(i + 3, j) };
+                acc4 += unsafe { *self.get_unchecked(i + 4, j) * *rhs.get_unchecked(i + 4, j) };
+                acc5 += unsafe { *self.get_unchecked(i + 5, j) * *rhs.get_unchecked(i + 5, j) };
+                acc6 += unsafe { *self.get_unchecked(i + 6, j) * *rhs.get_unchecked(i + 6, j) };
+                acc7 += unsafe { *self.get_unchecked(i + 7, j) * *rhs.get_unchecked(i + 7, j) };
+                i += 8;
+            }
+
+            res += acc0 + acc4;
+            res += acc1 + acc5;
+            res += acc2 + acc6;
+            res += acc3 + acc7;
+
+            for k in i .. self.nrows() {
+                res += unsafe { *self.get_unchecked(k, j) * *rhs.get_unchecked(k, j) }
+            }
+        }
+
+        res
+    }
+
+    /// The dot product between the transpose of `self` and `rhs`.
+    #[inline]
+    pub fn tr_dot<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<N, R2, C2, SB>) -> N
+        where SB: Storage<N, R2, C2>,
+              ShapeConstraint: DimEq<C, R2> + DimEq<R, C2> {
+        let (nrows, ncols) = self.shape();
+        assert!((ncols, nrows) == rhs.shape(), "Transposed dot product dimension mismatch.");
+
+        let mut res = N::zero();
+
+        for j in 0 .. self.nrows() {
+            for i in 0 .. self.ncols() {
+                res += unsafe { *self.get_unchecked(j, i) * *rhs.get_unchecked(i, j) }
+            }
+        }
+
+        res
+    }
+}
+
+fn array_axpy<N>(y: &mut [N], a: N, x: &[N], beta: N, stride1: usize, stride2: usize, len: usize)
+    where N: Scalar + Zero + ClosedAdd + ClosedMul {
+    for i in 0 .. len {
+        unsafe {
+            let y = y.get_unchecked_mut(i * stride1);
+            *y = a * *x.get_unchecked(i * stride2) + beta * *y;
+        }
+    }
+}
+
+fn array_ax<N>(y: &mut [N], a: N, x: &[N], stride1: usize, stride2: usize, len: usize)
+    where N: Scalar + Zero + ClosedAdd + ClosedMul {
+    for i in 0 .. len {
+        unsafe {
+            *y.get_unchecked_mut(i * stride1) = a * *x.get_unchecked(i * stride2);
+        }
+    }
+}
+
+impl<N, D: Dim, S> Vector<N, D, S>
+    where N: Scalar + Zero + ClosedAdd + ClosedMul,
+          S: StorageMut<N, D> {
+    /// Computes `self = a * x + b * self`.
+    ///
+    /// If be is zero, `self` is never read from.
+    #[inline]
+    pub fn axpy<D2: Dim, SB>(&mut self, a: N, x: &Vector<N, D2, SB>, b: N)
+        where SB: Storage<N, D2>,
+              ShapeConstraint: DimEq<D, D2> {
+
+        assert_eq!(self.nrows(), x.nrows(), "Axpy: mismatched vector shapes.");
+
+        let rstride1 = self.strides().0;
+        let rstride2 = x.strides().0;
+
+        let y = self.data.as_mut_slice();
+        let x = x.data.as_slice();
+
+        if !b.is_zero() {
+            array_axpy(y, a, x, b, rstride1, rstride2, x.len());
+        }
+        else {
+            array_ax(y, a, x, rstride1, rstride2, x.len());
+        }
+    }
+
+    /// Computes `self = alpha * a * x + beta * self`, where `a` is a matrix, `x` a vector, and
+    /// `alpha, beta` two scalars.
+    ///
+    /// If `beta` is zero, `self` is never read.
+    #[inline]
+    pub fn gemv<R2: Dim, C2: Dim, D3: Dim, SB, SC>(&mut self,
+                                                   alpha: N,
+                                                   a:     &Matrix<N, R2, C2, SB>,
+                                                   x:     &Vector<N, D3, SC>,
+                                                   beta:  N)
+        where N:  One,
+              SB: Storage<N, R2, C2>,
+              SC: Storage<N, D3>,
+              ShapeConstraint: DimEq<D, R2> +
+                               AreMultipliable<R2, C2, D3, U1> {
+        let dim1 = self.nrows();
+        let (nrows2, ncols2) = a.shape();
+        let dim3 = x.nrows();
+
+        assert!(ncols2 == dim3 && dim1 == nrows2, "Gemv: dimensions mismatch.");
+
+        if ncols2 == 0 {
+            return;
+        }
+
+        // FIXME: avoid bound checks.
+        let col2 = a.column(0);
+        let val  = unsafe { *x.vget_unchecked(0) };
+        self.axpy(alpha * val, &col2, beta);
+
+        for j in 1 .. ncols2 {
+            let col2 = a.column(j);
+            let val  = unsafe { *x.vget_unchecked(j) };
+
+            self.axpy(alpha * val, &col2, N::one());
+        }
+    }
+
+    /// Computes `self = alpha * a * x + beta * self`, where `a` is a **symmetric** matrix, `x` a
+    /// vector, and `alpha, beta` two scalars.
+    ///
+    /// If `beta` is zero, `self` is never read. If `self` is read, only its lower-triangular part
+    /// (including the diagonal) is actually read.
+    #[inline]
+    pub fn gemv_symm<D2: Dim, D3: Dim, SB, SC>(&mut self,
+                                               alpha: N,
+                                               a:     &Matrix<N, D2, D2, SB>,
+                                               x:     &Vector<N, D3, SC>,
+                                               beta:  N)
+        where N:  One,
+              SB: Storage<N, D2, D2>,
+              SC: Storage<N, D3>,
+              ShapeConstraint: DimEq<D, D2> +
+                               AreMultipliable<D2, D2, D3, U1> {
+        let dim1 = self.nrows();
+        let dim2 = a.nrows();
+        let dim3 = x.nrows();
+
+        assert!(a.is_square(), "Syetric gemv: the input matrix must be square.");
+        assert!(dim2 == dim3 && dim1 == dim2, "Symmetric gemv: dimensions mismatch.");
+
+        if dim2 == 0 {
+            return;
+        }
+
+        // FIXME: avoid bound checks.
+        let col2 = a.column(0);
+        let val  = unsafe { *x.vget_unchecked(0) };
+        self.axpy(alpha * val, &col2, beta);
+        self[0] += alpha * x.rows_range(1 ..).dot(&a.slice_range(1 .., 0));
+
+        for j in 1 .. dim2 {
+            let col2 = a.column(j);
+            let dot  = x.rows_range(j ..).dot(&col2.rows_range(j ..));
+
+            let val;
+            unsafe {
+                val = *x.vget_unchecked(j);
+                *self.vget_unchecked_mut(j) += alpha * dot;
+            }
+            self.rows_range_mut(j + 1 ..).axpy(alpha * val, &col2.rows_range(j + 1 ..), N::one());
+        }
+    }
+}
+
+impl<N, R1: Dim, C1: Dim, S: StorageMut<N, R1, C1>> Matrix<N, R1, C1, S>
+    where N: Scalar + Zero + ClosedAdd + ClosedMul {
+
+    /// Computes `self = alpha * x * y.transpose() + beta * self`.
+    ///
+    /// If `beta` is zero, `self` is never read.
+    #[inline]
+    pub fn ger<D2: Dim, D3: Dim, SB, SC>(&mut self, alpha: N, x: &Vector<N, D2, SB>, y: &Vector<N, D3, SC>, beta: N)
+        where N: One,
+              SB: Storage<N, D2>,
+              SC: Storage<N, D3>,
+              ShapeConstraint: DimEq<R1, D2> + DimEq<C1, D3> {
+        let (nrows1, ncols1) = self.shape();
+        let dim2 = x.nrows();
+        let dim3 = y.nrows();
+
+        assert!(nrows1 == dim2 && ncols1 == dim3, "ger: dimensions mismatch.");
+
+        for j in 0 .. ncols1 {
+            // FIXME: avoid bound checks.
+            let val = unsafe { *y.vget_unchecked(j) };
+            self.column_mut(j).axpy(alpha * val, x, beta);
+        }
+    }
+
+    /// Computes `self = alpha * a * b + beta * self`, where `a, b, self` are matrices.
+    /// `alpha` and `beta` are scalar.
+    ///
+    /// If `beta` is zero, `self` is never read.
+    #[inline]
+    pub fn gemm<R2: Dim, C2: Dim, R3: Dim, C3: Dim, SB, SC>(&mut self,
+                                                            alpha: N,
+                                                            a: &Matrix<N, R2, C2, SB>,
+                                                            b: &Matrix<N, R3, C3, SC>,
+                                                            beta: N)
+        where N:  One,
+              SB: Storage<N, R2, C2>,
+              SC: Storage<N, R3, C3>,
+              ShapeConstraint: SameNumberOfRows<R1, R2>    +
+                               SameNumberOfColumns<C1, C3> +
+                               AreMultipliable<R2, C2, R3, C3> {
+       let (nrows1, ncols1) = self.shape();
+       let (nrows2, ncols2) = a.shape();
+       let (nrows3, ncols3) = b.shape();
+
+       assert_eq!(ncols2, nrows3, "gemm: dimensions mismatch for multiplication.");
+       assert_eq!((nrows1, ncols1), (nrows2, ncols3), "gemm: dimensions mismatch for addition.");
+
+       // We assume large matrices will be Dynamic but small matrices static.
+       // We could use matrixmultiply for large statically-sized matrices but the performance
+       // threshold to activate it would be different from SMALL_DIM because our code optimizes
+       // better for statically-sized matrices.
+       let is_dynamic = R1::is::<Dynamic>() || C1::is::<Dynamic>() ||
+                        R2::is::<Dynamic>() || C2::is::<Dynamic>() ||
+                        R3::is::<Dynamic>() || C3::is::<Dynamic>();
+       // Thershold determined ampirically.
+       const SMALL_DIM: usize = 5;
+
+       if is_dynamic &&
+          nrows1 > SMALL_DIM && ncols1 > SMALL_DIM &&
+          nrows2 > SMALL_DIM && ncols2 > SMALL_DIM {
+           if N::is::<f32>() {
+               let (rsa, csa) = a.strides();
+               let (rsb, csb) = b.strides();
+               let (rsc, csc) = self.strides();
+
+               unsafe {
+                   matrixmultiply::sgemm(
+                       nrows2,
+                       ncols2,
+                       ncols3,
+                       mem::transmute_copy(&alpha),
+                       a.data.ptr() as *const f32,
+                       rsa as isize, csa as isize,
+                       b.data.ptr() as *const f32,
+                       rsb as isize, csb as isize,
+                       mem::transmute_copy(&beta),
+                       self.data.ptr_mut() as *mut f32,
+                       rsc as isize, csc as isize);
+               }
+           }
+           else if N::is::<f64>() {
+               let (rsa, csa) = a.strides();
+               let (rsb, csb) = b.strides();
+               let (rsc, csc) = self.strides();
+
+               unsafe {
+                   matrixmultiply::dgemm(
+                       nrows2,
+                       ncols2,
+                       ncols3,
+                       mem::transmute_copy(&alpha),
+                       a.data.ptr() as *const f64,
+                       rsa as isize, csa as isize,
+                       b.data.ptr() as *const f64,
+                       rsb as isize, csb as isize,
+                       mem::transmute_copy(&beta),
+                       self.data.ptr_mut() as *mut f64,
+                       rsc as isize, csc as isize);
+               }
+           }
+       }
+       else {
+           for j1 in 0 .. ncols1 {
+               // FIXME: avoid bound checks.
+               self.column_mut(j1).gemv(alpha, a, &b.column(j1), beta);
+           }
+       }
+    }
+}
+
+
+impl<N, R1: Dim, C1: Dim, S: StorageMut<N, R1, C1>> Matrix<N, R1, C1, S>
+    where N: Scalar + Zero + ClosedAdd + ClosedMul {
+    /// Computes `self = alpha * x * y.transpose() + beta * self`, where `self` is a **symmetric**
+    /// matrix.
+    ///
+    /// If `beta` is zero, `self` is never read. The result is symmetric. Only the lower-triangular
+    /// (including the diagonal) part of `self` is read/written.
+    #[inline]
+    pub fn ger_symm<D2: Dim, D3: Dim, SB, SC>(&mut self,
+                                              alpha: N,
+                                              x:     &Vector<N, D2, SB>,
+                                              y:     &Vector<N, D3, SC>,
+                                              beta:  N)
+        where N: One,
+              SB: Storage<N, D2>,
+              SC: Storage<N, D3>,
+              ShapeConstraint: DimEq<R1, D2> + DimEq<C1, D3> {
+        let dim1 = self.nrows();
+        let dim2 = x.nrows();
+        let dim3 = y.nrows();
+
+        assert!(self.is_square(), "Symmetric ger: the input matrix must be square.");
+        assert!(dim1 == dim2 && dim1 == dim3, "ger: dimensions mismatch.");
+
+        for j in 0 .. dim1 {
+            // FIXME: avoid bound checks.
+            let val = unsafe { *y.vget_unchecked(j) };
+            let subdim = Dynamic::new(dim1 - j);
+            self.generic_slice_mut((j, j), (subdim, U1)).axpy(alpha * val, &x.rows_range(j ..), beta);
+        }
+    }
+}

src/core/cg.rs

@@ -7,20 +7,20 @@
 
 use num::One;
 
-use core::{Scalar, SquareMatrix, OwnedSquareMatrix, ColumnVector, Unit};
-use core::dimension::{DimName, DimNameSub, DimNameDiff, U1, U2, U3, U4};
-use core::storage::{Storage, StorageMut, OwnedStorage};
-use core::allocator::{Allocator, OwnedAllocator};
-use geometry::{PointBase, OrthographicBase, PerspectiveBase, IsometryBase, OwnedRotation, OwnedPoint};
+use core::{DefaultAllocator, Scalar, SquareMatrix, Vector, Unit,
+           VectorN, MatrixN, Vector3, Matrix3, Matrix4};
+use core::dimension::{DimName, DimNameSub, DimNameDiff, U1};
+use core::storage::{Storage, StorageMut};
+use core::allocator::Allocator;
+use geometry::{Point, Isometry, Point3, Rotation2, Rotation3, Orthographic3, Perspective3, IsometryMatrix3};
 
 use alga::general::{Real, Field};
 use alga::linear::Transformation;
 
 
-impl<N, D: DimName, S> SquareMatrix<N, D, S>
+impl<N, D: DimName> MatrixN<N, D>
     where N: Scalar + Field,
-          S: OwnedStorage<N, D, D>,
-          S::Alloc: OwnedAllocator<N, D, D, S> {
+          DefaultAllocator: Allocator<N, D, D> {
     /// Creates a new homogeneous matrix that applies the same scaling factor on each dimension.
     #[inline]
     pub fn new_scaling(scaling: N) -> Self {
@@ -32,9 +32,9 @@ impl<N, D: DimName, S> SquareMatrix<N, D, S>
 
     /// Creates a new homogeneous matrix that applies a distinct scaling factor for each dimension.
     #[inline]
-    pub fn new_nonuniform_scaling<SB>(scaling: &ColumnVector<N, DimNameDiff<D, U1>, SB>) -> Self
+    pub fn new_nonuniform_scaling<SB>(scaling: &Vector<N, DimNameDiff<D, U1>, SB>) -> Self
         where D:  DimNameSub<U1>,
-              SB: Storage<N, DimNameDiff<D, U1>, U1> {
+              SB: Storage<N, DimNameDiff<D, U1>> {
         let mut res = Self::one();
         for i in 0 .. scaling.len() {
             res[(i, i)] = scaling[i];
@@ -45,10 +45,9 @@ impl<N, D: DimName, S> SquareMatrix<N, D, S>
 
     /// Creates a new homogeneous matrix that applies a pure translation.
     #[inline]
-    pub fn new_translation<SB>(translation: &ColumnVector<N, DimNameDiff<D, U1>, SB>) -> Self
+    pub fn new_translation<SB>(translation: &Vector<N, DimNameDiff<D, U1>, SB>) -> Self
         where D:  DimNameSub<U1>,
-              SB: Storage<N, DimNameDiff<D, U1>, U1>,
-              S::Alloc: Allocator<N, DimNameDiff<D, U1>, U1> {
+              SB: Storage<N, DimNameDiff<D, U1>> {
         let mut res = Self::one();
         res.fixed_slice_mut::<DimNameDiff<D, U1>, U1>(0, D::dim() - 1).copy_from(translation);
 
@@ -56,44 +55,30 @@ impl<N, D: DimName, S> SquareMatrix<N, D, S>
     }
 }
 
-impl<N, S> SquareMatrix<N, U3, S>
-    where N: Real,
-          S: OwnedStorage<N, U3, U3>,
-          S::Alloc: OwnedAllocator<N, U3, U3, S> {
+impl<N: Real> Matrix3<N> {
     /// Builds a 2 dimensional homogeneous rotation matrix from an angle in radian.
     #[inline]
-    pub fn new_rotation(angle: N) -> Self
-        where S::Alloc: Allocator<N, U2, U2> {
-        OwnedRotation::<N, U2, S::Alloc>::new(angle).to_homogeneous()
+    pub fn new_rotation(angle: N) -> Self {
+        Rotation2::new(angle).to_homogeneous()
     }
 }
 
-impl<N, S> SquareMatrix<N, U4, S>
-    where N: Real,
-          S: OwnedStorage<N, U4, U4>,
-          S::Alloc: OwnedAllocator<N, U4, U4, S> {
-
+impl<N: Real> Matrix4<N> {
     /// Builds a 3D homogeneous rotation matrix from an axis and an angle (multiplied together).
     /// 
     /// Returns the identity matrix if the given argument is zero.
     #[inline]
-    pub fn new_rotation<SB>(axisangle: ColumnVector<N, U3, SB>) -> Self
-        where SB: Storage<N, U3, U1>,
-              S::Alloc: Allocator<N, U3, U3> {
-        OwnedRotation::<N, U3, S::Alloc>::new(axisangle).to_homogeneous()
+    pub fn new_rotation(axisangle: Vector3<N>) -> Self {
+        Rotation3::new(axisangle).to_homogeneous()
     }
 
     /// Builds a 3D homogeneous rotation matrix from an axis and an angle (multiplied together).
     /// 
     /// Returns the identity matrix if the given argument is zero.
     #[inline]
-    pub fn new_rotation_wrt_point<SB>(axisangle: ColumnVector<N, U3, SB>, pt: OwnedPoint<N, U3, S::Alloc>) -> Self
-        where SB: Storage<N, U3, U1>,
-              S::Alloc: Allocator<N, U3, U3> +
-                        Allocator<N, U3, U1> +
-                        Allocator<N, U1, U3> {
-        let rot = OwnedRotation::<N, U3, S::Alloc>::from_scaled_axis(axisangle);
-        IsometryBase::rotation_wrt_point(rot, pt).to_homogeneous()
+    pub fn new_rotation_wrt_point(axisangle: Vector3<N>, pt: Point3<N>) -> Self {
+        let rot = Rotation3::from_scaled_axis(axisangle);
+        Isometry::rotation_wrt_point(rot, pt).to_homogeneous()
     }
 
     /// Builds a 3D homogeneous rotation matrix from an axis and an angle (multiplied together).
@@ -101,37 +86,32 @@ impl<N, S> SquareMatrix<N, U4, S>
     /// Returns the identity matrix if the given argument is zero.
     /// This is identical to `Self::new_rotation`.
     #[inline]
-    pub fn from_scaled_axis<SB>(axisangle: ColumnVector<N, U3, SB>) -> Self
-        where SB: Storage<N, U3, U1>,
-              S::Alloc: Allocator<N, U3, U3> {
-        OwnedRotation::<N, U3, S::Alloc>::from_scaled_axis(axisangle).to_homogeneous()
+    pub fn from_scaled_axis(axisangle: Vector3<N>) -> Self {
+        Rotation3::from_scaled_axis(axisangle).to_homogeneous()
     }
 
     /// Creates a new rotation from Euler angles.
     ///
     /// The primitive rotations are applied in order: 1 roll − 2 pitch − 3 yaw.
-    pub fn from_euler_angles(roll: N, pitch: N, yaw: N) -> Self
-        where S::Alloc: Allocator<N, U3, U3> {
-        OwnedRotation::<N, U3, S::Alloc>::from_euler_angles(roll, pitch, yaw).to_homogeneous()
+    pub fn from_euler_angles(roll: N, pitch: N, yaw: N) -> Self {
+        Rotation3::from_euler_angles(roll, pitch, yaw).to_homogeneous()
     }
 
     /// Builds a 3D homogeneous rotation matrix from an axis and a rotation angle.
-    pub fn from_axis_angle<SB>(axis: &Unit<ColumnVector<N, U3, SB>>, angle: N) -> Self
-        where SB: Storage<N, U3, U1>,
-              S::Alloc: Allocator<N, U3, U3> {
-        OwnedRotation::<N, U3, S::Alloc>::from_axis_angle(axis, angle).to_homogeneous()
+    pub fn from_axis_angle(axis: &Unit<Vector3<N>>, angle: N) -> Self {
+        Rotation3::from_axis_angle(axis, angle).to_homogeneous()
     }
 
     /// Creates a new homogeneous matrix for an orthographic projection.
     #[inline]
     pub fn new_orthographic(left: N, right: N, bottom: N, top: N, znear: N, zfar: N) -> Self {
-        OrthographicBase::new(left, right, bottom, top, znear, zfar).unwrap()
+        Orthographic3::new(left, right, bottom, top, znear, zfar).unwrap()
     }
 
     /// Creates a new homogeneous matrix for a perspective projection.
     #[inline]
     pub fn new_perspective(aspect: N, fovy: N, znear: N, zfar: N) -> Self {
-        PerspectiveBase::new(aspect, fovy, znear, zfar).unwrap()
+        Perspective3::new(aspect, fovy, znear, zfar).unwrap()
     }
 
     /// Creates an isometry that corresponds to the local frame of an observer standing at the
@@ -140,57 +120,30 @@ impl<N, S> SquareMatrix<N, U4, S>
     /// It maps the view direction `target - eye` to the positive `z` axis and the origin to the
     /// `eye`.
     #[inline]
-    pub fn new_observer_frame<SB>(eye:    &PointBase<N, U3, SB>,
-                                  target: &PointBase<N, U3, SB>,
-                                  up:     &ColumnVector<N, U3, SB>)
-                                  -> Self
-        where SB: OwnedStorage<N, U3, U1, Alloc = S::Alloc>,
-              SB::Alloc: OwnedAllocator<N, U3, U1, SB> +
-                         Allocator<N, U1, U3> +
-                         Allocator<N, U3, U3> {
-        IsometryBase::<N, U3, SB, OwnedRotation<N, U3, SB::Alloc>>
-                    ::new_observer_frame(eye, target, up).to_homogeneous()
+    pub fn new_observer_frame(eye: &Point3<N>, target: &Point3<N>, up: &Vector3<N>) -> Self {
+        IsometryMatrix3::new_observer_frame(eye, target, up).to_homogeneous()
     }
 
     /// Builds a right-handed look-at view matrix.
     #[inline]
-    pub fn look_at_rh<SB>(eye:    &PointBase<N, U3, SB>,
-                          target: &PointBase<N, U3, SB>,
-                          up:     &ColumnVector<N, U3, SB>)
-                          -> Self
-        where SB: OwnedStorage<N, U3, U1, Alloc = S::Alloc>,
-              SB::Alloc: OwnedAllocator<N, U3, U1, SB> +
-                         Allocator<N, U1, U3> +
-                         Allocator<N, U3, U3> {
-        IsometryBase::<N, U3, SB, OwnedRotation<N, U3, SB::Alloc>>
-                    ::look_at_rh(eye, target, up).to_homogeneous()
+    pub fn look_at_rh(eye: &Point3<N>, target: &Point3<N>, up: &Vector3<N>) -> Self {
+        IsometryMatrix3::look_at_rh(eye, target, up).to_homogeneous()
     }
 
     /// Builds a left-handed look-at view matrix.
     #[inline]
-    pub fn look_at_lh<SB>(eye:    &PointBase<N, U3, SB>,
-                          target: &PointBase<N, U3, SB>,
-                          up:     &ColumnVector<N, U3, SB>)
-                          -> Self
-        where SB: OwnedStorage<N, U3, U1, Alloc = S::Alloc>,
-              SB::Alloc: OwnedAllocator<N, U3, U1, SB> +
-                         Allocator<N, U1, U3> +
-                         Allocator<N, U3, U3> {
-        IsometryBase::<N, U3, SB, OwnedRotation<N, U3, SB::Alloc>>
-                    ::look_at_lh(eye, target, up).to_homogeneous()
+    pub fn look_at_lh(eye: &Point3<N>, target: &Point3<N>, up: &Vector3<N>) -> Self {
+        IsometryMatrix3::look_at_lh(eye, target, up).to_homogeneous()
     }
 }
 
 
-impl<N, D: DimName, S> SquareMatrix<N, D, S>
-    where N: Scalar + Field,
-          S: Storage<N, D, D> {
-
+impl<N: Scalar + Field, D: DimName, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
     /// Computes the transformation equal to `self` followed by an uniform scaling factor.
     #[inline]
-    pub fn append_scaling(&self, scaling: N) -> OwnedSquareMatrix<N, D, S::Alloc>
+    pub fn append_scaling(&self, scaling: N) -> MatrixN<N, D>
         where D: DimNameSub<U1>,
-              S::Alloc: Allocator<N, DimNameDiff<D, U1>, D> {
+              DefaultAllocator: Allocator<N, D, D> {
         let mut res = self.clone_owned();
         res.append_scaling_mut(scaling);
         res
@@ -198,9 +151,9 @@ impl<N, D: DimName, S> SquareMatrix<N, D, S>
 
     /// Computes the transformation equal to an uniform scaling factor followed by `self`.
     #[inline]
-    pub fn prepend_scaling(&self, scaling: N) -> OwnedSquareMatrix<N, D, S::Alloc>
+    pub fn prepend_scaling(&self, scaling: N) -> MatrixN<N, D>
         where D: DimNameSub<U1>,
-              S::Alloc: Allocator<N, D, DimNameDiff<D, U1>> {
+              DefaultAllocator: Allocator<N, D, D> {
         let mut res = self.clone_owned();
         res.prepend_scaling_mut(scaling);
         res
@@ -208,11 +161,10 @@ impl<N, D: DimName, S> SquareMatrix<N, D, S>
 
     /// Computes the transformation equal to `self` followed by a non-uniform scaling factor.
     #[inline]
-    pub fn append_nonuniform_scaling<SB>(&self, scaling: &ColumnVector<N, DimNameDiff<D, U1>, SB>)
-        -> OwnedSquareMatrix<N, D, S::Alloc>
+    pub fn append_nonuniform_scaling<SB>(&self, scaling: &Vector<N, DimNameDiff<D, U1>, SB>) -> MatrixN<N, D>
         where D: DimNameSub<U1>,
-              SB: Storage<N, DimNameDiff<D, U1>, U1>,
-              S::Alloc: Allocator<N, U1, D> {
+              SB: Storage<N, DimNameDiff<D, U1>>,
+              DefaultAllocator: Allocator<N, D, D> {
         let mut res = self.clone_owned();
         res.append_nonuniform_scaling_mut(scaling);
         res
@@ -220,11 +172,10 @@ impl<N, D: DimName, S> SquareMatrix<N, D, S>
 
     /// Computes the transformation equal to a non-uniform scaling factor followed by `self`.
     #[inline]
-    pub fn prepend_nonuniform_scaling<SB>(&self, scaling: &ColumnVector<N, DimNameDiff<D, U1>, SB>)
-        -> OwnedSquareMatrix<N, D, S::Alloc>
+    pub fn prepend_nonuniform_scaling<SB>(&self, scaling: &Vector<N, DimNameDiff<D, U1>, SB>) -> MatrixN<N, D>
         where D: DimNameSub<U1>,
-              SB: Storage<N, DimNameDiff<D, U1>, U1>,
-              S::Alloc: Allocator<N, D, U1> {
+              SB: Storage<N, DimNameDiff<D, U1>>,
+              DefaultAllocator: Allocator<N, D, D> {
         let mut res = self.clone_owned();
         res.prepend_nonuniform_scaling_mut(scaling);
         res
@@ -232,11 +183,10 @@ impl<N, D: DimName, S> SquareMatrix<N, D, S>
 
     /// Computes the transformation equal to `self` followed by a translation.
     #[inline]
-    pub fn append_translation<SB>(&self, shift: &ColumnVector<N, DimNameDiff<D, U1>, SB>)
-        -> OwnedSquareMatrix<N, D, S::Alloc>
+    pub fn append_translation<SB>(&self, shift: &Vector<N, DimNameDiff<D, U1>, SB>) -> MatrixN<N, D>
         where D: DimNameSub<U1>,
-              SB: Storage<N, DimNameDiff<D, U1>, U1>,
-              S::Alloc: Allocator<N, DimNameDiff<D, U1>, U1> {
+              SB: Storage<N, DimNameDiff<D, U1>>,
+              DefaultAllocator: Allocator<N, D, D> {
         let mut res = self.clone_owned();
         res.append_translation_mut(shift);
         res
@@ -244,28 +194,23 @@ impl<N, D: DimName, S> SquareMatrix<N, D, S>
 
     /// Computes the transformation equal to a translation followed by `self`.
     #[inline]
-    pub fn prepend_translation<SB>(&self, shift: &ColumnVector<N, DimNameDiff<D, U1>, SB>)
-        -> OwnedSquareMatrix<N, D, S::Alloc>
+    pub fn prepend_translation<SB>(&self, shift: &Vector<N, DimNameDiff<D, U1>, SB>) -> MatrixN<N, D>
         where D: DimNameSub<U1>,
-              SB: Storage<N, DimNameDiff<D, U1>, U1>,
-              S::Alloc: Allocator<N, DimNameDiff<D, U1>, U1> +
-                        Allocator<N, DimNameDiff<D, U1>, DimNameDiff<D, U1>> +
-                        Allocator<N, U1, DimNameDiff<D, U1>> {
+              SB: Storage<N, DimNameDiff<D, U1>>,
+              DefaultAllocator: Allocator<N, D, D> +
+                                Allocator<N, DimNameDiff<D, U1>> {
         let mut res = self.clone_owned();
         res.prepend_translation_mut(shift);
         res
     }
 }
 
-impl<N, D: DimName, S> SquareMatrix<N, D, S>
-    where N: Scalar + Field,
-          S: StorageMut<N, D, D> {
+impl<N: Scalar + Field, D: DimName, S: StorageMut<N, D, D>> SquareMatrix<N, D, S> {
 
     /// Computes in-place the transformation equal to `self` followed by an uniform scaling factor.
     #[inline]
     pub fn append_scaling_mut(&mut self, scaling: N)
-        where D: DimNameSub<U1>,
-              S::Alloc: Allocator<N, DimNameDiff<D, U1>, D> {
+        where D: DimNameSub<U1> {
         let mut to_scale = self.fixed_rows_mut::<DimNameDiff<D, U1>>(0);
         to_scale *= scaling;
     }
@@ -273,18 +218,16 @@ impl<N, D: DimName, S> SquareMatrix<N, D, S>
     /// Computes in-place the transformation equal to an uniform scaling factor followed by `self`.
     #[inline]
     pub fn prepend_scaling_mut(&mut self, scaling: N)
-        where D: DimNameSub<U1>,
-              S::Alloc: Allocator<N, D, DimNameDiff<D, U1>> {
+        where D: DimNameSub<U1> {
         let mut to_scale = self.fixed_columns_mut::<DimNameDiff<D, U1>>(0);
         to_scale *= scaling;
     }
 
     /// Computes in-place the transformation equal to `self` followed by a non-uniform scaling factor.
     #[inline]
-    pub fn append_nonuniform_scaling_mut<SB>(&mut self, scaling: &ColumnVector<N, DimNameDiff<D, U1>, SB>)
+    pub fn append_nonuniform_scaling_mut<SB>(&mut self, scaling: &Vector<N, DimNameDiff<D, U1>, SB>)
         where D:  DimNameSub<U1>,
-              SB: Storage<N, DimNameDiff<D, U1>, U1>,
-              S::Alloc: Allocator<N, U1, D> {
+              SB: Storage<N, DimNameDiff<D, U1>> {
         for i in 0 .. scaling.len() {
             let mut to_scale = self.fixed_rows_mut::<U1>(i);
             to_scale *= scaling[i];
@@ -293,10 +236,9 @@ impl<N, D: DimName, S> SquareMatrix<N, D, S>
 
     /// Computes in-place the transformation equal to a non-uniform scaling factor followed by `self`.
     #[inline]
-    pub fn prepend_nonuniform_scaling_mut<SB>(&mut self, scaling: &ColumnVector<N, DimNameDiff<D, U1>, SB>)
+    pub fn prepend_nonuniform_scaling_mut<SB>(&mut self, scaling: &Vector<N, DimNameDiff<D, U1>, SB>)
         where D:  DimNameSub<U1>,
-              SB: Storage<N, DimNameDiff<D, U1>, U1>,
-              S::Alloc: Allocator<N, D, U1> {
+              SB: Storage<N, DimNameDiff<D, U1>> {
         for i in 0 .. scaling.len() {
             let mut to_scale = self.fixed_columns_mut::<U1>(i);
             to_scale *= scaling[i];
@@ -305,10 +247,9 @@ impl<N, D: DimName, S> SquareMatrix<N, D, S>
 
     /// Computes the transformation equal to `self` followed by a translation.
     #[inline]
-    pub fn append_translation_mut<SB>(&mut self, shift: &ColumnVector<N, DimNameDiff<D, U1>, SB>)
+    pub fn append_translation_mut<SB>(&mut self, shift: &Vector<N, DimNameDiff<D, U1>, SB>)
         where D: DimNameSub<U1>,
-              SB: Storage<N, DimNameDiff<D, U1>, U1>,
-              S::Alloc: Allocator<N, DimNameDiff<D, U1>, U1> {
+              SB: Storage<N, DimNameDiff<D, U1>> {
         for i in 0 .. D::dim() {
             for j in 0 .. D::dim() - 1 {
                 self[(j, i)] += shift[j] * self[(D::dim() - 1, i)];
@@ -318,12 +259,10 @@ impl<N, D: DimName, S> SquareMatrix<N, D, S>
 
     /// Computes the transformation equal to a translation followed by `self`.
     #[inline]
-    pub fn prepend_translation_mut<SB>(&mut self, shift: &ColumnVector<N, DimNameDiff<D, U1>, SB>)
+    pub fn prepend_translation_mut<SB>(&mut self, shift: &Vector<N, DimNameDiff<D, U1>, SB>)
         where D: DimNameSub<U1>,
-              SB: Storage<N, DimNameDiff<D, U1>, U1>,
-              S::Alloc: Allocator<N, DimNameDiff<D, U1>, U1> +
-                        Allocator<N, DimNameDiff<D, U1>, DimNameDiff<D, U1>> +
-                        Allocator<N, U1, DimNameDiff<D, U1>> {
+              SB: Storage<N, DimNameDiff<D, U1>>,
+              DefaultAllocator: Allocator<N, DimNameDiff<D, U1>> {
         let scale = self.fixed_slice::<U1, DimNameDiff<D, U1>>(D::dim() - 1, 0).tr_dot(&shift);
         let post_translation = self.fixed_slice::<DimNameDiff<D, U1>, DimNameDiff<D, U1>>(0, 0) * shift;
 
@@ -335,19 +274,12 @@ impl<N, D: DimName, S> SquareMatrix<N, D, S>
 }
 
 
-impl<N, D, SA, SB> Transformation<PointBase<N, DimNameDiff<D, U1>, SB>> for SquareMatrix<N, D, SA>
-    where N:  Real,
-          D:  DimNameSub<U1>,
-          SA: OwnedStorage<N, D, D>,
-          SB: OwnedStorage<N, DimNameDiff<D, U1>, U1, Alloc = SA::Alloc>,
-          SA::Alloc: OwnedAllocator<N, D, D, SA> +
-                     Allocator<N, DimNameDiff<D, U1>, DimNameDiff<D, U1>> +
-                     Allocator<N, DimNameDiff<D, U1>, U1> +
-                     Allocator<N, U1, DimNameDiff<D, U1>>,
-          SB::Alloc: OwnedAllocator<N, DimNameDiff<D, U1>, U1, SB> {
+impl<N: Real, D: DimNameSub<U1>> Transformation<Point<N, DimNameDiff<D, U1>>> for MatrixN<N, D>
+    where DefaultAllocator: Allocator<N, D, D> +
+                            Allocator<N, DimNameDiff<D, U1>> +
+                            Allocator<N, DimNameDiff<D, U1>, DimNameDiff<D, U1>> {
     #[inline]
-    fn transform_vector(&self, v: &ColumnVector<N, DimNameDiff<D, U1>, SB>)
-        -> ColumnVector<N, DimNameDiff<D, U1>, SB> {
+    fn transform_vector(&self, v: &VectorN<N, DimNameDiff<D, U1>>) -> VectorN<N, DimNameDiff<D, U1>> {
         let transform  = self.fixed_slice::<DimNameDiff<D, U1>, DimNameDiff<D, U1>>(0, 0);
         let normalizer = self.fixed_slice::<U1, DimNameDiff<D, U1>>(D::dim() - 1, 0);
         let n = normalizer.tr_dot(&v);
@@ -360,8 +292,7 @@ impl<N, D, SA, SB> Transformation<PointBase<N, DimNameDiff<D, U1>, SB>> for Squa
     }
 
     #[inline]
-    fn transform_point(&self, pt: &PointBase<N, DimNameDiff<D, U1>, SB>)
-        -> PointBase<N, DimNameDiff<D, U1>, SB> {
+    fn transform_point(&self, pt: &Point<N, DimNameDiff<D, U1>>) -> Point<N, DimNameDiff<D, U1>> {
         let transform   = self.fixed_slice::<DimNameDiff<D, U1>, DimNameDiff<D, U1>>(0, 0);
         let translation = self.fixed_slice::<DimNameDiff<D, U1>, U1>(0, D::dim() - 1);
         let normalizer  = self.fixed_slice::<U1, DimNameDiff<D, U1>>(D::dim() - 1, 0);

src/core/componentwise.rs

@@ -4,21 +4,22 @@ use num::Signed;
 
 use alga::general::{ClosedMul, ClosedDiv};
 
-use core::{Scalar, Matrix, OwnedMatrix, MatrixSum};
+use core::{DefaultAllocator, Scalar, Matrix, MatrixMN, MatrixSum};
 use core::dimension::Dim;
 use core::storage::{Storage, StorageMut};
-use core::allocator::SameShapeAllocator;
+use core::allocator::{Allocator, SameShapeAllocator};
 use core::constraint::{ShapeConstraint, SameNumberOfRows, SameNumberOfColumns};
 
 
 /// The type of the result of a matrix componentwise operation.
-pub type MatrixComponentOp<N, R1, C1, R2, C2, SA> = MatrixSum<N, R1, C1, R2, C2, SA>;
+pub type MatrixComponentOp<N, R1, C1, R2, C2> = MatrixSum<N, R1, C1, R2, C2>;
 
 impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /// Computes the componentwise absolute value.
     #[inline]
-    pub fn abs(&self) -> OwnedMatrix<N, R, C, S::Alloc>
-        where N: Signed {
+    pub fn abs(&self) -> MatrixMN<N, R, C>
+        where N: Signed,
+              DefaultAllocator: Allocator<N, R, C> {
         let mut res = self.clone_owned();
 
         for e in res.iter_mut() {
@@ -33,27 +34,32 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
 
 macro_rules! component_binop_impl(
     ($($binop: ident, $binop_mut: ident, $Trait: ident . $binop_assign: ident, $desc:expr, $desc_mut:expr);* $(;)*) => {$(
-        impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
+        impl<N: Scalar, R1: Dim, C1: Dim, SA: Storage<N, R1, C1>> Matrix<N, R1, C1, SA> {
             #[doc = $desc]
             #[inline]
-            pub fn $binop<R2, C2, SB>(&self, rhs: &Matrix<N, R2, C2, SB>) -> MatrixComponentOp<N, R, C, R2, C2, S>
+            pub fn $binop<R2, C2, SB>(&self, rhs: &Matrix<N, R2, C2, SB>) -> MatrixComponentOp<N, R1, C1, R2, C2>
                 where N: $Trait,
                       R2: Dim, C2: Dim,
                       SB: Storage<N, R2, C2>,
-                      S::Alloc: SameShapeAllocator<N, R, C, R2, C2, S>,
-                      ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2> {
+                      DefaultAllocator: SameShapeAllocator<N, R1, C1, R2, C2>,
+                      ShapeConstraint:  SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
         
+                assert_eq!(self.shape(), rhs.shape(), "Componentwise mul/div: mismatched matrix dimensions.");
                 let mut res = self.clone_owned_sum();
 
-                for (res, rhs) in res.iter_mut().zip(rhs.iter()) {
-                    res.$binop_assign(*rhs);
+                for j in 0 .. res.ncols() {
+                    for i in 0 .. res.nrows() {
+                        unsafe {
+                            res.get_unchecked_mut(i, j).$binop_assign(*rhs.get_unchecked(i, j));
+                        }
+                    }
                 }
 
                 res
             }
         }
 
-        impl<N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
+        impl<N: Scalar, R1: Dim, C1: Dim, SA: StorageMut<N, R1, C1>> Matrix<N, R1, C1, SA> {
             #[doc = $desc_mut]
             #[inline]
             pub fn $binop_mut<R2, C2, SB>(&mut self, rhs: &Matrix<N, R2, C2, SB>)
@@ -61,9 +67,16 @@ macro_rules! component_binop_impl(
                       R2: Dim,
                       C2: Dim,
                       SB: Storage<N, R2, C2>,
-                      ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2> {
-                for (me, rhs) in self.iter_mut().zip(rhs.iter()) {
-                    me.$binop_assign(*rhs);
+                      ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
+
+                assert_eq!(self.shape(), rhs.shape(), "Componentwise mul/div: mismatched matrix dimensions.");
+
+                for j in 0 .. self.ncols() {
+                    for i in 0 .. self.nrows() {
+                        unsafe {
+                            self.get_unchecked_mut(i, j).$binop_assign(*rhs.get_unchecked(i, j));
+                        }
+                    }
                 }
             }
         }

src/core/constraint.rs

@@ -6,8 +6,7 @@ use core::dimension::{Dim, DimName, Dynamic};
 pub struct ShapeConstraint;
 
 /// Constraints `C1` and `R2` to be equivalent.
-pub trait AreMultipliable<R1: Dim, C1: Dim,
-                          R2: Dim, C2: Dim> {
+pub trait AreMultipliable<R1: Dim, C1: Dim, R2: Dim, C2: Dim>: DimEq<C1, R2> {
 }
 
 
@@ -15,11 +14,30 @@ impl<R1: Dim, C1: Dim, R2: Dim, C2: Dim> AreMultipliable<R1, C1, R2, C2> for Sha
 where ShapeConstraint: DimEq<C1, R2> {
 }
 
+/// Constraints `D1` and `D2` to be equivalent.
+pub trait DimEq<D1: Dim, D2: Dim> {
+    /// This is either equal to `D1` or `D2`, always choosing the one (if any) which is a type-level
+    /// constant.
+    type Representative: Dim;
+}
+
+impl<D: Dim> DimEq<D, D> for ShapeConstraint {
+    type Representative = D;
+}
+
+impl<D: DimName> DimEq<D, Dynamic> for ShapeConstraint {
+    type Representative = D;
+}
+
+impl<D: DimName> DimEq<Dynamic, D> for ShapeConstraint {
+    type Representative = D;
+}
+
 macro_rules! equality_trait_decl(
     ($($doc: expr, $Trait: ident),* $(,)*) => {$(
         // XXX: we can't do something like `DimEq<D1> for D2` because we would require a blancket impl…
         #[doc = $doc]
-        pub trait $Trait<D1: Dim, D2: Dim> {
+        pub trait $Trait<D1: Dim, D2: Dim>: DimEq<D1, D2> + DimEq<D2, D1> {
             /// This is either equal to `D1` or `D2`, always choosing the one (if any) which is a type-level
             /// constant.
             type Representative: Dim;
@@ -40,9 +58,6 @@ macro_rules! equality_trait_decl(
 );
 
 equality_trait_decl!(
-    "Constraints `D1` and `D2` to be equivalent.",
-    DimEq,
-
     "Constraints `D1` and `D2` to be equivalent. \
      They are both assumed to be the number of \
      rows of a matrix.",

src/core/construction.rs

@@ -1,5 +1,7 @@
 #[cfg(feature = "arbitrary")]
 use quickcheck::{Arbitrary, Gen};
+#[cfg(feature = "arbitrary")]
+use core::storage::Owned;
 
 use std::iter;
 use num::{Zero, One, Bounded};
@@ -8,38 +10,44 @@ use typenum::{self, Cmp, Greater};
 
 use alga::general::{ClosedAdd, ClosedMul};
 
-use core::{Scalar, Matrix, SquareMatrix, ColumnVector, Unit};
+use core::{DefaultAllocator, Scalar, Matrix, Vector, Unit, MatrixMN, MatrixN, VectorN};
 use core::dimension::{Dim, DimName, Dynamic, U1, U2, U3, U4, U5, U6};
-use core::allocator::{Allocator, OwnedAllocator};
-use core::storage::{Storage, OwnedStorage};
+use core::allocator::Allocator;
+use core::storage::Storage;
 
 /*
  *
  * Generic constructors.
  *
  */
-impl<N: Scalar, R: Dim, C: Dim, S: OwnedStorage<N, R, C>> Matrix<N, R, C, S>
-    // XXX: needed because of a compiler bug. See the rust compiler issue #26026.
-    where S::Alloc: OwnedAllocator<N, R, C, S> {
+impl<N: Scalar, R: Dim, C: Dim> MatrixMN<N, R, C>
+    where DefaultAllocator: Allocator<N, R, C> {
     /// Creates a new uninitialized matrix. If the matrix has a compile-time dimension, this panics
     /// if `nrows != R::to_usize()` or `ncols != C::to_usize()`.
     #[inline]
-    pub unsafe fn new_uninitialized_generic(nrows: R, ncols: C) -> Matrix<N, R, C, S> {
-        Matrix::from_data(S::Alloc::allocate_uninitialized(nrows, ncols))
+    pub unsafe fn new_uninitialized_generic(nrows: R, ncols: C) -> Self {
+        Self::from_data(DefaultAllocator::allocate_uninitialized(nrows, ncols))
     }
 
     /// Creates a matrix with all its elements set to `elem`.
     #[inline]
-    pub fn from_element_generic(nrows: R, ncols: C, elem: N) -> Matrix<N, R, C, S> {
+    pub fn from_element_generic(nrows: R, ncols: C, elem: N) -> Self {
         let len = nrows.value() * ncols.value();
-        Matrix::from_iterator_generic(nrows, ncols, iter::repeat(elem).take(len))
+        Self::from_iterator_generic(nrows, ncols, iter::repeat(elem).take(len))
+    }
+
+    /// Creates a matrix with all its elements set to 0.
+    #[inline]
+    pub fn zeros_generic(nrows: R, ncols: C) -> Self
+        where N: Zero {
+        Self::from_element_generic(nrows, ncols, N::zero())
     }
 
     /// Creates a matrix with all its elements filled by an iterator.
     #[inline]
-    pub fn from_iterator_generic<I>(nrows: R, ncols: C, iter: I) -> Matrix<N, R, C, S>
+    pub fn from_iterator_generic<I>(nrows: R, ncols: C, iter: I) -> Self
         where I: IntoIterator<Item = N> {
-        Matrix::from_data(S::Alloc::allocate_from_iterator(nrows, ncols, iter))
+        Self::from_data(DefaultAllocator::allocate_from_iterator(nrows, ncols, iter))
     }
 
     /// Creates a matrix with its elements filled with the components provided by a slice in
@@ -48,7 +56,7 @@ impl<N: Scalar, R: Dim, C: Dim, S: OwnedStorage<N, R, C>> Matrix<N, R, C, S>
     /// The order of elements in the slice must follow the usual mathematic writing, i.e.,
     /// row-by-row.
     #[inline]
-    pub fn from_row_slice_generic(nrows: R, ncols: C, slice: &[N]) -> Matrix<N, R, C, S> {
+    pub fn from_row_slice_generic(nrows: R, ncols: C, slice: &[N]) -> Self {
         assert!(slice.len() == nrows.value() * ncols.value(),
                 "Matrix init. error: the slice did not contain the right number of elements.");
 
@@ -69,14 +77,14 @@ impl<N: Scalar, R: Dim, C: Dim, S: OwnedStorage<N, R, C>> Matrix<N, R, C, S>
     /// Creates a matrix with its elements filled with the components provided by a slice. The
     /// components must have the same layout as the matrix data storage (i.e. row-major or column-major).
     #[inline]
-    pub fn from_column_slice_generic(nrows: R, ncols: C, slice: &[N]) -> Matrix<N, R, C, S> {
-        Matrix::from_iterator_generic(nrows, ncols, slice.iter().cloned())
+    pub fn from_column_slice_generic(nrows: R, ncols: C, slice: &[N]) -> Self {
+        Self::from_iterator_generic(nrows, ncols, slice.iter().cloned())
     }
 
     /// Creates a matrix filled with the results of a function applied to each of its component
     /// coordinates.
     #[inline]
-    pub fn from_fn_generic<F>(nrows: R, ncols: C, mut f: F) -> Matrix<N, R, C, S>
+    pub fn from_fn_generic<F>(nrows: R, ncols: C, mut f: F) -> Self
         where F: FnMut(usize, usize) -> N {
         let mut res = unsafe { Self::new_uninitialized_generic(nrows, ncols) };
 
@@ -94,7 +102,7 @@ impl<N: Scalar, R: Dim, C: Dim, S: OwnedStorage<N, R, C>> Matrix<N, R, C, S>
     /// If the matrix is not square, the largest square submatrix starting at index `(0, 0)` is set
     /// to the identity matrix. All other entries are set to zero.
     #[inline]
-    pub fn identity_generic(nrows: R, ncols: C) -> Matrix<N, R, C, S>
+    pub fn identity_generic(nrows: R, ncols: C) -> Self
         where N: Zero + One {
         Self::from_diagonal_element_generic(nrows, ncols, N::one())
     }
@@ -104,10 +112,9 @@ impl<N: Scalar, R: Dim, C: Dim, S: OwnedStorage<N, R, C>> Matrix<N, R, C, S>
     /// If the matrix is not square, the largest square submatrix starting at index `(0, 0)` is set
     /// to the identity matrix. All other entries are set to zero.
     #[inline]
-    pub fn from_diagonal_element_generic(nrows: R, ncols: C, elt: N) -> Matrix<N, R, C, S>
+    pub fn from_diagonal_element_generic(nrows: R, ncols: C, elt: N) -> Self
         where N: Zero + One {
-        let mut res = unsafe { Self::new_uninitialized_generic(nrows, ncols) };
-        res.fill(N::zero());
+        let mut res = Self::zeros_generic(nrows, ncols);
 
         for i in 0 .. ::min(nrows.value(), ncols.value()) {
             unsafe { *res.get_unchecked_mut(i, i) = elt }
@@ -116,12 +123,29 @@ impl<N: Scalar, R: Dim, C: Dim, S: OwnedStorage<N, R, C>> Matrix<N, R, C, S>
         res
     }
 
+    /// Creates a new matrix that may be rectangular. The first `elts.len()` diagonal elements are
+    /// filled with the content of `elts`. Others are set to 0.
+    ///
+    /// Panics if `elts.len()` is larger than the minimum among `nrows` and `ncols`.
+    #[inline]
+    pub fn from_partial_diagonal_generic(nrows: R, ncols: C, elts: &[N]) -> Self
+        where N: Zero {
+        let mut res = Self::zeros_generic(nrows, ncols);
+        assert!(elts.len() <= ::min(nrows.value(), ncols.value()), "Too many diagonal elements provided.");
+
+        for (i, elt) in elts.iter().enumerate() {
+            unsafe { *res.get_unchecked_mut(i, i) = *elt }
+        }
+
+        res
+    }
+
     /// Builds a new matrix from its rows.
     ///
     /// Panics if not enough rows are provided (for statically-sized matrices), or if all rows do
     /// not have the same dimensions.
     #[inline]
-    pub fn from_rows<SB>(rows: &[Matrix<N, U1, C, SB>]) -> Matrix<N, R, C, S>
+    pub fn from_rows<SB>(rows: &[Matrix<N, U1, C, SB>]) -> Self
         where SB: Storage<N, U1, C> {
 
         assert!(rows.len() > 0, "At least one row must be given.");
@@ -144,8 +168,8 @@ impl<N: Scalar, R: Dim, C: Dim, S: OwnedStorage<N, R, C>> Matrix<N, R, C, S>
     /// Panics if not enough columns are provided (for statically-sized matrices), or if all
     /// columns do not have the same dimensions.
     #[inline]
-    pub fn from_columns<SB>(columns: &[ColumnVector<N, R, SB>]) -> Matrix<N, R, C, S>
-        where SB: Storage<N, R, U1> {
+    pub fn from_columns<SB>(columns: &[Vector<N, R, SB>]) -> Self
+        where SB: Storage<N, R> {
 
         assert!(columns.len() > 0, "At least one column must be given.");
         let ncols = C::try_to_usize().unwrap_or(columns.len());
@@ -160,31 +184,27 @@ impl<N: Scalar, R: Dim, C: Dim, S: OwnedStorage<N, R, C>> Matrix<N, R, C, S>
         // FIXME: optimize that.
         Self::from_fn_generic(R::from_usize(nrows), C::from_usize(ncols), |i, j| columns[j][i])
     }
-}
 
-impl<N, R: Dim, C: Dim, S> Matrix<N, R, C, S>
-    where N: Scalar + Rand,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
     /// Creates a matrix filled with random values.
     #[inline]
-    pub fn new_random_generic(nrows: R, ncols: C) -> Matrix<N, R, C, S> {
-        Matrix::from_fn_generic(nrows, ncols, |_, _| rand::random())
+    pub fn new_random_generic(nrows: R, ncols: C) -> Self
+        where N: Rand {
+        Self::from_fn_generic(nrows, ncols, |_, _| rand::random())
     }
 }
 
-impl<N, D: Dim, S> SquareMatrix<N, D, S>
-    where N: Scalar + Zero,
-          S: OwnedStorage<N, D, D>,
-          S::Alloc: OwnedAllocator<N, D, D, S> {
+impl<N, D: Dim> MatrixN<N, D>
+    where N: Scalar,
+          DefaultAllocator: Allocator<N, D, D> {
     /// Creates a square matrix with its diagonal set to `diag` and all other entries set to 0.
     #[inline]
-    pub fn from_diagonal<SB: Storage<N, D, U1>>(diag: &ColumnVector<N, D, SB>) -> Self {
+    pub fn from_diagonal<SB: Storage<N, D>>(diag: &Vector<N, D, SB>) -> Self
+        where N: Zero {
         let (dim, _) = diag.data.shape();
-        let mut res = Self::from_element_generic(dim, dim, N::zero());
+        let mut res = Self::zeros_generic(dim, dim);
 
         for i in 0 .. diag.len() {
-            unsafe { *res.get_unchecked_mut(i, i) = *diag.get_unchecked(i, 0); }
+            unsafe { *res.get_unchecked_mut(i, i) = *diag.vget_unchecked(i); }
         }
 
         res
@@ -199,25 +219,31 @@ impl<N, D: Dim, S> SquareMatrix<N, D, S>
  */
 macro_rules! impl_constructors(
     ($($Dims: ty),*; $(=> $DimIdent: ident: $DimBound: ident),*; $($gargs: expr),*; $($args: ident),*) => {
-        impl<N: Scalar, $($DimIdent: $DimBound, )* S> Matrix<N $(, $Dims)*, S>
-            where S: OwnedStorage<N $(, $Dims)*>,
-                  S::Alloc: OwnedAllocator<N $(, $Dims)*, S> {
+        impl<N: Scalar, $($DimIdent: $DimBound, )*> MatrixMN<N $(, $Dims)*>
+            where DefaultAllocator: Allocator<N $(, $Dims)*> {
 
             /// Creates a new uninitialized matrix.
             #[inline]
-            pub unsafe fn new_uninitialized($($args: usize),*) -> Matrix<N $(, $Dims)*, S> {
+            pub unsafe fn new_uninitialized($($args: usize),*) -> Self {
                 Self::new_uninitialized_generic($($gargs),*)
             }
 
             /// Creates a matrix with all its elements set to `elem`.
             #[inline]
-            pub fn from_element($($args: usize,)* elem: N) -> Matrix<N $(, $Dims)*, S> {
+            pub fn from_element($($args: usize,)* elem: N) -> Self {
                 Self::from_element_generic($($gargs, )* elem)
             }
 
+            /// Creates a matrix with all its elements set to `0`.
+            #[inline]
+            pub fn zeros($($args: usize),*) -> Self
+                where N: Zero {
+                Self::zeros_generic($($gargs),*)
+            }
+
             /// Creates a matrix with all its elements filled by an iterator.
             #[inline]
-            pub fn from_iterator<I>($($args: usize,)* iter: I) -> Matrix<N $(, $Dims)*, S>
+            pub fn from_iterator<I>($($args: usize,)* iter: I) -> Self
                 where I: IntoIterator<Item = N> {
                 Self::from_iterator_generic($($gargs, )* iter)
             }
@@ -228,14 +254,14 @@ macro_rules! impl_constructors(
             /// The order of elements in the slice must follow the usual mathematic writing, i.e.,
             /// row-by-row.
             #[inline]
-            pub fn from_row_slice($($args: usize,)* slice: &[N]) -> Matrix<N $(, $Dims)*, S> {
+            pub fn from_row_slice($($args: usize,)* slice: &[N]) -> Self {
                 Self::from_row_slice_generic($($gargs, )* slice)
             }
 
             /// Creates a matrix with its elements filled with the components provided by a slice
             /// in column-major order.
             #[inline]
-            pub fn from_column_slice($($args: usize,)* slice: &[N]) -> Matrix<N $(, $Dims)*, S> {
+            pub fn from_column_slice($($args: usize,)* slice: &[N]) -> Self {
                 Self::from_column_slice_generic($($gargs, )* slice)
             }
 
@@ -243,7 +269,7 @@ macro_rules! impl_constructors(
             /// component coordinates.
             // FIXME: don't take a dimension of the matrix is statically sized.
             #[inline]
-            pub fn from_fn<F>($($args: usize,)* f: F) -> Matrix<N $(, $Dims)*, S>
+            pub fn from_fn<F>($($args: usize,)* f: F) -> Self
                 where F: FnMut(usize, usize) -> N {
                 Self::from_fn_generic($($gargs, )* f)
             }
@@ -252,7 +278,7 @@ macro_rules! impl_constructors(
             /// submatrix (starting at the first row and column) is set to the identity while all
             /// other entries are set to zero.
             #[inline]
-            pub fn identity($($args: usize,)*) -> Matrix<N $(, $Dims)*, S>
+            pub fn identity($($args: usize,)*) -> Self
                 where N: Zero + One {
                 Self::identity_generic($($gargs),* )
             }
@@ -260,19 +286,28 @@ macro_rules! impl_constructors(
             /// Creates a matrix filled with its diagonal filled with `elt` and all other
             /// components set to zero.
             #[inline]
-            pub fn from_diagonal_element($($args: usize,)* elt: N) -> Matrix<N $(, $Dims)*, S>
+            pub fn from_diagonal_element($($args: usize,)* elt: N) -> Self
                 where N: Zero + One {
                 Self::from_diagonal_element_generic($($gargs, )* elt)
             }
+
+            /// Creates a new matrix that may be rectangular. The first `elts.len()` diagonal
+            /// elements are filled with the content of `elts`. Others are set to 0.
+            ///
+            /// Panics if `elts.len()` is larger than the minimum among `nrows` and `ncols`.
+            #[inline]
+            pub fn from_partial_diagonal($($args: usize,)* elts: &[N]) -> Self
+                where N: Zero {
+                Self::from_partial_diagonal_generic($($gargs, )* elts)
+            }
         }
 
-        impl<N: Scalar + Rand, $($DimIdent: $DimBound, )* S> Matrix<N $(, $Dims)*, S>
-            where S: OwnedStorage<N $(, $Dims)*>,
-                  S::Alloc: OwnedAllocator<N $(, $Dims)*, S> {
+        impl<N: Scalar + Rand, $($DimIdent: $DimBound, )*> MatrixMN<N $(, $Dims)*>
+            where DefaultAllocator: Allocator<N $(, $Dims)*> {
 
             /// Creates a matrix filled with random values.
             #[inline]
-            pub fn new_random($($args: usize),*) -> Matrix<N $(, $Dims)*, S> {
+            pub fn new_random($($args: usize),*) -> Self {
                 Self::new_random_generic($($gargs),*)
             }
         }
@@ -305,10 +340,9 @@ impl_constructors!(Dynamic, Dynamic;
  * Zero, One, Rand traits.
  *
  */
-impl<N, R: DimName, C: DimName, S> Zero for Matrix<N, R, C, S>
+impl<N, R: DimName, C: DimName> Zero for MatrixMN<N, R, C>
     where N: Scalar + Zero + ClosedAdd,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+          DefaultAllocator: Allocator<N, R, C> {
     #[inline]
     fn zero() -> Self {
         Self::from_element(N::zero())
@@ -320,20 +354,18 @@ impl<N, R: DimName, C: DimName, S> Zero for Matrix<N, R, C, S>
     }
 }
 
-impl<N, D: DimName, S> One for Matrix<N, D, D, S>
+impl<N, D: DimName> One for MatrixN<N, D>
     where N: Scalar + Zero + One + ClosedMul + ClosedAdd,
-          S: OwnedStorage<N, D, D>,
-          S::Alloc: OwnedAllocator<N, D, D, S> {
+          DefaultAllocator: Allocator<N, D, D> {
     #[inline]
     fn one() -> Self {
         Self::identity()
     }
 }
 
-impl<N, R: DimName, C: DimName, S> Bounded for Matrix<N, R, C, S>
+impl<N, R: DimName, C: DimName> Bounded for MatrixMN<N, R, C>
     where N: Scalar + Bounded,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+          DefaultAllocator: Allocator<N, R, C> {
     #[inline]
     fn max_value() -> Self {
         Self::from_element(N::max_value())
@@ -345,9 +377,8 @@ impl<N, R: DimName, C: DimName, S> Bounded for Matrix<N, R, C, S>
     }
 }
 
-impl<N: Scalar + Rand, R: Dim, C: Dim, S> Rand for Matrix<N, R, C, S>
-    where S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+impl<N: Scalar + Rand, R: Dim, C: Dim> Rand for MatrixMN<N, R, C>
+    where DefaultAllocator: Allocator<N, R, C> {
     #[inline]
     fn rand<G: Rng>(rng: &mut G) -> Self {
         let nrows = R::try_to_usize().unwrap_or(rng.gen_range(0, 10));
@@ -359,11 +390,11 @@ impl<N: Scalar + Rand, R: Dim, C: Dim, S> Rand for Matrix<N, R, C, S>
 
 
 #[cfg(feature = "arbitrary")]
-impl<N, R, C, S> Arbitrary for Matrix<N, R, C, S>
+impl<N, R, C> Arbitrary for MatrixMN<N, R, C>
     where R: Dim, C: Dim,
           N: Scalar + Arbitrary + Send,
-          S: OwnedStorage<N, R, C> + Send,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+          DefaultAllocator: Allocator<N, R, C>,
+          Owned<N, R, C>: Clone + Send {
     #[inline]
     fn arbitrary<G: Gen>(g: &mut G) -> Self {
         let nrows = R::try_to_usize().unwrap_or(g.gen_range(0, 10));
@@ -381,13 +412,12 @@ impl<N, R, C, S> Arbitrary for Matrix<N, R, C, S>
  */
 macro_rules! componentwise_constructors_impl(
     ($($R: ty, $C: ty, $($args: ident:($irow: expr,$icol: expr)),*);* $(;)*) => {$(
-        impl<N, S> Matrix<N, $R, $C, S>
+        impl<N> MatrixMN<N, $R, $C>
             where N: Scalar,
-                  S: OwnedStorage<N, $R, $C>,
-                  S::Alloc: OwnedAllocator<N, $R, $C, S> {
+                  DefaultAllocator: Allocator<N, $R, $C> {
             /// Initializes this matrix from its components.
             #[inline]
-            pub fn new($($args: N),*) -> Matrix<N, $R, $C, S> {
+            pub fn new($($args: N),*) -> Self {
                 unsafe {
                     let mut res = Self::new_uninitialized();
                     $( *res.get_unchecked_mut($irow, $icol) = $args; )*
@@ -549,16 +579,15 @@ componentwise_constructors_impl!(
  * Axis constructors.
  *
  */
-impl<N, R: DimName, S> ColumnVector<N, R, S>
+impl<N, R: DimName> VectorN<N, R>
 where N: Scalar + Zero + One,
-      S: OwnedStorage<N, R, U1>,
-      S::Alloc: OwnedAllocator<N, R, U1, S> {
+      DefaultAllocator: Allocator<N, R> {
     /// The column vector with a 1 as its first component, and zero elsewhere.
     #[inline]
     pub fn x() -> Self
       where R::Value: Cmp<typenum::U0, Output = Greater> {
         let mut res = Self::from_element(N::zero());
-        unsafe { *res.get_unchecked_mut(0, 0) = N::one(); }
+        unsafe { *res.vget_unchecked_mut(0) = N::one(); }
 
         res
     }
@@ -568,7 +597,7 @@ where N: Scalar + Zero + One,
     pub fn y() -> Self
       where R::Value: Cmp<typenum::U1, Output = Greater> {
         let mut res = Self::from_element(N::zero());
-        unsafe { *res.get_unchecked_mut(1, 0) = N::one(); }
+        unsafe { *res.vget_unchecked_mut(1) = N::one(); }
 
         res
     }
@@ -578,7 +607,7 @@ where N: Scalar + Zero + One,
     pub fn z() -> Self
       where R::Value: Cmp<typenum::U2, Output = Greater> {
         let mut res = Self::from_element(N::zero());
-        unsafe { *res.get_unchecked_mut(2, 0) = N::one(); }
+        unsafe { *res.vget_unchecked_mut(2) = N::one(); }
 
         res
     }
@@ -588,7 +617,7 @@ where N: Scalar + Zero + One,
     pub fn w() -> Self
       where R::Value: Cmp<typenum::U3, Output = Greater> {
         let mut res = Self::from_element(N::zero());
-        unsafe { *res.get_unchecked_mut(3, 0) = N::one(); }
+        unsafe { *res.vget_unchecked_mut(3) = N::one(); }
 
         res
     }
@@ -598,7 +627,7 @@ where N: Scalar + Zero + One,
     pub fn a() -> Self
       where R::Value: Cmp<typenum::U4, Output = Greater> {
         let mut res = Self::from_element(N::zero());
-        unsafe { *res.get_unchecked_mut(4, 0) = N::one(); }
+        unsafe { *res.vget_unchecked_mut(4) = N::one(); }
 
         res
     }
@@ -608,7 +637,7 @@ where N: Scalar + Zero + One,
     pub fn b() -> Self
       where R::Value: Cmp<typenum::U5, Output = Greater> {
         let mut res = Self::from_element(N::zero());
-        unsafe { *res.get_unchecked_mut(5, 0) = N::one(); }
+        unsafe { *res.vget_unchecked_mut(5) = N::one(); }
 
         res
     }

src/core/conversion.rs

@@ -3,37 +3,35 @@ use std::mem;
 use std::convert::{From, Into, AsRef, AsMut};
 use alga::general::{SubsetOf, SupersetOf};
 
-use core::{Scalar, Matrix};
+use core::{DefaultAllocator, Scalar, Matrix, MatrixMN};
 use core::dimension::{Dim,
     U1,  U2,  U3,  U4,
     U5,  U6,  U7,  U8,
     U9,  U10, U11, U12,
     U13, U14, U15, U16
 };
-use core::constraint::{ShapeConstraint, SameNumberOfRows, SameNumberOfColumns};
-use core::storage::{Storage, StorageMut, OwnedStorage};
 use core::iter::{MatrixIter, MatrixIterMut};
-use core::allocator::{OwnedAllocator, SameShapeAllocator};
+use core::constraint::{ShapeConstraint, SameNumberOfRows, SameNumberOfColumns};
+use core::storage::{ContiguousStorage, ContiguousStorageMut, Storage, StorageMut};
+use core::allocator::{Allocator, SameShapeAllocator};
 
 
 // FIXME: too bad this won't work allo slice conversions.
-impl<N1, N2, R1, C1, R2, C2, SA, SB> SubsetOf<Matrix<N2, R2, C2, SB>> for Matrix<N1, R1, C1, SA>
+impl<N1, N2, R1, C1, R2, C2> SubsetOf<MatrixMN<N2, R2, C2>> for MatrixMN<N1, R1, C1>
     where R1: Dim, C1: Dim, R2: Dim, C2: Dim,
           N1: Scalar,
           N2: Scalar + SupersetOf<N1>,
-          SA: OwnedStorage<N1, R1, C1>,
-          SB: OwnedStorage<N2, R2, C2>,
-          SB::Alloc: OwnedAllocator<N2, R2, C2, SB>,
-          SA::Alloc: OwnedAllocator<N1, R1, C1, SA> +
-                     SameShapeAllocator<N1, R1, C1, R2, C2, SA>,
+          DefaultAllocator: Allocator<N2, R2, C2> +
+                            Allocator<N1, R1, C1> +
+                            SameShapeAllocator<N1, R1, C1, R2, C2>,
           ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
     #[inline]
-    fn to_superset(&self) -> Matrix<N2, R2, C2, SB> {
+    fn to_superset(&self) -> MatrixMN<N2, R2, C2> {
         let (nrows, ncols) = self.shape();
         let nrows2 = R2::from_usize(nrows);
         let ncols2 = C2::from_usize(ncols);
 
-        let mut res = unsafe { Matrix::<N2, R2, C2, SB>::new_uninitialized_generic(nrows2, ncols2) };
+        let mut res = unsafe { MatrixMN::<N2, R2, C2>::new_uninitialized_generic(nrows2, ncols2) };
         for i in 0 .. nrows {
             for j in 0 .. ncols {
                 unsafe {
@@ -46,12 +44,12 @@ impl<N1, N2, R1, C1, R2, C2, SA, SB> SubsetOf<Matrix<N2, R2, C2, SB>> for Matrix
     }
 
     #[inline]
-    fn is_in_subset(m: &Matrix<N2, R2, C2, SB>) -> bool {
+    fn is_in_subset(m: &MatrixMN<N2, R2, C2>) -> bool {
         m.iter().all(|e| e.is_in_subset())
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(m: &Matrix<N2, R2, C2, SB>) -> Self {
+    unsafe fn from_superset_unchecked(m: &MatrixMN<N2, R2, C2>) -> Self {
         let (nrows2, ncols2) = m.shape();
         let nrows = R1::from_usize(nrows2);
         let ncols = C1::from_usize(ncols2);
@@ -90,10 +88,9 @@ impl<'a, N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> IntoIterator for &'a
 
 macro_rules! impl_from_into_asref_1D(
     ($(($NRows: ident, $NCols: ident) => $SZ: expr);* $(;)*) => {$(
-        impl<N, S> From<[N; $SZ]> for Matrix<N, $NRows, $NCols, S>
+        impl<N> From<[N; $SZ]> for MatrixMN<N, $NRows, $NCols>
         where N: Scalar,
-              S: OwnedStorage<N, $NRows, $NCols>,
-              S::Alloc: OwnedAllocator<N, $NRows, $NCols, S> {
+              DefaultAllocator: Allocator<N, $NRows, $NCols> {
             #[inline]
             fn from(arr: [N; $SZ]) -> Self {
                 unsafe {
@@ -107,8 +104,7 @@ macro_rules! impl_from_into_asref_1D(
 
         impl<N, S> Into<[N; $SZ]> for Matrix<N, $NRows, $NCols, S>
         where N: Scalar,
-              S: OwnedStorage<N, $NRows, $NCols>,
-              S::Alloc: OwnedAllocator<N, $NRows, $NCols, S> {
+              S: ContiguousStorage<N, $NRows, $NCols> {
             #[inline]
             fn into(self) -> [N; $SZ] {
                 unsafe {
@@ -122,8 +118,7 @@ macro_rules! impl_from_into_asref_1D(
 
         impl<N, S> AsRef<[N; $SZ]> for Matrix<N, $NRows, $NCols, S>
         where N: Scalar,
-              S: OwnedStorage<N, $NRows, $NCols>,
-              S::Alloc: OwnedAllocator<N, $NRows, $NCols, S> {
+              S: ContiguousStorage<N, $NRows, $NCols> {
             #[inline]
             fn as_ref(&self) -> &[N; $SZ] {
                 unsafe {
@@ -134,8 +129,7 @@ macro_rules! impl_from_into_asref_1D(
 
         impl<N, S> AsMut<[N; $SZ]> for Matrix<N, $NRows, $NCols, S>
         where N: Scalar,
-              S: OwnedStorage<N, $NRows, $NCols>,
-              S::Alloc: OwnedAllocator<N, $NRows, $NCols, S> {
+              S: ContiguousStorageMut<N, $NRows, $NCols> {
             #[inline]
             fn as_mut(&mut self) -> &mut [N; $SZ] {
                 unsafe {
@@ -165,10 +159,8 @@ impl_from_into_asref_1D!(
 
 macro_rules! impl_from_into_asref_2D(
     ($(($NRows: ty, $NCols: ty) => ($SZRows: expr, $SZCols: expr));* $(;)*) => {$(
-        impl<N, S> From<[[N; $SZRows]; $SZCols]> for Matrix<N, $NRows, $NCols, S>
-        where N: Scalar,
-              S: OwnedStorage<N, $NRows, $NCols>,
-              S::Alloc: OwnedAllocator<N, $NRows, $NCols, S> {
+        impl<N: Scalar> From<[[N; $SZRows]; $SZCols]> for MatrixMN<N, $NRows, $NCols>
+        where DefaultAllocator: Allocator<N, $NRows, $NCols> {
             #[inline]
             fn from(arr: [[N; $SZRows]; $SZCols]) -> Self {
                 unsafe {
@@ -180,10 +172,8 @@ macro_rules! impl_from_into_asref_2D(
             }
         }
 
-        impl<N, S> Into<[[N; $SZRows]; $SZCols]> for Matrix<N, $NRows, $NCols, S>
-        where N: Scalar,
-              S: OwnedStorage<N, $NRows, $NCols>,
-              S::Alloc: OwnedAllocator<N, $NRows, $NCols, S> {
+        impl<N: Scalar, S> Into<[[N; $SZRows]; $SZCols]> for Matrix<N, $NRows, $NCols, S>
+        where S: ContiguousStorage<N, $NRows, $NCols> {
             #[inline]
             fn into(self) -> [[N; $SZRows]; $SZCols] {
                 unsafe {
@@ -195,10 +185,8 @@ macro_rules! impl_from_into_asref_2D(
             }
         }
 
-        impl<N, S> AsRef<[[N; $SZRows]; $SZCols]> for Matrix<N, $NRows, $NCols, S>
-        where N: Scalar,
-              S: OwnedStorage<N, $NRows, $NCols>,
-              S::Alloc: OwnedAllocator<N, $NRows, $NCols, S> {
+        impl<N: Scalar, S> AsRef<[[N; $SZRows]; $SZCols]> for Matrix<N, $NRows, $NCols, S>
+        where S: ContiguousStorage<N, $NRows, $NCols> {
             #[inline]
             fn as_ref(&self) -> &[[N; $SZRows]; $SZCols] {
                 unsafe {
@@ -207,10 +195,8 @@ macro_rules! impl_from_into_asref_2D(
             }
         }
 
-        impl<N, S> AsMut<[[N; $SZRows]; $SZCols]> for Matrix<N, $NRows, $NCols, S>
-        where N: Scalar,
-              S: OwnedStorage<N, $NRows, $NCols>,
-              S::Alloc: OwnedAllocator<N, $NRows, $NCols, S> {
+        impl<N: Scalar, S> AsMut<[[N; $SZRows]; $SZCols]> for Matrix<N, $NRows, $NCols, S>
+        where S: ContiguousStorageMut<N, $NRows, $NCols> {
             #[inline]
             fn as_mut(&mut self) -> &mut [[N; $SZRows]; $SZCols] {
                 unsafe {
@@ -222,7 +208,7 @@ macro_rules! impl_from_into_asref_2D(
 );
 
 
-// Implement for matrices with shape 2x2 .. 4x4.
+// Implement for matrices with shape 2x2 .. 6x6.
 impl_from_into_asref_2D!(
     (U2, U2) => (2, 2); (U2, U3) => (2, 3); (U2, U4) => (2, 4); (U2, U5) => (2, 5); (U2, U6) => (2, 6);
     (U3, U2) => (3, 2); (U3, U3) => (3, 3); (U3, U4) => (3, 4); (U3, U5) => (3, 5); (U3, U6) => (3, 6);

src/core/coordinates.rs

@@ -9,8 +9,7 @@ use std::ops::{Deref, DerefMut};
 
 use core::{Scalar, Matrix};
 use core::dimension::{U1, U2, U3, U4, U5, U6};
-use core::storage::OwnedStorage;
-use core::allocator::OwnedAllocator;
+use core::storage::{ContiguousStorage, ContiguousStorageMut};
 
 /*
  *
@@ -35,22 +34,20 @@ macro_rules! coords_impl(
 macro_rules! deref_impl(
     ($R: ty, $C: ty; $Target: ident) => {
         impl<N: Scalar, S> Deref for Matrix<N, $R, $C, S>
-            where S: OwnedStorage<N, $R, $C>,
-                  S::Alloc: OwnedAllocator<N, $R, $C, S> {
+            where S: ContiguousStorage<N, $R, $C> {
             type Target = $Target<N>;
 
             #[inline]
             fn deref(&self) -> &Self::Target {
-                unsafe { mem::transmute(self) }
+                unsafe { mem::transmute(self.data.ptr()) }
             }
         }
 
         impl<N: Scalar, S> DerefMut for Matrix<N, $R, $C, S>
-            where S: OwnedStorage<N, $R, $C>,
-                  S::Alloc: OwnedAllocator<N, $R, $C, S> {
+            where S: ContiguousStorageMut<N, $R, $C> {
             #[inline]
             fn deref_mut(&mut self) -> &mut Self::Target {
-                unsafe { mem::transmute(self) }
+                unsafe { mem::transmute(self.data.ptr_mut()) }
             }
         }
     }

src/core/decompositions.rs

@@ -1,373 +0,0 @@
-use std::cmp;
-
-use alga::general::Real;
-use core::{SquareMatrix, OwnedSquareMatrix, ColumnVector, OwnedColumnVector};
-use dimension::{Dim, Dynamic, U1};
-use storage::{Storage, OwnedStorage};
-use allocator::{Allocator, OwnedAllocator};
-
-
-
-impl<N, D: Dim, S> SquareMatrix<N, D, S>
-    where N: Real,
-          S: OwnedStorage<N, D, D>,
-          S::Alloc: OwnedAllocator<N, D, D, S> {
-    /// Get the householder matrix corresponding to a reflexion to the hyperplane
-    /// defined by `vector`. It can be a reflexion contained in a subspace.
-    ///
-    /// # Arguments
-    /// * `dimension` - the dimension of the space the resulting matrix operates in
-    /// * `start` - the starting dimension of the subspace of the reflexion
-    /// * `vector` - the vector defining the reflection.
-    pub fn new_householder_generic<SB, D2>(dimension: D, start: usize, vector: &ColumnVector<N, D2, SB>)
-        -> OwnedSquareMatrix<N, D, S::Alloc>
-        where D2: Dim,
-              SB: Storage<N, D2, U1> {
-        let mut qk = Self::identity_generic(dimension, dimension);
-        let subdim = vector.shape().0;
-
-        let stop = subdim + start;
-
-        assert!(dimension.value() >= stop, "Householder matrix creation: subspace dimension index out of bounds.");
-
-        for j in start .. stop {
-            for i in start .. stop {
-                unsafe {
-                    let vv   = *vector.get_unchecked(i - start, 0) * *vector.get_unchecked(j - start, 0);
-                    let qkij = *qk.get_unchecked(i, j);
-                    *qk.get_unchecked_mut(i, j) = qkij - vv - vv;
-                }
-            }
-        }
-
-        qk
-    }
-}
-
-
-impl<N: Real, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
-    /// QR decomposition using Householder reflections.
-    pub fn qr(self) -> (OwnedSquareMatrix<N, D, S::Alloc>, OwnedSquareMatrix<N, D, S::Alloc>)
-        where S::Alloc: Allocator<N, Dynamic, U1> +
-                        Allocator<N, D, U1> {
-
-        let (nrows, ncols) = self.data.shape();
-
-        // XXX: too restrictive.
-        assert!(nrows.value() >= ncols.value(), "");
-
-        let mut q = OwnedSquareMatrix::<N, D, S::Alloc>::identity_generic(nrows, ncols);
-        let mut r = self.into_owned();
-
-        // Temporary buffer that contains a column.
-        let mut col = unsafe {
-            OwnedColumnVector::<N, D, S::Alloc>::new_uninitialized_generic(nrows, U1)
-        };
-
-        for ite in 0 .. cmp::min(nrows.value() - 1, ncols.value()) {
-            let subdim = Dynamic::new(nrows.value() - ite);
-            let mut v  = col.rows_mut(0, subdim.value());
-            v.copy_from(&r.generic_slice((ite, ite), (subdim, U1)));
-
-            let alpha =
-                if unsafe { *v.get_unchecked(ite, 0) } >= ::zero() {
-                    -v.norm()
-                }
-                else {
-                    v.norm()
-                };
-
-            unsafe {
-                let x = *v.get_unchecked(0, 0);
-                *v.get_unchecked_mut(0, 0) = x - alpha;
-            }
-
-            if !v.normalize_mut().is_zero() {
-                let mut qk = OwnedSquareMatrix::<N, D, S::Alloc>::new_householder_generic(nrows, ite, &v);
-                r = &qk * r;
-
-                // FIXME: add a method `q.mul_tr(qk) := q * qk.transpose` ?
-                qk.transpose_mut();
-                q = q * qk;
-            }
-        }
-
-        (q, r)
-    }
-
-    /// Eigendecomposition of a square symmetric matrix.
-    pub fn eig(&self, eps: N, niter: usize)
-               -> (OwnedSquareMatrix<N, D, S::Alloc>, OwnedColumnVector<N, D, S::Alloc>)
-        where S::Alloc: Allocator<N, D, U1> +
-                        Allocator<N, Dynamic, U1> {
-
-        assert!(self.is_square(),
-                "Unable to compute the eigenvectors and eigenvalues of a non-square matrix.");
-
-        let dim = self.data.shape().0;
-
-        let (mut eigenvectors, mut eigenvalues) = self.hessenberg();
-
-        if dim.value() == 1 {
-            return (eigenvectors, eigenvalues.diagonal());
-        }
-
-        // Allocate arrays for Givens rotation components
-        let mut c = unsafe { OwnedColumnVector::<N, D, S::Alloc>::new_uninitialized_generic(dim, U1) };
-        let mut s = unsafe { OwnedColumnVector::<N, D, S::Alloc>::new_uninitialized_generic(dim, U1) };
-
-        let mut iter = 0;
-        let mut curdim = dim.value() - 1;
-
-        for _ in 0 .. dim.value() {
-
-            let mut stop = false;
-
-            while !stop && iter < niter {
-
-                let lambda;
-
-                unsafe {
-                    let a = *eigenvalues.get_unchecked(curdim - 1, curdim - 1);
-                    let b = *eigenvalues.get_unchecked(curdim - 1, curdim);
-                    let c = *eigenvalues.get_unchecked(curdim, curdim - 1);
-                    let d = *eigenvalues.get_unchecked(curdim, curdim);
-
-                    let trace = a + d;
-                    let determinant = a * d - b * c;
-
-                    let constquarter: N = ::convert(0.25f64);
-                    let consthalf:    N = ::convert(0.5f64);
-
-                    let e = (constquarter * trace * trace - determinant).sqrt();
-
-                    let lambda1 = consthalf * trace + e;
-                    let lambda2 = consthalf * trace - e;
-
-                    if (lambda1 - d).abs() < (lambda2 - d).abs() {
-                        lambda = lambda1;
-                    }
-                    else {
-                        lambda = lambda2;
-                    }
-
-                }
-
-                // Shift matrix
-                for k in 0 .. curdim + 1 {
-                    unsafe {
-                        let a = *eigenvalues.get_unchecked(k, k);
-                        *eigenvalues.get_unchecked_mut(k, k) = a - lambda;
-                    }
-                }
-
-
-                // Givens rotation from left
-                for k in 0 .. curdim {
-                    let x_i = unsafe { *eigenvalues.get_unchecked(k, k) };
-                    let x_j = unsafe { *eigenvalues.get_unchecked(k + 1, k) };
-
-                    let ctmp;
-                    let stmp;
-
-                    if x_j.abs() < eps {
-                        ctmp = N::one();
-                        stmp = N::zero();
-                    }
-                    else if x_i.abs() < eps {
-                        ctmp = N::zero();
-                        stmp = -N::one();
-                    }
-                    else {
-                        let r = x_i.hypot(x_j);
-                        ctmp = x_i / r;
-                        stmp = -x_j / r;
-                    }
-
-                    c[k] = ctmp;
-                    s[k] = stmp;
-
-                    for j in k .. (curdim + 1) {
-                        unsafe {
-                            let a = *eigenvalues.get_unchecked(k, j);
-                            let b = *eigenvalues.get_unchecked(k + 1, j);
-
-                            *eigenvalues.get_unchecked_mut(k, j)     = ctmp * a - stmp * b;
-                            *eigenvalues.get_unchecked_mut(k + 1, j) = stmp * a + ctmp * b;
-                        }
-
-                    }
-                }
-
-                // Givens rotation from right applied to eigenvalues
-                for k in 0 .. curdim {
-                    for i in 0 .. (k + 2) {
-                        unsafe {
-                            let a = *eigenvalues.get_unchecked(i, k);
-                            let b = *eigenvalues.get_unchecked(i, k + 1);
-
-                            *eigenvalues.get_unchecked_mut(i, k)     = c[k] * a - s[k] * b;
-                            *eigenvalues.get_unchecked_mut(i, k + 1) = s[k] * a + c[k] * b;
-                        }
-                    }
-                }
-
-
-                // Shift back
-                for k in 0 .. curdim + 1 {
-                    unsafe {
-                        let a = *eigenvalues.get_unchecked(k, k);
-                        *eigenvalues.get_unchecked_mut(k, k) = a + lambda;
-                    }
-                }
-
-
-                // Givens rotation from right applied to eigenvectors
-                for k in 0 .. curdim {
-                    for i in 0 .. dim.value() {
-
-                        unsafe {
-                            let a = *eigenvectors.get_unchecked(i, k);
-                            let b = *eigenvectors.get_unchecked(i, k + 1);
-
-                            *eigenvectors.get_unchecked_mut(i, k)     = c[k] * a - s[k] * b;
-                            *eigenvectors.get_unchecked_mut(i, k + 1) = s[k] * a + c[k] * b;
-                        }
-                    }
-                }
-
-                iter = iter + 1;
-                stop = true;
-
-                for j in 0 .. curdim {
-                    // Check last row.
-                    if unsafe { *eigenvalues.get_unchecked(curdim, j) }.abs() >= eps {
-                        stop = false;
-                        break;
-                    }
-
-                    // Check last column.
-                    if unsafe { *eigenvalues.get_unchecked(j, curdim) }.abs() >= eps {
-                        stop = false;
-                        break;
-                    }
-                }
-            }
-
-
-            if stop {
-                if curdim > 1 {
-                    curdim = curdim - 1;
-                }
-                else {
-                    break;
-                }
-            }
-        }
-
-        (eigenvectors, eigenvalues.diagonal())
-    }
-
-    /// Cholesky decomposition G of a square symmetric positive definite matrix A, such that A = G * G^T
-    ///
-    /// Matrix symmetricness is not checked. Returns `None` if `self` is not definite positive.
-    #[inline]
-    pub fn cholesky(&self) -> Result<OwnedSquareMatrix<N, D, S::Alloc>, &'static str> {
-        let out = self.transpose();
-
-        if !out.relative_eq(self, N::default_epsilon(), N::default_max_relative()) {
-            return Err("Cholesky: Input matrix is not symmetric");
-        }
-
-        self.do_cholesky(out)
-    }
-
-    /// Cholesky decomposition G of a square symmetric positive definite matrix A, such that A = G * G^T
-    #[inline]
-    pub fn cholesky_unchecked(&self) -> Result<OwnedSquareMatrix<N, D, S::Alloc>, &'static str> {
-        let out = self.transpose();
-        self.do_cholesky(out)
-    }
-
-    #[inline(always)]
-    fn do_cholesky(&self, mut out: OwnedSquareMatrix<N, D, S::Alloc>)
-                   -> Result<OwnedSquareMatrix<N, D, S::Alloc>, &'static str> {
-        assert!(self.is_square(), "The input matrix must be square.");
-
-        for i in 0 .. out.nrows() {
-            for j in 0 .. (i + 1) {
-
-                let mut sum = out[(i, j)];
-
-                for k in 0 .. j {
-                    sum = sum - out[(i, k)] * out[(j, k)];
-                }
-
-                if i > j {
-                    out[(i, j)] = sum / out[(j, j)];
-                }
-                else if sum > N::zero() {
-                    out[(i, i)] = sum.sqrt();
-                }
-                else {
-                    return Err("Cholesky: Input matrix is not positive definite to machine precision.");
-                }
-            }
-        }
-
-        for i in 0 .. out.nrows() {
-            for j in i + 1 .. out.ncols() {
-                out[(i, j)] = N::zero();
-            }
-        }
-
-        Ok(out)
-    }
-
-    /// Hessenberg
-    /// Returns the matrix `self` in Hessenberg form and the corresponding similarity transformation
-    ///
-    /// # Returns
-    /// The tuple (`q`, `h`) that `q * h * q^T = self`
-    pub fn hessenberg(&self) -> (OwnedSquareMatrix<N, D, S::Alloc>, OwnedSquareMatrix<N, D, S::Alloc>)
-        where S::Alloc: Allocator<N, D, U1> + Allocator<N, Dynamic, U1> {
-
-        let (nrows, ncols) = self.data.shape();
-        let mut h = self.clone_owned();
-
-        let mut q = OwnedSquareMatrix::<N, D, S::Alloc>::identity_generic(nrows, ncols);
-
-        if ncols.value() <= 2 {
-            return (q, h);
-        }
-
-        // Temporary buffer that contains a column.
-        let mut col = unsafe {
-            OwnedColumnVector::<N, D, S::Alloc>::new_uninitialized_generic(nrows, U1)
-        };
-
-        for ite in 0 .. (ncols.value() - 2) {
-            let subdim = Dynamic::new(nrows.value() - (ite + 1));
-            let mut v = col.rows_mut(0, subdim.value());
-            v.copy_from(&h.generic_slice((ite + 1, ite), (subdim, U1)));
-
-            let alpha = v.norm();
-
-            unsafe {
-                let x = *v.get_unchecked(0, 0);
-                *v.get_unchecked_mut(0, 0) = x - alpha;
-            }
-
-            if !v.normalize_mut().is_zero() {
-                // XXX: we output the householder matrix to a pre-allocated matrix instead of
-                // return a value to `p`. This would avoid allocation at each iteration.
-                let p = OwnedSquareMatrix::<N, D, S::Alloc>::new_householder_generic(nrows, ite + 1, &v);
-
-                q = q * &p;
-                h = &p * h * p;
-            }
-        }
-
-        (q, h)
-    }
-}

src/core/default_allocator.rs

@@ -4,6 +4,8 @@
 //! heap-allocated buffers for matrices with at least one dimension unknown at compile-time.
 
 use std::mem;
+use std::ptr;
+use std::cmp;
 use std::ops::Mul;
 
 use typenum::Prod;
@@ -11,7 +13,8 @@ use generic_array::ArrayLength;
 
 use core::Scalar;
 use core::dimension::{Dim, DimName, Dynamic};
-use core::allocator::Allocator;
+use core::allocator::{Allocator, Reallocator};
+use core::storage::{Storage, StorageMut};
 use core::matrix_array::MatrixArray;
 use core::matrix_vec::MatrixVec;
 
@@ -107,3 +110,110 @@ impl<N: Scalar, R: DimName> Allocator<N, R, Dynamic> for DefaultAllocator {
         MatrixVec::new(nrows, ncols, res)
     }
 }
+
+/*
+ *
+ * Reallocator.
+ *
+ */
+// Anything -> Static × Static
+impl<N: Scalar, RFrom, CFrom, RTo, CTo> Reallocator<N, RFrom, CFrom, RTo, CTo> for DefaultAllocator
+    where RFrom: Dim,
+          CFrom: Dim,
+          RTo:   DimName,
+          CTo:   DimName,
+          Self: Allocator<N, RFrom, CFrom>,
+          RTo::Value: Mul<CTo::Value>,
+          Prod<RTo::Value, CTo::Value>: ArrayLength<N> {
+
+    #[inline]
+    unsafe fn reallocate_copy(rto: RTo, cto: CTo, buf: <Self as Allocator<N, RFrom, CFrom>>::Buffer) -> MatrixArray<N, RTo, CTo> {
+        let mut res = <Self as Allocator<N, RTo, CTo>>::allocate_uninitialized(rto, cto);
+
+        let (rfrom, cfrom) = buf.shape();
+
+        let len_from = rfrom.value() * cfrom.value();
+        let len_to   = rto.value()   * cto.value();
+        ptr::copy_nonoverlapping(buf.ptr(), res.ptr_mut(), cmp::min(len_from, len_to));
+
+        res
+    }
+}
+
+
+// Static × Static -> Dynamic × Any
+impl<N: Scalar, RFrom, CFrom, CTo> Reallocator<N, RFrom, CFrom, Dynamic, CTo> for DefaultAllocator
+    where RFrom: DimName,
+          CFrom: DimName,
+          CTo:   Dim,
+          RFrom::Value: Mul<CFrom::Value>,
+          Prod<RFrom::Value, CFrom::Value>: ArrayLength<N> {
+
+    #[inline]
+    unsafe fn reallocate_copy(rto: Dynamic, cto: CTo, buf: MatrixArray<N, RFrom, CFrom>) -> MatrixVec<N, Dynamic, CTo> {
+        let mut res = <Self as Allocator<N, Dynamic, CTo>>::allocate_uninitialized(rto, cto);
+
+        let (rfrom, cfrom) = buf.shape();
+
+        let len_from = rfrom.value() * cfrom.value();
+        let len_to   = rto.value()   * cto.value();
+        ptr::copy_nonoverlapping(buf.ptr(), res.ptr_mut(), cmp::min(len_from, len_to));
+
+        res
+    }
+}
+
+// Static × Static -> Static × Dynamic
+impl<N: Scalar, RFrom, CFrom, RTo> Reallocator<N, RFrom, CFrom, RTo, Dynamic> for DefaultAllocator
+    where RFrom: DimName,
+          CFrom: DimName,
+          RTo:   DimName,
+          RFrom::Value: Mul<CFrom::Value>,
+          Prod<RFrom::Value, CFrom::Value>: ArrayLength<N> {
+
+    #[inline]
+    unsafe fn reallocate_copy(rto: RTo, cto: Dynamic, buf: MatrixArray<N, RFrom, CFrom>) -> MatrixVec<N, RTo, Dynamic> {
+        let mut res = <Self as Allocator<N, RTo, Dynamic>>::allocate_uninitialized(rto, cto);
+
+        let (rfrom, cfrom) = buf.shape();
+
+        let len_from = rfrom.value() * cfrom.value();
+        let len_to   = rto.value()   * cto.value();
+        ptr::copy_nonoverlapping(buf.ptr(), res.ptr_mut(), cmp::min(len_from, len_to));
+
+        res
+    }
+}
+
+// All conversion from a dynamic buffer to a dynamic buffer.
+impl<N: Scalar, CFrom: Dim, CTo: Dim> Reallocator<N, Dynamic, CFrom, Dynamic, CTo> for DefaultAllocator {
+    #[inline]
+    unsafe fn reallocate_copy(rto: Dynamic, cto: CTo, buf: MatrixVec<N, Dynamic, CFrom>) -> MatrixVec<N, Dynamic, CTo> {
+        let new_buf = buf.resize(rto.value() * cto.value());
+        MatrixVec::new(rto, cto, new_buf)
+    }
+}
+
+impl<N: Scalar, CFrom: Dim, RTo: DimName> Reallocator<N, Dynamic, CFrom, RTo, Dynamic> for DefaultAllocator {
+    #[inline]
+    unsafe fn reallocate_copy(rto: RTo, cto: Dynamic, buf: MatrixVec<N, Dynamic, CFrom>) -> MatrixVec<N, RTo, Dynamic> {
+        let new_buf = buf.resize(rto.value() * cto.value());
+        MatrixVec::new(rto, cto, new_buf)
+    }
+}
+
+impl<N: Scalar, RFrom: DimName, CTo: Dim> Reallocator<N, RFrom, Dynamic, Dynamic, CTo> for DefaultAllocator {
+    #[inline]
+    unsafe fn reallocate_copy(rto: Dynamic, cto: CTo, buf: MatrixVec<N, RFrom, Dynamic>) -> MatrixVec<N, Dynamic, CTo> {
+        let new_buf = buf.resize(rto.value() * cto.value());
+        MatrixVec::new(rto, cto, new_buf)
+    }
+}
+
+impl<N: Scalar, RFrom: DimName, RTo: DimName> Reallocator<N, RFrom, Dynamic, RTo, Dynamic> for DefaultAllocator {
+    #[inline]
+    unsafe fn reallocate_copy(rto: RTo, cto: Dynamic, buf: MatrixVec<N, RFrom, Dynamic>) -> MatrixVec<N, RTo, Dynamic> {
+        let new_buf = buf.resize(rto.value() * cto.value());
+        MatrixVec::new(rto, cto, new_buf)
+    }
+}

src/core/dimension.rs

@@ -3,9 +3,11 @@
 //! Traits and tags for identifying the dimension of all algebraic entities.
 
 use std::fmt::Debug;
-use std::any::Any;
+use std::any::{TypeId, Any};
+use std::cmp;
 use std::ops::{Add, Sub, Mul, Div};
-use typenum::{self, Unsigned, UInt, B1, Bit, UTerm, Sum, Prod, Diff, Quot};
+use typenum::{self, Unsigned, UInt, B1, Bit, UTerm, Sum, Prod, Diff, Quot,
+              Min, Minimum, Max, Maximum};
 
 #[cfg(feature = "serde-serialize")]
 use serde::{Serialize, Serializer, Deserialize, Deserializer};
@@ -55,6 +57,11 @@ impl IsNotStaticOne for Dynamic { }
 /// Trait implemented by any type that can be used as a dimension. This includes type-level
 /// integers and `Dynamic` (for dimensions not known at compile-time).
 pub trait Dim: Any + Debug + Copy + PartialEq + Send {
+    #[inline(always)]
+    fn is<D: Dim>() -> bool {
+        TypeId::of::<Self>() == TypeId::of::<D>()
+    }
+
     /// Gets the compile-time value of `Self`. Returns `None` if it is not known, i.e., if `Self =
     /// Dynamic`.
     fn try_to_usize() -> Option<usize>;
@@ -85,6 +92,24 @@ impl Dim for Dynamic {
     }
 }
 
+impl Add<usize> for Dynamic {
+    type Output = Dynamic;
+
+    #[inline]
+    fn add(self, rhs: usize) -> Dynamic {
+        Dynamic::new(self.value + rhs)
+    }
+}
+
+impl Sub<usize> for Dynamic {
+    type Output = Dynamic;
+
+    #[inline]
+    fn sub(self, rhs: usize) -> Dynamic {
+        Dynamic::new(self.value - rhs)
+    }
+}
+
 /*
  *
  * Operations.
@@ -93,7 +118,7 @@ impl Dim for Dynamic {
 
 macro_rules! dim_ops(
     ($($DimOp:    ident, $DimNameOp: ident,
-       $Op:       ident, $op: ident,
+       $Op:       ident, $op: ident, $op_path: path,
        $DimResOp: ident, $DimNameResOp: ident,
        $ResOp: ident);* $(;)*) => {$(
         pub type $DimResOp<D1, D2> = <D1 as $DimOp<D2>>::Output;
@@ -120,7 +145,7 @@ macro_rules! dim_ops(
 
             #[inline]
             fn $op(self, other: D) -> Dynamic {
-                Dynamic::new(self.value.$op(other.value()))
+                Dynamic::new($op_path(self.value, other.value()))
             }
         }
 
@@ -129,7 +154,7 @@ macro_rules! dim_ops(
 
             #[inline]
             fn $op(self, other: Dynamic) -> Dynamic {
-                Dynamic::new(self.value().$op(other.value))
+                Dynamic::new($op_path(self.value(), other.value))
             }
         }
 
@@ -155,10 +180,12 @@ macro_rules! dim_ops(
 );
 
 dim_ops!(
-    DimAdd, DimNameAdd, Add, add, DimSum,  DimNameSum,  Sum;
-    DimMul, DimNameMul, Mul, mul, DimProd, DimNameProd, Prod;
-    DimSub, DimNameSub, Sub, sub, DimDiff, DimNameDiff, Diff;
-    DimDiv, DimNameDiv, Div, div, DimQuot, DimNameQuot, Quot;
+    DimAdd, DimNameAdd, Add, add, Add::add, DimSum,     DimNameSum,     Sum;
+    DimMul, DimNameMul, Mul, mul, Mul::mul, DimProd,    DimNameProd,    Prod;
+    DimSub, DimNameSub, Sub, sub, Sub::sub, DimDiff,    DimNameDiff,    Diff;
+    DimDiv, DimNameDiv, Div, div, Div::div, DimQuot,    DimNameQuot,    Quot;
+    DimMin, DimNameMin, Min, min, cmp::min, DimMinimum, DimNameNimimum, Minimum;
+    DimMax, DimNameMax, Max, max, cmp::max, DimMaximum, DimNameMaximum, Maximum;
 );
 
 

src/core/edition.rs

@@ -0,0 +1,539 @@
+use num::{Zero, One};
+use std::cmp;
+use std::ptr;
+
+use core::{DefaultAllocator, Scalar, Matrix, DMatrix, MatrixMN, Vector};
+use core::dimension::{Dim, DimName, DimSub, DimDiff, DimAdd, DimSum, DimMin, DimMinimum, U1, Dynamic};
+use core::constraint::{ShapeConstraint, DimEq};
+use core::allocator::{Allocator, Reallocator};
+use core::storage::{Storage, StorageMut};
+
+impl<N: Scalar + Zero, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
+    /// Extracts the upper triangular part of this matrix (including the diagonal).
+    #[inline]
+    pub fn upper_triangle(&self) -> MatrixMN<N, R, C>
+        where DefaultAllocator: Allocator<N, R, C> {
+        let mut res = self.clone_owned();
+        res.fill_lower_triangle(N::zero(), 1);
+
+        res
+    }
+
+    /// Extracts the upper triangular part of this matrix (including the diagonal).
+    #[inline]
+    pub fn lower_triangle(&self) -> MatrixMN<N, R, C>
+        where DefaultAllocator: Allocator<N, R, C> {
+        let mut res = self.clone_owned();
+        res.fill_upper_triangle(N::zero(), 1);
+
+        res
+    }
+}
+
+impl<N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
+    /// Sets all the elements of this matrix to `val`.
+    #[inline]
+    pub fn fill(&mut self, val: N) {
+        for e in self.iter_mut() {
+            *e = val
+        }
+    }
+
+    /// Fills `self` with the identity matrix.
+    #[inline]
+    pub fn fill_with_identity(&mut self)
+        where N: Zero + One {
+        self.fill(N::zero());
+        self.fill_diagonal(N::one());
+    }
+
+    /// Sets all the diagonal elements of this matrix to `val`.
+    #[inline]
+    pub fn fill_diagonal(&mut self, val: N) {
+        let (nrows, ncols) = self.shape();
+        let n = cmp::min(nrows, ncols);
+
+        for i in 0 .. n {
+            unsafe { *self.get_unchecked_mut(i, i) = val }
+        }
+    }
+
+    /// Sets all the elements of the selected row to `val`.
+    #[inline]
+    pub fn fill_row(&mut self, i: usize, val: N) {
+        assert!(i < self.nrows(), "Row index out of bounds.");
+        for j in 0 .. self.ncols() {
+            unsafe { *self.get_unchecked_mut(i, j) = val }
+        }
+    }
+
+    /// Sets all the elements of the selected column to `val`.
+    #[inline]
+    pub fn fill_column(&mut self, j: usize, val: N) {
+        assert!(j < self.ncols(), "Row index out of bounds.");
+        for i in 0 .. self.nrows() {
+            unsafe { *self.get_unchecked_mut(i, j) = val }
+        }
+    }
+
+    /// Fills the diagonal of this matrix with the content of the given vector.
+    #[inline]
+    pub fn set_diagonal<R2: Dim, S2>(&mut self, diag: &Vector<N, R2, S2>)
+        where R:  DimMin<C>,
+              S2: Storage<N, R2>,
+              ShapeConstraint: DimEq<DimMinimum<R, C>, R2> {
+        let (nrows, ncols)  = self.shape();
+        let min_nrows_ncols = cmp::min(nrows, ncols);
+        assert_eq!(diag.len(), min_nrows_ncols, "Mismatched dimensions.");
+
+        for i in 0 .. min_nrows_ncols {
+            unsafe { *self.get_unchecked_mut(i, i) = *diag.vget_unchecked(i) }
+        }
+    }
+
+    /// Sets all the elements of the lower-triangular part of this matrix to `val`.
+    ///
+    /// The parameter `shift` allows some subdiagonals to be left untouched:
+    /// * If `shift = 0` then the diagonal is overwritten as well.
+    /// * If `shift = 1` then the diagonal is left untouched.
+    /// * If `shift > 1`, then the diagonal and the first `shift - 1` subdiagonals are left
+    /// untouched.
+    #[inline]
+    pub fn fill_lower_triangle(&mut self, val: N, shift: usize) {
+        for j in 0 .. self.ncols() {
+            for i in (j + shift) .. self.nrows() {
+                unsafe { *self.get_unchecked_mut(i, j) = val }
+            }
+        }
+    }
+
+    /// Sets all the elements of the lower-triangular part of this matrix to `val`.
+    ///
+    /// The parameter `shift` allows some superdiagonals to be left untouched:
+    /// * If `shift = 0` then the diagonal is overwritten as well.
+    /// * If `shift = 1` then the diagonal is left untouched.
+    /// * If `shift > 1`, then the diagonal and the first `shift - 1` superdiagonals are left
+    /// untouched.
+    #[inline]
+    pub fn fill_upper_triangle(&mut self, val: N, shift: usize) {
+        for j in shift .. self.ncols() {
+            // FIXME: is there a more efficient way to avoid the min ?
+            // (necessary for rectangular matrices)
+            for i in 0 .. cmp::min(j + 1 - shift, self.nrows()) {
+                unsafe { *self.get_unchecked_mut(i, j) = val }
+            }
+        }
+    }
+
+    /// Swaps two rows in-place.
+    #[inline]
+    pub fn swap_rows(&mut self, irow1: usize, irow2: usize) {
+        assert!(irow1 < self.nrows() && irow2 < self.nrows());
+
+        if irow1 != irow2 {
+            // FIXME: optimize that.
+            for i in 0 .. self.ncols() {
+                unsafe { self.swap_unchecked((irow1, i), (irow2, i)) }
+            }
+        }
+        // Otherwise do nothing.
+    }
+
+    /// Swaps two columns in-place.
+    #[inline]
+    pub fn swap_columns(&mut self, icol1: usize, icol2: usize) {
+        assert!(icol1 < self.ncols() && icol2 < self.ncols());
+
+        if icol1 != icol2 {
+            // FIXME: optimize that.
+            for i in 0 .. self.nrows() {
+                unsafe { self.swap_unchecked((i, icol1), (i, icol2)) }
+            }
+        }
+        // Otherwise do nothing.
+    }
+}
+
+impl<N: Scalar, D: Dim, S: StorageMut<N, D, D>> Matrix<N, D, D, S> {
+    /// Copies the upper-triangle of this matrix to its lower-triangular part.
+    ///
+    /// This makes the matrix symmetric. Panics if the matrix is not square.
+    pub fn fill_lower_triangle_with_upper_triangle(&mut self) {
+        assert!(self.is_square(), "The input matrix should be square.");
+
+        let dim = self.nrows();
+        for j in 0 .. dim {
+            for i in j + 1 .. dim {
+                unsafe {
+                    *self.get_unchecked_mut(i, j) = *self.get_unchecked(j, i);
+                }
+            }
+        }
+    }
+
+    /// Copies the upper-triangle of this matrix to its upper-triangular part.
+    ///
+    /// This makes the matrix symmetric. Panics if the matrix is not square.
+    pub fn fill_upper_triangle_with_lower_triangle(&mut self) {
+        assert!(self.is_square(), "The input matrix should be square.");
+
+        for j in 1 .. self.ncols() {
+            for i in 0 .. j {
+                unsafe {
+                    *self.get_unchecked_mut(i, j) = *self.get_unchecked(j, i);
+                }
+            }
+        }
+    }
+}
+
+/*
+ *
+ * FIXME: specialize all the following for slices.
+ *
+ */
+impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
+    /*
+     *
+     * Column removal.
+     *
+     */
+    /// Removes the `i`-th column from this matrix.
+    #[inline]
+    pub fn remove_column(self, i: usize) -> MatrixMN<N, R, DimDiff<C, U1>>
+        where C: DimSub<U1>,
+              DefaultAllocator: Reallocator<N, R, C, R, DimDiff<C, U1>> {
+        self.remove_fixed_columns::<U1>(i)
+    }
+
+    /// Removes a fixed number − `D::dim()` − of consecutive columns from this matrix, starting
+    /// with the `i`-th (included).
+    #[inline]
+    pub fn remove_fixed_columns<D>(self, i: usize) -> MatrixMN<N, R, DimDiff<C, D>>
+        where D: DimName,
+              C: DimSub<D>,
+              DefaultAllocator: Reallocator<N, R, C, R, DimDiff<C, D>> {
+
+        self.remove_columns_generic(i, D::name())
+    }
+
+    /// Removes `n` consecutive columns from this matrix, starting with the `i`-th (included).
+    #[inline]
+    pub fn remove_columns(self, i: usize, n: usize) -> MatrixMN<N, R, Dynamic>
+        where C: DimSub<Dynamic, Output = Dynamic>,
+              DefaultAllocator: Reallocator<N, R, C, R, Dynamic> {
+
+        self.remove_columns_generic(i, Dynamic::new(n))
+    }
+
+    /// Removes `nremove.value()` columns from this matrix, starting with the `i`-th (included).
+    ///
+    /// This is the generic implementation of `.remove_columns(...)` and
+    /// `.remove_fixed_columns(...)` which have nicer API interfaces.
+    #[inline]
+    pub fn remove_columns_generic<D>(self, i: usize, nremove: D) -> MatrixMN<N, R, DimDiff<C, D>>
+        where D: Dim,
+              C: DimSub<D>,
+              DefaultAllocator: Reallocator<N, R, C, R, DimDiff<C, D>> {
+
+        let mut m = self.into_owned();
+        let (nrows, ncols) = m.data.shape();
+        assert!(i + nremove.value() <= ncols.value(), "Column index out of range.");
+
+        if nremove.value() != 0 && i + nremove.value() < ncols.value() {
+            // The first `deleted_i * nrows` are left untouched.
+            let copied_value_start = i + nremove.value();
+
+            unsafe {
+                let ptr_in  = m.data.ptr().offset((copied_value_start * nrows.value()) as isize);
+                let ptr_out = m.data.ptr_mut().offset((i * nrows.value()) as isize);
+
+                ptr::copy(ptr_in, ptr_out, (ncols.value() - copied_value_start) * nrows.value());
+            }
+        }
+
+        unsafe {
+            Matrix::from_data(DefaultAllocator::reallocate_copy(nrows, ncols.sub(nremove), m.data))
+        }
+    }
+
+
+    /*
+     *
+     * Row removal.
+     *
+     */
+    /// Removes the `i`-th row from this matrix.
+    #[inline]
+    pub fn remove_row(self, i: usize) -> MatrixMN<N, DimDiff<R, U1>, C>
+        where R: DimSub<U1>,
+              DefaultAllocator: Reallocator<N, R, C, DimDiff<R, U1>, C> {
+        self.remove_fixed_rows::<U1>(i)
+    }
+
+    /// Removes a fixed number − `D::dim()` − of consecutive rows from this matrix, starting
+    /// with the `i`-th (included).
+    #[inline]
+    pub fn remove_fixed_rows<D>(self, i: usize) -> MatrixMN<N, DimDiff<R, D>, C>
+        where D: DimName,
+              R: DimSub<D>,
+              DefaultAllocator: Reallocator<N, R, C, DimDiff<R, D>, C> {
+
+        self.remove_rows_generic(i, D::name())
+    }
+
+    /// Removes `n` consecutive rows from this matrix, starting with the `i`-th (included).
+    #[inline]
+    pub fn remove_rows(self, i: usize, n: usize) -> MatrixMN<N, Dynamic, C>
+        where R: DimSub<Dynamic, Output = Dynamic>,
+              DefaultAllocator: Reallocator<N, R, C, Dynamic, C> {
+
+        self.remove_rows_generic(i, Dynamic::new(n))
+    }
+
+    /// Removes `nremove.value()` rows from this matrix, starting with the `i`-th (included).
+    ///
+    /// This is the generic implementation of `.remove_rows(...)` and `.remove_fixed_rows(...)`
+    /// which have nicer API interfaces.
+    #[inline]
+    pub fn remove_rows_generic<D>(self, i: usize, nremove: D) -> MatrixMN<N, DimDiff<R, D>, C>
+        where D: Dim,
+              R: DimSub<D>,
+              DefaultAllocator: Reallocator<N, R, C, DimDiff<R, D>, C> {
+        let mut m = self.into_owned();
+        let (nrows, ncols) = m.data.shape();
+        assert!(i + nremove.value() <= nrows.value(), "Row index out of range.");
+
+        if nremove.value() != 0 {
+            unsafe {
+                compress_rows(&mut m.data.as_mut_slice(), nrows.value(), ncols.value(), i, nremove.value());
+            }
+        }
+
+        unsafe {
+            Matrix::from_data(DefaultAllocator::reallocate_copy(nrows.sub(nremove), ncols, m.data))
+        }
+    }
+
+    /*
+     *
+     * Columns insertion.
+     *
+     */
+    /// Inserts a column filled with `val` at the `i-th` position.
+    #[inline]
+    pub fn insert_column(self, i: usize, val: N) -> MatrixMN<N, R, DimSum<C, U1>>
+        where C: DimAdd<U1>,
+              DefaultAllocator: Reallocator<N, R, C, R, DimSum<C, U1>> {
+        self.insert_fixed_columns::<U1>(i, val)
+    }
+
+    /// Inserts `D` column filled with `val` at the `i-th` position.
+    #[inline]
+    pub fn insert_fixed_columns<D>(self, i: usize, val: N) -> MatrixMN<N, R, DimSum<C, D>>
+        where D: DimName,
+              C: DimAdd<D>,
+              DefaultAllocator: Reallocator<N, R, C, R, DimSum<C, D>> {
+        let mut res = unsafe { self.insert_columns_generic_uninitialized(i, D::name()) };
+        res.fixed_columns_mut::<D>(i).fill(val);
+        res
+    }
+
+    /// Inserts `n` column filled with `val` at the `i-th` position.
+    #[inline]
+    pub fn insert_columns(self, i: usize, n: usize, val: N) -> MatrixMN<N, R, Dynamic>
+        where C: DimAdd<Dynamic, Output = Dynamic>,
+              DefaultAllocator: Reallocator<N, R, C, R, Dynamic> {
+        let mut res = unsafe { self.insert_columns_generic_uninitialized(i, Dynamic::new(n)) };
+        res.columns_mut(i, n).fill(val);
+        res
+    }
+
+    /// Inserts `ninsert.value()` columns at the `i-th` place of this matrix.
+    ///
+    /// The added column values are not initialized.
+    #[inline]
+    pub unsafe fn insert_columns_generic_uninitialized<D>(self, i: usize, ninsert: D)
+        -> MatrixMN<N, R, DimSum<C, D>>
+        where D: Dim,
+              C: DimAdd<D>,
+              DefaultAllocator: Reallocator<N, R, C, R, DimSum<C, D>> {
+
+        let m = self.into_owned();
+        let (nrows, ncols) = m.data.shape();
+        let mut res = Matrix::from_data(DefaultAllocator::reallocate_copy(nrows, ncols.add(ninsert), m.data));
+
+        assert!(i <= ncols.value(), "Column insertion index out of range.");
+
+        if ninsert.value() != 0 && i != ncols.value() {
+            let ptr_in  = res.data.ptr().offset((i * nrows.value()) as isize);
+            let ptr_out = res.data.ptr_mut().offset(((i + ninsert.value()) * nrows.value()) as isize);
+
+            ptr::copy(ptr_in, ptr_out, (ncols.value() - i) * nrows.value())
+        }
+
+        res
+    }
+
+    /*
+     *
+     * Rows insertion.
+     *
+     */
+    /// Inserts a row filled with `val` at the `i-th` position.
+    #[inline]
+    pub fn insert_row(self, i: usize, val: N) -> MatrixMN<N, DimSum<R, U1>, C>
+        where R: DimAdd<U1>,
+              DefaultAllocator: Reallocator<N, R, C, DimSum<R, U1>, C> {
+        self.insert_fixed_rows::<U1>(i, val)
+    }
+
+    /// Inserts `D` row filled with `val` at the `i-th` position.
+    #[inline]
+    pub fn insert_fixed_rows<D>(self, i: usize, val: N) -> MatrixMN<N, DimSum<R, D>, C>
+        where D: DimName,
+              R: DimAdd<D>,
+              DefaultAllocator: Reallocator<N, R, C, DimSum<R, D>, C> {
+        let mut res = unsafe { self.insert_rows_generic_uninitialized(i, D::name()) };
+        res.fixed_rows_mut::<D>(i).fill(val);
+        res
+    }
+
+    /// Inserts `n` rows filled with `val` at the `i-th` position.
+    #[inline]
+    pub fn insert_rows(self, i: usize, n: usize, val: N) -> MatrixMN<N, Dynamic, C>
+        where R: DimAdd<Dynamic, Output = Dynamic>,
+              DefaultAllocator: Reallocator<N, R, C, Dynamic, C> {
+        let mut res = unsafe { self.insert_rows_generic_uninitialized(i, Dynamic::new(n)) };
+        res.rows_mut(i, n).fill(val);
+        res
+    }
+
+    /// Inserts `ninsert.value()` rows at the `i-th` place of this matrix.
+    ///
+    /// The added rows values are not initialized.
+    #[inline]
+    pub unsafe fn insert_rows_generic_uninitialized<D>(self, i: usize, ninsert: D)
+        -> MatrixMN<N, DimSum<R, D>, C>
+        where D: Dim,
+              R: DimAdd<D>,
+              DefaultAllocator: Reallocator<N, R, C, DimSum<R, D>, C> {
+
+        let m = self.into_owned();
+        let (nrows, ncols) = m.data.shape();
+        let mut res = Matrix::from_data(DefaultAllocator::reallocate_copy(nrows.add(ninsert), ncols, m.data));
+
+        assert!(i <= nrows.value(), "Row insertion index out of range.");
+
+        if ninsert.value() != 0 {
+            extend_rows(&mut res.data.as_mut_slice(), nrows.value(), ncols.value(), i, ninsert.value());
+        }
+
+        res
+    }
+
+    /*
+     *
+     * Resizing.
+     *
+     */
+
+    pub fn resize(self, new_nrows: usize, new_ncols: usize, val: N) -> DMatrix<N>
+        where DefaultAllocator: Reallocator<N, R, C, Dynamic, Dynamic> {
+
+        self.resize_generic(Dynamic::new(new_nrows), Dynamic::new(new_ncols), val)
+    }
+
+    pub fn fixed_resize<R2: DimName, C2: DimName>(self, val: N) -> MatrixMN<N, R2, C2>
+        where DefaultAllocator: Reallocator<N, R, C, R2, C2> {
+
+        self.resize_generic(R2::name(), C2::name(), val)
+    }
+
+    /// Resizes `self` such that it has dimensions `new_nrows × now_ncols`. The values are copied
+    /// such that `self[(i, j)] == result[(i, j)]`. If the result has more rows and/or columns than
+    /// `self`, then the extra rows or columns are filled with `val`.
+    #[inline]
+    pub fn resize_generic<R2: Dim, C2: Dim>(self, new_nrows: R2, new_ncols: C2, val: N) -> MatrixMN<N, R2, C2>
+        where DefaultAllocator: Reallocator<N, R, C, R2, C2> {
+
+        let (nrows, ncols) = self.shape();
+        let mut data = self.data.into_owned();
+
+        if new_nrows.value() == nrows {
+            let res = unsafe { DefaultAllocator::reallocate_copy(new_nrows, new_ncols, data) };
+
+            Matrix::from_data(res)
+        }
+        else {
+            let mut res;
+
+            unsafe {
+                if new_nrows.value() < nrows {
+                    compress_rows(&mut data.as_mut_slice(), nrows, ncols, new_nrows.value(), nrows - new_nrows.value());
+                    res = Matrix::from_data(DefaultAllocator::reallocate_copy(new_nrows, new_ncols, data));
+                }
+                else {
+                    res = Matrix::from_data(DefaultAllocator::reallocate_copy(new_nrows, new_ncols, data));
+                    extend_rows(&mut res.data.as_mut_slice(), nrows, ncols, nrows, new_nrows.value() - nrows);
+                }
+            }
+
+            if new_ncols.value() > ncols {
+                res.columns_range_mut(ncols ..).fill(val);
+            }
+
+            if new_nrows.value() > nrows {
+                res.slice_range_mut(nrows .., .. cmp::min(ncols, new_ncols.value())).fill(val);
+            }
+
+            res
+        }
+    }
+}
+
+
+unsafe fn compress_rows<N: Scalar>(data: &mut [N], nrows: usize, ncols: usize, i: usize, nremove: usize) {
+    let new_nrows = nrows - nremove;
+    let ptr_in    = data.as_ptr();
+    let ptr_out   = data.as_mut_ptr();
+
+    let mut curr_i = i;
+
+    for k in 0 .. ncols - 1 {
+        ptr::copy(ptr_in.offset((curr_i + (k + 1) * nremove) as isize),
+                  ptr_out.offset(curr_i as isize),
+                  new_nrows);
+
+        curr_i += new_nrows;
+    }
+
+    // Deal with the last column from which less values have to be copied.
+    let remaining_len = nrows - i - nremove;
+    ptr::copy(ptr_in.offset((nrows * ncols - remaining_len) as isize),
+              ptr_out.offset(curr_i as isize),
+              remaining_len);
+}
+
+
+unsafe fn extend_rows<N: Scalar>(data: &mut [N], nrows: usize, ncols: usize, i: usize, ninsert: usize) {
+    let new_nrows = nrows + ninsert;
+    let ptr_in    = data.as_ptr();
+    let ptr_out   = data.as_mut_ptr();
+
+    let remaining_len = nrows - i;
+    let mut curr_i = new_nrows * ncols - remaining_len;
+
+    // Deal with the last column from which less values have to be copied.
+    ptr::copy(ptr_in.offset((nrows * ncols - remaining_len) as isize),
+              ptr_out.offset(curr_i as isize),
+              remaining_len);
+
+    for k in (0 .. ncols - 1).rev() {
+        curr_i -= new_nrows;
+
+        ptr::copy(ptr_in.offset((k * nrows + i) as isize),
+                  ptr_out.offset(curr_i as isize),
+                  nrows);
+    }
+}

src/core/inverse.rs

@@ -1,203 +0,0 @@
-use approx::ApproxEq;
-
-use alga::general::Field;
-
-use core::{Scalar, Matrix, SquareMatrix, OwnedSquareMatrix};
-use core::dimension::Dim;
-use core::storage::{Storage, StorageMut};
-
-
-impl<N, D: Dim, S> SquareMatrix<N, D, S>
-    where N: Scalar + Field + ApproxEq,
-          S: Storage<N, D, D> {
-    /// Attempts to invert this matrix.
-    #[inline]
-    pub fn try_inverse(self) -> Option<OwnedSquareMatrix<N, D, S::Alloc>> {
-        let mut res = self.into_owned();
-
-        if res.shape().0 <= 3 {
-            if res.try_inverse_mut() {
-                Some(res)
-            }
-            else {
-                None
-            }
-        }
-        else {
-            gauss_jordan_inverse(res)
-        }
-    }
-}
-
-
-impl<N, D: Dim, S> SquareMatrix<N, D, S>
-    where N: Scalar + Field + ApproxEq,
-          S: StorageMut<N, D, D> {
-    /// Attempts to invert this matrix in-place. Returns `false` and leaves `self` untouched if
-    /// inversion fails.
-    #[inline]
-    pub fn try_inverse_mut(&mut self) -> bool {
-        assert!(self.is_square(), "Unable to invert a non-square matrix.");
-
-        let dim = self.shape().0;
-
-        unsafe {
-            match dim {
-                0 => true,
-                1 => {
-                    let determinant = self.get_unchecked(0, 0).clone();
-                    if determinant == N::zero() {
-                        false
-                    }
-                    else {
-                        *self.get_unchecked_mut(0, 0) = N::one() / determinant;
-                        true
-                    }
-                },
-                2 => {
-                    let determinant = self.determinant();
-
-                    if determinant == N::zero() {
-                        false
-                    }
-                    else {
-                        let m11 = *self.get_unchecked(0, 0); let m12 = *self.get_unchecked(0, 1);
-                        let m21 = *self.get_unchecked(1, 0); let m22 = *self.get_unchecked(1, 1);
-
-                        *self.get_unchecked_mut(0, 0) =  m22 / determinant;
-                        *self.get_unchecked_mut(0, 1) = -m12 / determinant;
-
-                        *self.get_unchecked_mut(1, 0) = -m21 / determinant;
-                        *self.get_unchecked_mut(1, 1) =  m11 / determinant;
-
-                        true
-                    }
-                },
-                3 => {
-                    let m11 = *self.get_unchecked(0, 0);
-                    let m12 = *self.get_unchecked(0, 1);
-                    let m13 = *self.get_unchecked(0, 2);
-
-                    let m21 = *self.get_unchecked(1, 0);
-                    let m22 = *self.get_unchecked(1, 1);
-                    let m23 = *self.get_unchecked(1, 2);
-
-                    let m31 = *self.get_unchecked(2, 0);
-                    let m32 = *self.get_unchecked(2, 1);
-                    let m33 = *self.get_unchecked(2, 2);
-
-
-                    let minor_m12_m23 = m22 * m33 - m32 * m23;
-                    let minor_m11_m23 = m21 * m33 - m31 * m23;
-                    let minor_m11_m22 = m21 * m32 - m31 * m22;
-
-                    let determinant = m11 * minor_m12_m23 -
-                                      m12 * minor_m11_m23 +
-                                      m13 * minor_m11_m22;
-
-                    if determinant == N::zero() {
-                        false
-                    }
-                    else {
-                        *self.get_unchecked_mut(0, 0) = minor_m12_m23 / determinant;
-                        *self.get_unchecked_mut(0, 1) = (m13 * m32 - m33 * m12) / determinant;
-                        *self.get_unchecked_mut(0, 2) = (m12 * m23 - m22 * m13) / determinant;
-
-                        *self.get_unchecked_mut(1, 0) = -minor_m11_m23 / determinant;
-                        *self.get_unchecked_mut(1, 1) = (m11 * m33 - m31 * m13) / determinant;
-                        *self.get_unchecked_mut(1, 2) = (m13 * m21 - m23 * m11) / determinant;
-
-                        *self.get_unchecked_mut(2, 0) = minor_m11_m22  / determinant;
-                        *self.get_unchecked_mut(2, 1) = (m12 * m31 - m32 * m11) / determinant;
-                        *self.get_unchecked_mut(2, 2) = (m11 * m22 - m21 * m12) / determinant;
-
-                        true
-                    }
-                },
-                _ => {
-                    let oself = self.clone_owned();
-                    if let Some(res) = gauss_jordan_inverse(oself) {
-                        self.copy_from(&res);
-                        true
-                    }
-                    else {
-                        false
-                    }
-                }
-            }
-        }
-    }
-}
-
-
-/// Inverts the given matrix using Gauss-Jordan Ellimitation.
-fn gauss_jordan_inverse<N, D, S>(mut matrix: SquareMatrix<N, D, S>) -> Option<OwnedSquareMatrix<N, D, S::Alloc>>
-    where D: Dim,
-          N: Scalar + Field + ApproxEq,
-          S: StorageMut<N, D, D> {
-
-    assert!(matrix.is_square(), "Unable to invert a non-square matrix.");
-    let dim = matrix.data.shape().0;
-    let mut res: OwnedSquareMatrix<N, D, S::Alloc> = Matrix::identity_generic(dim, dim);
-    let dim = dim.value();
-
-    unsafe {
-        for k in 0 .. dim {
-            // Search a non-zero value on the k-th column.
-            // FIXME: would it be worth it to spend some more time searching for the
-            // max instead?
-
-            let mut n0 = k; // index of a non-zero entry.
-
-            while n0 != dim {
-                if !matrix.get_unchecked(n0, k).is_zero() {
-                    break;
-                }
-
-                n0 += 1;
-            }
-
-            if n0 == dim {
-                return None
-            }
-
-            // Swap pivot line.
-            if n0 != k {
-                for j in 0 .. dim {
-                    matrix.swap_unchecked((n0, j), (k, j));
-                    res.swap_unchecked((n0, j), (k, j));
-                }
-            }
-
-            let pivot = *matrix.get_unchecked(k, k);
-
-            for j in k .. dim {
-                let selfval = *matrix.get_unchecked(k, j) / pivot;
-                *matrix.get_unchecked_mut(k, j) = selfval;
-            }
-
-            for j in 0 .. dim {
-                let resval = *res.get_unchecked(k, j) / pivot;
-                *res.get_unchecked_mut(k, j) = resval;
-            }
-
-            for l in 0 .. dim {
-                if l != k {
-                    let normalizer = *matrix.get_unchecked(l, k);
-
-                    for j in k .. dim {
-                        let selfval = *matrix.get_unchecked(l, j) - *matrix.get_unchecked(k, j) * normalizer;
-                        *matrix.get_unchecked_mut(l, j) = selfval;
-                    }
-
-                    for j in 0 .. dim {
-                        let resval  = *res.get_unchecked(l, j) - *res.get_unchecked(k, j) * normalizer;
-                        *res.get_unchecked_mut(l, j) = resval;
-                    }
-                }
-            }
-        }
-
-        Some(res)
-    }
-}

src/core/iter.rs

@@ -81,6 +81,13 @@ macro_rules! iterator {
                 self.size_hint().0
             }
         }
+
+        impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + $Storage<N, R, C>> ExactSizeIterator for $Name<'a, N, R, C, S> {
+            #[inline]
+            fn len(&self) -> usize {
+                self.size
+            }
+        }
     }
 }
 

src/core/matrix_alga.rs

@@ -7,42 +7,39 @@ use alga::general::{AbstractMagma, AbstractGroupAbelian, AbstractGroup, Abstract
                     ClosedAdd, ClosedNeg, ClosedMul};
 use alga::linear::{VectorSpace, NormedSpace, InnerSpace, FiniteDimVectorSpace, FiniteDimInnerSpace};
 
-use core::{Scalar, Matrix, SquareMatrix};
+use core::{DefaultAllocator, Scalar, MatrixMN, MatrixN};
 use core::dimension::{Dim, DimName};
-use core::storage::OwnedStorage;
-use core::allocator::OwnedAllocator;
+use core::storage::{Storage, StorageMut};
+use core::allocator::Allocator;
 
 /*
  *
  * Additive structures.
  *
  */
-impl<N, R: DimName, C: DimName, S> Identity<Additive> for Matrix<N, R, C, S>
+impl<N, R: DimName, C: DimName> Identity<Additive> for MatrixMN<N, R, C>
     where N: Scalar + Zero,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+          DefaultAllocator: Allocator<N, R, C> {
     #[inline]
     fn identity() -> Self {
         Self::from_element(N::zero())
     }
 }
 
-impl<N, R: DimName, C: DimName, S> AbstractMagma<Additive> for Matrix<N, R, C, S>
+impl<N, R: DimName, C: DimName> AbstractMagma<Additive> for MatrixMN<N, R, C>
     where N: Scalar + ClosedAdd,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+          DefaultAllocator: Allocator<N, R, C> {
     #[inline]
     fn operate(&self, other: &Self) -> Self {
         self + other
     }
 }
 
-impl<N, R: DimName, C: DimName, S> Inverse<Additive> for Matrix<N, R, C, S>
+impl<N, R: DimName, C: DimName> Inverse<Additive> for MatrixMN<N, R, C>
     where N: Scalar + ClosedNeg,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+          DefaultAllocator: Allocator<N, R, C> {
     #[inline]
-    fn inverse(&self) -> Matrix<N, R, C, S> {
+    fn inverse(&self) -> MatrixMN<N, R, C> {
         -self
     }
 
@@ -54,10 +51,9 @@ impl<N, R: DimName, C: DimName, S> Inverse<Additive> for Matrix<N, R, C, S>
 
 macro_rules! inherit_additive_structure(
     ($($marker: ident<$operator: ident> $(+ $bounds: ident)*),* $(,)*) => {$(
-        impl<N, R: DimName, C: DimName, S> $marker<$operator> for Matrix<N, R, C, S>
+        impl<N, R: DimName, C: DimName> $marker<$operator> for MatrixMN<N, R, C>
             where N: Scalar + $marker<$operator> $(+ $bounds)*,
-                  S: OwnedStorage<N, R, C>,
-                  S::Alloc: OwnedAllocator<N, R, C, S> { }
+                  DefaultAllocator: Allocator<N, R, C> { }
     )*}
 );
 
@@ -70,10 +66,9 @@ inherit_additive_structure!(
     AbstractGroupAbelian<Additive> + Zero + ClosedAdd + ClosedNeg
 );
 
-impl<N, R: DimName, C: DimName, S> AbstractModule for Matrix<N, R, C, S>
+impl<N, R: DimName, C: DimName> AbstractModule for MatrixMN<N, R, C>
     where N: Scalar + RingCommutative,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+          DefaultAllocator: Allocator<N, R, C> {
     type AbstractRing = N;
 
     #[inline]
@@ -82,24 +77,21 @@ impl<N, R: DimName, C: DimName, S> AbstractModule for Matrix<N, R, C, S>
     }
 }
 
-impl<N, R: DimName, C: DimName, S> Module for Matrix<N, R, C, S>
+impl<N, R: DimName, C: DimName> Module for MatrixMN<N, R, C>
     where N: Scalar + RingCommutative,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+          DefaultAllocator: Allocator<N, R, C> {
     type Ring = N;
 }
 
-impl<N, R: DimName, C: DimName, S> VectorSpace for Matrix<N, R, C, S>
+impl<N, R: DimName, C: DimName> VectorSpace for MatrixMN<N, R, C>
     where N: Scalar + Field,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+          DefaultAllocator: Allocator<N, R, C> {
     type Field = N;
 }
 
-impl<N, R: DimName, C: DimName, S> FiniteDimVectorSpace for Matrix<N, R, C, S>
+impl<N, R: DimName, C: DimName> FiniteDimVectorSpace for MatrixMN<N, R, C>
     where N: Scalar + Field,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+          DefaultAllocator: Allocator<N, R, C> {
     #[inline]
     fn dimension() -> usize {
         R::dim() * C::dim()
@@ -131,10 +123,8 @@ impl<N, R: DimName, C: DimName, S> FiniteDimVectorSpace for Matrix<N, R, C, S>
     }
 }
 
-impl<N, R: DimName, C: DimName, S> NormedSpace for Matrix<N, R, C, S>
-    where N: Real,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+impl<N: Real, R: DimName, C: DimName> NormedSpace for MatrixMN<N, R, C>
+    where DefaultAllocator: Allocator<N, R, C> {
     #[inline]
     fn norm_squared(&self) -> N {
         self.norm_squared()
@@ -166,10 +156,8 @@ impl<N, R: DimName, C: DimName, S> NormedSpace for Matrix<N, R, C, S>
     }
 }
 
-impl<N, R: DimName, C: DimName, S> InnerSpace for Matrix<N, R, C, S>
-    where N: Real,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+impl<N: Real, R: DimName, C: DimName> InnerSpace for MatrixMN<N, R, C>
+    where DefaultAllocator: Allocator<N, R, C> {
     type Real = N;
 
     #[inline]
@@ -187,12 +175,10 @@ impl<N, R: DimName, C: DimName, S> InnerSpace for Matrix<N, R, C, S>
 // In particular:
 //   − use `x()` instead of `::canonical_basis_element`
 //   − use `::new(x, y, z)` instead of `::from_slice`
-impl<N, R: DimName, C: DimName, S> FiniteDimInnerSpace for Matrix<N, R, C, S>
-    where N: Real,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+impl<N: Real, R: DimName, C: DimName> FiniteDimInnerSpace for MatrixMN<N, R, C>
+    where DefaultAllocator: Allocator<N, R, C> {
     #[inline]
-    fn orthonormalize(vs: &mut [Matrix<N, R, C, S>]) -> usize {
+    fn orthonormalize(vs: &mut [MatrixMN<N, R, C>]) -> usize {
         let mut nbasis_elements = 0;
 
         for i in 0 .. vs.len() {
@@ -307,20 +293,18 @@ impl<N, R: DimName, C: DimName, S> FiniteDimInnerSpace for Matrix<N, R, C, S>
  *
  *
  */
-impl<N, D: DimName, S> Identity<Multiplicative> for SquareMatrix<N, D, S>
+impl<N, D: DimName> Identity<Multiplicative> for MatrixN<N, D>
     where N: Scalar + Zero + One,
-          S: OwnedStorage<N, D, D>,
-          S::Alloc: OwnedAllocator<N, D, D, S> {
+          DefaultAllocator: Allocator<N, D, D> {
     #[inline]
     fn identity() -> Self {
         Self::identity()
     }
 }
 
-impl<N, D: DimName, S> AbstractMagma<Multiplicative> for SquareMatrix<N, D, S>
-    where N: Scalar + Zero + ClosedAdd + ClosedMul,
-          S: OwnedStorage<N, D, D>,
-          S::Alloc: OwnedAllocator<N, D, D, S> {
+impl<N, D: DimName> AbstractMagma<Multiplicative> for MatrixN<N, D>
+    where N: Scalar + Zero + One + ClosedAdd + ClosedMul,
+          DefaultAllocator: Allocator<N, D, D> {
     #[inline]
     fn operate(&self, other: &Self) -> Self {
         self * other
@@ -329,10 +313,9 @@ impl<N, D: DimName, S> AbstractMagma<Multiplicative> for SquareMatrix<N, D, S>
 
 macro_rules! impl_multiplicative_structure(
     ($($marker: ident<$operator: ident> $(+ $bounds: ident)*),* $(,)*) => {$(
-        impl<N, D: DimName, S> $marker<$operator> for SquareMatrix<N, D, S>
-            where N: Scalar + Zero + ClosedAdd + ClosedMul + $marker<$operator> $(+ $bounds)*,
-                  S: OwnedStorage<N, D, D>,
-                  S::Alloc: OwnedAllocator<N, D, D, S> { }
+        impl<N, D: DimName> $marker<$operator> for MatrixN<N, D>
+            where N: Scalar + Zero + One + ClosedAdd + ClosedMul + $marker<$operator> $(+ $bounds)*,
+                  DefaultAllocator: Allocator<N, D, D> { }
     )*}
 );
 
@@ -341,421 +324,24 @@ impl_multiplicative_structure!(
     AbstractMonoid<Multiplicative> + One
 );
 
-// // FIXME: Field too strong?
-// impl<N, S> Matrix for Matrix<N, S>
-//     where N: Scalar + Field,
-//           S: Storage<N> {
-//     type Field     = N;
-//     type Row       = OwnedMatrix<N, Static<U1>, S::C, S::Alloc>;
-//     type Column    = OwnedMatrix<N, S::R, Static<U1>, S::Alloc>;
-//     type Transpose = OwnedMatrix<N, S::C, S::R, S::Alloc>;
-
-//     #[inline]
-//     fn nrows(&self) -> usize {
-//         self.shape().0
-//     }
-
-//     #[inline]
-//     fn ncolumns(&self) -> usize {
-//         self.shape().1
-//     }
-
-//     #[inline]
-//     fn row(&self, row: usize) -> Self::Row {
-//         let mut res: Self::Row = ::zero();
-
-//         for (column, e) in res.iter_mut().enumerate() {
-//             *e = self[(row, column)];
-//         }
-
-//         res
-//     }
-
-//     #[inline]
-//     fn column(&self, column: usize) -> Self::Column {
-//         let mut res: Self::Column = ::zero();
-
-//         for (row, e) in res.iter_mut().enumerate() {
-//             *e = self[(row, column)];
-//         }
-
-//         res
-//     }
-
-//     #[inline]
-//     unsafe fn get_unchecked(&self, i: usize, j: usize) -> Self::Field {
-//         self.get_unchecked(i, j)
-//     }
-
-//     #[inline]
-//     fn transpose(&self) -> Self::Transpose {
-//         self.transpose()
-//     }
-// }
-
-// impl<N, S> MatrixMut for Matrix<N, S>
-//     where N: Scalar + Field,
-//           S: StorageMut<N> {
-//     #[inline]
-//     fn set_row_mut(&mut self, irow: usize, row: &Self::Row) {
-//         assert!(irow < self.shape().0, "Row index out of bounds.");
-
-//         for (icol, e) in row.iter().enumerate() {
-//             unsafe { self.set_unchecked(irow, icol, *e) }
-//         }
-//     }
-
-//     #[inline]
-//     fn set_column_mut(&mut self, icol: usize, col: &Self::Column) {
-//         assert!(icol < self.shape().1, "Column index out of bounds.");
-//         for (irow, e) in col.iter().enumerate() {
-//             unsafe { self.set_unchecked(irow, icol, *e) }
-//         }
-//     }
-
-//     #[inline]
-//     unsafe fn set_unchecked(&mut self, i: usize, j: usize, val: Self::Field) {
-//         *self.get_unchecked_mut(i, j) = val
-//     }
-// }
-
-// // FIXME: Real is needed here only for invertibility...
-// impl<N: Real> SquareMatrixMut for $t<N> {
-//     #[inline]
-//     fn from_diagonal(diag: &Self::Coordinates) -> Self {
-//         let mut res: $t<N> = ::zero();
-//         res.set_diagonal_mut(diag);
-//         res
-//     }
-
-//     #[inline]
-//     fn set_diagonal_mut(&mut self, diag: &Self::Coordinates) {
-//         for (i, e) in diag.iter().enumerate() {
-//             unsafe { self.set_unchecked(i, i, *e) }
-//         }
-//     }
-// }
-
-
-
-// Specializations depending on the dimension.
-// matrix_group_approx_impl!(common: $t, 1, $vector, $($compN),+);
-
-// // FIXME: Real is needed here only for invertibility...
-// impl<N: Real> SquareMatrix for $t<N> {
-//     type Vector = $vector<N>;
-
-//     #[inline]
-//     fn diagonal(&self) -> Self::Coordinates {
-//         $vector::new(self.m11)
-//     }
-
-//     #[inline]
-//     fn determinant(&self) -> Self::Field {
-//         self.m11
-//     }
-
-//     #[inline]
-//     fn try_inverse(&self) -> Option<Self> {
-//         let mut res = *self;
-//         if res.try_inverse_mut() {
-//             Some(res)
-//         }
-//         else {
-//             None
-//         }
-//     }
-
-//     #[inline]
-//     fn try_inverse_mut(&mut self) -> bool {
-//         if relative_eq!(&self.m11, &::zero()) {
-//             false
-//         }
-//         else {
-//             self.m11 = ::one::<N>() / ::determinant(self);
-
-//             true
-//         }
-//     }
-
-//     #[inline]
-//     fn transpose_mut(&mut self) {
-//         // no-op
-//     }
-// }
-
-//  ident, 2, $vector: ident, $($compN: ident),+) => {
-// matrix_group_approx_impl!(common: $t, 2, $vector, $($compN),+);
-
-// // FIXME: Real is needed only for inversion here.
-// impl<N: Real> SquareMatrix for $t<N> {
-//     type Vector = $vector<N>;
-
-//     #[inline]
-//     fn diagonal(&self) -> Self::Coordinates {
-//         $vector::new(self.m11, self.m22)
-//     }
-
-//     #[inline]
-//     fn determinant(&self) -> Self::Field {
-//         self.m11 * self.m22 - self.m21 * self.m12
-//     }
-
-//     #[inline]
-//     fn try_inverse(&self) -> Option<Self> {
-//         let mut res = *self;
-//         if res.try_inverse_mut() {
-//             Some(res)
-//         }
-//         else {
-//             None
-//         }
-//     }
-
-//     #[inline]
-//     fn try_inverse_mut(&mut self) -> bool {
-//         let determinant = ::determinant(self);
-
-//         if relative_eq!(&determinant, &::zero()) {
-//             false
-//         }
-//         else {
-//             *self = Matrix2::new(
-//                 self.m22 / determinant , -self.m12 / determinant,
-//                 -self.m21 / determinant, self.m11 / determinant);
-
-//             true
-//         }
-//     }
-
-//     #[inline]
-//     fn transpose_mut(&mut self) {
-//         mem::swap(&mut self.m12, &mut self.m21)
-//     }
-// }
-
-//  ident, 3, $vector: ident, $($compN: ident),+) => {
-// matrix_group_approx_impl!(common: $t, 3, $vector, $($compN),+);
-
-// // FIXME: Real is needed only for inversion here.
-// impl<N: Real> SquareMatrix for $t<N> {
-//     type Vector = $vector<N>;
-
-//     #[inline]
-//     fn diagonal(&self) -> Self::Coordinates {
-//         $vector::new(self.m11, self.m22, self.m33)
-//     }
-
-//     #[inline]
-//     fn determinant(&self) -> Self::Field {
-//         let minor_m12_m23 = self.m22 * self.m33 - self.m32 * self.m23;
-//         let minor_m11_m23 = self.m21 * self.m33 - self.m31 * self.m23;
-//         let minor_m11_m22 = self.m21 * self.m32 - self.m31 * self.m22;
-
-//         self.m11 * minor_m12_m23 - self.m12 * minor_m11_m23 + self.m13 * minor_m11_m22
-//     }
-
-//     #[inline]
-//     fn try_inverse(&self) -> Option<Self> {
-//         let mut res = *self;
-//         if res.try_inverse_mut() {
-//             Some(res)
-//         }
-//         else {
-//             None
-//         }
-//     }
-
-//     #[inline]
-//     fn try_inverse_mut(&mut self) -> bool {
-//         let minor_m12_m23 = self.m22 * self.m33 - self.m32 * self.m23;
-//         let minor_m11_m23 = self.m21 * self.m33 - self.m31 * self.m23;
-//         let minor_m11_m22 = self.m21 * self.m32 - self.m31 * self.m22;
-
-//         let determinant = self.m11 * minor_m12_m23 -
-//                           self.m12 * minor_m11_m23 +
-//                           self.m13 * minor_m11_m22;
-
-//         if relative_eq!(&determinant, &::zero()) {
-//             false
-//         }
-//         else {
-//             *self = Matrix3::new(
-//                 (minor_m12_m23 / determinant),
-//                 ((self.m13 * self.m32 - self.m33 * self.m12) / determinant),
-//                 ((self.m12 * self.m23 - self.m22 * self.m13) / determinant),
-
-//                 (-minor_m11_m23 / determinant),
-//                 ((self.m11 * self.m33 - self.m31 * self.m13) / determinant),
-//                 ((self.m13 * self.m21 - self.m23 * self.m11) / determinant),
-
-//                 (minor_m11_m22  / determinant),
-//                 ((self.m12 * self.m31 - self.m32 * self.m11) / determinant),
-//                 ((self.m11 * self.m22 - self.m21 * self.m12) / determinant)
-//                 );
-
-//             true
-//         }
-//     }
-
-//     #[inline]
-//     fn transpose_mut(&mut self) {
-//         mem::swap(&mut self.m12, &mut self.m21);
-//         mem::swap(&mut self.m13, &mut self.m31);
-//         mem::swap(&mut self.m23, &mut self.m32);
-//     }
-// }
-
-//  ident, $dimension: expr, $vector: ident, $($compN: ident),+) => {
-// matrix_group_approx_impl!(common: $t, $dimension, $vector, $($compN),+);
-
-// // FIXME: Real is needed only for inversion here.
-// impl<N: Real> SquareMatrix for $t<N> {
-//     type Vector = $vector<N>;
-
-//     #[inline]
-//     fn diagonal(&self) -> Self::Coordinates {
-//         let mut diagonal: $vector<N> = ::zero();
-
-//         for i in 0 .. $dimension {
-//             unsafe { diagonal.unsafe_set(i, self.get_unchecked(i, i)) }
-//         }
-
-//         diagonal
-//     }
-
-//     #[inline]
-//     fn determinant(&self) -> Self::Field {
-//         // FIXME: extremely naive implementation.
-//         let mut det = ::zero();
-
-//         for icol in 0 .. $dimension {
-//             let e = unsafe { self.unsafe_at((0, icol)) };
-
-//             if e != ::zero() {
-//                 let minor_mat = self.delete_row_column(0, icol);
-//                 let minor     = minor_mat.determinant();
-
-//                 if icol % 2 == 0 {
-//                     det += minor;
-//                 }
-//                 else {
-//                     det -= minor;
-//                 }
-//             }
-//         }
-
-//         det
-//     }
-
-//     #[inline]
-//     fn try_inverse(&self) -> Option<Self> {
-//         let mut res = *self;
-//         if res.try_inverse_mut() {
-//             Some(res)
-//         }
-//         else {
-//             None
-//         }
-//     }
-
-//     #[inline]
-//     fn try_inverse_mut(&mut self) -> bool {
-//         let mut res: $t<N> = ::one();
-
-//         // Inversion using Gauss-Jordan elimination
-//         for k in 0 .. $dimension {
-//             // search a non-zero value on the k-th column
-//             // FIXME: would it be worth it to spend some more time searching for the
-//             // max instead?
-
-//             let mut n0 = k; // index of a non-zero entry
-
-//             while n0 != $dimension {
-//                 if self[(n0, k)] != ::zero() {
-//                     break;
-//                 }
-
-//                 n0 = n0 + 1;
-//             }
-
-//             if n0 == $dimension {
-//                 return false
-//             }
-
-//             // swap pivot line
-//             if n0 != k {
-//                 for j in 0 .. $dimension {
-//                     self.swap((n0, j), (k, j));
-//                     res.swap((n0, j), (k, j));
-//                 }
-//             }
-
-//             let pivot = self[(k, k)];
-
-//             for j in k .. $dimension {
-//                 let selfval = self[(k, j)] / pivot;
-//                 self[(k, j)] = selfval;
-//             }
-
-//             for j in 0 .. $dimension {
-//                 let resval = res[(k, j)] / pivot;
-//                 res[(k, j)] = resval;
-//             }
-
-//             for l in 0 .. $dimension {
-//                 if l != k {
-//                     let normalizer = self[(l, k)];
-
-//                     for j in k .. $dimension {
-//                         let selfval = self[(l, j)] - self[(k, j)] * normalizer;
-//                         self[(l, j)] = selfval;
-//                     }
-
-//                     for j in 0 .. $dimension {
-//                         let resval  = res[(l, j)] - res[(k, j)] * normalizer;
-//                         res[(l, j)] = resval;
-//                     }
-//                 }
-//             }
-//         }
-
-//         *self = res;
-
-//         true
-//     }
-
-//     #[inline]
-//     fn transpose_mut(&mut self) {
-//         for i in 1 .. $dimension {
-//             for j in 0 .. i {
-//                 self.swap((i, j), (j, i))
-//             }
-//         }
-//     }
-
-
-
 
 /*
  *
  * Ordering
  *
  */
-impl<N, R: Dim, C: Dim, S> MeetSemilattice for Matrix<N, R, C, S>
+impl<N, R: Dim, C: Dim> MeetSemilattice for MatrixMN<N, R, C>
     where N: Scalar + MeetSemilattice,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+          DefaultAllocator: Allocator<N, R, C> {
     #[inline]
     fn meet(&self, other: &Self) -> Self {
         self.zip_map(other, |a, b| a.meet(&b))
     }
 }
 
-impl<N, R: Dim, C: Dim, S> JoinSemilattice for Matrix<N, R, C, S>
+impl<N, R: Dim, C: Dim> JoinSemilattice for MatrixMN<N, R, C>
     where N: Scalar + JoinSemilattice,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+          DefaultAllocator: Allocator<N, R, C> {
     #[inline]
     fn join(&self, other: &Self) -> Self {
         self.zip_map(other, |a, b| a.join(&b))
@@ -763,10 +349,9 @@ impl<N, R: Dim, C: Dim, S> JoinSemilattice for Matrix<N, R, C, S>
 }
 
 
-impl<N, R: Dim, C: Dim, S> Lattice for Matrix<N, R, C, S>
+impl<N, R: Dim, C: Dim> Lattice for MatrixMN<N, R, C>
     where N: Scalar + Lattice,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S> {
+          DefaultAllocator: Allocator<N, R, C> {
     #[inline]
     fn meet_join(&self, other: &Self) -> (Self, Self) {
         let shape = self.data.shape();

src/core/matrix_array.rs

@@ -18,7 +18,7 @@ use generic_array::{ArrayLength, GenericArray};
 
 use core::Scalar;
 use core::dimension::{DimName, U1};
-use core::storage::{Storage, StorageMut, Owned, OwnedStorage};
+use core::storage::{Storage, StorageMut, Owned, ContiguousStorage, ContiguousStorageMut};
 use core::allocator::Allocator;
 use core::default_allocator::DefaultAllocator;
 
@@ -136,22 +136,10 @@ unsafe impl<N, R, C> Storage<N, R, C> for MatrixArray<N, R, C>
           R: DimName,
           C: DimName,
           R::Value: Mul<C::Value>,
-          Prod<R::Value, C::Value>: ArrayLength<N> {
+          Prod<R::Value, C::Value>: ArrayLength<N>,
+          DefaultAllocator: Allocator<N, R, C, Buffer = Self> {
     type RStride = U1;
     type CStride = R;
-    type Alloc   = DefaultAllocator;
-
-    #[inline]
-    fn into_owned(self) -> Owned<N, R, C, Self::Alloc> {
-        self
-    }
-
-    #[inline]
-    fn clone_owned(&self) -> Owned<N, R, C, Self::Alloc> {
-        let it = self.iter().cloned();
-
-        Self::Alloc::allocate_from_iterator(self.shape().0, self.shape().1, it)
-    }
 
     #[inline]
     fn ptr(&self) -> *const N {
@@ -167,30 +155,44 @@ unsafe impl<N, R, C> Storage<N, R, C> for MatrixArray<N, R, C>
     fn strides(&self) -> (Self::RStride, Self::CStride) {
         (Self::RStride::name(), Self::CStride::name())
     }
+
+    #[inline]
+    fn is_contiguous(&self) -> bool {
+        true
     }
 
+    #[inline]
+    fn into_owned(self) -> Owned<N, R, C>
+        where DefaultAllocator: Allocator<N, R, C> {
+        self
+    }
+
+    #[inline]
+    fn clone_owned(&self) -> Owned<N, R, C>
+        where DefaultAllocator: Allocator<N, R, C> {
+        let it = self.iter().cloned();
+
+        DefaultAllocator::allocate_from_iterator(self.shape().0, self.shape().1, it)
+    }
+
+    #[inline]
+    fn as_slice(&self) -> &[N] {
+        &self[..]
+    }
+}
+
+
 unsafe impl<N, R, C> StorageMut<N, R, C> for MatrixArray<N, R, C>
     where N: Scalar,
           R: DimName,
           C: DimName,
           R::Value: Mul<C::Value>,
-          Prod<R::Value, C::Value>: ArrayLength<N> {
+          Prod<R::Value, C::Value>: ArrayLength<N>,
+          DefaultAllocator: Allocator<N, R, C, Buffer = Self> {
     #[inline]
     fn ptr_mut(&mut self) -> *mut N {
         self[..].as_mut_ptr()
     }
-}
-
-unsafe impl<N, R, C> OwnedStorage<N, R, C> for MatrixArray<N, R, C>
-    where N: Scalar,
-          R: DimName,
-          C: DimName,
-          R::Value: Mul<C::Value>,
-          Prod<R::Value, C::Value>: ArrayLength<N> {
-    #[inline]
-    fn as_slice(&self) -> &[N] {
-        &self[..]
-    }
 
     #[inline]
     fn as_mut_slice(&mut self) -> &mut [N] {
@@ -198,6 +200,24 @@ unsafe impl<N, R, C> OwnedStorage<N, R, C> for MatrixArray<N, R, C>
     }
 }
 
+unsafe impl<N, R, C> ContiguousStorage<N, R, C> for MatrixArray<N, R, C>
+    where N: Scalar,
+          R: DimName,
+          C: DimName,
+          R::Value: Mul<C::Value>,
+          Prod<R::Value, C::Value>: ArrayLength<N>,
+          DefaultAllocator: Allocator<N, R, C, Buffer = Self> {
+}
+
+unsafe impl<N, R, C> ContiguousStorageMut<N, R, C> for MatrixArray<N, R, C>
+    where N: Scalar,
+          R: DimName,
+          C: DimName,
+          R::Value: Mul<C::Value>,
+          Prod<R::Value, C::Value>: ArrayLength<N>,
+          DefaultAllocator: Allocator<N, R, C, Buffer = Self> {
+}
+
 
 /*
  *

src/core/matrix_slice.rs

@@ -1,28 +1,31 @@
 use std::marker::PhantomData;
+use std::ops::{Range, RangeFrom, RangeTo, RangeFull};
+use std::slice;
 
 use core::{Scalar, Matrix};
 use core::dimension::{Dim, DimName, Dynamic, DimMul, DimProd, U1};
 use core::iter::MatrixIter;
 use core::storage::{Storage, StorageMut, Owned};
 use core::allocator::Allocator;
+use core::default_allocator::DefaultAllocator;
 
 macro_rules! slice_storage_impl(
     ($doc: expr; $Storage: ident as $SRef: ty; $T: ident.$get_addr: ident ($Ptr: ty as $Ref: ty)) => {
         #[doc = $doc]
-        pub struct $T<'a, N: Scalar, R: Dim, C: Dim, RStride: Dim, CStride: Dim, Alloc> {
+        #[derive(Debug)]
+        pub struct $T<'a, N: Scalar, R: Dim, C: Dim, RStride: Dim, CStride: Dim> {
             ptr:       $Ptr,
             shape:     (R, C),
             strides:   (RStride, CStride),
-            _phantoms: PhantomData<($Ref, Alloc)>,
+            _phantoms: PhantomData<$Ref>,
         }
 
-        // Dynamic and () are arbitrary. It's just to be able to call the constructors with
-        // `Slice::`
-        impl<'a, N: Scalar, R: Dim, C: Dim> $T<'a, N, R, C, Dynamic, Dynamic, ()> {
+        // Dynamic is arbitrary. It's just to be able to call the constructors with `Slice::`
+        impl<'a, N: Scalar, R: Dim, C: Dim> $T<'a, N, R, C, Dynamic, Dynamic> {
             /// Create a new matrix slice without bound checking.
             #[inline]
             pub unsafe fn new_unchecked<RStor, CStor, S>(storage: $SRef, start: (usize, usize), shape: (R, C))
-                -> $T<'a, N, R, C, S::RStride, S::CStride, S::Alloc>
+                -> $T<'a, N, R, C, S::RStride, S::CStride>
                 where RStor: Dim,
                       CStor: Dim,
                       S:     $Storage<N, RStor, CStor> {
@@ -37,17 +40,29 @@ macro_rules! slice_storage_impl(
                                                                                         start:   (usize, usize),
                                                                                         shape:   (R, C),
                                                                                         strides: (RStride, CStride))
-                -> $T<'a, N, R, C, RStride, CStride, S::Alloc>
+                -> $T<'a, N, R, C, RStride, CStride>
                 where RStor: Dim,
                       CStor: Dim,
                       S: $Storage<N, RStor, CStor>,
                       RStride: Dim,
                       CStride: Dim {
 
+                $T::from_raw_parts(storage.$get_addr(start.0, start.1), shape, strides)
+            }
+
+            /// Create a new matrix slice without bound checking and from a raw pointer.
+            #[inline]
+            pub unsafe fn from_raw_parts<RStride, CStride>(ptr:     $Ptr,
+                                                           shape:   (R, C),
+                                                           strides: (RStride, CStride))
+                -> $T<'a, N, R, C, RStride, CStride>
+                where RStride: Dim,
+                      CStride: Dim {
+
                 $T {
-                    ptr:       storage.$get_addr(start.0, start.1),
+                    ptr:       ptr,
                     shape:     shape,
-                    strides:   (strides.0, strides.1),
+                    strides:   strides,
                     _phantoms: PhantomData
                 }
             }
@@ -65,11 +80,11 @@ slice_storage_impl!("A mutable matrix data storage for mutable matrix slice. Onl
 );
 
 
-impl<'a, N: Scalar, R: Dim, C: Dim, RStride: Dim, CStride: Dim, Alloc> Copy
-for SliceStorage<'a, N, R, C, RStride, CStride, Alloc> { }
+impl<'a, N: Scalar, R: Dim, C: Dim, RStride: Dim, CStride: Dim> Copy
+for SliceStorage<'a, N, R, C, RStride, CStride> { }
 
-impl<'a, N: Scalar, R: Dim, C: Dim, RStride: Dim, CStride: Dim, Alloc> Clone
-for SliceStorage<'a, N, R, C, RStride, CStride, Alloc> {
+impl<'a, N: Scalar, R: Dim, C: Dim, RStride: Dim, CStride: Dim> Clone
+for SliceStorage<'a, N, R, C, RStride, CStride> {
     #[inline]
     fn clone(&self) -> Self {
         SliceStorage {
@@ -83,26 +98,11 @@ for SliceStorage<'a, N, R, C, RStride, CStride, Alloc> {
 
 macro_rules! storage_impl(
     ($($T: ident),* $(,)*) => {$(
-        unsafe impl<'a, N, R: Dim, C: Dim, RStride: Dim, CStride: Dim, Alloc> Storage<N, R, C>
-            for $T<'a, N, R, C, RStride, CStride, Alloc>
-            where N:     Scalar,
-                  Alloc: Allocator<N, R, C> {
+        unsafe impl<'a, N: Scalar, R: Dim, C: Dim, RStride: Dim, CStride: Dim> Storage<N, R, C>
+            for $T<'a, N, R, C, RStride, CStride> {
 
             type RStride = RStride;
             type CStride = CStride;
-            type Alloc   = Alloc;
-
-            #[inline]
-            fn into_owned(self) -> Owned<N, R, C, Self::Alloc> {
-                self.clone_owned()
-            }
-
-            #[inline]
-            fn clone_owned(&self) -> Owned<N, R, C, Self::Alloc> {
-                let (nrows, ncols) = self.shape();
-                let it = MatrixIter::new(self).cloned();
-                Alloc::allocate_from_iterator(nrows, ncols, it)
-            }
 
             #[inline]
             fn ptr(&self) -> *const N {
@@ -118,20 +118,74 @@ macro_rules! storage_impl(
             fn strides(&self) -> (Self::RStride, Self::CStride) {
                 self.strides
             }
+
+            #[inline]
+            fn is_contiguous(&self) -> bool {
+                // Common cases that can be deduced at compile-time even if one of the dimensions
+                // is Dynamic.
+                if (RStride::is::<U1>() && C::is::<U1>()) || // Column vector.
+                   (CStride::is::<U1>() && R::is::<U1>()) {  // Row vector.
+                    true
+                }
+                else {
+                    let (nrows, _)     = self.shape();
+                    let (srows, scols) = self.strides();
+
+                    srows.value() == 1 && scols.value() == nrows.value()
+                }
+            }
+
+
+
+            #[inline]
+            fn into_owned(self) -> Owned<N, R, C>
+                where DefaultAllocator: Allocator<N, R, C> {
+                self.clone_owned()
+            }
+
+            #[inline]
+            fn clone_owned(&self) -> Owned<N, R, C>
+                where DefaultAllocator: Allocator<N, R, C> {
+                let (nrows, ncols) = self.shape();
+                let it = MatrixIter::new(self).cloned();
+                DefaultAllocator::allocate_from_iterator(nrows, ncols, it)
+            }
+
+            #[inline]
+            fn as_slice(&self) -> &[N] {
+                let (nrows, ncols) = self.shape();
+                if nrows.value() != 0 && ncols.value() != 0 {
+                    let sz = self.linear_index(nrows.value() - 1, ncols.value() - 1);
+                    unsafe { slice::from_raw_parts(self.ptr, sz + 1) }
+                }
+                else {
+                    unsafe { slice::from_raw_parts(self.ptr, 0) }
+                }
+            }
         }
     )*}
 );
 
 storage_impl!(SliceStorage, SliceStorageMut);
 
-unsafe impl<'a, N, R: Dim, C: Dim, RStride: Dim, CStride: Dim, Alloc> StorageMut<N, R, C>
-    for SliceStorageMut<'a, N, R, C, RStride, CStride, Alloc>
-    where N: Scalar,
-          Alloc: Allocator<N, R, C> {
+unsafe impl<'a, N: Scalar, R: Dim, C: Dim, RStride: Dim, CStride: Dim> StorageMut<N, R, C>
+    for SliceStorageMut<'a, N, R, C, RStride, CStride> {
     #[inline]
     fn ptr_mut(&mut self) -> *mut N {
         self.ptr
     }
+
+    #[inline]
+    fn as_mut_slice(&mut self) -> &mut [N] {
+        let (nrows, ncols) = self.shape();
+        if nrows.value() != 0 && ncols.value() != 0 {
+            let sz = self.linear_index(nrows.value() - 1, ncols.value() - 1);
+            unsafe { slice::from_raw_parts_mut(self.ptr, sz + 1) }
+        }
+        else {
+            unsafe { slice::from_raw_parts_mut(self.ptr, 0) }
+        }
+    }
 }
 
 
@@ -139,35 +193,44 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     #[inline]
     fn assert_slice_index(&self, start: (usize, usize), shape: (usize, usize), steps: (usize, usize)) {
         let my_shape = self.shape();
-        assert!(start.0 + (shape.0 - 1) * steps.0 <= my_shape.0, "Matrix slicing out of bounds.");
-        assert!(start.1 + (shape.1 - 1) * steps.1 <= my_shape.1, "Matrix slicing out of bounds.");
+        // NOTE: we previously did: (shape.0 - 1) * steps.0
+        // which was wrong because underflow may occur for zero-sized matrices.
+        // Istead, we moved the subtraction into an addition on the right hand side.
+        assert!(start.0 + shape.0 * steps.0 <= my_shape.0 + steps.0, "Matrix slicing out of bounds.");
+        assert!(start.1 + shape.1 * steps.1 <= my_shape.1 + steps.1, "Matrix slicing out of bounds.");
     }
 }
 
 
 macro_rules! matrix_slice_impl(
-    ($me: ident: $Me: ty, $MatrixSlice: ident, $SliceStorage: ident, $Storage: ident, $data: expr;
+    ($me: ident: $Me: ty, $MatrixSlice: ident, $SliceStorage: ident, $Storage: ident.$get_addr: ident (), $data: expr;
      $row: ident,
+     $row_part: ident,
      $rows: ident,
      $rows_with_step: ident,
      $fixed_rows: ident,
      $fixed_rows_with_step: ident,
      $rows_generic: ident,
+     $rows_generic_with_step: ident,
      $column: ident,
+     $column_part: ident,
      $columns: ident,
      $columns_with_step: ident,
      $fixed_columns: ident,
      $fixed_columns_with_step: ident,
      $columns_generic: ident,
+     $columns_generic_with_step: ident,
      $slice: ident,
      $slice_with_steps: ident,
      $fixed_slice: ident,
      $fixed_slice_with_steps: ident,
      $generic_slice: ident,
-     $generic_slice_with_steps: ident) => {
+     $generic_slice_with_steps: ident,
+     $rows_range_pair: ident,
+     $columns_range_pair: ident) => {
         /// A matrix slice.
-        pub type $MatrixSlice<'a, N, R, C, RStride, CStride, Alloc>
-        = Matrix<N, R, C, $SliceStorage<'a, N, R, C, RStride, CStride, Alloc>>;
+        pub type $MatrixSlice<'a, N, R, C, RStride, CStride>
+        = Matrix<N, R, C, $SliceStorage<'a, N, R, C, RStride, CStride>>;
 
         impl<N: Scalar, R: Dim, C: Dim, S: $Storage<N, R, C>> Matrix<N, R, C, S> {
             /*
@@ -175,65 +238,75 @@ macro_rules! matrix_slice_impl(
              * Row slicing.
              *
              */
-            /// Returns a slice containing the i-th column of this matrix.
+            /// Returns a slice containing the i-th row of this matrix.
             #[inline]
-            pub fn $row($me: $Me, i: usize) -> $MatrixSlice<N, U1, C, S::RStride, S::CStride, S::Alloc> {
+            pub fn $row($me: $Me, i: usize) -> $MatrixSlice<N, U1, C, S::RStride, S::CStride> {
                 $me.$fixed_rows::<U1>(i)
             }
 
+            /// Returns a slice containing the `n` first elements of the i-th row of this matrix.
+            #[inline]
+            pub fn $row_part($me: $Me, i: usize, n: usize) -> $MatrixSlice<N, U1, Dynamic, S::RStride, S::CStride> {
+                $me.$generic_slice((i, 0), (U1, Dynamic::new(n)))
+            }
+
             /// Extracts from this matrix a set of consecutive rows.
             #[inline]
             pub fn $rows($me: $Me, first_row: usize, nrows: usize)
-                -> $MatrixSlice<N, Dynamic, C, S::RStride, S::CStride, S::Alloc> {
+                -> $MatrixSlice<N, Dynamic, C, S::RStride, S::CStride> {
 
-                let my_shape = $me.data.shape();
-                $me.assert_slice_index((first_row, 0), (nrows, my_shape.1.value()), (1, 1));
-                let shape = (Dynamic::new(nrows), my_shape.1);
-
-                unsafe {
-                    let data = $SliceStorage::new_unchecked($data, (first_row, 0), shape);
-                    Matrix::from_data_statically_unchecked(data)
-                }
+                $me.$rows_generic(first_row, Dynamic::new(nrows))
             }
 
             /// Extracts from this matrix a set of consecutive rows regularly spaced by `step` rows.
             #[inline]
             pub fn $rows_with_step($me: $Me, first_row: usize, nrows: usize, step: usize)
-                -> $MatrixSlice<N, Dynamic, C, Dynamic, S::CStride, S::Alloc> {
+                -> $MatrixSlice<N, Dynamic, C, Dynamic, S::CStride> {
 
-                $me.$rows_generic(first_row, Dynamic::new(nrows), Dynamic::new(step))
+                $me.$rows_generic_with_step(first_row, Dynamic::new(nrows), Dynamic::new(step))
             }
 
             /// Extracts a compile-time number of consecutive rows from this matrix.
             #[inline]
             pub fn $fixed_rows<RSlice>($me: $Me, first_row: usize)
-                -> $MatrixSlice<N, RSlice, C, S::RStride, S::CStride, S::Alloc>
+                -> $MatrixSlice<N, RSlice, C, S::RStride, S::CStride>
                 where RSlice: DimName {
 
-                let my_shape = $me.data.shape();
-                $me.assert_slice_index((first_row, 0), (RSlice::dim(), my_shape.1.value()), (1, 1));
-                let shape = (RSlice::name(), my_shape.1);
-
-                unsafe {
-                    let data = $SliceStorage::new_unchecked($data, (first_row, 0), shape);
-                    Matrix::from_data_statically_unchecked(data)
-                }
+                $me.$rows_generic(first_row, RSlice::name())
             }
 
             /// Extracts from this matrix a compile-time number of rows regularly spaced by `step` rows.
             #[inline]
             pub fn $fixed_rows_with_step<RSlice>($me: $Me, first_row: usize, step: usize)
-                -> $MatrixSlice<N, RSlice, C, Dynamic, S::CStride, S::Alloc>
+                -> $MatrixSlice<N, RSlice, C, Dynamic, S::CStride>
                 where RSlice: DimName {
 
-                $me.$rows_generic(first_row, RSlice::name(), Dynamic::new(step))
+                $me.$rows_generic_with_step(first_row, RSlice::name(), Dynamic::new(step))
             }
 
             /// Extracts from this matrix `nrows` rows regularly spaced by `step` rows. Both argument may
             /// or may not be values known at compile-time.
             #[inline]
-            pub fn $rows_generic<RSlice, RStep>($me: $Me, row_start: usize, nrows: RSlice, step: RStep)
-                -> $MatrixSlice<N, RSlice, C, DimProd<RStep, S::RStride>, S::CStride, S::Alloc>
+            pub fn $rows_generic<RSlice>($me: $Me, row_start: usize, nrows: RSlice)
+                -> $MatrixSlice<N, RSlice, C, S::RStride, S::CStride>
+                where RSlice: Dim {
+
+                let my_shape   = $me.data.shape();
+                $me.assert_slice_index((row_start, 0), (nrows.value(), my_shape.1.value()), (1, 1));
+
+                let shape = (nrows, my_shape.1);
+
+                unsafe {
+                    let data = $SliceStorage::new_unchecked($data, (row_start, 0), shape);
+                    Matrix::from_data_statically_unchecked(data)
+                }
+            }
+
+            /// Extracts from this matrix `nrows` rows regularly spaced by `step` rows. Both argument may
+            /// or may not be values known at compile-time.
+            #[inline]
+            pub fn $rows_generic_with_step<RSlice, RStep>($me: $Me, row_start: usize, nrows: RSlice, step: RStep)
+                -> $MatrixSlice<N, RSlice, C, DimProd<RStep, S::RStride>, S::CStride>
                 where RSlice: Dim,
                       RStep: DimMul<S::RStride> {
 
@@ -257,64 +330,74 @@ macro_rules! matrix_slice_impl(
              */
             /// Returns a slice containing the i-th column of this matrix.
             #[inline]
-            pub fn $column($me: $Me, i: usize) -> $MatrixSlice<N, R, U1, S::RStride, S::CStride, S::Alloc> {
+            pub fn $column($me: $Me, i: usize) -> $MatrixSlice<N, R, U1, S::RStride, S::CStride> {
                 $me.$fixed_columns::<U1>(i)
             }
 
+            /// Returns a slice containing the `n` first elements of the i-th column of this matrix.
+            #[inline]
+            pub fn $column_part($me: $Me, i: usize, n: usize) -> $MatrixSlice<N, Dynamic, U1, S::RStride, S::CStride> {
+                $me.$generic_slice((0, i), (Dynamic::new(n), U1))
+            }
+
             /// Extracts from this matrix a set of consecutive columns.
             #[inline]
             pub fn $columns($me: $Me, first_col: usize, ncols: usize)
-                -> $MatrixSlice<N, R, Dynamic, S::RStride, S::CStride, S::Alloc> {
+                -> $MatrixSlice<N, R, Dynamic, S::RStride, S::CStride> {
 
-                let my_shape = $me.data.shape();
-                $me.assert_slice_index((0, first_col), (my_shape.0.value(), ncols), (1, 1));
-                let shape = (my_shape.0, Dynamic::new(ncols));
-
-                unsafe {
-                    let data = $SliceStorage::new_unchecked($data, (0, first_col), shape);
-                    Matrix::from_data_statically_unchecked(data)
-                }
+                $me.$columns_generic(first_col, Dynamic::new(ncols))
             }
 
             /// Extracts from this matrix a set of consecutive columns regularly spaced by `step` columns.
             #[inline]
             pub fn $columns_with_step($me: $Me, first_col: usize, ncols: usize, step: usize)
-                -> $MatrixSlice<N, R, Dynamic, S::RStride, Dynamic, S::Alloc> {
+                -> $MatrixSlice<N, R, Dynamic, S::RStride, Dynamic> {
 
-                $me.$columns_generic(first_col, Dynamic::new(ncols), Dynamic::new(step))
+                $me.$columns_generic_with_step(first_col, Dynamic::new(ncols), Dynamic::new(step))
             }
 
             /// Extracts a compile-time number of consecutive columns from this matrix.
             #[inline]
             pub fn $fixed_columns<CSlice>($me: $Me, first_col: usize)
-                -> $MatrixSlice<N, R, CSlice, S::RStride, S::CStride, S::Alloc>
+                -> $MatrixSlice<N, R, CSlice, S::RStride, S::CStride>
                 where CSlice: DimName {
 
-                let my_shape = $me.data.shape();
-                $me.assert_slice_index((0, first_col), (my_shape.0.value(), CSlice::dim()), (1, 1));
-                let shape = (my_shape.0, CSlice::name());
-
-                unsafe {
-                    let data = $SliceStorage::new_unchecked($data, (0, first_col), shape);
-                    Matrix::from_data_statically_unchecked(data)
-                }
+                $me.$columns_generic(first_col, CSlice::name())
             }
 
             /// Extracts from this matrix a compile-time number of columns regularly spaced by `step`
             /// columns.
             #[inline]
             pub fn $fixed_columns_with_step<CSlice>($me: $Me, first_col: usize, step: usize)
-                -> $MatrixSlice<N, R, CSlice, S::RStride, Dynamic, S::Alloc>
+                -> $MatrixSlice<N, R, CSlice, S::RStride, Dynamic>
                 where CSlice: DimName {
 
-                $me.$columns_generic(first_col, CSlice::name(), Dynamic::new(step))
+                $me.$columns_generic_with_step(first_col, CSlice::name(), Dynamic::new(step))
             }
 
+            /// Extracts from this matrix `ncols` columns. The number of columns may or may not be
+            /// known at compile-time.
+            #[inline]
+            pub fn $columns_generic<CSlice>($me: $Me, first_col: usize, ncols: CSlice)
+                -> $MatrixSlice<N, R, CSlice, S::RStride, S::CStride>
+                where CSlice: Dim {
+
+                let my_shape = $me.data.shape();
+                $me.assert_slice_index((0, first_col), (my_shape.0.value(), ncols.value()), (1, 1));
+                let shape = (my_shape.0, ncols);
+
+                unsafe {
+                    let data = $SliceStorage::new_unchecked($data, (0, first_col), shape);
+                    Matrix::from_data_statically_unchecked(data)
+                }
+            }
+
+
             /// Extracts from this matrix `ncols` columns regularly spaced by `step` columns. Both argument may
             /// or may not be values known at compile-time.
             #[inline]
-            pub fn $columns_generic<CSlice, CStep>($me: $Me, first_col: usize, ncols: CSlice, step: CStep)
-                -> $MatrixSlice<N, R, CSlice, S::RStride, DimProd<CStep, S::CStride>, S::Alloc>
+            pub fn $columns_generic_with_step<CSlice, CStep>($me: $Me, first_col: usize, ncols: CSlice, step: CStep)
+                -> $MatrixSlice<N, R, CSlice, S::RStride, DimProd<CStep, S::CStride>>
                 where CSlice: Dim,
                       CStep:  DimMul<S::CStride> {
 
@@ -341,7 +424,7 @@ macro_rules! matrix_slice_impl(
             /// consecutive elements.
             #[inline]
             pub fn $slice($me: $Me, start: (usize, usize), shape: (usize, usize))
-                -> $MatrixSlice<N, Dynamic, Dynamic, S::RStride, S::CStride, S::Alloc> {
+                -> $MatrixSlice<N, Dynamic, Dynamic, S::RStride, S::CStride> {
 
                 $me.assert_slice_index(start, shape, (1, 1));
                 let shape = (Dynamic::new(shape.0), Dynamic::new(shape.1));
@@ -359,7 +442,7 @@ macro_rules! matrix_slice_impl(
             /// original matrix.
             #[inline]
             pub fn $slice_with_steps($me: $Me, start: (usize, usize), shape: (usize, usize), steps: (usize, usize))
-                -> $MatrixSlice<N, Dynamic, Dynamic, Dynamic, Dynamic, S::Alloc> {
+                -> $MatrixSlice<N, Dynamic, Dynamic, Dynamic, Dynamic> {
                 let shape = (Dynamic::new(shape.0), Dynamic::new(shape.1));
                 let steps = (Dynamic::new(steps.0), Dynamic::new(steps.1));
 
@@ -370,7 +453,7 @@ macro_rules! matrix_slice_impl(
             /// CSlice::dim())` consecutive components.
             #[inline]
             pub fn $fixed_slice<RSlice, CSlice>($me: $Me, irow: usize, icol: usize)
-                -> $MatrixSlice<N, RSlice, CSlice, S::RStride, S::CStride, S::Alloc>
+                -> $MatrixSlice<N, RSlice, CSlice, S::RStride, S::CStride>
                 where RSlice: DimName,
                       CSlice: DimName {
 
@@ -389,7 +472,7 @@ macro_rules! matrix_slice_impl(
             /// the original matrix.
             #[inline]
             pub fn $fixed_slice_with_steps<RSlice, CSlice>($me: $Me, start: (usize, usize), steps: (usize, usize))
-                -> $MatrixSlice<N, RSlice, CSlice, Dynamic, Dynamic, S::Alloc>
+                -> $MatrixSlice<N, RSlice, CSlice, Dynamic, Dynamic>
                 where RSlice: DimName,
                       CSlice: DimName {
                 let shape = (RSlice::name(), CSlice::name());
@@ -400,7 +483,7 @@ macro_rules! matrix_slice_impl(
             /// Creates a slice that may or may not have a fixed size and stride.
             #[inline]
             pub fn $generic_slice<RSlice, CSlice>($me: $Me, start: (usize, usize), shape: (RSlice, CSlice))
-                -> $MatrixSlice<N, RSlice, CSlice, S::RStride, S::CStride, S::Alloc>
+                -> $MatrixSlice<N, RSlice, CSlice, S::RStride, S::CStride>
                 where RSlice: Dim,
                       CSlice: Dim {
 
@@ -418,12 +501,13 @@ macro_rules! matrix_slice_impl(
                                                                            start: (usize, usize),
                                                                            shape: (RSlice, CSlice),
                                                                            steps: (RStep, CStep))
-                -> $MatrixSlice<N, RSlice, CSlice, DimProd<RStep, S::RStride>, DimProd<CStep, S::CStride>, S::Alloc>
+                -> $MatrixSlice<N, RSlice, CSlice, DimProd<RStep, S::RStride>, DimProd<CStep, S::CStride>>
                 where RSlice: Dim,
                       CSlice: Dim,
                       RStep: DimMul<S::RStride>,
                       CStep: DimMul<S::CStride> {
 
+                assert!(steps.0.value() > 0 && steps.1.value() > 0, "Matrix slicing steps must not be zero.");
                 $me.assert_slice_index(start, (shape.0.value(), shape.1.value()), (steps.0.value(), steps.1.value()));
 
                 let my_strides = $me.data.strides();
@@ -434,49 +518,297 @@ macro_rules! matrix_slice_impl(
                     Matrix::from_data_statically_unchecked(data)
                 }
             }
+
+            /*
+             *
+             * Splitting.
+             *
+             */
+            /// Splits this NxM matrix into two parts delimited by two ranges.
+            ///
+            /// Panics if the ranges overlap or if the first range is empty.
+            #[inline]
+            pub fn $rows_range_pair<Range1: SliceRange<R>, Range2: SliceRange<R>>($me: $Me, r1: Range1, r2: Range2)
+                -> ($MatrixSlice<N, Range1::Size, C, S::RStride, S::CStride>,
+                    $MatrixSlice<N, Range2::Size, C, S::RStride, S::CStride>) {
+
+                let (nrows, ncols) = $me.data.shape();
+                let strides        = $me.data.strides();
+
+                let start1 = r1.begin(nrows);
+                let start2 = r2.begin(nrows);
+
+                let end1 = r1.end(nrows);
+                let end2 = r2.end(nrows);
+
+                let nrows1 = r1.size(nrows);
+                let nrows2 = r2.size(nrows);
+
+                assert!(start2 >= end1 || start1 >= end2, "Rows range pair: the slice ranges must not overlap.");
+                assert!(end2 <= nrows.value(), "Rows range pair: index out of range.");
+
+                unsafe {
+                    let ptr1 = $data.$get_addr(start1, 0);
+                    let ptr2 = $data.$get_addr(start2, 0);
+
+                    let data1  = $SliceStorage::from_raw_parts(ptr1, (nrows1, ncols), strides);
+                    let data2  = $SliceStorage::from_raw_parts(ptr2, (nrows2, ncols), strides);
+                    let slice1 = Matrix::from_data_statically_unchecked(data1);
+                    let slice2 = Matrix::from_data_statically_unchecked(data2);
+
+                    (slice1, slice2)
+                }
+            }
+
+            /// Splits this NxM matrix into two parts delimited by two ranges.
+            ///
+            /// Panics if the ranges overlap or if the first range is empty.
+            #[inline]
+            pub fn $columns_range_pair<Range1: SliceRange<C>, Range2: SliceRange<C>>($me: $Me, r1: Range1, r2: Range2)
+                -> ($MatrixSlice<N, R, Range1::Size, S::RStride, S::CStride>,
+                    $MatrixSlice<N, R, Range2::Size, S::RStride, S::CStride>) {
+
+                let (nrows, ncols) = $me.data.shape();
+                let strides        = $me.data.strides();
+
+                let start1 = r1.begin(ncols);
+                let start2 = r2.begin(ncols);
+
+                let end1 = r1.end(ncols);
+                let end2 = r2.end(ncols);
+
+                let ncols1 = r1.size(ncols);
+                let ncols2 = r2.size(ncols);
+
+                assert!(start2 >= end1 || start1 >= end2, "Columns range pair: the slice ranges must not overlap.");
+                assert!(end2 <= ncols.value(), "Columns range pair: index out of range.");
+
+                unsafe {
+                    let ptr1 = $data.$get_addr(0, start1);
+                    let ptr2 = $data.$get_addr(0, start2);
+
+                    let data1  = $SliceStorage::from_raw_parts(ptr1, (nrows, ncols1), strides);
+                    let data2  = $SliceStorage::from_raw_parts(ptr2, (nrows, ncols2), strides);
+                    let slice1 = Matrix::from_data_statically_unchecked(data1);
+                    let slice2 = Matrix::from_data_statically_unchecked(data2);
+
+                    (slice1, slice2)
+                }
+            }
         }
     }
 );
 
 matrix_slice_impl!(
-     self: &Self, MatrixSlice, SliceStorage, Storage, &self.data;
+     self: &Self, MatrixSlice, SliceStorage, Storage.get_address_unchecked(), &self.data;
      row,
+     row_part,
      rows,
      rows_with_step,
      fixed_rows,
      fixed_rows_with_step,
      rows_generic,
+     rows_generic_with_step,
      column,
+     column_part,
      columns,
      columns_with_step,
      fixed_columns,
      fixed_columns_with_step,
      columns_generic,
+     columns_generic_with_step,
      slice,
      slice_with_steps,
      fixed_slice,
      fixed_slice_with_steps,
      generic_slice,
-     generic_slice_with_steps);
+     generic_slice_with_steps,
+     rows_range_pair,
+     columns_range_pair);
 
 
 matrix_slice_impl!(
-     self: &mut Self, MatrixSliceMut, SliceStorageMut, StorageMut, &mut self.data;
+     self: &mut Self, MatrixSliceMut, SliceStorageMut, StorageMut.get_address_unchecked_mut(), &mut self.data;
      row_mut,
+     row_part_mut,
      rows_mut,
      rows_with_step_mut,
      fixed_rows_mut,
      fixed_rows_with_step_mut,
      rows_generic_mut,
+     rows_generic_with_step_mut,
      column_mut,
+     column_part_mut,
      columns_mut,
      columns_with_step_mut,
      fixed_columns_mut,
      fixed_columns_with_step_mut,
      columns_generic_mut,
+     columns_generic_with_step_mut,
      slice_mut,
      slice_with_steps_mut,
      fixed_slice_mut,
      fixed_slice_with_steps_mut,
      generic_slice_mut,
-     generic_slice_with_steps_mut);
+     generic_slice_with_steps_mut,
+     rows_range_pair_mut,
+     columns_range_pair_mut);
+
+
+pub trait SliceRange<D: Dim> {
+    type Size: Dim;
+
+    fn begin(&self, shape: D) -> usize;
+    // NOTE: this is the index immediatly after the last index.
+    fn end(&self, shape: D) -> usize;
+    fn size(&self, shape: D) -> Self::Size;
+}
+
+impl<D: Dim> SliceRange<D> for usize {
+    type Size = U1;
+
+    #[inline(always)]
+    fn begin(&self, _: D) -> usize {
+        *self
+    }
+
+    #[inline(always)]
+    fn end(&self, _: D) -> usize {
+        *self + 1
+    }
+
+    #[inline(always)]
+    fn size(&self, _: D) -> Self::Size {
+        U1
+    }
+}
+
+impl<D: Dim> SliceRange<D> for Range<usize> {
+    type Size = Dynamic;
+
+    #[inline(always)]
+    fn begin(&self, _: D) -> usize {
+        self.start
+    }
+
+    #[inline(always)]
+    fn end(&self, _: D) -> usize {
+        self.end
+    }
+
+    #[inline(always)]
+    fn size(&self, _: D) -> Self::Size {
+        Dynamic::new(self.end - self.start)
+    }
+}
+
+impl<D: Dim> SliceRange<D> for RangeFrom<usize> {
+    type Size = Dynamic;
+
+    #[inline(always)]
+    fn begin(&self, _: D) -> usize {
+        self.start
+    }
+
+    #[inline(always)]
+    fn end(&self, dim: D) -> usize {
+        dim.value()
+    }
+
+    #[inline(always)]
+    fn size(&self, dim: D) -> Self::Size {
+        Dynamic::new(dim.value() - self.start)
+    }
+}
+
+impl<D: Dim> SliceRange<D> for RangeTo<usize> {
+    type Size = Dynamic;
+
+    #[inline(always)]
+    fn begin(&self, _: D) -> usize {
+        0
+    }
+
+    #[inline(always)]
+    fn end(&self, _: D) -> usize {
+        self.end
+    }
+
+    #[inline(always)]
+    fn size(&self, _: D) -> Self::Size {
+        Dynamic::new(self.end)
+    }
+}
+
+impl<D: Dim> SliceRange<D> for RangeFull {
+    type Size = D;
+
+    #[inline(always)]
+    fn begin(&self, _: D) -> usize {
+        0
+    }
+
+    #[inline(always)]
+    fn end(&self, dim: D) -> usize {
+        dim.value()
+    }
+
+    #[inline(always)]
+    fn size(&self, dim: D) -> Self::Size {
+        dim
+    }
+}
+
+
+impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
+    #[inline]
+    pub fn slice_range<RowRange, ColRange>(&self, rows: RowRange, cols: ColRange)
+        -> MatrixSlice<N, RowRange::Size, ColRange::Size, S::RStride, S::CStride>
+        where RowRange: SliceRange<R>,
+              ColRange: SliceRange<C> {
+
+        let (nrows, ncols) = self.data.shape();
+        self.generic_slice((rows.begin(nrows), cols.begin(ncols)),
+                           (rows.size(nrows), cols.size(ncols)))
+    }
+
+    #[inline]
+    pub fn rows_range<RowRange: SliceRange<R>>(&self, rows: RowRange)
+        -> MatrixSlice<N, RowRange::Size, C, S::RStride, S::CStride> {
+
+        self.slice_range(rows, ..)
+    }
+
+    #[inline]
+    pub fn columns_range<ColRange: SliceRange<C>>(&self, cols: ColRange)
+        -> MatrixSlice<N, R, ColRange::Size, S::RStride, S::CStride> {
+
+        self.slice_range(.., cols)
+    }
+}
+
+impl<N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
+    pub fn slice_range_mut<RowRange, ColRange>(&mut self, rows: RowRange, cols: ColRange)
+        -> MatrixSliceMut<N, RowRange::Size, ColRange::Size, S::RStride, S::CStride>
+        where RowRange: SliceRange<R>,
+              ColRange: SliceRange<C> {
+
+        let (nrows, ncols) = self.data.shape();
+        self.generic_slice_mut((rows.begin(nrows), cols.begin(ncols)),
+                               (rows.size(nrows), cols.size(ncols)))
+    }
+
+    #[inline]
+    pub fn rows_range_mut<RowRange: SliceRange<R>>(&mut self, rows: RowRange)
+        -> MatrixSliceMut<N, RowRange::Size, C, S::RStride, S::CStride> {
+
+        self.slice_range_mut(rows, ..)
+    }
+
+    #[inline]
+    pub fn columns_range_mut<ColRange: SliceRange<C>>(&mut self, cols: ColRange)
+        -> MatrixSliceMut<N, R, ColRange::Size, S::RStride, S::CStride> {
+
+        self.slice_range_mut(.., cols)
+    }
+}

src/core/matrix_vec.rs

@@ -2,7 +2,8 @@ use std::ops::Deref;
 
 use core::Scalar;
 use core::dimension::{Dim, DimName, Dynamic, U1};
-use core::storage::{Storage, StorageMut, Owned, OwnedStorage};
+use core::storage::{Storage, StorageMut, Owned, ContiguousStorage, ContiguousStorageMut};
+use core::allocator::Allocator;
 use core::default_allocator::DefaultAllocator;
 
 /*
@@ -45,6 +46,26 @@ impl<N, R: Dim, C: Dim> MatrixVec<N, R, C> {
     pub unsafe fn data_mut(&mut self) -> &mut Vec<N> {
         &mut self.data
     }
+
+    /// Resizes the undelying mutable data storage and unrwaps it.
+    ///
+    /// If `sz` is larger than the current size, additional elements are uninitialized.
+    /// If `sz` is smaller than the current size, additional elements are trucated.
+    #[inline]
+    pub unsafe fn resize(mut self, sz: usize) -> Vec<N>{
+        let len = self.len();
+
+        if sz < len {
+            self.data.set_len(sz);
+            self.data.shrink_to_fit();
+        }
+        else {
+            self.data.reserve_exact(sz - len);
+            self.data.set_len(sz);
+        }
+
+        self.data
+    }
 }
 
 impl<N, R: Dim, C: Dim> Deref for MatrixVec<N, R, C> {
@@ -62,24 +83,14 @@ impl<N, R: Dim, C: Dim> Deref for MatrixVec<N, R, C> {
  * Dynamic − Dynamic
  *
  */
-unsafe impl<N: Scalar, C: Dim> Storage<N, Dynamic, C> for MatrixVec<N, Dynamic, C> {
+unsafe impl<N: Scalar, C: Dim> Storage<N, Dynamic, C> for MatrixVec<N, Dynamic, C>
+    where DefaultAllocator: Allocator<N, Dynamic, C, Buffer = Self> {
     type RStride = U1;
     type CStride = Dynamic;
-    type Alloc   = DefaultAllocator;
-
-    #[inline]
-    fn into_owned(self) -> Owned<N, Dynamic, C, Self::Alloc> {
-        self
-    }
-
-    #[inline]
-    fn clone_owned(&self) -> Owned<N, Dynamic, C, Self::Alloc> {
-        self.clone()
-    }
 
     #[inline]
     fn ptr(&self) -> *const N {
-        self[..].as_ptr()
+        self.data.as_ptr()
     }
 
     #[inline]
@@ -91,27 +102,39 @@ unsafe impl<N: Scalar, C: Dim> Storage<N, Dynamic, C> for MatrixVec<N, Dynamic,
     fn strides(&self) -> (Self::RStride, Self::CStride) {
         (Self::RStride::name(), self.nrows)
     }
-}
-
-
-unsafe impl<N: Scalar, R: DimName> Storage<N, R, Dynamic> for MatrixVec<N, R, Dynamic> {
-    type RStride = U1;
-    type CStride = R;
-    type Alloc   = DefaultAllocator;
 
     #[inline]
-    fn into_owned(self) -> Owned<N, R, Dynamic, Self::Alloc> {
+    fn is_contiguous(&self) -> bool {
+        true
+    }
+
+    #[inline]
+    fn into_owned(self) -> Owned<N, Dynamic, C>
+        where DefaultAllocator: Allocator<N, Dynamic, C> {
         self
     }
 
     #[inline]
-    fn clone_owned(&self) -> Owned<N, R, Dynamic, Self::Alloc> {
+    fn clone_owned(&self) -> Owned<N, Dynamic, C>
+        where DefaultAllocator: Allocator<N, Dynamic, C> {
         self.clone()
     }
 
+    #[inline]
+    fn as_slice(&self) -> &[N] {
+        &self[..]
+    }
+}
+
+
+unsafe impl<N: Scalar, R: DimName> Storage<N, R, Dynamic> for MatrixVec<N, R, Dynamic>
+    where DefaultAllocator: Allocator<N, R, Dynamic, Buffer = Self> {
+    type RStride = U1;
+    type CStride = R;
+
     #[inline]
     fn ptr(&self) -> *const N {
-        self[..].as_ptr()
+        self.data.as_ptr()
     }
 
     #[inline]
@@ -123,6 +146,28 @@ unsafe impl<N: Scalar, R: DimName> Storage<N, R, Dynamic> for MatrixVec<N, R, Dy
     fn strides(&self) -> (Self::RStride, Self::CStride) {
         (Self::RStride::name(), self.nrows)
     }
+
+    #[inline]
+    fn is_contiguous(&self) -> bool {
+        true
+    }
+
+    #[inline]
+    fn into_owned(self) -> Owned<N, R, Dynamic>
+        where DefaultAllocator: Allocator<N, R, Dynamic> {
+        self
+    }
+
+    #[inline]
+    fn clone_owned(&self) -> Owned<N, R, Dynamic>
+        where DefaultAllocator: Allocator<N, R, Dynamic> {
+        self.clone()
+    }
+
+    #[inline]
+    fn as_slice(&self) -> &[N] {
+        &self[..]
+    }
 }
 
 
@@ -130,20 +175,14 @@ unsafe impl<N: Scalar, R: DimName> Storage<N, R, Dynamic> for MatrixVec<N, R, Dy
 
 /*
  *
- * StorageMut, OwnedStorage.
+ * StorageMut, ContiguousStorage.
  *
  */
-unsafe impl<N: Scalar, C: Dim> StorageMut<N, Dynamic, C> for MatrixVec<N, Dynamic, C> {
+unsafe impl<N: Scalar, C: Dim> StorageMut<N, Dynamic, C> for MatrixVec<N, Dynamic, C>
+    where DefaultAllocator: Allocator<N, Dynamic, C, Buffer = Self> {
     #[inline]
     fn ptr_mut(&mut self) -> *mut N {
-        self.as_mut_slice().as_mut_ptr()
-    }
-}
-
-unsafe impl<N: Scalar, C: Dim> OwnedStorage<N, Dynamic, C> for MatrixVec<N, Dynamic, C> {
-    #[inline]
-    fn as_slice(&self) -> &[N] {
-        &self[..]
+        self.data.as_mut_ptr()
     }
 
     #[inline]
@@ -152,18 +191,20 @@ unsafe impl<N: Scalar, C: Dim> OwnedStorage<N, Dynamic, C> for MatrixVec<N, Dyna
     }
 }
 
+unsafe impl<N: Scalar, C: Dim> ContiguousStorage<N, Dynamic, C> for MatrixVec<N, Dynamic, C>
+    where DefaultAllocator: Allocator<N, Dynamic, C, Buffer = Self> {
+}
 
-unsafe impl<N: Scalar, R: DimName> StorageMut<N, R, Dynamic> for MatrixVec<N, R, Dynamic> {
+unsafe impl<N: Scalar, C: Dim> ContiguousStorageMut<N, Dynamic, C> for MatrixVec<N, Dynamic, C>
+    where DefaultAllocator: Allocator<N, Dynamic, C, Buffer = Self> {
+}
+
+
+unsafe impl<N: Scalar, R: DimName> StorageMut<N, R, Dynamic> for MatrixVec<N, R, Dynamic>
+    where DefaultAllocator: Allocator<N, R, Dynamic, Buffer = Self> {
     #[inline]
     fn ptr_mut(&mut self) -> *mut N {
-        self.as_mut_slice().as_mut_ptr()
-    }
-}
-
-unsafe impl<N: Scalar, R: DimName> OwnedStorage<N, R, Dynamic> for MatrixVec<N, R, Dynamic> {
-    #[inline]
-    fn as_slice(&self) -> &[N] {
-        &self[..]
+        self.data.as_mut_ptr()
     }
 
     #[inline]
@@ -171,3 +212,11 @@ unsafe impl<N: Scalar, R: DimName> OwnedStorage<N, R, Dynamic> for MatrixVec<N,
         &mut self.data[..]
     }
 }
+
+unsafe impl<N: Scalar, R: DimName> ContiguousStorage<N, R, Dynamic> for MatrixVec<N, R, Dynamic>
+    where DefaultAllocator: Allocator<N, R, Dynamic, Buffer = Self> {
+}
+
+unsafe impl<N: Scalar, R: DimName> ContiguousStorageMut<N, R, Dynamic> for MatrixVec<N, R, Dynamic>
+    where DefaultAllocator: Allocator<N, R, Dynamic, Buffer = Self> {
+}

src/core/mod.rs

@@ -6,6 +6,7 @@ pub mod allocator;
 pub mod storage;
 pub mod coordinates;
 mod ops;
+mod blas;
 pub mod iter;
 pub mod default_allocator;
 
@@ -15,8 +16,6 @@ mod construction;
 mod properties;
 mod alias;
 mod matrix_alga;
-mod determinant;
-mod inverse;
 mod conversion;
 mod matrix_slice;
 mod matrix_array;
@@ -24,8 +23,7 @@ mod matrix_vec;
 mod cg;
 mod unit;
 mod componentwise;
-
-mod decompositions;
+mod edition;
 
 #[doc(hidden)]
 pub mod helper;

src/core/ops.rs

@@ -1,15 +1,16 @@
 use std::iter;
 use std::ops::{Add, AddAssign, Sub, SubAssign, Mul, MulAssign, Div, DivAssign, Neg,
                Index, IndexMut};
-use num::{Zero, One};
+use std::cmp::PartialOrd;
+use num::{Zero, One, Signed};
 
 use alga::general::{ClosedMul, ClosedDiv, ClosedAdd, ClosedSub, ClosedNeg};
 
-use core::{Scalar, Matrix, OwnedMatrix, SquareMatrix, MatrixSum, MatrixMul, MatrixTrMul};
-use core::dimension::{Dim, DimMul, DimName, DimProd};
-use core::constraint::{ShapeConstraint, SameNumberOfRows, SameNumberOfColumns, AreMultipliable};
-use core::storage::{Storage, StorageMut, OwnedStorage};
-use core::allocator::{SameShapeAllocator, Allocator, OwnedAllocator};
+use core::{DefaultAllocator, Scalar, Matrix, MatrixN, MatrixMN, MatrixSum};
+use core::dimension::{Dim, DimName, DimProd, DimMul};
+use core::constraint::{ShapeConstraint, SameNumberOfRows, SameNumberOfColumns, AreMultipliable, DimEq};
+use core::storage::{Storage, StorageMut, ContiguousStorageMut};
+use core::allocator::{SameShapeAllocator, Allocator, SameShapeR, SameShapeC};
 
 /*
  *
@@ -70,8 +71,9 @@ impl<N, R: Dim, C: Dim, S> IndexMut<(usize, usize)> for Matrix<N, R, C, S>
  */
 impl<N, R: Dim, C: Dim, S> Neg for Matrix<N, R, C, S>
     where N: Scalar + ClosedNeg,
-          S: Storage<N, R, C> {
-    type Output = OwnedMatrix<N, R, C, S::Alloc>;
+          S: Storage<N, R, C>,
+          DefaultAllocator: Allocator<N, R, C> {
+    type Output = MatrixMN<N, R, C>;
 
     #[inline]
     fn neg(self) -> Self::Output {
@@ -83,8 +85,9 @@ impl<N, R: Dim, C: Dim, S> Neg for Matrix<N, R, C, S>
 
 impl<'a, N, R: Dim, C: Dim, S> Neg for &'a Matrix<N, R, C, S>
     where N: Scalar + ClosedNeg,
-          S: Storage<N, R, C> {
-    type Output = OwnedMatrix<N, R, C, S::Alloc>;
+          S: Storage<N, R, C>,
+          DefaultAllocator: Allocator<N, R, C> {
+    type Output = MatrixMN<N, R, C>;
 
     #[inline]
     fn neg(self) -> Self::Output {
@@ -109,33 +112,156 @@ impl<N, R: Dim, C: Dim, S> Matrix<N, R, C, S>
  * Addition & Substraction
  *
  */
+
 macro_rules! componentwise_binop_impl(
     ($Trait: ident, $method: ident, $bound: ident;
-     $TraitAssign: ident, $method_assign: ident) => {
+     $TraitAssign: ident, $method_assign: ident, $method_assign_statically_unchecked: ident,
+     $method_assign_statically_unchecked_rhs: ident;
+     $method_to: ident, $method_to_statically_unchecked: ident) => {
+
+        impl<N, R1: Dim, C1: Dim, SA: Storage<N, R1, C1>> Matrix<N, R1, C1, SA>
+            where N: Scalar + $bound {
+
+            /*
+             *
+             * Methods without dimension checking at compile-time.
+             * This is useful for code reuse because the sum representative system does not plays
+             * easily with static checks.
+             *
+             */
+            #[inline]
+            fn $method_to_statically_unchecked<R2: Dim, C2: Dim, SB,
+                                               R3: Dim, C3: Dim, SC>(&self,
+                                                                     rhs: &Matrix<N, R2, C2, SB>,
+                                                                     out: &mut Matrix<N, R3, C3, SC>)
+                where SB: Storage<N, R2, C2>,
+                      SC: StorageMut<N, R3, C3> {
+                assert!(self.shape() == rhs.shape(), "Matrix addition/subtraction dimensions mismatch.");
+                assert!(self.shape() == out.shape(), "Matrix addition/subtraction output dimensions mismatch.");
+
+                // This is the most common case and should be deduced at compile-time.
+                // FIXME: use specialization instead?
+                if self.data.is_contiguous() && rhs.data.is_contiguous() && out.data.is_contiguous() {
+                    let arr1 = self.data.as_slice();
+                    let arr2 = rhs.data.as_slice();
+                    let mut out = out.data.as_mut_slice();
+                    for i in 0 .. arr1.len() {
+                        unsafe {
+                            *out.get_unchecked_mut(i) = arr1.get_unchecked(i).$method(*arr2.get_unchecked(i));
+                        }
+                    }
+                }
+                else {
+                    for j in 0 .. self.ncols() {
+                        for i in 0 .. self.nrows() {
+                            unsafe {
+                                let val = self.get_unchecked(i, j).$method(*rhs.get_unchecked(i, j));
+                                *out.get_unchecked_mut(i, j) = val;
+                            }
+                        }
+                    }
+                }
+            }
+
+
+            #[inline]
+            fn $method_assign_statically_unchecked<R2, C2, SB>(&mut self, rhs: &Matrix<N, R2, C2, SB>)
+                where R2: Dim,
+                      C2: Dim,
+                      SA: StorageMut<N, R1, C1>,
+                      SB: Storage<N, R2, C2> {
+                assert!(self.shape() == rhs.shape(), "Matrix addition/subtraction dimensions mismatch.");
+
+                // This is the most common case and should be deduced at compile-time.
+                // FIXME: use specialization instead?
+                if self.data.is_contiguous() && rhs.data.is_contiguous() {
+                    let mut arr1 = self.data.as_mut_slice();
+                    let arr2 = rhs.data.as_slice();
+                    for i in 0 .. arr2.len() {
+                        unsafe {
+                            arr1.get_unchecked_mut(i).$method_assign(*arr2.get_unchecked(i));
+                        }
+                    }
+                }
+                else {
+                    for j in 0 .. rhs.ncols() {
+                        for i in 0 .. rhs.nrows() {
+                            unsafe {
+                                self.get_unchecked_mut(i, j).$method_assign(*rhs.get_unchecked(i, j))
+                            }
+                        }
+                    }
+                }
+            }
+
+
+            #[inline]
+            fn $method_assign_statically_unchecked_rhs<R2, C2, SB>(&self, rhs: &mut Matrix<N, R2, C2, SB>)
+                where R2: Dim,
+                      C2: Dim,
+                      SB: StorageMut<N, R2, C2> {
+                assert!(self.shape() == rhs.shape(), "Matrix addition/subtraction dimensions mismatch.");
+
+                // This is the most common case and should be deduced at compile-time.
+                // FIXME: use specialization instead?
+                if self.data.is_contiguous() && rhs.data.is_contiguous() {
+                    let arr1 = self.data.as_slice();
+                    let mut arr2 = rhs.data.as_mut_slice();
+                    for i in 0 .. arr1.len() {
+                        unsafe {
+                            let res = arr1.get_unchecked(i).$method(*arr2.get_unchecked(i));
+                            *arr2.get_unchecked_mut(i) = res;
+                        }
+                    }
+                }
+                else {
+                    for j in 0 .. self.ncols() {
+                        for i in 0 .. self.nrows() {
+                            unsafe {
+                                let mut r = rhs.get_unchecked_mut(i, j);
+                                *r = self.get_unchecked(i, j).$method(*r)
+                            }
+                        }
+                    }
+                }
+            }
+
+
+            /*
+             *
+             * Methods without dimension checking at compile-time.
+             * This is useful for code reuse because the sum representative system does not plays
+             * easily with static checks.
+             *
+             */
+            /// Equivalent to `self + rhs` but stores the result into `out` to avoid allocations.
+            #[inline]
+            pub fn $method_to<R2: Dim, C2: Dim, SB,
+                              R3: Dim, C3: Dim, SC>(&self,
+                                                    rhs: &Matrix<N, R2, C2, SB>,
+                                                    out: &mut Matrix<N, R3, C3, SC>)
+                where SB: Storage<N, R2, C2>,
+                      SC: StorageMut<N, R3, C3>,
+                      ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> +
+                                       SameNumberOfRows<R1, R3> + SameNumberOfColumns<C1, C3> {
+                self.$method_to_statically_unchecked(rhs, out)
+            }
+        }
+
         impl<'b, N, R1, C1, R2, C2, SA, SB> $Trait<&'b Matrix<N, R2, C2, SB>> for Matrix<N, R1, C1, SA>
             where R1: Dim, C1: Dim, R2: Dim, C2: Dim,
                   N: Scalar + $bound,
                   SA: Storage<N, R1, C1>,
                   SB: Storage<N, R2, C2>,
-                  SA::Alloc: SameShapeAllocator<N, R1, C1, R2, C2, SA>,
+                  DefaultAllocator: SameShapeAllocator<N, R1, C1, R2, C2>,
                   ShapeConstraint:  SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
-            type Output = MatrixSum<N, R1, C1, R2, C2, SA>;
+            type Output = MatrixSum<N, R1, C1, R2, C2>;
 
             #[inline]
-            fn $method(self, right: &'b Matrix<N, R2, C2, SB>) -> Self::Output {
-                assert!(self.shape() == right.shape(), "Matrix addition/subtraction dimensions mismatch.");
+            fn $method(self, rhs: &'b Matrix<N, R2, C2, SB>) -> Self::Output {
+                assert!(self.shape() == rhs.shape(), "Matrix addition/subtraction dimensions mismatch.");
                 let mut res = self.into_owned_sum::<R2, C2>();
-
-                // XXX: optimize our iterator!
-                //
-                // Using our own iterator prevents loop unrolling, wich breaks some optimization
-                // (like SIMD). On the other hand, using the slice iterator is 4x faster.
-
-                // for (left, right) in res.iter_mut().zip(right.iter()) {
-                for (left, right) in res.as_mut_slice().iter_mut().zip(right.iter()) {
-                    *left = left.$method(*right)
-                }
-
+                res.$method_assign_statically_unchecked(rhs);
                 res
             }
         }
@@ -145,26 +271,16 @@ macro_rules! componentwise_binop_impl(
                   N: Scalar + $bound,
                   SA: Storage<N, R1, C1>,
                   SB: Storage<N, R2, C2>,
-                  SB::Alloc: SameShapeAllocator<N, R2, C2, R1, C1, SB>,
+                  DefaultAllocator: SameShapeAllocator<N, R2, C2, R1, C1>,
                   ShapeConstraint:  SameNumberOfRows<R2, R1> + SameNumberOfColumns<C2, C1> {
-            type Output = MatrixSum<N, R2, C2, R1, C1, SB>;
+            type Output = MatrixSum<N, R2, C2, R1, C1>;
 
             #[inline]
-            fn $method(self, right: Matrix<N, R2, C2, SB>) -> Self::Output {
-                assert!(self.shape() == right.shape(), "Matrix addition/subtraction dimensions mismatch.");
-                let mut res = right.into_owned_sum::<R1, C1>();
-
-                // XXX: optimize our iterator!
-                //
-                // Using our own iterator prevents loop unrolling, wich breaks some optimization
-                // (like SIMD). On the other hand, using the slice iterator is 4x faster.
-
-                // for (left, right) in self.iter().zip(res.iter_mut()) {
-                for (left, right) in self.iter().zip(res.as_mut_slice().iter_mut()) {
-                    *right = left.$method(*right)
-                }
-
-                res
+            fn $method(self, rhs: Matrix<N, R2, C2, SB>) -> Self::Output {
+                let mut rhs = rhs.into_owned_sum::<R1, C1>();
+                assert!(self.shape() == rhs.shape(), "Matrix addition/subtraction dimensions mismatch.");
+                self.$method_assign_statically_unchecked_rhs(&mut rhs);
+                rhs
             }
         }
 
@@ -173,13 +289,13 @@ macro_rules! componentwise_binop_impl(
                   N: Scalar + $bound,
                   SA: Storage<N, R1, C1>,
                   SB: Storage<N, R2, C2>,
-                  SA::Alloc: SameShapeAllocator<N, R1, C1, R2, C2, SA>,
+                  DefaultAllocator: SameShapeAllocator<N, R1, C1, R2, C2>,
                   ShapeConstraint:  SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
-            type Output = MatrixSum<N, R1, C1, R2, C2, SA>;
+            type Output = MatrixSum<N, R1, C1, R2, C2>;
 
             #[inline]
-            fn $method(self, right: Matrix<N, R2, C2, SB>) -> Self::Output {
-                self.$method(&right)
+            fn $method(self, rhs: Matrix<N, R2, C2, SB>) -> Self::Output {
+                self.$method(&rhs)
             }
         }
 
@@ -188,13 +304,21 @@ macro_rules! componentwise_binop_impl(
                   N: Scalar + $bound,
                   SA: Storage<N, R1, C1>,
                   SB: Storage<N, R2, C2>,
-                  SA::Alloc: SameShapeAllocator<N, R1, C1, R2, C2, SA>,
+                  DefaultAllocator: SameShapeAllocator<N, R1, C1, R2, C2>,
                   ShapeConstraint:  SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
-            type Output = MatrixSum<N, R1, C1, R2, C2, SA>;
+            type Output = MatrixSum<N, R1, C1, R2, C2>;
 
             #[inline]
-            fn $method(self, right: &'b Matrix<N, R2, C2, SB>) -> Self::Output {
-                self.clone_owned().$method(right)
+            fn $method(self, rhs: &'b Matrix<N, R2, C2, SB>) -> Self::Output {
+                let mut res = unsafe {
+                    let (nrows, ncols) = self.shape();
+                    let nrows: SameShapeR<R1, R2> = Dim::from_usize(nrows);
+                    let ncols: SameShapeC<C1, C2> = Dim::from_usize(ncols);
+                    Matrix::new_uninitialized_generic(nrows, ncols)
+                };
+
+                self.$method_to_statically_unchecked(rhs, &mut res);
+                res
             }
         }
 
@@ -206,11 +330,8 @@ macro_rules! componentwise_binop_impl(
                   ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
 
             #[inline]
-            fn $method_assign(&mut self, right: &'b Matrix<N, R2, C2, SB>) {
-                assert!(self.shape() == right.shape(), "Matrix addition/subtraction dimensions mismatch.");
-                for (left, right) in self.iter_mut().zip(right.iter()) {
-                    left.$method_assign(*right)
-                }
+            fn $method_assign(&mut self, rhs: &'b Matrix<N, R2, C2, SB>) {
+                self.$method_assign_statically_unchecked(rhs)
             }
         }
 
@@ -222,32 +343,34 @@ macro_rules! componentwise_binop_impl(
                   ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
 
             #[inline]
-            fn $method_assign(&mut self, right: Matrix<N, R2, C2, SB>) {
-                self.$method_assign(&right)
+            fn $method_assign(&mut self, rhs: Matrix<N, R2, C2, SB>) {
+                self.$method_assign(&rhs)
             }
         }
     }
 );
 
-componentwise_binop_impl!(Add, add, ClosedAdd; AddAssign, add_assign);
-componentwise_binop_impl!(Sub, sub, ClosedSub; SubAssign, sub_assign);
+componentwise_binop_impl!(Add, add, ClosedAdd;
+                          AddAssign, add_assign, add_assign_statically_unchecked, add_assign_statically_unchecked_mut;
+                          add_to, add_to_statically_unchecked);
+componentwise_binop_impl!(Sub, sub, ClosedSub;
+                          SubAssign, sub_assign, sub_assign_statically_unchecked, sub_assign_statically_unchecked_mut;
+                          sub_to, sub_to_statically_unchecked);
 
-impl<N, R: DimName, C: DimName, S> iter::Sum for Matrix<N, R, C, S>
+impl<N, R: DimName, C: DimName> iter::Sum for MatrixMN<N, R, C>
     where N: Scalar + ClosedAdd + Zero,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S>
+          DefaultAllocator: Allocator<N, R, C>
 {
-    fn sum<I: Iterator<Item = Matrix<N, R, C, S>>>(iter: I) -> Matrix<N, R, C, S> {
+    fn sum<I: Iterator<Item = MatrixMN<N, R, C>>>(iter: I) -> MatrixMN<N, R, C> {
         iter.fold(Matrix::zero(), |acc, x| acc + x)
     }
 }
 
-impl<'a, N, R: DimName, C: DimName, S> iter::Sum<&'a Matrix<N, R, C, S>> for Matrix<N, R, C, S>
+impl<'a, N, R: DimName, C: DimName> iter::Sum<&'a MatrixMN<N, R, C>> for MatrixMN<N, R, C>
     where N: Scalar + ClosedAdd + Zero,
-          S: OwnedStorage<N, R, C>,
-          S::Alloc: OwnedAllocator<N, R, C, S>
+          DefaultAllocator: Allocator<N, R, C>
 {
-    fn sum<I: Iterator<Item = &'a Matrix<N, R, C, S>>>(iter: I) -> Matrix<N, R, C, S> {
+    fn sum<I: Iterator<Item = &'a MatrixMN<N, R, C>>>(iter: I) -> MatrixMN<N, R, C> {
         iter.fold(Matrix::zero(), |acc, x| acc + x)
     }
 }
@@ -266,8 +389,9 @@ macro_rules! componentwise_scalarop_impl(
      $TraitAssign: ident, $method_assign: ident) => {
         impl<N, R: Dim, C: Dim, S> $Trait<N> for Matrix<N, R, C, S>
             where N: Scalar + $bound,
-                  S: Storage<N, R, C> {
-            type Output = OwnedMatrix<N, R, C, S::Alloc>;
+                  S: Storage<N, R, C>,
+                  DefaultAllocator: Allocator<N, R, C> {
+            type Output = MatrixMN<N, R, C>;
 
             #[inline]
             fn $method(self, rhs: N) -> Self::Output {
@@ -289,8 +413,9 @@ macro_rules! componentwise_scalarop_impl(
 
         impl<'a, N, R: Dim, C: Dim, S> $Trait<N> for &'a Matrix<N, R, C, S>
             where N: Scalar + $bound,
-                  S: Storage<N, R, C> {
-            type Output = OwnedMatrix<N, R, C, S::Alloc>;
+                  S: Storage<N, R, C>,
+                  DefaultAllocator: Allocator<N, R, C> {
+            type Output = MatrixMN<N, R, C>;
 
             #[inline]
             fn $method(self, rhs: N) -> Self::Output {
@@ -302,9 +427,11 @@ macro_rules! componentwise_scalarop_impl(
             where N: Scalar + $bound,
                   S: StorageMut<N, R, C> {
             #[inline]
-            fn $method_assign(&mut self, right: N) {
-                for left in self.iter_mut() {
-                    left.$method_assign(right)
+            fn $method_assign(&mut self, rhs: N) {
+                for j in 0 .. self.ncols() {
+                    for i in 0 .. self.nrows() {
+                        unsafe { self.get_unchecked_mut(i, j).$method_assign(rhs) };
+                    }
                 }
             }
         }
@@ -316,35 +443,35 @@ componentwise_scalarop_impl!(Div, div, ClosedDiv; DivAssign, div_assign);
 
 macro_rules! left_scalar_mul_impl(
     ($($T: ty),* $(,)*) => {$(
-        impl<R: Dim, C: Dim, S> Mul<Matrix<$T, R, C, S>> for $T
-            where S: Storage<$T, R, C> {
-            type Output = OwnedMatrix<$T, R, C, S::Alloc>;
+        impl<R: Dim, C: Dim, S: Storage<$T, R, C>> Mul<Matrix<$T, R, C, S>> for $T
+            where DefaultAllocator: Allocator<$T, R, C> {
+            type Output = MatrixMN<$T, R, C>;
 
             #[inline]
-            fn mul(self, right: Matrix<$T, R, C, S>) -> Self::Output {
-                let mut res = right.into_owned();
+            fn mul(self, rhs: Matrix<$T, R, C, S>) -> Self::Output {
+                let mut res = rhs.into_owned();
 
                 // XXX: optimize our iterator!
                 //
                 // Using our own iterator prevents loop unrolling, wich breaks some optimization
                 // (like SIMD). On the other hand, using the slice iterator is 4x faster.
 
-                // for right in res.iter_mut() {
-                for right in res.as_mut_slice().iter_mut() {
-                    *right = self * *right
+                // for rhs in res.iter_mut() {
+                for rhs in res.as_mut_slice().iter_mut() {
+                    *rhs = self * *rhs
                 }
 
                 res
             }
         }
 
-        impl<'b, R: Dim, C: Dim, S> Mul<&'b Matrix<$T, R, C, S>> for $T
-            where S: Storage<$T, R, C> {
-            type Output = OwnedMatrix<$T, R, C, S::Alloc>;
+        impl<'b, R: Dim, C: Dim, S: Storage<$T, R, C>> Mul<&'b Matrix<$T, R, C, S>> for $T
+            where DefaultAllocator: Allocator<$T, R, C> {
+            type Output = MatrixMN<$T, R, C>;
 
             #[inline]
-            fn mul(self, right: &'b Matrix<$T, R, C, S>) -> Self::Output {
-                self * right.clone_owned()
+            fn mul(self, rhs: &'b Matrix<$T, R, C, S>) -> Self::Output {
+                self * rhs.clone_owned()
             }
         }
     )*}
@@ -361,84 +488,66 @@ left_scalar_mul_impl!(
 // Matrix × Matrix
 impl<'a, 'b, N, R1: Dim, C1: Dim, R2: Dim, C2: Dim, SA, SB> Mul<&'b Matrix<N, R2, C2, SB>>
 for &'a Matrix<N, R1, C1, SA>
-    where N:  Scalar + Zero + ClosedAdd + ClosedMul,
-          SB: Storage<N, R2, C2>,
+    where N:  Scalar + Zero + One + ClosedAdd + ClosedMul,
           SA: Storage<N, R1, C1>,
-          SA::Alloc: Allocator<N, R1, C2>,
+          SB: Storage<N, R2, C2>,
+          DefaultAllocator: Allocator<N, R1, C2>,
           ShapeConstraint:  AreMultipliable<R1, C1, R2, C2> {
-    type Output = MatrixMul<N, R1, C1, C2, SA>;
+    type Output = MatrixMN<N, R1, C2>;
 
     #[inline]
-    fn mul(self, right: &'b Matrix<N, R2, C2, SB>) -> Self::Output {
-        let (nrows1, ncols1) = self.shape();
-        let (nrows2, ncols2) = right.shape();
-
-        assert!(ncols1 == nrows2, "Matrix multiplication dimensions mismatch.");
-
-        let mut res: MatrixMul<N, R1, C1, C2, SA> = unsafe {
-            Matrix::new_uninitialized_generic(self.data.shape().0, right.data.shape().1)
+    fn mul(self, rhs: &'b Matrix<N, R2, C2, SB>) -> Self::Output {
+        let mut res = unsafe {
+            Matrix::new_uninitialized_generic(self.data.shape().0, rhs.data.shape().1)
         };
 
-        for i in 0 .. nrows1 {
-            for j in 0 .. ncols2 {
-                let mut acc = N::zero();
-
-                unsafe {
-                    for k in 0 .. ncols1 {
-                        acc = acc + *self.get_unchecked(i, k) * *right.get_unchecked(k, j);
-                    }
-
-                    *res.get_unchecked_mut(i, j) = acc;
-                }
-            }
-        }
-
+        self.mul_to(rhs, &mut res);
         res
     }
 }
 
 impl<'a, N, R1: Dim, C1: Dim, R2: Dim, C2: Dim, SA, SB> Mul<Matrix<N, R2, C2, SB>>
 for &'a Matrix<N, R1, C1, SA>
-    where N:  Scalar + Zero + ClosedAdd + ClosedMul,
+    where N:  Scalar + Zero + One + ClosedAdd + ClosedMul,
           SB: Storage<N, R2, C2>,
           SA: Storage<N, R1, C1>,
-          SA::Alloc: Allocator<N, R1, C2>,
+          DefaultAllocator: Allocator<N, R1, C2>,
           ShapeConstraint:  AreMultipliable<R1, C1, R2, C2> {
-    type Output = MatrixMul<N, R1, C1, C2, SA>;
+    type Output = MatrixMN<N, R1, C2>;
 
     #[inline]
-    fn mul(self, right: Matrix<N, R2, C2, SB>) -> Self::Output {
-        self * &right
+    fn mul(self, rhs: Matrix<N, R2, C2, SB>) -> Self::Output {
+        self * &rhs
     }
 }
 
 impl<'b, N, R1: Dim, C1: Dim, R2: Dim, C2: Dim, SA, SB> Mul<&'b Matrix<N, R2, C2, SB>>
 for Matrix<N, R1, C1, SA>
-    where N:  Scalar + Zero + ClosedAdd + ClosedMul,
+    where N:  Scalar + Zero + One + ClosedAdd + ClosedMul,
           SB: Storage<N, R2, C2>,
           SA: Storage<N, R1, C1>,
-          SA::Alloc: Allocator<N, R1, C2>,
+          DefaultAllocator: Allocator<N, R1, C2>,
           ShapeConstraint:  AreMultipliable<R1, C1, R2, C2> {
-    type Output = MatrixMul<N, R1, C1, C2, SA>;
+    type Output = MatrixMN<N, R1, C2>;
 
     #[inline]
-    fn mul(self, right: &'b Matrix<N, R2, C2, SB>) -> Self::Output {
-        &self * right
+    fn mul(self, rhs: &'b Matrix<N, R2, C2, SB>) -> Self::Output {
+        &self * rhs
     }
 }
 
 impl<N, R1: Dim, C1: Dim, R2: Dim, C2: Dim, SA, SB> Mul<Matrix<N, R2, C2, SB>>
 for Matrix<N, R1, C1, SA>
-    where N:  Scalar + Zero + ClosedAdd + ClosedMul,
+    where N:  Scalar + Zero + One + ClosedAdd + ClosedMul,
           SB: Storage<N, R2, C2>,
           SA: Storage<N, R1, C1>,
-          SA::Alloc: Allocator<N, R1, C2>,
+          DefaultAllocator: Allocator<N, R1, C2>,
           ShapeConstraint:  AreMultipliable<R1, C1, R2, C2> {
-    type Output = MatrixMul<N, R1, C1, C2, SA>;
+    type Output = MatrixMN<N, R1, C2>;
 
     #[inline]
-    fn mul(self, right: Matrix<N, R2, C2, SB>) -> Self::Output {
-        &self * &right
+    fn mul(self, rhs: Matrix<N, R2, C2, SB>) -> Self::Output {
+        &self * &rhs
     }
 }
 
@@ -447,84 +556,106 @@ for Matrix<N, R1, C1, SA>
 //    − we can't use `a *= b` when C2 is not equal to C1.
 impl<N, R1, C1, R2, SA, SB> MulAssign<Matrix<N, R2, C1, SB>> for Matrix<N, R1, C1, SA>
     where R1: Dim, C1: Dim, R2: Dim,
-          N:  Scalar + Zero + ClosedAdd + ClosedMul,
+          N:  Scalar + Zero + One + ClosedAdd + ClosedMul,
           SB: Storage<N, R2, C1>,
-          SA: OwnedStorage<N, R1, C1>,
+          SA: ContiguousStorageMut<N, R1, C1> + Clone,
           ShapeConstraint:  AreMultipliable<R1, C1, R2, C1>,
-          SA::Alloc: OwnedAllocator<N, R1, C1, SA> {
+          DefaultAllocator: Allocator<N, R1, C1, Buffer = SA> {
     #[inline]
-    fn mul_assign(&mut self, right: Matrix<N, R2, C1, SB>) {
-        *self = &*self * right
+    fn mul_assign(&mut self, rhs: Matrix<N, R2, C1, SB>) {
+        *self = &*self * rhs
     }
 }
 
 impl<'b, N, R1, C1, R2, SA, SB> MulAssign<&'b Matrix<N, R2, C1, SB>> for Matrix<N, R1, C1, SA>
     where R1: Dim, C1: Dim, R2: Dim,
-          N:  Scalar + Zero + ClosedAdd + ClosedMul,
+          N:  Scalar + Zero + One + ClosedAdd + ClosedMul,
           SB: Storage<N, R2, C1>,
-          SA: OwnedStorage<N, R1, C1>,
+          SA: ContiguousStorageMut<N, R1, C1> + Clone,
           ShapeConstraint: AreMultipliable<R1, C1, R2, C1>,
           // FIXME: this is too restrictive. See comments for the non-ref version.
-          SA::Alloc: OwnedAllocator<N, R1, C1, SA> {
+          DefaultAllocator: Allocator<N, R1, C1, Buffer = SA> {
     #[inline]
-    fn mul_assign(&mut self, right: &'b Matrix<N, R2, C1, SB>) {
-        *self = &*self * right
+    fn mul_assign(&mut self, rhs: &'b Matrix<N, R2, C1, SB>) {
+        *self = &*self * rhs
     }
 }
 
 
 // Transpose-multiplication.
 impl<N, R1: Dim, C1: Dim, SA> Matrix<N, R1, C1, SA>
-    where N:  Scalar,
+    where N:  Scalar + Zero + One + ClosedAdd + ClosedMul,
           SA: Storage<N, R1, C1> {
-    /// Equivalent to `self.transpose() * right`.
+    /// Equivalent to `self.transpose() * rhs`.
     #[inline]
-    pub fn tr_mul<R2: Dim, C2: Dim, SB>(&self, right: &Matrix<N, R2, C2, SB>) -> MatrixTrMul<N, R1, C1, C2, SA>
-        where N: Zero + ClosedAdd + ClosedMul,
-              SB: Storage<N, R2, C2>,
-              SA::Alloc: Allocator<N, C1, C2>,
-              ShapeConstraint: AreMultipliable<C1, R1, R2, C2> {
+    pub fn tr_mul<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<N, R2, C2, SB>) -> MatrixMN<N, C1, C2>
+        where SB: Storage<N, R2, C2>,
+              DefaultAllocator: Allocator<N, C1, C2>,
+              ShapeConstraint: SameNumberOfRows<R1, R2> {
+
+        let mut res = unsafe {
+            Matrix::new_uninitialized_generic(self.data.shape().1, rhs.data.shape().1)
+        };
+
+        self.tr_mul_to(rhs, &mut res);
+        res
+    }
+
+    /// Equivalent to `self.transpose() * rhs` but stores the result into `out` to avoid
+    /// allocations.
+    #[inline]
+    pub fn tr_mul_to<R2: Dim, C2: Dim, SB,
+                     R3: Dim, C3: Dim, SC>(&self,
+                                           rhs: &Matrix<N, R2, C2, SB>,
+                                           out: &mut Matrix<N, R3, C3, SC>)
+        where SB: Storage<N, R2, C2>,
+              SC: StorageMut<N, R3, C3>,
+              ShapeConstraint: SameNumberOfRows<R1, R2> +
+                               DimEq<C1, R3> +
+                               DimEq<C2, C3> {
         let (nrows1, ncols1) = self.shape();
-        let (nrows2, ncols2) = right.shape();
+        let (nrows2, ncols2) = rhs.shape();
+        let (nrows3, ncols3) = out.shape();
 
         assert!(nrows1 == nrows2, "Matrix multiplication dimensions mismatch.");
-
-        let mut res: MatrixTrMul<N, R1, C1, C2, SA> = unsafe {
-            Matrix::new_uninitialized_generic(self.data.shape().1, right.data.shape().1)
-        };
+        assert!(nrows3 == ncols1 && ncols3 == ncols2, "Matrix multiplication output dimensions mismatch.");
 
         for i in 0 .. ncols1 {
             for j in 0 .. ncols2 {
-                let mut acc = N::zero();
-
-                unsafe {
-                    for k in 0 .. nrows1 {
-                        acc += *self.get_unchecked(k, i) * *right.get_unchecked(k, j);
-                    }
-
-                    *res.get_unchecked_mut(i, j) = acc;
+                let dot = self.column(i).dot(&rhs.column(j));
+                unsafe { *out.get_unchecked_mut(i, j) = dot };
             }
         }
     }
 
-        res
+    /// Equivalent to `self * rhs` but stores the result into `out` to avoid allocations.
+    #[inline]
+    pub fn mul_to<R2: Dim, C2: Dim, SB,
+                  R3: Dim, C3: Dim, SC>(&self,
+                                        rhs: &Matrix<N, R2, C2, SB>,
+                                        out: &mut Matrix<N, R3, C3, SC>)
+        where SB: Storage<N, R2, C2>,
+              SC: StorageMut<N, R3, C3>,
+              ShapeConstraint: SameNumberOfRows<R3, R1>    +
+                               SameNumberOfColumns<C3, C2> +
+                               AreMultipliable<R1, C1, R2, C2> {
+        out.gemm(N::one(), self, rhs, N::zero());
     }
 
 
     /// The kronecker product of two matrices (aka. tensor product of the corresponding linear
     /// maps).
     pub fn kronecker<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<N, R2, C2, SB>)
-                                           -> OwnedMatrix<N, DimProd<R1, R2>, DimProd<C1, C2>, SA::Alloc>
+                                           -> MatrixMN<N, DimProd<R1, R2>, DimProd<C1, C2>>
         where N:  ClosedMul,
               R1: DimMul<R2>,
               C1: DimMul<C2>,
               SB: Storage<N, R2, C2>,
-              SA::Alloc: Allocator<N, DimProd<R1, R2>, DimProd<C1, C2>> {
+              DefaultAllocator: Allocator<N, DimProd<R1, R2>, DimProd<C1, C2>> {
         let (nrows1, ncols1) = self.data.shape();
         let (nrows2, ncols2) = rhs.data.shape();
 
-        let mut res: OwnedMatrix<_, _, _, SA::Alloc> =
-            unsafe { Matrix::new_uninitialized_generic(nrows1.mul(nrows2), ncols1.mul(ncols2)) };
+        let mut res = unsafe { Matrix::new_uninitialized_generic(nrows1.mul(nrows2), ncols1.mul(ncols2)) };
 
         {
             let mut data_res = res.data.ptr_mut();
@@ -549,22 +680,76 @@ impl<N, R1: Dim, C1: Dim, SA> Matrix<N, R1, C1, SA>
     }
 }
 
-impl<N, D: DimName, S> iter::Product for SquareMatrix<N, D, S>
+impl<N: Scalar + ClosedAdd, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
+    /// Adds a scalar to `self`.
+    #[inline]
+    pub fn add_scalar(&self, rhs: N) -> MatrixMN<N, R, C>
+        where DefaultAllocator: Allocator<N, R, C> {
+        let mut res = self.clone_owned();
+        res.add_scalar_mut(rhs);
+        res
+    }
+
+    /// Adds a scalar to `self` in-place.
+    #[inline]
+    pub fn add_scalar_mut(&mut self, rhs: N)
+        where S: StorageMut<N, R, C> {
+        for e in self.iter_mut() {
+            *e += rhs
+        }
+    }
+}
+
+
+impl<N, D: DimName> iter::Product for MatrixN<N, D>
     where N: Scalar + Zero + One + ClosedMul + ClosedAdd,
-          S: OwnedStorage<N, D, D>,
-          S::Alloc: OwnedAllocator<N, D, D, S>
+          DefaultAllocator: Allocator<N, D, D>
 {
-    fn product<I: Iterator<Item = SquareMatrix<N, D, S>>>(iter: I) -> SquareMatrix<N, D, S> {
+    fn product<I: Iterator<Item = MatrixN<N, D>>>(iter: I) -> MatrixN<N, D> {
         iter.fold(Matrix::one(), |acc, x| acc * x)
     }
 }
 
-impl<'a, N, D: DimName, S> iter::Product<&'a SquareMatrix<N, D, S>> for SquareMatrix<N, D, S>
+impl<'a, N, D: DimName> iter::Product<&'a MatrixN<N, D>> for MatrixN<N, D>
     where N: Scalar + Zero + One + ClosedMul + ClosedAdd,
-          S: OwnedStorage<N, D, D>,
-          S::Alloc: OwnedAllocator<N, D, D, S>
+          DefaultAllocator: Allocator<N, D, D>
 {
-    fn product<I: Iterator<Item = &'a SquareMatrix<N, D, S>>>(iter: I) -> SquareMatrix<N, D, S> {
+    fn product<I: Iterator<Item = &'a MatrixN<N, D>>>(iter: I) -> MatrixN<N, D> {
         iter.fold(Matrix::one(), |acc, x| acc * x)
     }
 }
+
+impl<N: Scalar + PartialOrd + Signed, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
+    /// Returns the absolute value of the coefficient with the largest absolute value.
+    #[inline]
+    pub fn amax(&self) -> N {
+        let mut max = N::zero();
+
+        for e in self.iter() {
+            let ae = e.abs();
+
+            if ae > max {
+                max = ae;
+            }
+        }
+
+        max
+    }
+
+    /// Returns the absolute value of the coefficient with the smallest absolute value.
+    #[inline]
+    pub fn amin(&self) -> N {
+        let mut it = self.iter();
+        let mut min = it.next().expect("amin: empty matrices not supported.").abs();
+
+        for e in it {
+            let ae = e.abs();
+
+            if ae < min {
+                min = ae;
+            }
+        }
+
+        min
+    }
+}

src/core/properties.rs

@@ -2,33 +2,38 @@
 use num::{Zero, One};
 use approx::ApproxEq;
 
-use alga::general::{ClosedAdd, ClosedMul, ClosedSub, Field};
+use alga::general::{ClosedAdd, ClosedMul, Real};
 
-use core::{Scalar, Matrix, SquareMatrix};
-use core::dimension::Dim;
+use core::{DefaultAllocator, Scalar, Matrix, SquareMatrix};
+use core::dimension::{Dim, DimMin};
 use core::storage::Storage;
+use core::allocator::Allocator;
 
 
 impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /// Indicates if this is a square matrix.
     #[inline]
-    pub fn is_square(&self) -> bool {
-        let shape = self.shape();
-        shape.0 == shape.1
-    }
+    pub fn is_empty(&self) -> bool {
+        let (nrows, ncols) = self.shape();
+        nrows == 0 || ncols == 0
+    }
+
+    /// Indicates if this is a square matrix.
+    #[inline]
+    pub fn is_square(&self) -> bool {
+        let (nrows, ncols) = self.shape();
+        nrows == ncols
     }
 
-impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S>
     // FIXME: ApproxEq prevents us from using those methods on integer matrices…
-    where N: ApproxEq,
-          N::Epsilon: Copy {
     /// Indicated if this is the identity matrix within a relative error of `eps`.
     ///
     /// If the matrix is diagonal, this checks that diagonal elements (i.e. at coordinates `(i, i)`
     /// for i from `0` to `min(R, C)`) are equal one; and that all other elements are zero.
     #[inline]
     pub fn is_identity(&self, eps: N::Epsilon) -> bool
-        where N: Zero + One {
+    where N: Zero + One + ApproxEq,
+          N::Epsilon: Copy {
         let (nrows, ncols) = self.shape();
         let d;
 
@@ -75,32 +80,35 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S>
 
         true
     }
-}
 
-
-impl<N: Scalar + ApproxEq, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S>
-    where N: Zero + One + ClosedAdd + ClosedMul,
-          N::Epsilon: Copy {
-    /// Checks that this matrix is orthogonal, i.e., that it is square and `M × Mᵀ = Id`.
+    /// Checks that `Mᵀ × M = Id`.
     ///
     /// In this definition `Id` is approximately equal to the identity matrix with a relative error
     /// equal to `eps`.
     #[inline]
-    pub fn is_orthogonal(&self, eps: N::Epsilon) -> bool {
-        self.is_square() && (self.tr_mul(self)).is_identity(eps)
+    pub fn is_orthogonal(&self, eps: N::Epsilon) -> bool
+        where N: Zero + One + ClosedAdd + ClosedMul + ApproxEq,
+              S: Storage<N, R, C>,
+              N::Epsilon: Copy,
+              DefaultAllocator: Allocator<N, C, C> {
+        (self.tr_mul(self)).is_identity(eps)
+    }
 }
 
+
+impl<N: Real, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S>
+    where DefaultAllocator: Allocator<N, D, D> {
     /// Checks that this matrix is orthogonal and has a determinant equal to 1.
     #[inline]
-    pub fn is_special_orthogonal(&self, eps: N::Epsilon) -> bool
-        where N: ClosedSub + PartialOrd {
-            self.is_orthogonal(eps) && self.determinant() > N::zero()
+    pub fn is_special_orthogonal(&self, eps: N) -> bool
+        where D: DimMin<D, Output = D>,
+              DefaultAllocator: Allocator<(usize, usize), D> {
+            self.is_square() && self.is_orthogonal(eps) && self.determinant() > N::zero()
     }
 
     /// Returns `true` if this matrix is invertible.
     #[inline]
-    pub fn is_invertible(&self) -> bool
-        where N: Field {
+    pub fn is_invertible(&self) -> bool {
         // FIXME: improve this?
         self.clone_owned().try_inverse().is_some()
     }

src/core/scalar.rs

@@ -1,3 +1,4 @@
+use std::any::TypeId;
 use std::fmt::Debug;
 use std::any::Any;
 
@@ -5,5 +6,9 @@ use std::any::Any;
 ///
 /// This does not make any assumption on the algebraic properties of `Self`.
 pub trait Scalar: Copy + PartialEq + Debug + Any {
+    #[inline]
+    fn is<T: Scalar>() -> bool {
+        TypeId::of::<Self>() == TypeId::of::<T>()
+    }
 }
 impl<T: Copy + PartialEq + Debug + Any> Scalar for T { }

src/core/storage.rs

@@ -1,39 +1,28 @@
 //! Abstract definition of a matrix data storage.
 
+use std::fmt::Debug;
 use std::mem;
-use std::any::Any;
 
 use core::Scalar;
-use dimension::Dim;
-use allocator::{Allocator, SameShapeR, SameShapeC};
+use core::default_allocator::DefaultAllocator;
+use core::dimension::{Dim, U1};
+use core::allocator::{Allocator, SameShapeR, SameShapeC};
 
 /*
- * Aliases for sum storage.
+ * Aliases for allocation results.
  */
 /// The data storage for the sum of two matrices with dimensions `(R1, C1)` and `(R2, C2)`.
-pub type SumStorage<N, R1, C1, R2, C2, SA> =
-    <<SA as Storage<N, R1, C1>>::Alloc as Allocator<N, SameShapeR<R1, R2>, SameShapeC<C1, C2>>>::Buffer;
+pub type SameShapeStorage<N, R1, C1, R2, C2> = <DefaultAllocator as Allocator<N, SameShapeR<R1, R2>, SameShapeC<C1, C2>>>::Buffer;
 
-/*
- * Aliases for multiplication storage.
- */
-/// The data storage for the multiplication of two matrices with dimensions `(R1, C1)` on the left
-/// hand side, and with `C2` columns on the right hand side.
-pub type MulStorage<N, R1, C1, C2, SA> =
-    <<SA as Storage<N, R1, C1>>::Alloc as Allocator<N, R1, C2>>::Buffer;
-
-/// The data storage for the multiplication of two matrices with dimensions `(R1, C1)` on the left
-/// hand side, and with `C2` columns on the right hand side. The first matrix is implicitly
-/// transposed.
-pub type TrMulStorage<N, R1, C1, C2, SA> =
-    <<SA as Storage<N, R1, C1>>::Alloc as Allocator<N, C1, C2>>::Buffer;
-
-/*
- * Alias for allocation result.
- */
+// FIXME: better name than Owned ?
 /// The owned data storage that can be allocated from `S`.
-pub type Owned<N, R, C, A> =
-    <A as Allocator<N, R, C>>::Buffer;
+pub type Owned<N, R, C = U1> = <DefaultAllocator as Allocator<N, R, C>>::Buffer;
+
+/// The row-stride of the owned data storage for a buffer of dimension `(R, C)`.
+pub type RStride<N, R, C = U1> = <<DefaultAllocator as Allocator<N, R, C>>::Buffer as Storage<N, R, C>>::RStride;
+
+/// The column-stride of the owned data storage for a buffer of dimension `(R, C)`.
+pub type CStride<N, R, C = U1> = <<DefaultAllocator as Allocator<N, R, C>>::Buffer as Storage<N, R, C>>::CStride;
 
 
 /// The trait shared by all matrix data storage.
@@ -45,22 +34,13 @@ pub type Owned<N, R, C, A> =
 /// should **not** allow the user to modify the size of the underlying buffer with safe methods
 /// (for example the `MatrixVec::data_mut` method is unsafe because the user could change the
 /// vector's size so that it no longer contains enough elements: this will lead to UB.
-pub unsafe trait Storage<N: Scalar, R: Dim, C: Dim>: Sized {
+pub unsafe trait Storage<N: Scalar, R: Dim, C: Dim = U1>: Debug + Sized {
     /// The static stride of this storage's rows.
     type RStride: Dim;
 
     /// The static stride of this storage's columns.
     type CStride: Dim;
 
-    /// The allocator for this family of storage.
-    type Alloc: Allocator<N, R, C>;
-
-    /// Builds a matrix data storage that does not contain any reference.
-    fn into_owned(self) -> Owned<N, R, C, Self::Alloc>;
-
-    /// Clones this data storage into one that does not contain any reference.
-    fn clone_owned(&self) -> Owned<N, R, C, Self::Alloc>;
-
     /// The matrix data pointer.
     fn ptr(&self) -> *const N;
 
@@ -110,6 +90,24 @@ pub unsafe trait Storage<N: Scalar, R: Dim, C: Dim>: Sized {
     unsafe fn get_unchecked(&self, irow: usize, icol: usize) -> &N {
         self.get_unchecked_linear(self.linear_index(irow, icol))
     }
+
+    /// Indicates whether this data buffer stores its elements contiguously.
+    #[inline]
+    fn is_contiguous(&self) -> bool;
+
+    /// Retrieves the data buffer as a contiguous slice.
+    ///
+    /// The matrix components may not be stored in a contiguous way, depending on the strides.
+    #[inline]
+    fn as_slice(&self) -> &[N];
+
+    /// Builds a matrix data storage that does not contain any reference.
+    fn into_owned(self) -> Owned<N, R, C>
+        where DefaultAllocator: Allocator<N, R, C>;
+
+    /// Clones this data storage into one that does not contain any reference.
+    fn clone_owned(&self) -> Owned<N, R, C>
+        where DefaultAllocator: Allocator<N, R, C>;
 }
 
 
@@ -118,7 +116,7 @@ pub unsafe trait Storage<N: Scalar, R: Dim, C: Dim>: Sized {
 /// Note that a mutable access does not mean that the matrix owns its data. For example, a mutable
 /// matrix slice can provide mutable access to its elements even if it does not own its data (it
 /// contains only an internal reference to them).
-pub unsafe trait StorageMut<N: Scalar, R: Dim, C: Dim>: Storage<N, R, C> {
+pub unsafe trait StorageMut<N: Scalar, R: Dim, C: Dim = U1>: Storage<N, R, C> {
     /// The matrix mutable data pointer.
     fn ptr_mut(&mut self) -> *mut N;
 
@@ -163,22 +161,24 @@ pub unsafe trait StorageMut<N: Scalar, R: Dim, C: Dim>: Storage<N, R, C> {
 
         self.swap_unchecked_linear(lid1, lid2)
     }
-}
 
-/// A matrix storage that does not contain any reference and that is stored contiguously in memory.
+    /// Retrieves the mutable data buffer as a contiguous slice.
     ///
-/// The storage requirement means that for any value of `i` in `[0, nrows * ncols[`, the value
-/// `.get_unchecked_linear` succeeds. This trait is unsafe because failing to comply to this may
-/// cause Undefined Behaviors.
-pub unsafe trait OwnedStorage<N: Scalar, R: Dim, C: Dim>: StorageMut<N, R, C> + Clone + Any
-    where Self::Alloc: Allocator<N, R, C, Buffer = Self> {
-    // NOTE: We could auto-impl those two methods but we don't to make sure the user is aware that
-    // data must be contiguous.
-    /// Converts this data storage to a slice.
-    #[inline]
-    fn as_slice(&self) -> &[N];
-
-    /// Converts this data storage to a mutable slice.
+    /// Matrix components may not be contiguous, depending on its strides.
     #[inline]
     fn as_mut_slice(&mut self) -> &mut [N];
 }
+
+/// A matrix storage that is stored contiguously in memory.
+///
+/// The storage requirement means that for any value of `i` in `[0, nrows * ncols[`, the value
+/// `.get_unchecked_linear` returns one of the matrix component. This trait is unsafe because
+/// failing to comply to this may cause Undefined Behaviors.
+pub unsafe trait ContiguousStorage<N: Scalar, R: Dim, C: Dim = U1>: Storage<N, R, C> { }
+
+/// A mutable matrix storage that is stored contiguously in memory.
+///
+/// The storage requirement means that for any value of `i` in `[0, nrows * ncols[`, the value
+/// `.get_unchecked_linear` returns one of the matrix component. This trait is unsafe because
+/// failing to comply to this may cause Undefined Behaviors.
+pub unsafe trait ContiguousStorageMut<N: Scalar, R: Dim, C: Dim = U1>: ContiguousStorage<N, R, C> + StorageMut<N, R, C> { }

src/debug/mod.rs

@@ -0,0 +1,8 @@
+//! Various tools useful for testing/debugging/benchmarking.
+
+
+mod random_orthogonal;
+mod random_sdp;
+
+pub use self::random_orthogonal::*;
+pub use self::random_sdp::*;

src/debug/random_orthogonal.rs

@@ -0,0 +1,51 @@
+#[cfg(feature = "arbitrary")]
+use quickcheck::{Arbitrary, Gen};
+#[cfg(feature = "arbitrary")]
+use core::storage::Owned;
+
+use num_complex::Complex;
+use alga::general::Real;
+use core::{DefaultAllocator, MatrixN};
+use core::dimension::{Dim, Dynamic, U2};
+use core::allocator::Allocator;
+use geometry::UnitComplex;
+
+/// A random orthogonal matrix.
+#[derive(Clone, Debug)]
+pub struct RandomOrthogonal<N: Real, D: Dim = Dynamic>
+    where DefaultAllocator: Allocator<N, D, D> {
+    m: MatrixN<N, D>
+}
+
+
+impl<N: Real, D: Dim> RandomOrthogonal<N, D>
+    where DefaultAllocator: Allocator<N, D, D> {
+    /// Retrieve the generated matrix.
+    pub fn unwrap(self) -> MatrixN<N, D> {
+        self.m
+    }
+
+    /// Creates a new random orthogonal matrix from its dimension and a random reals generators.
+    pub fn new<Rand: FnMut() -> N>(dim: D, mut rand: Rand) -> Self {
+        let mut res = MatrixN::identity_generic(dim, dim);
+
+        // Create an orthogonal matrix by compositing planar 2D rotations.
+        for i in 0 .. dim.value() - 1 {
+            let c = Complex::new(rand(), rand());
+            let rot: UnitComplex<N> = UnitComplex::from_complex(c);
+            rot.rotate(&mut res.fixed_rows_mut::<U2>(i));
+        }
+
+        RandomOrthogonal { m: res }
+    }
+}
+
+#[cfg(feature = "arbitrary")]
+impl<N: Real + Arbitrary + Send, D: Dim> Arbitrary for RandomOrthogonal<N, D>
+    where DefaultAllocator: Allocator<N, D, D>,
+          Owned<N, D, D>: Clone + Send {
+    fn arbitrary<G: Gen>(g: &mut G) -> Self {
+        let dim = D::try_to_usize().unwrap_or(g.gen_range(1, 50));
+        Self::new(D::from_usize(dim), || N::arbitrary(g))
+    }
+}

src/debug/random_sdp.rs

@@ -0,0 +1,54 @@
+#[cfg(feature = "arbitrary")]
+use quickcheck::{Arbitrary, Gen};
+#[cfg(feature = "arbitrary")]
+use core::storage::Owned;
+
+use alga::general::Real;
+use core::{DefaultAllocator, MatrixN};
+use core::dimension::{Dim, Dynamic};
+use core::allocator::Allocator;
+
+use debug::RandomOrthogonal;
+
+
+/// A random, well-conditioned, symmetric definite-positive matrix.
+#[derive(Clone, Debug)]
+pub struct RandomSDP<N: Real, D: Dim = Dynamic>
+    where DefaultAllocator: Allocator<N, D, D> {
+    m: MatrixN<N, D>
+}
+
+
+impl<N: Real, D: Dim> RandomSDP<N, D>
+    where DefaultAllocator: Allocator<N, D, D> {
+
+    /// Retrieve the generated matrix.
+    pub fn unwrap(self) -> MatrixN<N, D> {
+        self.m
+    }
+
+    /// Creates a new well conditioned symmetric definite-positive matrix from its dimension and a
+    /// random reals generators.
+    pub fn new<Rand: FnMut() -> N>(dim: D, mut rand: Rand) -> Self {
+        let mut m = RandomOrthogonal::new(dim, || rand()).unwrap();
+        let mt = m.transpose();
+
+        for i in 0 .. dim.value() {
+            let mut col = m.column_mut(i);
+            let eigenval = N::one() + rand().abs();
+            col *= eigenval;
+        }
+
+        RandomSDP { m: m * mt }
+    }
+}
+
+#[cfg(feature = "arbitrary")]
+impl<N: Real + Arbitrary + Send, D: Dim> Arbitrary for RandomSDP<N, D>
+    where DefaultAllocator: Allocator<N, D, D>,
+          Owned<N, D, D>: Clone + Send {
+    fn arbitrary<G: Gen>(g: &mut G) -> Self {
+        let dim = D::try_to_usize().unwrap_or(g.gen_range(1, 50));
+        Self::new(D::from_usize(dim), || N::arbitrary(g))
+    }
+}

src/geometry/isometry.rs

@@ -1,30 +1,40 @@
 use std::fmt;
+use std::hash;
 use std::marker::PhantomData;
 use approx::ApproxEq;
 
+#[cfg(feature = "serde-serialize")]
+use serde;
+
 use alga::general::{Real, SubsetOf};
 use alga::linear::Rotation;
 
-use core::{Scalar, OwnedSquareMatrix};
+use core::{DefaultAllocator, MatrixN};
 use core::dimension::{DimName, DimNameSum, DimNameAdd, U1};
-use core::storage::{Storage, OwnedStorage};
-use core::allocator::{Allocator, OwnedAllocator};
-use geometry::{TranslationBase, PointBase};
-
-
-/// An isometry that uses a data storage deduced from the allocator `A`.
-pub type OwnedIsometryBase<N, D, A, R> =
-    IsometryBase<N, D, <A as Allocator<N, D, U1>>::Buffer, R>;
+use core::storage::Owned;
+use core::allocator::Allocator;
+use geometry::{Translation, Point};
 
 /// A direct isometry, i.e., a rotation followed by a translation.
 #[repr(C)]
-#[derive(Hash, Debug, Clone, Copy)]
+#[derive(Debug)]
 #[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
-pub struct IsometryBase<N: Scalar, D: DimName, S, R> {
+#[cfg_attr(feature = "serde-serialize",
+    serde(bound(
+        serialize = "R: serde::Serialize,
+                     DefaultAllocator: Allocator<N, D>,
+                     Owned<N, D>: serde::Serialize")))]
+#[cfg_attr(feature = "serde-serialize",
+    serde(bound(
+        deserialize = "R: serde::Deserialize<'de>,
+                       DefaultAllocator: Allocator<N, D>,
+                       Owned<N, D>: serde::Deserialize<'de>")))]
+pub struct Isometry<N: Real, D: DimName, R>
+    where DefaultAllocator: Allocator<N, D> {
     /// The pure rotational part of this isometry.
     pub rotation:    R,
     /// The pure translational part of this isometry.
-    pub translation: TranslationBase<N, D, S>,
+    pub translation: Translation<N, D>,
 
 
     // One dummy private field just to prevent explicit construction.
@@ -32,15 +42,34 @@ pub struct IsometryBase<N: Scalar, D: DimName, S, R> {
     _noconstruct: PhantomData<N>
 }
 
-impl<N, D: DimName, S, R> IsometryBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real + hash::Hash, D: DimName + hash::Hash, R: hash::Hash> hash::Hash for Isometry<N, D, R>
+    where DefaultAllocator: Allocator<N, D>,
+          Owned<N, D>: hash::Hash {
+    fn hash<H: hash::Hasher>(&self, state: &mut H) {
+        self.translation.hash(state);
+        self.rotation.hash(state);
+    }
+}
+
+impl<N: Real, D: DimName + Copy, R: Rotation<Point<N, D>> + Copy> Copy for Isometry<N, D, R>
+    where DefaultAllocator: Allocator<N, D>,
+          Owned<N, D>: Copy {
+}
+
+impl<N: Real, D: DimName, R: Rotation<Point<N, D>> + Clone> Clone for Isometry<N, D, R>
+    where DefaultAllocator: Allocator<N, D> {
+    #[inline]
+    fn clone(&self) -> Self {
+        Isometry::from_parts(self.translation.clone(), self.rotation.clone())
+    }
+}
+
+impl<N: Real, D: DimName, R: Rotation<Point<N, D>>> Isometry<N, D, R>
+    where DefaultAllocator: Allocator<N, D> {
     /// Creates a new isometry from its rotational and translational parts.
     #[inline]
-    pub fn from_parts(translation: TranslationBase<N, D, S>, rotation: R) -> IsometryBase<N, D, S, R> {
-        IsometryBase {
+    pub fn from_parts(translation: Translation<N, D>, rotation: R) -> Isometry<N, D, R> {
+        Isometry {
             rotation:     rotation,
             translation:  translation,
             _noconstruct: PhantomData
@@ -49,7 +78,7 @@ impl<N, D: DimName, S, R> IsometryBase<N, D, S, R>
 
     /// Inverts `self`.
     #[inline]
-    pub fn inverse(&self) -> IsometryBase<N, D, S, R> {
+    pub fn inverse(&self) -> Isometry<N, D, R> {
         let mut res = self.clone();
         res.inverse_mut();
         res
@@ -65,7 +94,7 @@ impl<N, D: DimName, S, R> IsometryBase<N, D, S, R>
 
     /// Appends to `self` the given translation in-place.
     #[inline]
-    pub fn append_translation_mut(&mut self, t: &TranslationBase<N, D, S>) {
+    pub fn append_translation_mut(&mut self, t: &Translation<N, D>) {
         self.translation.vector += &t.vector
     }
 
@@ -79,7 +108,7 @@ impl<N, D: DimName, S, R> IsometryBase<N, D, S, R>
     /// Appends in-place to `self` a rotation centered at the point `p`, i.e., the rotation that
     /// lets `p` invariant.
     #[inline]
-    pub fn append_rotation_wrt_point_mut(&mut self, r: &R, p: &PointBase<N, D, S>) {
+    pub fn append_rotation_wrt_point_mut(&mut self, r: &R, p: &Point<N, D>) {
         self.translation.vector -= &p.coords;
         self.append_rotation_mut(r);
         self.translation.vector += &p.coords;
@@ -89,7 +118,7 @@ impl<N, D: DimName, S, R> IsometryBase<N, D, S, R>
     /// `self.translation`.
     #[inline]
     pub fn append_rotation_wrt_center_mut(&mut self, r: &R) {
-        let center = PointBase::from_coordinates(self.translation.vector.clone());
+        let center = Point::from_coordinates(self.translation.vector.clone());
         self.append_rotation_wrt_point_mut(r, &center)
     }
 }
@@ -98,16 +127,15 @@ impl<N, D: DimName, S, R> IsometryBase<N, D, S, R>
 // and makes it hard to use it, e.g., for Transform × Isometry implementation.
 // This is OK since all constructors of the isometry enforce the Rotation bound already (and
 // explicit struct construction is prevented by the dummy ZST field).
-impl<N, D: DimName, S, R> IsometryBase<N, D, S, R>
-    where N: Scalar,
-          S: Storage<N, D, U1> {
+impl<N: Real, D: DimName, R> Isometry<N, D, R>
+    where DefaultAllocator: Allocator<N, D> {
     /// Converts this isometry into its equivalent homogeneous transformation matrix.
     #[inline]
-    pub fn to_homogeneous(&self) -> OwnedSquareMatrix<N, DimNameSum<D, U1>, S::Alloc>
+    pub fn to_homogeneous(&self) -> MatrixN<N, DimNameSum<D, U1>>
         where D: DimNameAdd<U1>,
-              R: SubsetOf<OwnedSquareMatrix<N, DimNameSum<D, U1>, S::Alloc>>,
-              S::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
-        let mut res: OwnedSquareMatrix<N, _, S::Alloc> = ::convert_ref(&self.rotation);
+              R: SubsetOf<MatrixN<N, DimNameSum<D, U1>>>,
+              DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
+        let mut res: MatrixN<N, _> = ::convert_ref(&self.rotation);
         res.fixed_slice_mut::<D, U1>(0, D::dim()).copy_from(&self.translation.vector);
 
         res
@@ -115,30 +143,24 @@ impl<N, D: DimName, S, R> IsometryBase<N, D, S, R>
 }
 
 
-impl<N, D: DimName, S, R> Eq for IsometryBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>> + Eq,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R> Eq for Isometry<N, D, R>
+    where R: Rotation<Point<N, D>> + Eq,
+          DefaultAllocator: Allocator<N, D> {
 }
 
-impl<N, D: DimName, S, R> PartialEq for IsometryBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>> + PartialEq,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R> PartialEq for Isometry<N, D, R>
+    where R: Rotation<Point<N, D>> + PartialEq,
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
-    fn eq(&self, right: &IsometryBase<N, D, S, R>) -> bool {
+    fn eq(&self, right: &Isometry<N, D, R>) -> bool {
         self.translation == right.translation &&
         self.rotation    == right.rotation
     }
 }
 
-impl<N, D: DimName, S, R> ApproxEq for IsometryBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>> + ApproxEq<Epsilon = N::Epsilon>,
-          S::Alloc: OwnedAllocator<N, D, U1, S>,
+impl<N: Real, D: DimName, R> ApproxEq for Isometry<N, D, R>
+    where R: Rotation<Point<N, D>> + ApproxEq<Epsilon = N::Epsilon>,
+          DefaultAllocator: Allocator<N, D>,
           N::Epsilon: Copy {
     type Epsilon = N::Epsilon;
 
@@ -175,32 +197,16 @@ impl<N, D: DimName, S, R> ApproxEq for IsometryBase<N, D, S, R>
  * Display
  *
  */
-impl<N, D: DimName, S, R> fmt::Display for IsometryBase<N, D, S, R>
-    where N: Real + fmt::Display,
-          S: OwnedStorage<N, D, U1>,
-          R: fmt::Display,
-          S::Alloc: OwnedAllocator<N, D, U1, S> + Allocator<usize, D, U1> {
+impl<N: Real + fmt::Display, D: DimName, R> fmt::Display for Isometry<N, D, R>
+    where R: fmt::Display,
+          DefaultAllocator: Allocator<N, D> +
+                            Allocator<usize, D> {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         let precision = f.precision().unwrap_or(3);
 
-        try!(writeln!(f, "IsometryBase {{"));
+        try!(writeln!(f, "Isometry {{"));
         try!(write!(f, "{:.*}", precision, self.translation));
         try!(write!(f, "{:.*}", precision, self.rotation));
         writeln!(f, "}}")
     }
 }
-
-
-//         /*
-//          *
-//          * Absolute
-//          *
-//          */
-//         impl<N: Absolute> Absolute for $t<N> {
-//             type AbsoluteValue = $submatrix<N::AbsoluteValue>;
-//
-//             #[inline]
-//             fn abs(m: &$t<N>) -> $submatrix<N::AbsoluteValue> {
-//                 Absolute::abs(&m.submatrix)
-//             }
-//         }

src/geometry/isometry_alga.rs

@@ -1,14 +1,14 @@
 use alga::general::{AbstractMagma, AbstractGroup, AbstractLoop, AbstractMonoid, AbstractQuasigroup,
                     AbstractSemigroup, Real, Inverse, Multiplicative, Identity, Id};
-use alga::linear::{Transformation, Similarity, AffineTransformation, DirectIsometry, Isometry,
+use alga::linear::{Transformation, Similarity, AffineTransformation, DirectIsometry,
                    Rotation, ProjectiveTransformation};
+use alga::linear::Isometry as AlgaIsometry;
 
-use core::ColumnVector;
-use core::dimension::{DimName, U1};
-use core::storage::OwnedStorage;
-use core::allocator::OwnedAllocator;
+use core::{DefaultAllocator, VectorN};
+use core::dimension::DimName;
+use core::allocator::Allocator;
 
-use geometry::{IsometryBase, TranslationBase, PointBase};
+use geometry::{Isometry, Translation, Point};
 
 
 /*
@@ -16,22 +16,18 @@ use geometry::{IsometryBase, TranslationBase, PointBase};
  * Algebraic structures.
  *
  */
-impl<N, D: DimName, S, R> Identity<Multiplicative> for IsometryBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R> Identity<Multiplicative> for Isometry<N, D, R>
+    where R: Rotation<Point<N, D>>,
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn identity() -> Self {
         Self::identity()
     }
 }
 
-impl<N, D: DimName, S, R> Inverse<Multiplicative> for IsometryBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R> Inverse<Multiplicative> for Isometry<N, D, R>
+    where R: Rotation<Point<N, D>>,
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn inverse(&self) -> Self {
         self.inverse()
@@ -43,11 +39,9 @@ impl<N, D: DimName, S, R> Inverse<Multiplicative> for IsometryBase<N, D, S, R>
     }
 }
 
-impl<N, D: DimName, S, R> AbstractMagma<Multiplicative> for IsometryBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R> AbstractMagma<Multiplicative> for Isometry<N, D, R>
+    where R: Rotation<Point<N, D>>,
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn operate(&self, rhs: &Self) -> Self {
         self * rhs
@@ -56,11 +50,9 @@ impl<N, D: DimName, S, R> AbstractMagma<Multiplicative> for IsometryBase<N, D, S
 
 macro_rules! impl_multiplicative_structures(
     ($($marker: ident<$operator: ident>),* $(,)*) => {$(
-        impl<N, D: DimName, S, R> $marker<$operator> for IsometryBase<N, D, S, R>
-            where N: Real,
-                  S: OwnedStorage<N, D, U1>,
-                  R: Rotation<PointBase<N, D, S>>,
-                  S::Alloc: OwnedAllocator<N, D, U1, S> { }
+        impl<N: Real, D: DimName, R> $marker<$operator> for Isometry<N, D, R>
+            where R: Rotation<Point<N, D>>,
+                  DefaultAllocator: Allocator<N, D> { }
     )*}
 );
 
@@ -77,49 +69,43 @@ impl_multiplicative_structures!(
  * Transformation groups.
  *
  */
-impl<N, D: DimName, S, R> Transformation<PointBase<N, D, S>> for IsometryBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R> Transformation<Point<N, D>> for Isometry<N, D, R>
+    where R: Rotation<Point<N, D>>,
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
-    fn transform_point(&self, pt: &PointBase<N, D, S>) -> PointBase<N, D, S> {
+    fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
         self * pt
     }
 
     #[inline]
-    fn transform_vector(&self, v: &ColumnVector<N, D, S>) -> ColumnVector<N, D, S> {
+    fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
         self * v
     }
 }
 
-impl<N, D: DimName, S, R> ProjectiveTransformation<PointBase<N, D, S>> for IsometryBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R> ProjectiveTransformation<Point<N, D>> for Isometry<N, D, R>
+    where R: Rotation<Point<N, D>>,
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
-    fn inverse_transform_point(&self, pt: &PointBase<N, D, S>) -> PointBase<N, D, S> {
+    fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
         self.rotation.inverse_transform_point(&(pt - &self.translation.vector))
     }
 
     #[inline]
-    fn inverse_transform_vector(&self, v: &ColumnVector<N, D, S>) -> ColumnVector<N, D, S> {
+    fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
         self.rotation.inverse_transform_vector(v)
     }
 }
 
-impl<N, D: DimName, S, R> AffineTransformation<PointBase<N, D, S>> for IsometryBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R> AffineTransformation<Point<N, D>> for Isometry<N, D, R>
+    where R: Rotation<Point<N, D>>,
+          DefaultAllocator: Allocator<N, D> {
     type Rotation          = R;
     type NonUniformScaling = Id;
-    type Translation       = TranslationBase<N, D, S>;
+    type Translation       = Translation<N, D>;
 
     #[inline]
-    fn decompose(&self) -> (TranslationBase<N, D, S>, R, Id, R) {
+    fn decompose(&self) -> (Translation<N, D>, R, Id, R) {
         (self.translation.clone(), self.rotation.clone(), Id::new(), R::identity())
     }
 
@@ -136,7 +122,7 @@ impl<N, D: DimName, S, R> AffineTransformation<PointBase<N, D, S>> for IsometryB
     #[inline]
     fn append_rotation(&self, r: &Self::Rotation) -> Self {
         let shift = r.transform_vector(&self.translation.vector);
-        IsometryBase::from_parts(TranslationBase::from_vector(shift), r.clone() * self.rotation.clone())
+        Isometry::from_parts(Translation::from_vector(shift), r.clone() * self.rotation.clone())
     }
 
     #[inline]
@@ -155,22 +141,20 @@ impl<N, D: DimName, S, R> AffineTransformation<PointBase<N, D, S>> for IsometryB
     }
 
     #[inline]
-    fn append_rotation_wrt_point(&self, r: &Self::Rotation, p: &PointBase<N, D, S>) -> Option<Self> {
+    fn append_rotation_wrt_point(&self, r: &Self::Rotation, p: &Point<N, D>) -> Option<Self> {
         let mut res = self.clone();
         res.append_rotation_wrt_point_mut(r, p);
         Some(res)
     }
 }
 
-impl<N, D: DimName, S, R> Similarity<PointBase<N, D, S>> for IsometryBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R> Similarity<Point<N, D>> for Isometry<N, D, R>
+    where R: Rotation<Point<N, D>>,
+          DefaultAllocator: Allocator<N, D> {
     type Scaling = Id;
 
     #[inline]
-    fn translation(&self) -> TranslationBase<N, D, S> {
+    fn translation(&self) -> Translation<N, D> {
         self.translation.clone()
     }
 
@@ -187,12 +171,10 @@ impl<N, D: DimName, S, R> Similarity<PointBase<N, D, S>> for IsometryBase<N, D,
 
 macro_rules! marker_impl(
     ($($Trait: ident),*) => {$(
-        impl<N, D: DimName, S, R> $Trait<PointBase<N, D, S>> for IsometryBase<N, D, S, R>
-        where N: Real,
-              S: OwnedStorage<N, D, U1>,
-              R: Rotation<PointBase<N, D, S>>,
-              S::Alloc: OwnedAllocator<N, D, U1, S> { }
+        impl<N: Real, D: DimName, R> $Trait<Point<N, D>> for Isometry<N, D, R>
+        where R: Rotation<Point<N, D>>,
+              DefaultAllocator: Allocator<N, D> { }
     )*}
 );
 
-marker_impl!(Isometry, DirectIsometry);
+marker_impl!(AlgaIsometry, DirectIsometry);

src/geometry/isometry_alias.rs

@@ -1,19 +1,16 @@
-use core::MatrixArray;
-use core::dimension::{U1, U2, U3};
+use core::dimension::{U2, U3};
 
-use geometry::{Rotation, IsometryBase, UnitQuaternion, UnitComplex};
+use geometry::{Isometry, Rotation2, Rotation3, UnitQuaternion, UnitComplex};
 
-/// A D-dimensional isometry.
-pub type Isometry<N, D> = IsometryBase<N, D, MatrixArray<N, D, U1>, Rotation<N, D>>;
 
 /// A 2-dimensional isometry using a unit complex number for its rotational part.
-pub type Isometry2<N> = IsometryBase<N, U2, MatrixArray<N, U2, U1>, UnitComplex<N>>;
+pub type Isometry2<N> = Isometry<N, U2, UnitComplex<N>>;
 
 /// A 3-dimensional isometry using a unit quaternion for its rotational part.
-pub type Isometry3<N> = IsometryBase<N, U3, MatrixArray<N, U3, U1>, UnitQuaternion<N>>;
+pub type Isometry3<N> = Isometry<N, U3, UnitQuaternion<N>>;
 
-/// A 2-dimensional isometry using a rotation matrix for its rotation part.
-pub type IsometryMatrix2<N> = Isometry<N, U2>;
+/// A 2-dimensional isometry using a rotation matrix for its rotational part.
+pub type IsometryMatrix2<N> = Isometry<N, U2, Rotation2<N>>;
 
-/// A 3-dimensional isometry using a rotation matrix for its rotation part.
-pub type IsometryMatrix3<N> = Isometry<N, U3>;
+/// A 3-dimensional isometry using a rotation matrix for its rotational part.
+pub type IsometryMatrix3<N> = Isometry<N, U3, Rotation3<N>>;

src/geometry/isometry_construction.rs

@@ -1,5 +1,7 @@
 #[cfg(feature = "arbitrary")]
 use quickcheck::{Arbitrary, Gen};
+#[cfg(feature = "arbitrary")]
+use core::storage::Owned;
 
 use num::One;
 use rand::{Rng, Rand};
@@ -7,31 +9,33 @@ use rand::{Rng, Rand};
 use alga::general::Real;
 use alga::linear::Rotation as AlgaRotation;
 
-use core::ColumnVector;
-use core::dimension::{DimName, U1, U2, U3, U4};
-use core::allocator::{OwnedAllocator, Allocator};
-use core::storage::OwnedStorage;
+use core::{DefaultAllocator, Vector2, Vector3};
+use core::dimension::{DimName, U2, U3};
+use core::allocator::Allocator;
 
-use geometry::{PointBase, TranslationBase, RotationBase, IsometryBase, UnitQuaternionBase, UnitComplex};
+use geometry::{Point, Translation, Rotation, Isometry, UnitQuaternion, UnitComplex,
+               Point3, Rotation2, Rotation3};
 
 
-impl<N, D: DimName, S, R> IsometryBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: AlgaRotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R: AlgaRotation<Point<N, D>>> Isometry<N, D, R>
+    where DefaultAllocator: Allocator<N, D> {
     /// Creates a new identity isometry.
     #[inline]
     pub fn identity() -> Self {
-        Self::from_parts(TranslationBase::identity(), R::identity())
+        Self::from_parts(Translation::identity(), R::identity())
+    }
+
+    /// The isometry that applies the rotation `r` with its axis passing through the point `p`.
+    /// This effectively lets `p` invariant.
+    #[inline]
+    pub fn rotation_wrt_point(r: R, p: Point<N, D>) -> Self {
+        let shift = r.transform_vector(&-&p.coords);
+        Self::from_parts(Translation::from_vector(shift + p.coords), r)
     }
 }
 
-impl<N, D: DimName, S, R> One for IsometryBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: AlgaRotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R: AlgaRotation<Point<N, D>>> One for Isometry<N, D, R>
+    where DefaultAllocator: Allocator<N, D> {
     /// Creates a new identity isometry.
     #[inline]
     fn one() -> Self {
@@ -39,37 +43,21 @@ impl<N, D: DimName, S, R> One for IsometryBase<N, D, S, R>
     }
 }
 
-impl<N, D: DimName, S, R> Rand for IsometryBase<N, D, S, R>
-    where N: Real + Rand,
-          S: OwnedStorage<N, D, U1>,
-          R: AlgaRotation<PointBase<N, D, S>> + Rand,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real + Rand, D: DimName, R> Rand for Isometry<N, D, R>
+    where R: AlgaRotation<Point<N, D>> + Rand,
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn rand<G: Rng>(rng: &mut G) -> Self {
         Self::from_parts(rng.gen(), rng.gen())
     }
 }
 
-impl<N, D: DimName, S, R> IsometryBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: AlgaRotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
-    /// The isometry that applies the rotation `r` with its axis passing through the point `p`.
-    /// This effectively lets `p` invariant.
-    #[inline]
-    pub fn rotation_wrt_point(r: R, p: PointBase<N, D, S>) -> Self {
-        let shift = r.transform_vector(&-&p.coords);
-        Self::from_parts(TranslationBase::from_vector(shift + p.coords), r)
-    }
-}
-
 #[cfg(feature = "arbitrary")]
-impl<N, D: DimName, S, R> Arbitrary for IsometryBase<N, D, S, R>
+impl<N, D: DimName, R> Arbitrary for Isometry<N, D, R>
     where N: Real + Arbitrary + Send,
-          S: OwnedStorage<N, D, U1> + Send,
-          R: AlgaRotation<PointBase<N, D, S>> + Arbitrary + Send,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+          R: AlgaRotation<Point<N, D>> + Arbitrary + Send,
+          Owned<N, D>: Send,
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn arbitrary<G: Gen>(rng: &mut G) -> Self {
         Self::from_parts(Arbitrary::arbitrary(rng), Arbitrary::arbitrary(rng))
@@ -83,45 +71,31 @@ impl<N, D: DimName, S, R> Arbitrary for IsometryBase<N, D, S, R>
  */
 
 // 2D rotation.
-impl<N, S, SR> IsometryBase<N, U2, S, RotationBase<N, U2, SR>>
-    where N: Real,
-          S:  OwnedStorage<N, U2, U1, Alloc = SR::Alloc>,
-          SR: OwnedStorage<N, U2, U2>,
-          S::Alloc:  OwnedAllocator<N, U2, U1, S>,
-          SR::Alloc: OwnedAllocator<N, U2, U2, SR> {
+impl<N: Real> Isometry<N, U2, Rotation2<N>> {
     /// Creates a new isometry from a translation and a rotation angle.
     #[inline]
-    pub fn new(translation: ColumnVector<N, U2, S>, angle: N) -> Self {
-        Self::from_parts(TranslationBase::from_vector(translation), RotationBase::<N, U2, SR>::new(angle))
+    pub fn new(translation: Vector2<N>, angle: N) -> Self {
+        Self::from_parts(Translation::from_vector(translation), Rotation::<N, U2>::new(angle))
     }
 }
 
-impl<N, S> IsometryBase<N, U2, S, UnitComplex<N>>
-    where N: Real,
-          S: OwnedStorage<N, U2, U1>,
-          S::Alloc:  OwnedAllocator<N, U2, U1, S> {
+impl<N: Real> Isometry<N, U2, UnitComplex<N>> {
     /// Creates a new isometry from a translation and a rotation angle.
     #[inline]
-    pub fn new(translation: ColumnVector<N, U2, S>, angle: N) -> Self {
-        Self::from_parts(TranslationBase::from_vector(translation), UnitComplex::from_angle(angle))
+    pub fn new(translation: Vector2<N>, angle: N) -> Self {
+        Self::from_parts(Translation::from_vector(translation), UnitComplex::from_angle(angle))
     }
 }
 
 // 3D rotation.
 macro_rules! isometry_construction_impl(
     ($RotId: ident < $($RotParams: ident),*>, $RRDim: ty, $RCDim: ty) => {
-        impl<N, S, SR> IsometryBase<N, U3, S, $RotId<$($RotParams),*>>
-            where N: Real,
-                  S:  OwnedStorage<N, U3, U1, Alloc = SR::Alloc>,
-                  SR: OwnedStorage<N, $RRDim, $RCDim>,
-                  S::Alloc:  OwnedAllocator<N, U3, U1, S>,
-                  SR::Alloc: OwnedAllocator<N, $RRDim, $RCDim, SR> +
-                             Allocator<N, U3, U3> {
+        impl<N: Real> Isometry<N, U3, $RotId<$($RotParams),*>> {
             /// Creates a new isometry from a translation and a rotation axis-angle.
             #[inline]
-            pub fn new(translation: ColumnVector<N, U3, S>, axisangle: ColumnVector<N, U3, S>) -> Self {
+            pub fn new(translation: Vector3<N>, axisangle: Vector3<N>) -> Self {
                 Self::from_parts(
-                    TranslationBase::from_vector(translation),
+                    Translation::from_vector(translation),
                     $RotId::<$($RotParams),*>::from_scaled_axis(axisangle))
             }
 
@@ -137,12 +111,12 @@ macro_rules! isometry_construction_impl(
             ///   * up - Vertical direction. The only requirement of this parameter is to not be collinear
             ///   to `eye - at`. Non-collinearity is not checked.
             #[inline]
-            pub fn new_observer_frame(eye:    &PointBase<N, U3, S>,
-                                      target: &PointBase<N, U3, S>,
-                                      up:     &ColumnVector<N, U3, S>)
+            pub fn new_observer_frame(eye:    &Point3<N>,
+                                      target: &Point3<N>,
+                                      up:     &Vector3<N>)
                                       -> Self {
                 Self::from_parts(
-                    TranslationBase::from_vector(eye.coords.clone()),
+                    Translation::from_vector(eye.coords.clone()),
                     $RotId::new_observer_frame(&(target - eye), up))
             }
 
@@ -157,14 +131,14 @@ macro_rules! isometry_construction_impl(
             ///   * up - A vector approximately aligned with required the vertical axis. The only
             ///   requirement of this parameter is to not be collinear to `target - eye`.
             #[inline]
-            pub fn look_at_rh(eye:    &PointBase<N, U3, S>,
-                              target: &PointBase<N, U3, S>,
-                              up:     &ColumnVector<N, U3, S>)
+            pub fn look_at_rh(eye:    &Point3<N>,
+                              target: &Point3<N>,
+                              up:     &Vector3<N>)
                               -> Self {
                 let rotation = $RotId::look_at_rh(&(target - eye), up);
                 let trans    = &rotation * (-eye);
 
-                Self::from_parts(TranslationBase::from_vector(trans.coords), rotation)
+                Self::from_parts(Translation::from_vector(trans.coords), rotation)
             }
 
             /// Builds a left-handed look-at view matrix.
@@ -178,18 +152,18 @@ macro_rules! isometry_construction_impl(
             ///   * up - A vector approximately aligned with required the vertical axis. The only
             ///   requirement of this parameter is to not be collinear to `target - eye`.
             #[inline]
-            pub fn look_at_lh(eye:    &PointBase<N, U3, S>,
-                              target: &PointBase<N, U3, S>,
-                              up:     &ColumnVector<N, U3, S>)
+            pub fn look_at_lh(eye:    &Point3<N>,
+                              target: &Point3<N>,
+                              up:     &Vector3<N>)
                               -> Self {
                 let rotation = $RotId::look_at_lh(&(target - eye), up);
                 let trans    = &rotation * (-eye);
 
-                Self::from_parts(TranslationBase::from_vector(trans.coords), rotation)
+                Self::from_parts(Translation::from_vector(trans.coords), rotation)
             }
         }
     }
 );
 
-isometry_construction_impl!(RotationBase<N, U3, SR>, U3, U3);
-isometry_construction_impl!(UnitQuaternionBase<N, SR>, U4, U1);
+isometry_construction_impl!(Rotation3<N>, U3, U3);
+isometry_construction_impl!(UnitQuaternion<N>, U4, U1);

src/geometry/isometry_conversion.rs

@@ -1,50 +1,47 @@
 use alga::general::{Real, SubsetOf, SupersetOf};
 use alga::linear::Rotation;
 
-use core::{SquareMatrix, OwnedSquareMatrix};
-use core::dimension::{DimName, DimNameAdd, DimNameSum, U1};
-use core::storage::OwnedStorage;
-use core::allocator::{Allocator, OwnedAllocator};
+use core::{DefaultAllocator, MatrixN};
+use core::dimension::{DimName, DimNameAdd, DimNameSum, DimMin, U1};
+use core::allocator::Allocator;
 
-use geometry::{PointBase, TranslationBase, IsometryBase, SimilarityBase, TransformBase, SuperTCategoryOf, TAffine};
+use geometry::{Point, Translation, Isometry, Similarity, Transform, SuperTCategoryOf, TAffine};
 
 /*
  * This file provides the following conversions:
  * =============================================
  *
- * IsometryBase -> IsometryBase
- * IsometryBase -> SimilarityBase
- * IsometryBase -> TransformBase
- * IsometryBase -> Matrix (homogeneous)
+ * Isometry -> Isometry
+ * Isometry -> Similarity
+ * Isometry -> Transform
+ * Isometry -> Matrix (homogeneous)
  */
 
 
-impl<N1, N2, D: DimName, SA, SB, R1, R2> SubsetOf<IsometryBase<N2, D, SB, R2>> for IsometryBase<N1, D, SA, R1>
+impl<N1, N2, D: DimName, R1, R2> SubsetOf<Isometry<N2, D, R2>> for Isometry<N1, D, R1>
     where N1: Real,
           N2: Real + SupersetOf<N1>,
-          R1: Rotation<PointBase<N1, D, SA>> + SubsetOf<R2>,
-          R2: Rotation<PointBase<N2, D, SB>>,
-          SA: OwnedStorage<N1, D, U1>,
-          SB: OwnedStorage<N2, D, U1>,
-          SA::Alloc: OwnedAllocator<N1, D, U1, SA>,
-          SB::Alloc: OwnedAllocator<N2, D, U1, SB> {
+          R1: Rotation<Point<N1, D>> + SubsetOf<R2>,
+          R2: Rotation<Point<N2, D>>,
+          DefaultAllocator: Allocator<N1, D> +
+                            Allocator<N2, D> {
     #[inline]
-    fn to_superset(&self) -> IsometryBase<N2, D, SB, R2> {
-        IsometryBase::from_parts(
+    fn to_superset(&self) -> Isometry<N2, D, R2> {
+        Isometry::from_parts(
             self.translation.to_superset(),
             self.rotation.to_superset()
         )
     }
 
     #[inline]
-    fn is_in_subset(iso: &IsometryBase<N2, D, SB, R2>) -> bool {
-        ::is_convertible::<_, TranslationBase<N1, D, SA>>(&iso.translation) &&
+    fn is_in_subset(iso: &Isometry<N2, D, R2>) -> bool {
+        ::is_convertible::<_, Translation<N1, D>>(&iso.translation) &&
         ::is_convertible::<_, R1>(&iso.rotation)
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(iso: &IsometryBase<N2, D, SB, R2>) -> Self {
-        IsometryBase::from_parts(
+    unsafe fn from_superset_unchecked(iso: &Isometry<N2, D, R2>) -> Self {
+        Isometry::from_parts(
             iso.translation.to_subset_unchecked(),
             iso.rotation.to_subset_unchecked()
         )
@@ -52,95 +49,91 @@ impl<N1, N2, D: DimName, SA, SB, R1, R2> SubsetOf<IsometryBase<N2, D, SB, R2>> f
 }
 
 
-impl<N1, N2, D: DimName, SA, SB, R1, R2> SubsetOf<SimilarityBase<N2, D, SB, R2>> for IsometryBase<N1, D, SA, R1>
+impl<N1, N2, D: DimName, R1, R2> SubsetOf<Similarity<N2, D, R2>> for Isometry<N1, D, R1>
     where N1: Real,
           N2: Real + SupersetOf<N1>,
-          R1: Rotation<PointBase<N1, D, SA>> + SubsetOf<R2>,
-          R2: Rotation<PointBase<N2, D, SB>>,
-          SA: OwnedStorage<N1, D, U1>,
-          SB: OwnedStorage<N2, D, U1>,
-          SA::Alloc: OwnedAllocator<N1, D, U1, SA>,
-          SB::Alloc: OwnedAllocator<N2, D, U1, SB> {
+          R1: Rotation<Point<N1, D>> + SubsetOf<R2>,
+          R2: Rotation<Point<N2, D>>,
+          DefaultAllocator: Allocator<N1, D> +
+                            Allocator<N2, D> {
     #[inline]
-    fn to_superset(&self) -> SimilarityBase<N2, D, SB, R2> {
-        SimilarityBase::from_isometry(
+    fn to_superset(&self) -> Similarity<N2, D, R2> {
+        Similarity::from_isometry(
             self.to_superset(),
             N2::one()
         )
     }
 
     #[inline]
-    fn is_in_subset(sim: &SimilarityBase<N2, D, SB, R2>) -> bool {
-        ::is_convertible::<_, IsometryBase<N1, D, SA, R1>>(&sim.isometry) &&
+    fn is_in_subset(sim: &Similarity<N2, D, R2>) -> bool {
+        ::is_convertible::<_, Isometry<N1, D, R1>>(&sim.isometry) &&
         sim.scaling() == N2::one()
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(sim: &SimilarityBase<N2, D, SB, R2>) -> Self {
+    unsafe fn from_superset_unchecked(sim: &Similarity<N2, D, R2>) -> Self {
         ::convert_ref_unchecked(&sim.isometry)
     }
 }
 
 
-impl<N1, N2, D, SA, SB, R, C> SubsetOf<TransformBase<N2, D, SB, C>> for IsometryBase<N1, D, SA, R>
+impl<N1, N2, D, R, C> SubsetOf<Transform<N2, D, C>> for Isometry<N1, D, R>
     where N1: Real,
           N2: Real + SupersetOf<N1>,
-          SA: OwnedStorage<N1, D, U1>,
-          SB: OwnedStorage<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>,
           C:  SuperTCategoryOf<TAffine>,
-          R: Rotation<PointBase<N1, D, SA>> +
-             SubsetOf<OwnedSquareMatrix<N1, DimNameSum<D, U1>, SA::Alloc>> + // needed by: .to_homogeneous()
-             SubsetOf<SquareMatrix<N2, DimNameSum<D, U1>, SB>>,              // needed by: ::convert_unchecked(mm)
-          D:  DimNameAdd<U1>,
-          SA::Alloc: OwnedAllocator<N1, D, U1, SA> +
+          R: Rotation<Point<N1, D>> +
+             SubsetOf<MatrixN<N1, DimNameSum<D, U1>>> +
+             SubsetOf<MatrixN<N2, DimNameSum<D, U1>>>,
+          D: DimNameAdd<U1> +
+             DimMin<D, Output = D>, // needed by .is_special_orthogonal()
+          DefaultAllocator: Allocator<N1, D>     +
                             Allocator<N1, D, D>  +                                // needed by R
                             Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>> + // needed by: .to_homogeneous()
-                     Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>,  // needed by R
-          SB::Alloc: OwnedAllocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>, SB> +
-                     Allocator<N2, D, D> +  // needed by: mm.fixed_slice_mut
-                     Allocator<N2, D, U1> + // needed by: m.fixed_slice
-                     Allocator<N2, U1, D> { // needed by: m.fixed_slice
+                            Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>> + // needed by R
+                            Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>> +
+                            Allocator<(usize, usize), D> + // needed by .is_special_orthogonal()
+                            Allocator<N2, D, D> +
+                            Allocator<N2, D>    {
     #[inline]
-    fn to_superset(&self) -> TransformBase<N2, D, SB, C> {
-        TransformBase::from_matrix_unchecked(self.to_homogeneous().to_superset())
+    fn to_superset(&self) -> Transform<N2, D, C> {
+        Transform::from_matrix_unchecked(self.to_homogeneous().to_superset())
     }
 
     #[inline]
-    fn is_in_subset(t: &TransformBase<N2, D, SB, C>) -> bool {
+    fn is_in_subset(t: &Transform<N2, D, C>) -> bool {
         <Self as SubsetOf<_>>::is_in_subset(t.matrix())
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(t: &TransformBase<N2, D, SB, C>) -> Self {
+    unsafe fn from_superset_unchecked(t: &Transform<N2, D, C>) -> Self {
         Self::from_superset_unchecked(t.matrix())
     }
 }
 
 
-impl<N1, N2, D, SA, SB, R> SubsetOf<SquareMatrix<N2, DimNameSum<D, U1>, SB>> for IsometryBase<N1, D, SA, R>
+impl<N1, N2, D, R> SubsetOf<MatrixN<N2, DimNameSum<D, U1>>> for Isometry<N1, D, R>
     where N1: Real,
           N2: Real + SupersetOf<N1>,
-          SA: OwnedStorage<N1, D, U1>,
-          SB: OwnedStorage<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>,
-          R: Rotation<PointBase<N1, D, SA>> +
-             SubsetOf<OwnedSquareMatrix<N1, DimNameSum<D, U1>, SA::Alloc>> + // needed by: .to_homogeneous()
-             SubsetOf<SquareMatrix<N2, DimNameSum<D, U1>, SB>>,              // needed by: ::convert_unchecked(mm)
-          D:  DimNameAdd<U1>,
-          SA::Alloc: OwnedAllocator<N1, D, U1, SA> +
+          R: Rotation<Point<N1, D>> +
+             SubsetOf<MatrixN<N1, DimNameSum<D, U1>>> +
+             SubsetOf<MatrixN<N2, DimNameSum<D, U1>>>,
+          D: DimNameAdd<U1> +
+             DimMin<D, Output = D>, // needed by .is_special_orthogonal()
+          DefaultAllocator: Allocator<N1, D>     +
                             Allocator<N1, D, D>  +                                // needed by R
                             Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>> + // needed by: .to_homogeneous()
-                     Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>,  // needed by R
-          SB::Alloc: OwnedAllocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>, SB> +
-                     Allocator<N2, D, D> +  // needed by: mm.fixed_slice_mut
-                     Allocator<N2, D, U1> + // needed by: m.fixed_slice
-                     Allocator<N2, U1, D> { // needed by: m.fixed_slice
+                            Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>> + // needed by R
+                            Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>> +
+                            Allocator<(usize, usize), D> + // needed by .is_special_orthogonal()
+                            Allocator<N2, D, D> +
+                            Allocator<N2, D>    {
     #[inline]
-    fn to_superset(&self) -> SquareMatrix<N2, DimNameSum<D, U1>, SB> {
+    fn to_superset(&self) -> MatrixN<N2, DimNameSum<D, U1>> {
         self.to_homogeneous().to_superset()
     }
 
     #[inline]
-    fn is_in_subset(m: &SquareMatrix<N2, DimNameSum<D, U1>, SB>) -> bool {
+    fn is_in_subset(m: &MatrixN<N2, DimNameSum<D, U1>>) -> bool {
         let rot    = m.fixed_slice::<D, D>(0, 0);
         let bottom = m.fixed_slice::<U1, D>(D::dim(), 0);
 
@@ -154,9 +147,9 @@ impl<N1, N2, D, SA, SB, R> SubsetOf<SquareMatrix<N2, DimNameSum<D, U1>, SB>> for
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(m: &SquareMatrix<N2, DimNameSum<D, U1>, SB>) -> Self {
+    unsafe fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self {
         let t = m.fixed_slice::<D, U1>(0, D::dim()).into_owned();
-        let t = TranslationBase::from_vector(::convert_unchecked(t));
+        let t = Translation::from_vector(::convert_unchecked(t));
 
         Self::from_parts(t, ::convert_unchecked(m.clone_owned()))
     }

src/geometry/isometry_ops.rs

@@ -1,14 +1,13 @@
 use std::ops::{Mul, MulAssign, Div, DivAssign};
 
 use alga::general::Real;
-use alga::linear::Rotation;
+use alga::linear::Rotation as AlgaRotation;
 
-use core::ColumnVector;
+use core::{DefaultAllocator, VectorN};
 use core::dimension::{DimName, U1, U3, U4};
-use core::storage::OwnedStorage;
-use core::allocator::OwnedAllocator;
+use core::allocator::Allocator;
 
-use geometry::{PointBase, RotationBase, IsometryBase, TranslationBase, UnitQuaternionBase};
+use geometry::{Point, Rotation, Isometry, Translation, UnitQuaternion};
 
 // FIXME: there are several cloning of rotations that we could probably get rid of (but we didn't
 // yet because that would require to add a bound like `where for<'a, 'b> &'a R: Mul<&'b R, Output = R>`
@@ -22,41 +21,41 @@ use geometry::{PointBase, RotationBase, IsometryBase, TranslationBase, UnitQuate
  *
  * (Operators)
  *
- * IsometryBase × IsometryBase
- * IsometryBase × R
+ * Isometry × Isometry
+ * Isometry × R
  *
  *
- * IsometryBase ÷ IsometryBase
- * IsometryBase ÷ R
+ * Isometry ÷ Isometry
+ * Isometry ÷ R
  *
- * IsometryBase × PointBase
- * IsometryBase × ColumnVector
+ * Isometry × Point
+ * Isometry × Vector
  *
  *
- * IsometryBase    × TranslationBase
- * TranslationBase × IsometryBase
- * TranslationBase × R           -> IsometryBase<R>
+ * Isometry    × Translation
+ * Translation × Isometry
+ * Translation × R           -> Isometry<R>
  *
- * NOTE: The following are provided explicitly because we can't have R × IsometryBase.
- * RotationBase   × IsometryBase<RotationBase>
- * UnitQuaternion × IsometryBase<UnitQuaternion>
+ * NOTE: The following are provided explicitly because we can't have R × Isometry.
+ * Rotation       × Isometry<Rotation>
+ * UnitQuaternion × Isometry<UnitQuaternion>
  *
- * RotationBase   ÷ IsometryBase<RotationBase>
- * UnitQuaternion ÷ IsometryBase<UnitQuaternion>
+ * Rotation       ÷ Isometry<Rotation>
+ * UnitQuaternion ÷ Isometry<UnitQuaternion>
  *
- * RotationBase   × TranslationBase -> IsometryBase<RotationBase>
- * UnitQuaternion × TranslationBase -> IsometryBase<UnitQuaternion>
+ * Rotation       × Translation -> Isometry<Rotation>
+ * UnitQuaternion × Translation -> Isometry<UnitQuaternion>
  *
  *
  * (Assignment Operators)
  *
- * IsometryBase ×= TranslationBase
+ * Isometry ×= Translation
  *
- * IsometryBase ×= IsometryBase
- * IsometryBase ×= R
+ * Isometry ×= Isometry
+ * Isometry ×= R
  *
- * IsometryBase ÷= IsometryBase
- * IsometryBase ÷= R
+ * Isometry ÷= Isometry
+ * Isometry ÷= R
  *
  */
 
@@ -65,11 +64,9 @@ macro_rules! isometry_binop_impl(
     ($Op: ident, $op: ident;
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Output: ty;
      $action: expr; $($lives: tt),*) => {
-        impl<$($lives ,)* N, D: DimName, S, R> $Op<$Rhs> for $Lhs
-            where N: Real,
-                  S: OwnedStorage<N, D, U1>,
-                  R: Rotation<PointBase<N, D, S>>,
-                  S::Alloc: OwnedAllocator<N, D, U1, S> {
+        impl<$($lives ,)* N: Real, D: DimName, R> $Op<$Rhs> for $Lhs
+            where R: AlgaRotation<Point<N, D>>,
+                  DefaultAllocator: Allocator<N, D> {
             type Output = $Output;
 
             #[inline]
@@ -114,22 +111,18 @@ macro_rules! isometry_binop_assign_impl_all(
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty;
      [val] => $action_val: expr;
      [ref] => $action_ref: expr;) => {
-        impl<N, D: DimName, S, R> $OpAssign<$Rhs> for $Lhs
-            where N: Real,
-                  S: OwnedStorage<N, D, U1>,
-                  R: Rotation<PointBase<N, D, S>>,
-                  S::Alloc: OwnedAllocator<N, D, U1, S> {
+        impl<N: Real, D: DimName, R> $OpAssign<$Rhs> for $Lhs
+            where R: AlgaRotation<Point<N, D>>,
+                  DefaultAllocator: Allocator<N, D> {
             #[inline]
             fn $op_assign(&mut $lhs, $rhs: $Rhs) {
                 $action_val
             }
         }
 
-        impl<'b, N, D: DimName, S, R> $OpAssign<&'b $Rhs> for $Lhs
-            where N: Real,
-                  S: OwnedStorage<N, D, U1>,
-                  R: Rotation<PointBase<N, D, S>>,
-                  S::Alloc: OwnedAllocator<N, D, U1, S> {
+        impl<'b, N: Real, D: DimName, R> $OpAssign<&'b $Rhs> for $Lhs
+            where R: AlgaRotation<Point<N, D>>,
+                  DefaultAllocator: Allocator<N, D> {
             #[inline]
             fn $op_assign(&mut $lhs, $rhs: &'b $Rhs) {
                 $action_ref
@@ -138,18 +131,18 @@ macro_rules! isometry_binop_assign_impl_all(
     }
 );
 
-// IsometryBase × IsometryBase
-// IsometryBase ÷ IsometryBase
+// Isometry × Isometry
+// Isometry ÷ Isometry
 isometry_binop_impl_all!(
     Mul, mul;
-    self: IsometryBase<N, D, S, R>, rhs: IsometryBase<N, D, S, R>, Output = IsometryBase<N, D, S, R>;
+    self: Isometry<N, D, R>, rhs: Isometry<N, D, R>, Output = Isometry<N, D, R>;
     [val val] => &self * &rhs;
     [ref val] => self * &rhs;
     [val ref] => &self * rhs;
     [ref ref] => {
         let shift = self.rotation.transform_vector(&rhs.translation.vector);
 
-        IsometryBase::from_parts(TranslationBase::from_vector(&self.translation.vector + shift),
+        Isometry::from_parts(Translation::from_vector(&self.translation.vector + shift),
                              self.rotation.clone() * rhs.rotation.clone()) // FIXME: too bad we have to clone.
     };
 );
@@ -157,7 +150,7 @@ isometry_binop_impl_all!(
 
 isometry_binop_impl_all!(
     Div, div;
-    self: IsometryBase<N, D, S, R>, rhs: IsometryBase<N, D, S, R>, Output = IsometryBase<N, D, S, R>;
+    self: Isometry<N, D, R>, rhs: Isometry<N, D, R>, Output = Isometry<N, D, R>;
     [val val] => self * rhs.inverse();
     [ref val] => self * rhs.inverse();
     [val ref] => self * rhs.inverse();
@@ -165,10 +158,10 @@ isometry_binop_impl_all!(
 );
 
 
-// IsometryBase ×= TranslationBase
+// Isometry ×= Translation
 isometry_binop_assign_impl_all!(
     MulAssign, mul_assign;
-    self: IsometryBase<N, D, S, R>, rhs: TranslationBase<N, D, S>;
+    self: Isometry<N, D, R>, rhs: Translation<N, D>;
     [val] => *self *= &rhs;
     [ref] => {
         let shift = self.rotation.transform_vector(&rhs.vector);
@@ -176,11 +169,11 @@ isometry_binop_assign_impl_all!(
     };
 );
 
-// IsometryBase ×= IsometryBase
-// IsometryBase ÷= IsometryBase
+// Isometry ×= Isometry
+// Isometry ÷= Isometry
 isometry_binop_assign_impl_all!(
     MulAssign, mul_assign;
-    self: IsometryBase<N, D, S, R>, rhs: IsometryBase<N, D, S, R>;
+    self: Isometry<N, D, R>, rhs: Isometry<N, D, R>;
     [val] => *self *= &rhs;
     [ref] => {
         let shift = self.rotation.transform_vector(&rhs.translation.vector);
@@ -191,55 +184,55 @@ isometry_binop_assign_impl_all!(
 
 isometry_binop_assign_impl_all!(
     DivAssign, div_assign;
-    self: IsometryBase<N, D, S, R>, rhs: IsometryBase<N, D, S, R>;
+    self: Isometry<N, D, R>, rhs: Isometry<N, D, R>;
     [val] => *self /= &rhs;
     [ref] => *self *= rhs.inverse();
 );
 
-// IsometryBase ×= R
-// IsometryBase ÷= R
+// Isometry ×= R
+// Isometry ÷= R
 isometry_binop_assign_impl_all!(
     MulAssign, mul_assign;
-    self: IsometryBase<N, D, S, R>, rhs: R;
+    self: Isometry<N, D, R>, rhs: R;
     [val] => self.rotation *= rhs;
     [ref] => self.rotation *= rhs.clone();
 );
 
 isometry_binop_assign_impl_all!(
     DivAssign, div_assign;
-    self: IsometryBase<N, D, S, R>, rhs: R;
+    self: Isometry<N, D, R>, rhs: R;
     // FIXME: don't invert explicitly?
     [val] => *self *= rhs.inverse();
     [ref] => *self *= rhs.inverse();
 );
 
 
-// IsometryBase × R
-// IsometryBase ÷ R
+// Isometry × R
+// Isometry ÷ R
 isometry_binop_impl_all!(
     Mul, mul;
-    self: IsometryBase<N, D, S, R>, rhs: R, Output = IsometryBase<N, D, S, R>;
-    [val val] => IsometryBase::from_parts(self.translation, self.rotation * rhs);
-    [ref val] => IsometryBase::from_parts(self.translation.clone(), self.rotation.clone() * rhs); // FIXME: do not clone.
-    [val ref] => IsometryBase::from_parts(self.translation, self.rotation * rhs.clone());
-    [ref ref] => IsometryBase::from_parts(self.translation.clone(), self.rotation.clone() * rhs.clone());
+    self: Isometry<N, D, R>, rhs: R, Output = Isometry<N, D, R>;
+    [val val] => Isometry::from_parts(self.translation, self.rotation * rhs);
+    [ref val] => Isometry::from_parts(self.translation.clone(), self.rotation.clone() * rhs); // FIXME: do not clone.
+    [val ref] => Isometry::from_parts(self.translation, self.rotation * rhs.clone());
+    [ref ref] => Isometry::from_parts(self.translation.clone(), self.rotation.clone() * rhs.clone());
 );
 
 
 isometry_binop_impl_all!(
     Div, div;
-    self: IsometryBase<N, D, S, R>, rhs: R, Output = IsometryBase<N, D, S, R>;
-    [val val] => IsometryBase::from_parts(self.translation, self.rotation / rhs);
-    [ref val] => IsometryBase::from_parts(self.translation.clone(), self.rotation.clone() / rhs);
-    [val ref] => IsometryBase::from_parts(self.translation, self.rotation / rhs.clone());
-    [ref ref] => IsometryBase::from_parts(self.translation.clone(), self.rotation.clone() / rhs.clone());
+    self: Isometry<N, D, R>, rhs: R, Output = Isometry<N, D, R>;
+    [val val] => Isometry::from_parts(self.translation, self.rotation / rhs);
+    [ref val] => Isometry::from_parts(self.translation.clone(), self.rotation.clone() / rhs);
+    [val ref] => Isometry::from_parts(self.translation, self.rotation / rhs.clone());
+    [ref ref] => Isometry::from_parts(self.translation.clone(), self.rotation.clone() / rhs.clone());
 );
 
 
-// IsometryBase × PointBase
+// Isometry × Point
 isometry_binop_impl_all!(
     Mul, mul;
-    self: IsometryBase<N, D, S, R>, right: PointBase<N, D, S>, Output = PointBase<N, D, S>;
+    self: Isometry<N, D, R>, right: Point<N, D>, Output = Point<N, D>;
     [val val] => self.translation  * self.rotation.transform_point(&right);
     [ref val] => &self.translation * self.rotation.transform_point(&right);
     [val ref] => self.translation  * self.rotation.transform_point(right);
@@ -247,10 +240,12 @@ isometry_binop_impl_all!(
 );
 
 
-// IsometryBase × Vector
+// Isometry × Vector
 isometry_binop_impl_all!(
     Mul, mul;
-    self: IsometryBase<N, D, S, R>, right: ColumnVector<N, D, S>, Output = ColumnVector<N, D, S>;
+    // FIXME: because of `transform_vector`, we cant use a generic storage type for the rhs vector,
+    // i.e., right: Vector<N, D, S> where S: Storage<N, D>.
+    self: Isometry<N, D, R>, right: VectorN<N, D>, Output = VectorN<N, D>;
     [val val] => self.rotation.transform_vector(&right);
     [ref val] => self.rotation.transform_vector(&right);
     [val ref] => self.rotation.transform_vector(right);
@@ -258,38 +253,38 @@ isometry_binop_impl_all!(
 );
 
 
-// IsometryBase × TranslationBase
+// Isometry × Translation
 isometry_binop_impl_all!(
     Mul, mul;
-    self: IsometryBase<N, D, S, R>, right: TranslationBase<N, D, S>, Output = IsometryBase<N, D, S, R>;
+    self: Isometry<N, D, R>, right: Translation<N, D>, Output = Isometry<N, D, R>;
     [val val] => &self * &right;
     [ref val] => self * &right;
     [val ref] => &self * right;
     [ref ref] => {
         let new_tr = &self.translation.vector + self.rotation.transform_vector(&right.vector);
-        IsometryBase::from_parts(TranslationBase::from_vector(new_tr), self.rotation.clone())
+        Isometry::from_parts(Translation::from_vector(new_tr), self.rotation.clone())
     };
 );
 
-// TranslationBase × IsometryBase
+// Translation × Isometry
 isometry_binop_impl_all!(
     Mul, mul;
-    self: TranslationBase<N, D, S>, right: IsometryBase<N, D, S, R>, Output = IsometryBase<N, D, S, R>;
-    [val val] => IsometryBase::from_parts(self * right.translation, right.rotation);
-    [ref val] => IsometryBase::from_parts(self * &right.translation, right.rotation);
-    [val ref] => IsometryBase::from_parts(self * &right.translation, right.rotation.clone());
-    [ref ref] => IsometryBase::from_parts(self * &right.translation, right.rotation.clone());
+    self: Translation<N, D>, right: Isometry<N, D, R>, Output = Isometry<N, D, R>;
+    [val val] => Isometry::from_parts(self * right.translation, right.rotation);
+    [ref val] => Isometry::from_parts(self * &right.translation, right.rotation);
+    [val ref] => Isometry::from_parts(self * &right.translation, right.rotation.clone());
+    [ref ref] => Isometry::from_parts(self * &right.translation, right.rotation.clone());
 );
 
 
-// TranslationBase × R
+// Translation × R
 isometry_binop_impl_all!(
     Mul, mul;
-    self: TranslationBase<N, D, S>, right: R, Output = IsometryBase<N, D, S, R>;
-    [val val] => IsometryBase::from_parts(self, right);
-    [ref val] => IsometryBase::from_parts(self.clone(), right);
-    [val ref] => IsometryBase::from_parts(self, right.clone());
-    [ref ref] => IsometryBase::from_parts(self.clone(), right.clone());
+    self: Translation<N, D>, right: R, Output = Isometry<N, D, R>;
+    [val val] => Isometry::from_parts(self, right);
+    [ref val] => Isometry::from_parts(self.clone(), right);
+    [val ref] => Isometry::from_parts(self, right.clone());
+    [ref ref] => Isometry::from_parts(self.clone(), right.clone());
 );
 
 
@@ -300,12 +295,9 @@ macro_rules! isometry_from_composition_impl(
      ($R1: ty, $C1: ty),($R2: ty, $C2: ty) $(for $Dims: ident: $DimsBound: ident),*;
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Output: ty;
      $action: expr; $($lives: tt),*) => {
-        impl<$($lives ,)* N $(, $Dims: $DimsBound)*, SA, SB> $Op<$Rhs> for $Lhs
-            where N: Real,
-                  SA: OwnedStorage<N, $R1, $C1>,
-                  SB: OwnedStorage<N, $R2, $C2, Alloc = SA::Alloc>,
-                  SA::Alloc: OwnedAllocator<N, $R1, $C1, SA>,
-                  SB::Alloc: OwnedAllocator<N, $R2, $C2, SB> {
+        impl<$($lives ,)* N: Real $(, $Dims: $DimsBound)*> $Op<$Rhs> for $Lhs
+            where DefaultAllocator: Allocator<N, $R1, $C1> +
+                                    Allocator<N, $R2, $C2> {
             type Output = $Output;
 
             #[inline]
@@ -352,51 +344,51 @@ macro_rules! isometry_from_composition_impl_all(
 );
 
 
-// RotationBase × TranslationBase
+// Rotation × Translation
 isometry_from_composition_impl_all!(
     Mul, mul;
     (D, D), (D, U1) for D: DimName;
-    self: RotationBase<N, D, SA>, right: TranslationBase<N, D, SB>, Output = IsometryBase<N, D, SB, RotationBase<N, D, SA>>;
-    [val val] => IsometryBase::from_parts(TranslationBase::from_vector(&self * right.vector),  self);
-    [ref val] => IsometryBase::from_parts(TranslationBase::from_vector(self * right.vector),   self.clone());
-    [val ref] => IsometryBase::from_parts(TranslationBase::from_vector(&self * &right.vector), self);
-    [ref ref] => IsometryBase::from_parts(TranslationBase::from_vector(self * &right.vector),  self.clone());
+    self: Rotation<N, D>, right: Translation<N, D>, Output = Isometry<N, D, Rotation<N, D>>;
+    [val val] => Isometry::from_parts(Translation::from_vector(&self * right.vector),  self);
+    [ref val] => Isometry::from_parts(Translation::from_vector(self * right.vector),   self.clone());
+    [val ref] => Isometry::from_parts(Translation::from_vector(&self * &right.vector), self);
+    [ref ref] => Isometry::from_parts(Translation::from_vector(self * &right.vector),  self.clone());
 );
 
 
-// UnitQuaternionBase × TranslationBase
+// UnitQuaternion × Translation
 isometry_from_composition_impl_all!(
     Mul, mul;
     (U4, U1), (U3, U1);
-    self: UnitQuaternionBase<N, SA>, right: TranslationBase<N, U3, SB>,
-    Output = IsometryBase<N, U3, SB, UnitQuaternionBase<N, SA>>;
-    [val val] => IsometryBase::from_parts(TranslationBase::from_vector(&self *  right.vector), self);
-    [ref val] => IsometryBase::from_parts(TranslationBase::from_vector( self *  right.vector), self.clone());
-    [val ref] => IsometryBase::from_parts(TranslationBase::from_vector(&self * &right.vector), self);
-    [ref ref] => IsometryBase::from_parts(TranslationBase::from_vector( self * &right.vector), self.clone());
+    self: UnitQuaternion<N>, right: Translation<N, U3>,
+    Output = Isometry<N, U3, UnitQuaternion<N>>;
+    [val val] => Isometry::from_parts(Translation::from_vector(&self *  right.vector), self);
+    [ref val] => Isometry::from_parts(Translation::from_vector( self *  right.vector), self.clone());
+    [val ref] => Isometry::from_parts(Translation::from_vector(&self * &right.vector), self);
+    [ref ref] => Isometry::from_parts(Translation::from_vector( self * &right.vector), self.clone());
 );
 
-// RotationBase × IsometryBase
+// Rotation × Isometry
 isometry_from_composition_impl_all!(
     Mul, mul;
     (D, D), (D, U1) for D: DimName;
-    self: RotationBase<N, D, SA>, right: IsometryBase<N, D, SB, RotationBase<N, D, SA>>,
-    Output = IsometryBase<N, D, SB, RotationBase<N, D, SA>>;
+    self: Rotation<N, D>, right: Isometry<N, D, Rotation<N, D>>,
+    Output = Isometry<N, D, Rotation<N, D>>;
     [val val] => &self * &right;
     [ref val] =>  self * &right;
     [val ref] => &self * right;
     [ref ref] => {
         let shift = self * &right.translation.vector;
-        IsometryBase::from_parts(TranslationBase::from_vector(shift), self * &right.rotation)
+        Isometry::from_parts(Translation::from_vector(shift), self * &right.rotation)
     };
 );
 
-// RotationBase ÷ IsometryBase
+// Rotation ÷ Isometry
 isometry_from_composition_impl_all!(
     Div, div;
     (D, D), (D, U1) for D: DimName;
-    self: RotationBase<N, D, SA>, right: IsometryBase<N, D, SB, RotationBase<N, D, SA>>,
-    Output = IsometryBase<N, D, SB, RotationBase<N, D, SA>>;
+    self: Rotation<N, D>, right: Isometry<N, D, Rotation<N, D>>,
+    Output = Isometry<N, D, Rotation<N, D>>;
     // FIXME: don't call iverse explicitly?
     [val val] => self * right.inverse();
     [ref val] => self * right.inverse();
@@ -405,28 +397,28 @@ isometry_from_composition_impl_all!(
 );
 
 
-// UnitQuaternion × IsometryBase
+// UnitQuaternion × Isometry
 isometry_from_composition_impl_all!(
     Mul, mul;
     (U4, U1), (U3, U1);
-    self: UnitQuaternionBase<N, SA>, right: IsometryBase<N, U3, SB, UnitQuaternionBase<N, SA>>,
-    Output = IsometryBase<N, U3, SB, UnitQuaternionBase<N, SA>>;
+    self: UnitQuaternion<N>, right: Isometry<N, U3, UnitQuaternion<N>>,
+    Output = Isometry<N, U3, UnitQuaternion<N>>;
     [val val] => &self * &right;
     [ref val] =>  self * &right;
     [val ref] => &self * right;
     [ref ref] => {
         let shift = self * &right.translation.vector;
-        IsometryBase::from_parts(TranslationBase::from_vector(shift), self * &right.rotation)
+        Isometry::from_parts(Translation::from_vector(shift), self * &right.rotation)
     };
 );
 
 
-// UnitQuaternion ÷ IsometryBase
+// UnitQuaternion ÷ Isometry
 isometry_from_composition_impl_all!(
     Div, div;
     (U4, U1), (U3, U1);
-    self: UnitQuaternionBase<N, SA>, right: IsometryBase<N, U3, SB, UnitQuaternionBase<N, SA>>,
-    Output = IsometryBase<N, U3, SB, UnitQuaternionBase<N, SA>>;
+    self: UnitQuaternion<N>, right: Isometry<N, U3, UnitQuaternion<N>>,
+    Output = Isometry<N, U3, UnitQuaternion<N>>;
     // FIXME: don't call inverse explicitly?
     [val val] => self * right.inverse();
     [ref val] => self * right.inverse();

src/geometry/mod.rs

@@ -14,7 +14,7 @@ mod point_coordinates;
 mod rotation;
 mod rotation_construction;
 mod rotation_ops;
-mod rotation_alga; // FIXME: implement RotationBase methods.
+mod rotation_alga; // FIXME: implement Rotation methods.
 mod rotation_conversion;
 mod rotation_alias;
 mod rotation_specialization;
@@ -23,9 +23,8 @@ mod quaternion;
 mod quaternion_construction;
 mod quaternion_ops;
 mod quaternion_alga;
-mod quaternion_alias;
-mod quaternion_coordinates;
 mod quaternion_conversion;
+mod quaternion_coordinates;
 
 mod unit_complex;
 mod unit_complex_construction;
@@ -61,6 +60,8 @@ mod transform_alga;
 mod transform_conversion;
 mod transform_alias;
 
+mod reflection;
+
 mod orthographic;
 mod perspective;
 
@@ -71,7 +72,6 @@ pub use self::rotation::*;
 pub use self::rotation_alias::*;
 
 pub use self::quaternion::*;
-pub use self::quaternion_alias::*;
 
 pub use self::unit_complex::*;
 
@@ -87,5 +87,7 @@ pub use self::similarity_alias::*;
 pub use self::transform::*;
 pub use self::transform_alias::*;
 
-pub use self::orthographic::{OrthographicBase, Orthographic3};
-pub use self::perspective::{PerspectiveBase, Perspective3};
+pub use self::reflection::*;
+
+pub use self::orthographic::Orthographic3;
+pub use self::perspective::Perspective3;

src/geometry/op_macros.rs

@@ -8,7 +8,7 @@ macro_rules! md_impl(
     // Operator, operator method, and calar bounds.
      $Op: ident, $op: ident $(where N: $($ScalarBounds: ident),*)*;
      // Storage dimensions, and dimension bounds.
-     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) for $($Dims: ident: $DimsBound: ident $(<$BoundParam: ty>)*),+
+     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) for $($Dims: ident: $DimsBound: ident $(<$($BoundParam: ty),*>)*),+
      // [Optional] Extra allocator bounds.
      $(where $ConstraintType: ty: $ConstraintBound: ident<$($ConstraintBoundParams: ty $( = $EqBound: ty )*),*> )*;
      // Argument identifiers and types + output.
@@ -17,10 +17,11 @@ macro_rules! md_impl(
      $action: expr;
      // Lifetime.
      $($lives: tt),*) => {
-        impl<$($lives ,)* N $(, $Dims: $DimsBound $(<$BoundParam>)*)*, SA, SB> $Op<$Rhs> for $Lhs
-            where N:  Scalar + Zero + ClosedAdd + ClosedMul $($(+ $ScalarBounds)*)*,
-                  SA: Storage<N, $R1, $C1>,
-                  SB: Storage<N, $R2, $C2>,
+        impl<$($lives ,)* N $(, $Dims: $DimsBound $(<$($BoundParam),*>)*)*> $Op<$Rhs> for $Lhs
+            where N: Scalar + Zero + One + ClosedAdd + ClosedMul $($(+ $ScalarBounds)*)*,
+                  DefaultAllocator: Allocator<N, $R1, $C1> +
+                                    Allocator<N, $R2, $C2> +
+                                    Allocator<N, $R1, $C2>,
                   $( $ConstraintType: $ConstraintBound<$( $ConstraintBoundParams $( = $EqBound )*),*> ),*
                    {
             type Output = $Result;
@@ -41,7 +42,7 @@ macro_rules! md_impl_all(
      // Operator, operator method, and calar bounds.
      $Op: ident, $op: ident $(where N: $($ScalarBounds: ident),*)*;
      // Storage dimensions, and dimension bounds.
-     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) for $($Dims: ident: $DimsBound: ident $(<$BoundParam: ty>)*),+
+     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) for $($Dims: ident: $DimsBound: ident $(<$($BoundParam: ty),*>)*),+
      // [Optional] Extra allocator bounds.
      $(where $ConstraintType: ty: $ConstraintBound: ident<$($ConstraintBoundParams: ty $( = $EqBound: ty )*),*> )*;
      // Argument identifiers and types + output.
@@ -54,28 +55,28 @@ macro_rules! md_impl_all(
 
         md_impl!(
             $Op, $op $(where N: $($ScalarBounds),*)*;
-            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$BoundParam>)*),+
+            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$($BoundParam),*>)*),+
             $(where $ConstraintType: $ConstraintBound<$($ConstraintBoundParams $( = $EqBound )*),*>)*;
             $lhs: $Lhs, $rhs: $Rhs, Output = $Result;
             $action_val_val; );
 
         md_impl!(
             $Op, $op $(where N: $($ScalarBounds),*)*;
-            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$BoundParam>)*),+
+            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$($BoundParam),*>)*),+
             $(where $ConstraintType: $ConstraintBound<$($ConstraintBoundParams $( = $EqBound )*),*>)*;
             $lhs: &'a $Lhs, $rhs: $Rhs, Output = $Result;
             $action_ref_val; 'a);
 
         md_impl!(
             $Op, $op $(where N: $($ScalarBounds),*)*;
-            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$BoundParam>)*),+
+            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$($BoundParam),*>)*),+
             $(where $ConstraintType: $ConstraintBound<$($ConstraintBoundParams $( = $EqBound )*),*>)*;
             $lhs: $Lhs, $rhs: &'b $Rhs, Output = $Result;
             $action_val_ref; 'b);
 
         md_impl!(
             $Op, $op $(where N: $($ScalarBounds),*)*;
-            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$BoundParam>)*),+
+            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$($BoundParam),*>)*),+
             $(where $ConstraintType: $ConstraintBound<$($ConstraintBoundParams $( = $EqBound )*),*>)*;
             $lhs: &'a $Lhs, $rhs: &'b $Rhs, Output = $Result;
             $action_ref_ref; 'a, 'b);
@@ -89,19 +90,18 @@ macro_rules! md_assign_impl(
      // Operator, operator method, and scalar bounds.
      $Op: ident, $op: ident $(where N: $($ScalarBounds: ident),*)*;
      // Storage dimensions, and dimension bounds.
-     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) for $($Dims: ident: $DimsBound: ident $(<$BoundParam: ty>)*),+
+     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) for $($Dims: ident: $DimsBound: ident $(<$($BoundParam: ty),*>)*),+
      // [Optional] Extra allocator bounds.
-     $(where $ConstraintType: ty: $ConstraintBound: ident<$($ConstraintBoundParams: ty $( = $EqBound: ty )*),*> )*;
+     $(where $ConstraintType: ty: $ConstraintBound: ident $(<$($ConstraintBoundParams: ty $( = $EqBound: ty )*),*>)* )*;
      // Argument identifiers and types.
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty;
      // Actual implementation and lifetimes.
      $action: expr; $($lives: tt),*) => {
-        impl<$($lives ,)* N $(, $Dims: $DimsBound $(<$BoundParam>)*)*, SA, SB> $Op<$Rhs> for $Lhs
-            where N:  Scalar + Zero + ClosedAdd + ClosedMul $($(+ $ScalarBounds)*)*,
-                  SA: OwnedStorage<N, $R1, $C1>, // FIXME: this is too restrictive.
-                  SB: Storage<N, $R2, $C2>,
-                  SA::Alloc: OwnedAllocator<N, $R1, $C1, SA>,
-                  $( $ConstraintType: $ConstraintBound<$( $ConstraintBoundParams $( = $EqBound )*),*> ),*
+        impl<$($lives ,)* N $(, $Dims: $DimsBound $(<$($BoundParam),*>)*)*> $Op<$Rhs> for $Lhs
+            where N:  Scalar + Zero + One + ClosedAdd + ClosedMul $($(+ $ScalarBounds)*)*,
+                  DefaultAllocator: Allocator<N, $R1, $C1> +
+                                    Allocator<N, $R2, $C2>,
+                  $( $ConstraintType: $ConstraintBound $(<$( $ConstraintBoundParams $( = $EqBound )*),*>)* ),*
         {
             #[inline]
             fn $op(&mut $lhs, $rhs: $Rhs) {
@@ -118,9 +118,9 @@ macro_rules! md_assign_impl_all(
      // Operator, operator method, and scalar bounds.
      $Op: ident, $op: ident $(where N: $($ScalarBounds: ident),*)*;
      // Storage dimensions, and dimension bounds.
-     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) for $($Dims: ident: $DimsBound: ident $(<$BoundParam: ty>)*),+
+     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) for $($Dims: ident: $DimsBound: ident $(<$($BoundParam: ty),*>)*),+
      // [Optional] Extra allocator bounds.
-     $(where $ConstraintType: ty: $ConstraintBound: ident<$($ConstraintBoundParams: ty $( = $EqBound: ty )*),*> )*;
+     $(where $ConstraintType: ty: $ConstraintBound: ident$(<$($ConstraintBoundParams: ty $( = $EqBound: ty )*),*>)* )*;
      // Argument identifiers and types.
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty;
      // Actual implementation and lifetimes.
@@ -128,15 +128,15 @@ macro_rules! md_assign_impl_all(
      [ref] => $action_ref: expr;) => {
         md_assign_impl!(
             $Op, $op $(where N: $($ScalarBounds),*)*;
-            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$BoundParam>)*),+
-            $(where $ConstraintType: $ConstraintBound<$($ConstraintBoundParams $( = $EqBound )*),*>)*;
+            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$($BoundParam),*>)*),+
+            $(where $ConstraintType: $ConstraintBound $(<$($ConstraintBoundParams $( = $EqBound )*),*>)*)*;
             $lhs: $Lhs, $rhs: $Rhs;
             $action_val; );
 
         md_assign_impl!(
             $Op, $op $(where N: $($ScalarBounds),*)*;
-            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$BoundParam>)*),+
-            $(where $ConstraintType: $ConstraintBound<$($ConstraintBoundParams $( = $EqBound )*),*>)*;
+            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$($BoundParam),*>)*),+
+            $(where $ConstraintType: $ConstraintBound $(<$($ConstraintBoundParams $( = $EqBound )*),*>)*)*;
             $lhs: $Lhs, $rhs: &'b $Rhs;
             $action_ref; 'b);
     }
@@ -146,14 +146,14 @@ macro_rules! md_assign_impl_all(
 /// Macro for the implementation of addition and subtraction.
 macro_rules! add_sub_impl(
     ($Op: ident, $op: ident, $bound: ident;
-     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) $(-> ($RRes: ty))* for $($Dims: ident: $DimsBound: ident),+;
+     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) $(-> ($RRes: ty))* for $($Dims: ident: $DimsBound: ident $(<$($BoundParam: ty),*>)*),+;
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Result: ty;
      $action: expr; $($lives: tt),*) => {
-        impl<$($lives ,)* N $(, $Dims: $DimsBound)*, SA, SB> $Op<$Rhs> for $Lhs
+        impl<$($lives ,)* N $(, $Dims: $DimsBound $(<$($BoundParam),*>)*)*> $Op<$Rhs> for $Lhs
             where N: Scalar + $bound,
-                  SA: Storage<N, $R1, $C1>,
-                  SB: Storage<N, $R2, $C2>,
-                  SA::Alloc: SameShapeAllocator<N, $R1, $C1, $R2, $C2, SA>,
+                  DefaultAllocator: Allocator<N, $R1, $C1> +
+                                    Allocator<N, $R2, $C2> +
+                                    SameShapeAllocator<N, $R1, $C1, $R2, $C2>,
                   ShapeConstraint: SameNumberOfRows<$R1, $R2 $(, Representative = $RRes)*> +
                                    SameNumberOfColumns<$C1, $C2> {
             type Output = $Result;
@@ -173,11 +173,10 @@ macro_rules! add_sub_assign_impl(
      ($R1: ty, $C1: ty),($R2: ty, $C2: ty) for $($Dims: ident: $DimsBound: ident),+;
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty;
      $action: expr; $($lives: tt),*) => {
-        impl<$($lives ,)* N $(, $Dims: $DimsBound)*, SA, SB> $Op<$Rhs> for $Lhs
+        impl<$($lives ,)* N $(, $Dims: $DimsBound)*> $Op<$Rhs> for $Lhs
             where N: Scalar + $bound,
-                  SA: OwnedStorage<N, $R1, $C1>, // FIXME: this is too restrictive.
-                  SB: Storage<N, $R2, $C2>,
-                  SA::Alloc: OwnedAllocator<N, $R1, $C1, SA>,
+                  DefaultAllocator: Allocator<N, $R1, $C1> +
+                                    Allocator<N, $R2, $C2>,
                   ShapeConstraint: SameNumberOfRows<$R1, $R2> + SameNumberOfColumns<$C1, $C2> {
             #[inline]
             fn $op(&mut $lhs, $rhs: $Rhs) {

src/geometry/orthographic.rs

@@ -1,70 +1,65 @@
 #[cfg(feature="arbitrary")]
 use quickcheck::{Arbitrary, Gen};
 use rand::{Rand, Rng};
-
 #[cfg(feature = "serde-serialize")]
-use serde::{Serialize, Serializer, Deserialize, Deserializer};
+use serde;
+use std::fmt;
 
 use alga::general::Real;
 
-use core::{Scalar, SquareMatrix, OwnedSquareMatrix, ColumnVector, OwnedColumnVector, MatrixArray};
-use core::dimension::{U1, U3, U4};
-use core::storage::{OwnedStorage, Storage, StorageMut};
-use core::allocator::OwnedAllocator;
+use core::{Matrix4, Vector, Vector3};
+use core::dimension::U3;
+use core::storage::Storage;
 use core::helper;
 
-use geometry::{PointBase, OwnedPoint};
+use geometry::Point3;
 
 /// A 3D orthographic projection stored as an homogeneous 4x4 matrix.
-#[derive(Debug, Clone, Copy)] // FIXME: Hash
-pub struct OrthographicBase<N: Scalar, S: Storage<N, U4, U4>> {
-    matrix: SquareMatrix<N, U4, S>
+pub struct Orthographic3<N: Real> {
+    matrix: Matrix4<N>
 }
 
-#[cfg(feature = "serde-serialize")]
-impl<N, S> Serialize for OrthographicBase<N, S>
-    where N: Scalar,
-          S: Storage<N, U4, U4>,
-          SquareMatrix<N, U4, S>: Serialize,
-{
-    fn serialize<T>(&self, serializer: T) -> Result<T::Ok, T::Error>
-        where T: Serializer
-    {
-        self.matrix.serialize(serializer)
+impl<N: Real> Copy for Orthographic3<N> { }
+
+impl<N: Real> Clone for Orthographic3<N> {
+    #[inline]
+    fn clone(&self) -> Self {
+        Orthographic3::from_matrix_unchecked(self.matrix.clone())
     }
 }
 
-#[cfg(feature = "serde-serialize")]
-impl<'de, N, S> Deserialize<'de> for OrthographicBase<N, S>
-    where N: Scalar,
-          S: Storage<N, U4, U4>,
-          SquareMatrix<N, U4, S>: Deserialize<'de>,
-{
-    fn deserialize<T>(deserializer: T) -> Result<Self, T::Error>
-        where T: Deserializer<'de>
-    {
-        SquareMatrix::deserialize(deserializer).map(|x| OrthographicBase { matrix: x })
+impl<N: Real> fmt::Debug for Orthographic3<N> {
+    fn fmt(&self, f: &mut fmt::Formatter) -> Result<(), fmt::Error> {
+        self.matrix.fmt(f)
     }
 }
 
-/// A 3D orthographic projection stored as a static homogeneous 4x4 matrix.
-pub type Orthographic3<N> = OrthographicBase<N, MatrixArray<N, U4, U4>>;
-
-impl<N, S> Eq for OrthographicBase<N, S>
-    where N: Scalar + Eq,
-          S: Storage<N, U4, U4> { }
-
-impl<N: Scalar, S: Storage<N, U4, U4>> PartialEq for OrthographicBase<N, S> {
+impl<N: Real> PartialEq for Orthographic3<N> {
     #[inline]
     fn eq(&self, right: &Self) -> bool {
         self.matrix == right.matrix
     }
 }
 
-impl<N, S> OrthographicBase<N, S>
-    where N: Real,
-          S: OwnedStorage<N, U4, U4>,
-          S::Alloc: OwnedAllocator<N, U4, U4, S> {
+#[cfg(feature = "serde-serialize")]
+impl<N: Real + serde::Serialize> serde::Serialize for Orthographic3<N> {
+    fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
+        where S: serde::Serializer {
+            self.matrix.serialize(serializer)
+        }
+}
+
+#[cfg(feature = "serde-serialize")]
+impl<'a, N: Real + serde::Deserialize<'a>> serde::Deserialize<'a> for Orthographic3<N> {
+    fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
+        where Des: serde::Deserializer<'a> {
+            let matrix = Matrix4::<N>::deserialize(deserializer)?;
+
+            Ok(Orthographic3::from_matrix_unchecked(matrix))
+        }
+}
+
+impl<N: Real> Orthographic3<N> {
     /// Creates a new orthographic projection matrix.
     #[inline]
     pub fn new(left: N, right: N, bottom: N, top: N, znear: N, zfar: N) -> Self {
@@ -72,7 +67,7 @@ impl<N, S> OrthographicBase<N, S>
         assert!(bottom < top, "The top corner must be higher than the bottom corner.");
         assert!(znear < zfar, "The far plane must be farther than the near plane.");
 
-        let matrix = SquareMatrix::<N, U4, S>::identity();
+        let matrix = Matrix4::<N>::identity();
         let mut res = Self::from_matrix_unchecked(matrix);
 
         res.set_left_and_right(left, right);
@@ -87,8 +82,8 @@ impl<N, S> OrthographicBase<N, S>
     /// It is not checked whether or not the given matrix actually represents an orthographic
     /// projection.
     #[inline]
-    pub fn from_matrix_unchecked(matrix: SquareMatrix<N, U4, S>) -> Self {
-        OrthographicBase {
+    pub fn from_matrix_unchecked(matrix: Matrix4<N>) -> Self {
+        Orthographic3 {
             matrix: matrix
         }
     }
@@ -105,24 +100,10 @@ impl<N, S> OrthographicBase<N, S>
 
         Self::new(-width * half, width * half, -height * half, height * half, znear, zfar)
     }
-}
-
-impl<N: Real, S: Storage<N, U4, U4>> OrthographicBase<N, S> {
-    /// A reference to the underlying homogeneous transformation matrix.
-    #[inline]
-    pub fn as_matrix(&self) -> &SquareMatrix<N, U4, S> {
-        &self.matrix
-    }
-
-    /// Retrieves the underlying homogeneous matrix.
-    #[inline]
-    pub fn unwrap(self) -> SquareMatrix<N, U4, S> {
-        self.matrix
-    }
 
     /// Retrieves the inverse of the underlying homogeneous matrix.
     #[inline]
-    pub fn inverse(&self) -> OwnedSquareMatrix<N, U4, S::Alloc> {
+    pub fn inverse(&self) -> Matrix4<N> {
         let mut res = self.to_homogeneous();
 
         let inv_m11 = N::one() / self.matrix[(0, 0)];
@@ -142,10 +123,22 @@ impl<N: Real, S: Storage<N, U4, U4>> OrthographicBase<N, S> {
 
     /// Computes the corresponding homogeneous matrix.
     #[inline]
-    pub fn to_homogeneous(&self) -> OwnedSquareMatrix<N, U4, S::Alloc> {
+    pub fn to_homogeneous(&self) -> Matrix4<N> {
         self.matrix.clone_owned()
     }
 
+    /// A reference to the underlying homogeneous transformation matrix.
+    #[inline]
+    pub fn as_matrix(&self) -> &Matrix4<N> {
+        &self.matrix
+    }
+
+    /// Retrieves the underlying homogeneous matrix.
+    #[inline]
+    pub fn unwrap(self) -> Matrix4<N> {
+        self.matrix
+    }
+
     /// The smallest x-coordinate of the view cuboid.
     #[inline]
     pub fn left(&self) -> N {
@@ -185,10 +178,8 @@ impl<N: Real, S: Storage<N, U4, U4>> OrthographicBase<N, S> {
     // FIXME: when we get specialization, specialize the Mul impl instead.
     /// Projects a point. Faster than matrix multiplication.
     #[inline]
-    pub fn project_point<SB>(&self, p: &PointBase<N, U3, SB>) -> OwnedPoint<N, U3, SB::Alloc>
-        where SB: Storage<N, U3, U1> {
-
-        OwnedPoint::<N, U3, SB::Alloc>::new(
+    pub fn project_point(&self, p: &Point3<N>) -> Point3<N> {
+        Point3::new(
             self.matrix[(0, 0)] * p[0] + self.matrix[(0, 3)],
             self.matrix[(1, 1)] * p[1] + self.matrix[(1, 3)],
             self.matrix[(2, 2)] * p[2] + self.matrix[(2, 3)]
@@ -197,10 +188,9 @@ impl<N: Real, S: Storage<N, U4, U4>> OrthographicBase<N, S> {
 
     /// Un-projects a point. Faster than multiplication by the underlying matrix inverse.
     #[inline]
-    pub fn unproject_point<SB>(&self, p: &PointBase<N, U3, SB>) -> OwnedPoint<N, U3, SB::Alloc>
-        where SB: Storage<N, U3, U1> {
+    pub fn unproject_point(&self, p: &Point3<N>) -> Point3<N> {
 
-        OwnedPoint::<N, U3, SB::Alloc>::new(
+        Point3::new(
             (p[0] - self.matrix[(0, 3)]) / self.matrix[(0, 0)],
             (p[1] - self.matrix[(1, 3)]) / self.matrix[(1, 1)],
             (p[2] - self.matrix[(2, 3)]) / self.matrix[(2, 2)]
@@ -210,18 +200,16 @@ impl<N: Real, S: Storage<N, U4, U4>> OrthographicBase<N, S> {
     // FIXME: when we get specialization, specialize the Mul impl instead.
     /// Projects a vector. Faster than matrix multiplication.
     #[inline]
-    pub fn project_vector<SB>(&self, p: &ColumnVector<N, U3, SB>) -> OwnedColumnVector<N, U3, SB::Alloc>
-        where SB: Storage<N, U3, U1> {
+    pub fn project_vector<SB>(&self, p: &Vector<N, U3, SB>) -> Vector3<N>
+        where SB: Storage<N, U3> {
 
-        OwnedColumnVector::<N, U3, SB::Alloc>::new(
+        Vector3::new(
             self.matrix[(0, 0)] * p[0],
             self.matrix[(1, 1)] * p[1],
             self.matrix[(2, 2)] * p[2]
         )
     }
-}
 
-impl<N: Real, S: StorageMut<N, U4, U4>> OrthographicBase<N, S> {
     /// Sets the smallest x-coordinate of the view cuboid.
     #[inline]
     pub fn set_left(&mut self, left: N) {
@@ -289,10 +277,7 @@ impl<N: Real, S: StorageMut<N, U4, U4>> OrthographicBase<N, S> {
     }
 }
 
-impl<N, S> Rand for OrthographicBase<N, S>
-    where N: Real + Rand,
-          S: OwnedStorage<N, U4, U4>,
-          S::Alloc: OwnedAllocator<N, U4, U4, S> {
+impl<N: Real + Rand> Rand for Orthographic3<N> {
     fn rand<R: Rng>(r: &mut R) -> Self {
         let left   = Rand::rand(r);
         let right  = helper::reject_rand(r, |x: &N| *x > left);
@@ -306,10 +291,8 @@ impl<N, S> Rand for OrthographicBase<N, S>
 }
 
 #[cfg(feature="arbitrary")]
-impl<N, S> Arbitrary for OrthographicBase<N, S>
-    where N: Real + Arbitrary,
-          S: OwnedStorage<N, U4, U4> + Send,
-          S::Alloc: OwnedAllocator<N, U4, U4, S> {
+impl<N: Real + Arbitrary> Arbitrary for Orthographic3<N>
+    where Matrix4<N>: Send {
     fn arbitrary<G: Gen>(g: &mut G) -> Self {
         let left   = Arbitrary::arbitrary(g);
         let right  = helper::reject(g, |x: &N| *x > left);

src/geometry/perspective.rs

@@ -3,77 +3,71 @@ use quickcheck::{Arbitrary, Gen};
 use rand::{Rand, Rng};
 
 #[cfg(feature = "serde-serialize")]
-use serde::{Serialize, Serializer, Deserialize, Deserializer};
+use serde;
+use std::fmt;
 
 use alga::general::Real;
 
-use core::{Scalar, SquareMatrix, OwnedSquareMatrix, ColumnVector, OwnedColumnVector, MatrixArray};
-use core::dimension::{U1, U3, U4};
-use core::storage::{OwnedStorage, Storage, StorageMut};
-use core::allocator::OwnedAllocator;
+use core::{Scalar, Matrix4, Vector, Vector3};
+use core::dimension::U3;
+use core::storage::Storage;
 use core::helper;
 
-use geometry::{PointBase, OwnedPoint};
+use geometry::Point3;
 
 /// A 3D perspective projection stored as an homogeneous 4x4 matrix.
-#[derive(Debug, Clone, Copy)] // FIXME: Hash
-pub struct PerspectiveBase<N: Scalar, S: Storage<N, U4, U4>> {
-    matrix: SquareMatrix<N, U4, S>
+pub struct Perspective3<N: Scalar> {
+    matrix: Matrix4<N>
 }
 
-#[cfg(feature = "serde-serialize")]
-impl<N, S> Serialize for PerspectiveBase<N, S>
-    where N: Scalar,
-          S: Storage<N, U4, U4>,
-          SquareMatrix<N, U4, S>: Serialize,
-{
-    fn serialize<T>(&self, serializer: T) -> Result<T::Ok, T::Error>
-        where T: Serializer
-    {
-        self.matrix.serialize(serializer)
+impl<N: Real> Copy for Perspective3<N> { }
+
+impl<N: Real> Clone for Perspective3<N> {
+    #[inline]
+    fn clone(&self) -> Self {
+        Perspective3::from_matrix_unchecked(self.matrix.clone())
     }
 }
 
-#[cfg(feature = "serde-serialize")]
-impl<'de, N, S> Deserialize<'de> for PerspectiveBase<N, S>
-    where N: Scalar,
-          S: Storage<N, U4, U4>,
-          SquareMatrix<N, U4, S>: Deserialize<'de>,
-{
-    fn deserialize<T>(deserializer: T) -> Result<Self, T::Error>
-        where T: Deserializer<'de>
-    {
-        SquareMatrix::deserialize(deserializer).map(|x| PerspectiveBase { matrix: x })
+impl<N: Real> fmt::Debug for Perspective3<N> {
+    fn fmt(&self, f: &mut fmt::Formatter) -> Result<(), fmt::Error> {
+        self.matrix.fmt(f)
     }
 }
 
-/// A 3D perspective projection stored as a static homogeneous 4x4 matrix.
-pub type Perspective3<N> = PerspectiveBase<N, MatrixArray<N, U4, U4>>;
-
-impl<N, S> Eq for PerspectiveBase<N, S>
-    where N: Scalar + Eq,
-          S: Storage<N, U4, U4> { }
-
-impl<N, S> PartialEq for PerspectiveBase<N, S>
-    where N: Scalar,
-          S: Storage<N, U4, U4> {
+impl<N: Real> PartialEq for Perspective3<N> {
     #[inline]
     fn eq(&self, right: &Self) -> bool {
         self.matrix == right.matrix
     }
 }
 
-impl<N, S> PerspectiveBase<N, S>
-    where N: Real,
-          S: OwnedStorage<N, U4, U4>,
-          S::Alloc: OwnedAllocator<N, U4, U4, S> {
+#[cfg(feature = "serde-serialize")]
+impl<N: Real + serde::Serialize> serde::Serialize for Perspective3<N> {
+    fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
+        where S: serde::Serializer {
+            self.matrix.serialize(serializer)
+        }
+}
+
+#[cfg(feature = "serde-serialize")]
+impl<'a, N: Real + serde::Deserialize<'a>> serde::Deserialize<'a> for Perspective3<N> {
+    fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
+        where Des: serde::Deserializer<'a> {
+            let matrix = Matrix4::<N>::deserialize(deserializer)?;
+
+            Ok(Perspective3::from_matrix_unchecked(matrix))
+        }
+}
+
+impl<N: Real> Perspective3<N> {
     /// Creates a new perspective matrix from the aspect ratio, y field of view, and near/far planes.
     pub fn new(aspect: N, fovy: N, znear: N, zfar: N) -> Self {
         assert!(!relative_eq!(zfar - znear, N::zero()), "The near-plane and far-plane must not be superimposed.");
         assert!(!relative_eq!(aspect, N::zero()), "The apsect ratio must not be zero.");
 
-        let matrix = SquareMatrix::<N, U4, S>::identity();
-        let mut res = PerspectiveBase::from_matrix_unchecked(matrix);
+        let matrix = Matrix4::identity();
+        let mut res = Perspective3::from_matrix_unchecked(matrix);
 
         res.set_fovy(fovy);
         res.set_aspect(aspect);
@@ -91,32 +85,15 @@ impl<N, S> PerspectiveBase<N, S>
     /// It is not checked whether or not the given matrix actually represents an orthographic
     /// projection.
     #[inline]
-    pub fn from_matrix_unchecked(matrix: SquareMatrix<N, U4, S>) -> Self {
-        PerspectiveBase {
+    pub fn from_matrix_unchecked(matrix: Matrix4<N>) -> Self {
+        Perspective3 {
             matrix: matrix
         }
     }
-}
-
-impl<N, S> PerspectiveBase<N, S>
-    where N: Real,
-          S: Storage<N, U4, U4> {
-
-    /// A reference to the underlying homogeneous transformation matrix.
-    #[inline]
-    pub fn as_matrix(&self) -> &SquareMatrix<N, U4, S> {
-        &self.matrix
-    }
-
-    /// Retrieves the underlying homogeneous matrix.
-    #[inline]
-    pub fn unwrap(self) -> SquareMatrix<N, U4, S> {
-        self.matrix
-    }
 
     /// Retrieves the inverse of the underlying homogeneous matrix.
     #[inline]
-    pub fn inverse(&self) -> OwnedSquareMatrix<N, U4, S::Alloc> {
+    pub fn inverse(&self) -> Matrix4<N> {
         let mut res = self.to_homogeneous();
 
         res[(0, 0)] = N::one() / self.matrix[(0, 0)];
@@ -135,10 +112,22 @@ impl<N, S> PerspectiveBase<N, S>
 
     /// Computes the corresponding homogeneous matrix.
     #[inline]
-    pub fn to_homogeneous(&self) -> OwnedSquareMatrix<N, U4, S::Alloc> {
+    pub fn to_homogeneous(&self) -> Matrix4<N> {
         self.matrix.clone_owned()
     }
 
+    /// A reference to the underlying homogeneous transformation matrix.
+    #[inline]
+    pub fn as_matrix(&self) -> &Matrix4<N> {
+        &self.matrix
+    }
+
+    /// Retrieves the underlying homogeneous matrix.
+    #[inline]
+    pub fn unwrap(self) -> Matrix4<N> {
+        self.matrix
+    }
+
     /// Gets the `width / height` aspect ratio of the view frustrum.
     #[inline]
     pub fn aspect(&self) -> N {
@@ -174,11 +163,9 @@ impl<N, S> PerspectiveBase<N, S>
     // FIXME: when we get specialization, specialize the Mul impl instead.
     /// Projects a point. Faster than matrix multiplication.
     #[inline]
-    pub fn project_point<SB>(&self, p: &PointBase<N, U3, SB>) -> OwnedPoint<N, U3, SB::Alloc>
-        where SB: Storage<N, U3, U1> {
-
+    pub fn project_point(&self, p: &Point3<N>) -> Point3<N> {
         let inverse_denom = -N::one() / p[2];
-        OwnedPoint::<N, U3, SB::Alloc>::new(
+        Point3::new(
              self.matrix[(0, 0)] * p[0] * inverse_denom,
              self.matrix[(1, 1)] * p[1] * inverse_denom,
             (self.matrix[(2, 2)] * p[2] + self.matrix[(2, 3)]) * inverse_denom
@@ -187,12 +174,10 @@ impl<N, S> PerspectiveBase<N, S>
 
     /// Un-projects a point. Faster than multiplication by the matrix inverse.
     #[inline]
-    pub fn unproject_point<SB>(&self, p: &PointBase<N, U3, SB>) -> OwnedPoint<N, U3, SB::Alloc>
-        where SB: Storage<N, U3, U1> {
-
+    pub fn unproject_point(&self, p: &Point3<N>) -> Point3<N> {
         let inverse_denom = self.matrix[(2, 3)] / (p[2] + self.matrix[(2, 2)]);
 
-        OwnedPoint::<N, U3, SB::Alloc>::new(
+        Point3::new(
             p[0] * inverse_denom / self.matrix[(0, 0)],
             p[1] * inverse_denom / self.matrix[(1, 1)],
             -inverse_denom
@@ -202,22 +187,17 @@ impl<N, S> PerspectiveBase<N, S>
     // FIXME: when we get specialization, specialize the Mul impl instead.
     /// Projects a vector. Faster than matrix multiplication.
     #[inline]
-    pub fn project_vector<SB>(&self, p: &ColumnVector<N, U3, SB>) -> OwnedColumnVector<N, U3, SB::Alloc>
-        where SB: Storage<N, U3, U1> {
+    pub fn project_vector<SB>(&self, p: &Vector<N, U3, SB>) -> Vector3<N>
+        where SB: Storage<N, U3> {
 
         let inverse_denom = -N::one() / p[2];
-        OwnedColumnVector::<N, U3, SB::Alloc>::new(
+        Vector3::new(
             self.matrix[(0, 0)] * p[0] * inverse_denom,
             self.matrix[(1, 1)] * p[1] * inverse_denom,
             self.matrix[(2, 2)]
         )
     }
-}
 
-
-impl<N, S> PerspectiveBase<N, S>
-    where N: Real,
-          S: StorageMut<N, U4, U4> {
     /// Updates this perspective matrix with a new `width / height` aspect ratio of the view
     /// frustrum.
     #[inline]
@@ -256,10 +236,7 @@ impl<N, S> PerspectiveBase<N, S>
     }
 }
 
-impl<N, S> Rand for PerspectiveBase<N, S>
-    where N: Real + Rand,
-          S: OwnedStorage<N, U4, U4>,
-          S::Alloc: OwnedAllocator<N, U4, U4, S> {
+impl<N: Real + Rand> Rand for Perspective3<N> {
     fn rand<R: Rng>(r: &mut R) -> Self {
         let znear  = Rand::rand(r);
         let zfar   = helper::reject_rand(r, |&x: &N| !(x - znear).is_zero());
@@ -270,10 +247,7 @@ impl<N, S> Rand for PerspectiveBase<N, S>
 }
 
 #[cfg(feature="arbitrary")]
-impl<N, S> Arbitrary for PerspectiveBase<N, S>
-    where N: Real + Arbitrary,
-          S: OwnedStorage<N, U4, U4> + Send,
-          S::Alloc: OwnedAllocator<N, U4, U4, S> {
+impl<N: Real + Arbitrary> Arbitrary for Perspective3<N> {
     fn arbitrary<G: Gen>(g: &mut G) -> Self {
         let znear  = Arbitrary::arbitrary(g);
         let zfar   = helper::reject(g, |&x: &N| !(x - znear).is_zero());

src/geometry/point.rs

@@ -1,101 +1,103 @@
 use num::One;
+use std::hash;
 use std::fmt;
 use std::cmp::Ordering;
 use approx::ApproxEq;
 
 #[cfg(feature = "serde-serialize")]
-use serde::{Serialize, Serializer, Deserialize, Deserializer};
+use serde;
 
-use core::{Scalar, ColumnVector, OwnedColumnVector};
+use core::{DefaultAllocator, Scalar, VectorN};
 use core::iter::{MatrixIter, MatrixIterMut};
 use core::dimension::{DimName, DimNameSum, DimNameAdd, U1};
-use core::storage::{Storage, StorageMut, MulStorage};
-use core::allocator::{Allocator, SameShapeR};
-
-// XXX Bad name: we can't even add points…
-/// The type of the result of the sum of a point with a vector.
-pub type PointSum<N, D1, D2, SA> =
-    PointBase<N, SameShapeR<D1, D2>,
-    <<SA as Storage<N, D1, U1>>::Alloc as Allocator<N, SameShapeR<D1, D2>, U1>>::Buffer>;
-
-/// The type of the result of the multiplication of a point by a matrix.
-pub type PointMul<N, R1, C1, SA> = PointBase<N, R1, MulStorage<N, R1, C1, U1, SA>>;
-
-/// A point with an owned storage.
-pub type OwnedPoint<N, D, A> = PointBase<N, D, <A as Allocator<N, D, U1>>::Buffer>;
+use core::allocator::Allocator;
 
 /// A point in a n-dimensional euclidean space.
 #[repr(C)]
-#[derive(Hash, Debug)]
-pub struct PointBase<N: Scalar, D: DimName, S: Storage<N, D, U1>> {
+#[derive(Debug)]
+pub struct Point<N: Scalar, D: DimName>
+    where DefaultAllocator: Allocator<N, D> {
     /// The coordinates of this point, i.e., the shift from the origin.
-    pub coords: ColumnVector<N, D, S>
+    pub coords: VectorN<N, D>
 }
 
-impl<N, D, S> Copy for PointBase<N, D, S>
-    where N: Scalar,
-          D: DimName,
-          S: Storage<N, D, U1> + Copy { }
+impl<N: Scalar + hash::Hash, D: DimName + hash::Hash> hash::Hash for Point<N, D>
+    where DefaultAllocator: Allocator<N, D>,
+          <DefaultAllocator as Allocator<N, D>>::Buffer: hash::Hash {
+    fn hash<H: hash::Hasher>(&self, state: &mut H) {
+        self.coords.hash(state)
+    }
+}
 
-impl<N, D, S> Clone for PointBase<N, D, S>
-    where N: Scalar,
-          D: DimName,
-          S: Storage<N, D, U1> + Clone {
+impl<N: Scalar, D: DimName> Copy for Point<N, D>
+    where DefaultAllocator: Allocator<N, D>,
+          <DefaultAllocator as Allocator<N, D>>::Buffer: Copy { }
+
+impl<N: Scalar, D: DimName> Clone for Point<N, D>
+    where DefaultAllocator: Allocator<N, D>,
+          <DefaultAllocator as Allocator<N, D>>::Buffer: Clone {
     #[inline]
     fn clone(&self) -> Self {
-        PointBase::from_coordinates(self.coords.clone())
+        Point::from_coordinates(self.coords.clone())
     }
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<N, D, S> Serialize for PointBase<N, D, S>
-    where N: Scalar,
-          D: DimName,
-          S: Storage<N, D, U1>,
-          ColumnVector<N, D, S>: Serialize,
-{
-    fn serialize<T>(&self, serializer: T) -> Result<T::Ok, T::Error>
-        where T: Serializer
-    {
+impl<N: Scalar, D: DimName> serde::Serialize for Point<N, D>
+where DefaultAllocator: Allocator<N, D>,
+      <DefaultAllocator as Allocator<N, D>>::Buffer: serde::Serialize {
+
+    fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
+        where S: serde::Serializer {
             self.coords.serialize(serializer)
         }
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<'de, N, D, S> Deserialize<'de> for PointBase<N, D, S>
-    where N: Scalar,
-          D: DimName,
-          S: Storage<N, D, U1>,
-          ColumnVector<N, D, S>: Deserialize<'de>,
-{
-    fn deserialize<T>(deserializer: T) -> Result<Self, T::Error>
-        where T: Deserializer<'de>
-    {
-        ColumnVector::deserialize(deserializer).map(|x| PointBase { coords: x })
+impl<'a, N: Scalar, D: DimName> serde::Deserialize<'a> for Point<N, D>
+where DefaultAllocator: Allocator<N, D>,
+      <DefaultAllocator as Allocator<N, D>>::Buffer: serde::Deserialize<'a> {
+
+    fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
+        where Des: serde::Deserializer<'a> {
+            let coords = VectorN::<N, D>::deserialize(deserializer)?;
+
+            Ok(Point::from_coordinates(coords))
         }
 }
 
-impl<N: Scalar, D: DimName, S: Storage<N, D, U1>> PointBase<N, D, S> {
-    /// Creates a new point with the given coordinates.
-    #[inline]
-    pub fn from_coordinates(coords: ColumnVector<N, D, S>) -> PointBase<N, D, S> {
-        PointBase {
-            coords: coords
-        }
-    }
-}
-
-impl<N: Scalar, D: DimName, S: Storage<N, D, U1>> PointBase<N, D, S> {
-    /// Moves this point into one that owns its data.
-    #[inline]
-    pub fn into_owned(self) -> OwnedPoint<N, D, S::Alloc> {
-        PointBase::from_coordinates(self.coords.into_owned())
-    }
+impl<N: Scalar, D: DimName> Point<N, D>
+    where DefaultAllocator: Allocator<N, D> {
 
     /// Clones this point into one that owns its data.
     #[inline]
-    pub fn clone_owned(&self) -> OwnedPoint<N, D, S::Alloc> {
-        PointBase::from_coordinates(self.coords.clone_owned())
+    pub fn clone(&self) -> Point<N, D> {
+        Point::from_coordinates(self.coords.clone_owned())
+    }
+
+    /// Converts this point into a vector in homogeneous coordinates, i.e., appends a `1` at the
+    /// end of it.
+    #[inline]
+    pub fn to_homogeneous(&self) -> VectorN<N, DimNameSum<D, U1>>
+        where N: One,
+              D: DimNameAdd<U1>,
+              DefaultAllocator: Allocator<N, DimNameSum<D, U1>> {
+
+        let mut res = unsafe {
+            VectorN::<_, DimNameSum<D, U1>>::new_uninitialized()
+        };
+        res.fixed_slice_mut::<D, U1>(0, 0).copy_from(&self.coords);
+        res[(D::dim(), 0)] = N::one();
+
+        res
+    }
+
+    /// Creates a new point with the given coordinates.
+    #[inline]
+    pub fn from_coordinates(coords: VectorN<N, D>) -> Point<N, D> {
+        Point {
+            coords: coords
+        }
     }
 
     /// The dimension of this point.
@@ -113,44 +115,26 @@ impl<N: Scalar, D: DimName, S: Storage<N, D, U1>> PointBase<N, D, S> {
 
     /// Iterates through this point coordinates.
     #[inline]
-    pub fn iter(&self) -> MatrixIter<N, D, U1, S> {
+    pub fn iter(&self) -> MatrixIter<N, D, U1, <DefaultAllocator as Allocator<N, D>>::Buffer> {
         self.coords.iter()
     }
 
     /// Gets a reference to i-th element of this point without bound-checking.
     #[inline]
     pub unsafe fn get_unchecked(&self, i: usize) -> &N {
-        self.coords.get_unchecked(i, 0)
+        self.coords.vget_unchecked(i)
     }
 
-
-    /// Converts this point into a vector in homogeneous coordinates, i.e., appends a `1` at the
-    /// end of it.
-    #[inline]
-    pub fn to_homogeneous(&self) -> OwnedColumnVector<N, DimNameSum<D, U1>, S::Alloc>
-        where N: One,
-              D: DimNameAdd<U1>,
-              S::Alloc: Allocator<N, DimNameSum<D, U1>, U1> {
-
-        let mut res = unsafe { OwnedColumnVector::<N, _, S::Alloc>::new_uninitialized() };
-        res.fixed_slice_mut::<D, U1>(0, 0).copy_from(&self.coords);
-        res[(D::dim(), 0)] = N::one();
-
-        res
-    }
-}
-
-impl<N: Scalar, D: DimName, S: StorageMut<N, D, U1>> PointBase<N, D, S> {
     /// Mutably iterates through this point coordinates.
     #[inline]
-    pub fn iter_mut(&mut self) -> MatrixIterMut<N, D, U1, S> {
+    pub fn iter_mut(&mut self) -> MatrixIterMut<N, D, U1, <DefaultAllocator as Allocator<N, D>>::Buffer> {
         self.coords.iter_mut()
     }
 
     /// Gets a mutable reference to i-th element of this point without bound-checking.
     #[inline]
     pub unsafe fn get_unchecked_mut(&mut self, i: usize) -> &mut N {
-        self.coords.get_unchecked_mut(i, 0)
+        self.coords.vget_unchecked_mut(i)
     }
 
     /// Swaps two entries without bound-checking.
@@ -160,9 +144,8 @@ impl<N: Scalar, D: DimName, S: StorageMut<N, D, U1>> PointBase<N, D, S> {
     }
 }
 
-impl<N, D: DimName, S> ApproxEq for PointBase<N, D, S>
-    where N: Scalar + ApproxEq,
-          S: Storage<N, D, U1>,
+impl<N: Scalar + ApproxEq, D: DimName> ApproxEq for Point<N, D>
+    where DefaultAllocator: Allocator<N, D>,
           N::Epsilon: Copy {
     type Epsilon = N::Epsilon;
 
@@ -192,22 +175,19 @@ impl<N, D: DimName, S> ApproxEq for PointBase<N, D, S>
     }
 }
 
-impl<N, D: DimName, S> Eq for PointBase<N, D, S>
-    where N: Scalar + Eq,
-          S: Storage<N, D, U1> { }
+impl<N: Scalar + Eq, D: DimName> Eq for Point<N, D>
+    where DefaultAllocator: Allocator<N, D> { }
 
-impl<N, D: DimName, S> PartialEq for PointBase<N, D, S>
-    where N: Scalar,
-          S: Storage<N, D, U1> {
+impl<N: Scalar, D: DimName> PartialEq for Point<N, D>
+    where DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn eq(&self, right: &Self) -> bool {
         self.coords == right.coords
     }
 }
 
-impl<N, D: DimName, S> PartialOrd for PointBase<N, D, S>
-    where N: Scalar + PartialOrd,
-          S: Storage<N, D, U1> {
+impl<N: Scalar + PartialOrd, D: DimName> PartialOrd for Point<N, D>
+    where DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
         self.coords.partial_cmp(&other.coords)
@@ -239,9 +219,8 @@ impl<N, D: DimName, S> PartialOrd for PointBase<N, D, S>
  * Display
  *
  */
-impl<N, D: DimName, S> fmt::Display for PointBase<N, D, S>
-    where N: Scalar + fmt::Display,
-          S: Storage<N, D, U1> {
+impl<N: Scalar + fmt::Display, D: DimName> fmt::Display for Point<N, D>
+    where DefaultAllocator: Allocator<N, D> {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         try!(write!(f, "{{"));
 

src/geometry/point_alga.rs

@@ -1,26 +1,22 @@
 use alga::general::{Field, Real, MeetSemilattice, JoinSemilattice, Lattice};
 use alga::linear::{AffineSpace, EuclideanSpace};
 
-use core::{ColumnVector, Scalar};
-use core::dimension::{DimName, U1};
-use core::storage::OwnedStorage;
-use core::allocator::OwnedAllocator;
+use core::{DefaultAllocator, Scalar, VectorN};
+use core::dimension::DimName;
+use core::allocator::Allocator;
 
-use geometry::PointBase;
+use geometry::Point;
 
 
-impl<N, D: DimName, S> AffineSpace for PointBase<N, D, S>
+impl<N: Scalar + Field, D: DimName> AffineSpace for Point<N, D>
     where N: Scalar + Field,
-          S: OwnedStorage<N, D, U1>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
-    type Translation = ColumnVector<N, D, S>;
+          DefaultAllocator: Allocator<N, D> {
+    type Translation = VectorN<N, D>;
 }
 
-impl<N, D: DimName, S> EuclideanSpace for PointBase<N, D, S>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
-    type Coordinates = ColumnVector<N, D, S>;
+impl<N: Real, D: DimName> EuclideanSpace for Point<N, D>
+    where DefaultAllocator: Allocator<N, D> {
+    type Coordinates = VectorN<N, D>;
     type Real        = N;
 
     #[inline]
@@ -49,35 +45,32 @@ impl<N, D: DimName, S> EuclideanSpace for PointBase<N, D, S>
  * Ordering
  *
  */
-impl<N, D: DimName, S> MeetSemilattice for PointBase<N, D, S>
+impl<N, D: DimName> MeetSemilattice for Point<N, D>
     where N: Scalar + MeetSemilattice,
-          S: OwnedStorage<N, D, U1>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn meet(&self, other: &Self) -> Self {
-        PointBase::from_coordinates(self.coords.meet(&other.coords))
+        Point::from_coordinates(self.coords.meet(&other.coords))
     }
 }
 
-impl<N, D: DimName, S> JoinSemilattice for PointBase<N, D, S>
+impl<N, D: DimName> JoinSemilattice for Point<N, D>
     where N: Scalar + JoinSemilattice,
-          S: OwnedStorage<N, D, U1>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn join(&self, other: &Self) -> Self {
-        PointBase::from_coordinates(self.coords.join(&other.coords))
+        Point::from_coordinates(self.coords.join(&other.coords))
     }
 }
 
 
-impl<N, D: DimName, S> Lattice for PointBase<N, D, S>
+impl<N, D: DimName> Lattice for Point<N, D>
     where N: Scalar + Lattice,
-          S: OwnedStorage<N, D, U1>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn meet_join(&self, other: &Self) -> (Self, Self) {
         let (meet, join) = self.coords.meet_join(&other.coords);
 
-        (PointBase::from_coordinates(meet), PointBase::from_coordinates(join))
+        (Point::from_coordinates(meet), Point::from_coordinates(join))
     }
 }

src/geometry/point_alias.rs

@@ -1,10 +1,6 @@
-use core::MatrixArray;
 use core::dimension::{U1, U2, U3, U4, U5, U6};
 
-use geometry::PointBase;
-
-/// A statically sized D-dimensional column point.
-pub type Point<N, D> = PointBase<N, D, MatrixArray<N, D, U1>>;
+use geometry::Point;
 
 /// A statically sized 1-dimensional column point.
 pub type Point1<N> = Point<N, U1>;

src/geometry/point_construction.rs

@@ -5,28 +5,25 @@ use rand::{Rand, Rng};
 use num::{Zero, One, Bounded};
 
 use alga::general::ClosedDiv;
-use core::{Scalar, ColumnVector};
-use core::storage::{Storage, OwnedStorage};
-use core::allocator::{Allocator, OwnedAllocator};
+use core::{DefaultAllocator, Scalar, VectorN};
+use core::allocator::Allocator;
 use core::dimension::{DimName, DimNameAdd, DimNameSum, U1, U2, U3, U4, U5, U6};
 
-use geometry::PointBase;
+use geometry::Point;
 
-impl<N, D: DimName, S> PointBase<N, D, S>
-    where N: Scalar,
-          S: OwnedStorage<N, D, U1>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Scalar, D: DimName> Point<N, D>
+    where DefaultAllocator: Allocator<N, D> {
     /// Creates a new point with uninitialized coordinates.
     #[inline]
     pub unsafe fn new_uninitialized() -> Self {
-        Self::from_coordinates(ColumnVector::<_, D, _>::new_uninitialized())
+        Self::from_coordinates(VectorN::new_uninitialized())
     }
 
     /// Creates a new point with all coordinates equal to zero.
     #[inline]
     pub fn origin() -> Self
         where N: Zero {
-        Self::from_coordinates(ColumnVector::<_, D, _>::from_element(N::zero()))
+        Self::from_coordinates(VectorN::from_element(N::zero()))
     }
 
     /// Creates a new point from its homogeneous vector representation.
@@ -34,11 +31,10 @@ impl<N, D: DimName, S> PointBase<N, D, S>
     /// In practice, this builds a D-dimensional points with the same first D component as `v`
     /// divided by the last component of `v`. Returns `None` if this divisor is zero.
     #[inline]
-    pub fn from_homogeneous<SB>(v: ColumnVector<N, DimNameSum<D, U1>, SB>) -> Option<Self>
+    pub fn from_homogeneous(v: VectorN<N, DimNameSum<D, U1>>) -> Option<Self>
         where N: Scalar + Zero + One + ClosedDiv,
               D: DimNameAdd<U1>,
-              SB: Storage<N, DimNameSum<D, U1>, U1, Alloc = S::Alloc>,
-              S::Alloc: Allocator<N, DimNameSum<D, U1>, U1> {
+              DefaultAllocator: Allocator<N, DimNameSum<D, U1>> {
 
         if !v[D::dim()].is_zero() {
             let coords =  v.fixed_slice::<D, U1>(0, 0) / v[D::dim()];
@@ -56,39 +52,34 @@ impl<N, D: DimName, S> PointBase<N, D, S>
  * Traits that buid points.
  *
  */
-impl<N, D: DimName, S> Bounded for PointBase<N, D, S>
-    where N: Scalar + Bounded,
-          S: OwnedStorage<N, D, U1>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Scalar + Bounded, D: DimName> Bounded for Point<N, D>
+    where DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn max_value() -> Self {
-        Self::from_coordinates(ColumnVector::max_value())
+        Self::from_coordinates(VectorN::max_value())
     }
 
     #[inline]
     fn min_value() -> Self {
-        Self::from_coordinates(ColumnVector::min_value())
+        Self::from_coordinates(VectorN::min_value())
     }
 }
 
-impl<N, D: DimName, S> Rand for PointBase<N, D, S>
-    where N: Scalar + Rand,
-          S: OwnedStorage<N, D, U1>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Scalar + Rand, D: DimName> Rand for Point<N, D>
+    where DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn rand<G: Rng>(rng: &mut G) -> Self {
-        PointBase::from_coordinates(rng.gen())
+        Point::from_coordinates(rng.gen())
     }
 }
 
 #[cfg(feature="arbitrary")]
-impl<N, D: DimName, S> Arbitrary for PointBase<N, D, S>
-    where N: Scalar + Arbitrary + Send,
-          S: OwnedStorage<N, D, U1> + Send,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Scalar + Arbitrary + Send, D: DimName> Arbitrary for Point<N, D>
+    where DefaultAllocator: Allocator<N, D>,
+          <DefaultAllocator as Allocator<N, D>>::Buffer: Send {
     #[inline]
     fn arbitrary<G: Gen>(g: &mut G) -> Self {
-        PointBase::from_coordinates(ColumnVector::arbitrary(g))
+        Point::from_coordinates(VectorN::arbitrary(g))
     }
 }
 
@@ -99,13 +90,11 @@ impl<N, D: DimName, S> Arbitrary for PointBase<N, D, S>
  */
 macro_rules! componentwise_constructors_impl(
     ($($D: ty, $($args: ident:$irow: expr),*);* $(;)*) => {$(
-        impl<N, S> PointBase<N, $D, S>
-            where N: Scalar,
-                  S: OwnedStorage<N, $D, U1>,
-                  S::Alloc: OwnedAllocator<N, $D, U1, S> {
+        impl<N: Scalar> Point<N, $D>
+            where DefaultAllocator: Allocator<N, $D> {
             /// Initializes this matrix from its components.
             #[inline]
-            pub fn new($($args: N),*) -> PointBase<N, $D, S> {
+            pub fn new($($args: N),*) -> Point<N, $D> {
                 unsafe {
                     let mut res = Self::new_uninitialized();
                     $( *res.get_unchecked_mut($irow) = $args; )*

src/geometry/point_conversion.rs

@@ -1,72 +1,67 @@
 use num::{One, Zero};
 use alga::general::{SubsetOf, SupersetOf, ClosedDiv};
 
-use core::{Scalar, Matrix, ColumnVector, OwnedColumnVector};
+use core::{DefaultAllocator, Scalar, Matrix, VectorN};
 use core::dimension::{DimName, DimNameSum, DimNameAdd, U1};
-use core::storage::OwnedStorage;
-use core::allocator::{Allocator, OwnedAllocator};
+use core::allocator::Allocator;
 
-use geometry::{PointBase, OwnedPoint};
+use geometry::Point;
 
 /*
  * This file provides the following conversions:
  * =============================================
  *
- * PointBase -> PointBase
- * PointBase -> ColumnVector (homogeneous)
+ * Point -> Point
+ * Point -> Vector (homogeneous)
  */
 
-impl<N1, N2, D, SA, SB> SubsetOf<PointBase<N2, D, SB>> for PointBase<N1, D, SA>
+impl<N1, N2, D> SubsetOf<Point<N2, D>> for Point<N1, D>
     where D: DimName,
           N1: Scalar,
           N2: Scalar + SupersetOf<N1>,
-          SA: OwnedStorage<N1, D, U1>,
-          SB: OwnedStorage<N2, D, U1>,
-          SB::Alloc: OwnedAllocator<N2, D, U1, SB>,
-          SA::Alloc: OwnedAllocator<N1, D, U1, SA> {
+          DefaultAllocator: Allocator<N2, D> +
+                            Allocator<N1, D> {
     #[inline]
-    fn to_superset(&self) -> PointBase<N2, D, SB> {
-        PointBase::from_coordinates(self.coords.to_superset())
+    fn to_superset(&self) -> Point<N2, D> {
+        Point::from_coordinates(self.coords.to_superset())
     }
 
     #[inline]
-    fn is_in_subset(m: &PointBase<N2, D, SB>) -> bool {
+    fn is_in_subset(m: &Point<N2, D>) -> bool {
         // FIXME: is there a way to reuse the `.is_in_subset` from the matrix implementation of
         // SubsetOf?
         m.iter().all(|e| e.is_in_subset())
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(m: &PointBase<N2, D, SB>) -> Self {
-        PointBase::from_coordinates(Matrix::from_superset_unchecked(&m.coords))
+    unsafe fn from_superset_unchecked(m: &Point<N2, D>) -> Self {
+        Point::from_coordinates(Matrix::from_superset_unchecked(&m.coords))
     }
 }
 
 
-impl<N1, N2, D, SA, SB> SubsetOf<ColumnVector<N2, DimNameSum<D, U1>, SB>> for PointBase<N1, D, SA>
+impl<N1, N2, D> SubsetOf<VectorN<N2, DimNameSum<D, U1>>> for Point<N1, D>
     where D:  DimNameAdd<U1>,
           N1: Scalar,
           N2: Scalar + Zero + One + ClosedDiv + SupersetOf<N1>,
-          SA: OwnedStorage<N1, D, U1>,
-          SB: OwnedStorage<N2, DimNameSum<D, U1>, U1>,
-          SA::Alloc: OwnedAllocator<N1, D, U1, SA> +
-                     Allocator<N1, DimNameSum<D, U1>, U1>,
-          SB::Alloc: OwnedAllocator<N2, DimNameSum<D, U1>, U1, SB> +
-                     Allocator<N2, D, U1> {
+          DefaultAllocator: Allocator<N1, D>                 +
+                            Allocator<N1, DimNameSum<D, U1>> +
+                            Allocator<N2, DimNameSum<D, U1>> +
+                            Allocator<N2, D> {
     #[inline]
-    fn to_superset(&self) -> ColumnVector<N2, DimNameSum<D, U1>, SB> {
-        let p: OwnedPoint<N2, D, SB::Alloc> = self.to_superset();
+    fn to_superset(&self) -> VectorN<N2, DimNameSum<D, U1>> {
+        let p: Point<N2, D> = self.to_superset();
         p.to_homogeneous()
     }
 
     #[inline]
-    fn is_in_subset(v: &ColumnVector<N2, DimNameSum<D, U1>, SB>) -> bool {
-        ::is_convertible::<_, OwnedColumnVector<N1, DimNameSum<D, U1>, SA::Alloc>>(v) &&
+    fn is_in_subset(v: &VectorN<N2, DimNameSum<D, U1>>) -> bool {
+        ::is_convertible::<_, VectorN<N1, DimNameSum<D, U1>>>(v) &&
         !v[D::dim()].is_zero()
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(v: &ColumnVector<N2, DimNameSum<D, U1>, SB>) -> Self {
+    unsafe fn from_superset_unchecked(v: &VectorN<N2, DimNameSum<D, U1>>) -> Self {
         let coords =  v.fixed_slice::<D, U1>(0, 0) / v[D::dim()];
         Self::from_coordinates(::convert_unchecked(coords))
     }

src/geometry/point_coordinates.rs

@@ -1,25 +1,23 @@
 use std::mem;
 use std::ops::{Deref, DerefMut};
 
-use core::Scalar;
+use core::{DefaultAllocator, Scalar};
 use core::dimension::{U1, U2, U3, U4, U5, U6};
 use core::coordinates::{X, XY, XYZ, XYZW, XYZWA, XYZWAB};
-use core::allocator::OwnedAllocator;
-use core::storage::OwnedStorage;
+use core::allocator::Allocator;
 
-use geometry::PointBase;
+use geometry::Point;
 
 /*
  *
- * Give coordinates to PointBase{1 .. 6}
+ * Give coordinates to Point{1 .. 6}
  *
  */
 
 macro_rules! deref_impl(
     ($D: ty, $Target: ident $(, $comps: ident)*) => {
-        impl<N: Scalar, S> Deref for PointBase<N, $D, S>
-            where S: OwnedStorage<N, $D, U1>,
-                  S::Alloc: OwnedAllocator<N, $D, U1, S> {
+        impl<N: Scalar> Deref for Point<N, $D>
+            where DefaultAllocator: Allocator<N, $D> {
             type Target = $Target<N>;
 
             #[inline]
@@ -28,9 +26,8 @@ macro_rules! deref_impl(
             }
         }
 
-        impl<N: Scalar, S> DerefMut for PointBase<N, $D, S>
-            where S: OwnedStorage<N, $D, U1>,
-                  S::Alloc: OwnedAllocator<N, $D, U1, S> {
+        impl<N: Scalar> DerefMut for Point<N, $D>
+            where DefaultAllocator: Allocator<N, $D> {
             #[inline]
             fn deref_mut(&mut self) -> &mut Self::Target {
                 unsafe { mem::transmute(self) }

src/geometry/point_ops.rs

@@ -1,15 +1,15 @@
 use std::ops::{Neg, Add, AddAssign, Sub, SubAssign, Mul, MulAssign, Div, DivAssign, Index, IndexMut};
-use num::Zero;
+use num::{Zero, One};
 
 use alga::general::{ClosedNeg, ClosedAdd, ClosedSub, ClosedMul, ClosedDiv};
 
-use core::{Scalar, ColumnVector, Matrix, ColumnVectorSum};
+use core::{DefaultAllocator, Scalar, Vector, Matrix, VectorSum};
 use core::dimension::{Dim, DimName, U1};
 use core::constraint::{ShapeConstraint, SameNumberOfRows, SameNumberOfColumns, AreMultipliable};
-use core::storage::{Storage, StorageMut};
+use core::storage::Storage;
 use core::allocator::{SameShapeAllocator, Allocator};
 
-use geometry::{PointBase, OwnedPoint, PointMul};
+use geometry::Point;
 
 
 /*
@@ -17,9 +17,8 @@ use geometry::{PointBase, OwnedPoint, PointMul};
  * Indexing.
  *
  */
-impl<N, D: DimName, S> Index<usize> for PointBase<N, D, S>
-    where N: Scalar,
-          S: Storage<N, D, U1> {
+impl<N: Scalar, D: DimName> Index<usize> for Point<N, D>
+    where DefaultAllocator: Allocator<N, D> {
     type Output = N;
 
     #[inline]
@@ -28,9 +27,8 @@ impl<N, D: DimName, S> Index<usize> for PointBase<N, D, S>
     }
 }
 
-impl<N, D: DimName, S> IndexMut<usize> for PointBase<N, D, S>
-    where N: Scalar,
-          S: StorageMut<N, D, U1> {
+impl<N: Scalar, D: DimName> IndexMut<usize> for Point<N, D>
+    where DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn index_mut(&mut self, i: usize) -> &mut Self::Output {
         &mut self.coords[i]
@@ -38,28 +36,27 @@ impl<N, D: DimName, S> IndexMut<usize> for PointBase<N, D, S>
 }
 
 /*
+ *
  * Neg.
  *
  */
-impl<N, D: DimName, S> Neg for PointBase<N, D, S>
-    where N: Scalar + ClosedNeg,
-          S: Storage<N, D, U1> {
-    type Output = OwnedPoint<N, D, S::Alloc>;
+impl<N: Scalar + ClosedNeg, D: DimName> Neg for Point<N, D>
+    where DefaultAllocator: Allocator<N, D> {
+    type Output = Point<N, D>;
 
     #[inline]
     fn neg(self) -> Self::Output {
-        PointBase::from_coordinates(-self.coords)
+        Point::from_coordinates(-self.coords)
     }
 }
 
-impl<'a, N, D: DimName, S> Neg for &'a PointBase<N, D, S>
-    where N: Scalar + ClosedNeg,
-          S: Storage<N, D, U1> {
-    type Output = OwnedPoint<N, D, S::Alloc>;
+impl<'a, N: Scalar + ClosedNeg, D: DimName> Neg for &'a Point<N, D>
+    where DefaultAllocator: Allocator<N, D> {
+    type Output = Point<N, D>;
 
     #[inline]
     fn neg(self) -> Self::Output {
-        PointBase::from_coordinates(-&self.coords)
+        Point::from_coordinates(-&self.coords)
     }
 }
 
@@ -69,94 +66,94 @@ impl<'a, N, D: DimName, S> Neg for &'a PointBase<N, D, S>
  *
  */
 
-// PointBase - PointBase
+// Point - Point
 add_sub_impl!(Sub, sub, ClosedSub;
     (D, U1), (D, U1) for D: DimName;
-    self: &'a PointBase<N, D, SA>, right: &'b PointBase<N, D, SB>, Output = ColumnVectorSum<N, D, D, SA>;
+    self: &'a Point<N, D>, right: &'b Point<N, D>, Output = VectorSum<N, D, D>;
     &self.coords - &right.coords; 'a, 'b);
 
 add_sub_impl!(Sub, sub, ClosedSub;
     (D, U1), (D, U1) for D: DimName;
-    self: &'a PointBase<N, D, SB>, right: PointBase<N, D, SA>, Output = ColumnVectorSum<N, D, D, SA>;
+    self: &'a Point<N, D>, right: Point<N, D>, Output = VectorSum<N, D, D>;
     &self.coords - right.coords; 'a);
 
 add_sub_impl!(Sub, sub, ClosedSub;
     (D, U1), (D, U1) for D: DimName;
-    self: PointBase<N, D, SA>, right: &'b PointBase<N, D, SB>, Output = ColumnVectorSum<N, D, D, SA>;
+    self: Point<N, D>, right: &'b Point<N, D>, Output = VectorSum<N, D, D>;
     self.coords - &right.coords; 'b);
 
 add_sub_impl!(Sub, sub, ClosedSub;
     (D, U1), (D, U1) for D: DimName;
-    self: PointBase<N, D, SA>, right: PointBase<N, D, SB>, Output = ColumnVectorSum<N, D, D, SA>;
+    self: Point<N, D>, right: Point<N, D>, Output = VectorSum<N, D, D>;
     self.coords - right.coords; );
 
-// PointBase - Vector
+// Point - Vector
 add_sub_impl!(Sub, sub, ClosedSub;
-    (D1, U1), (D2, U1) -> (D1) for D1: DimName, D2: Dim;
-    self: &'a PointBase<N, D1, SA>, right: &'b ColumnVector<N, D2, SB>, Output = OwnedPoint<N, D1, SA::Alloc>;
+    (D1, U1), (D2, U1) -> (D1) for D1: DimName, D2: Dim, SB: Storage<N, D2>;
+    self: &'a Point<N, D1>, right: &'b Vector<N, D2, SB>, Output = Point<N, D1>;
     Self::Output::from_coordinates(&self.coords - right); 'a, 'b);
 
 add_sub_impl!(Sub, sub, ClosedSub;
-    (D1, U1), (D2, U1) -> (D1) for D1: DimName, D2: Dim;
-    self: &'a PointBase<N, D1, SA>, right: ColumnVector<N, D2, SB>, Output = OwnedPoint<N, D1, SA::Alloc>;
+    (D1, U1), (D2, U1) -> (D1) for D1: DimName, D2: Dim, SB: Storage<N, D2>;
+    self: &'a Point<N, D1>, right: Vector<N, D2, SB>, Output = Point<N, D1>;
     Self::Output::from_coordinates(&self.coords - &right); 'a); // FIXME: should not be a ref to `right`.
 
 add_sub_impl!(Sub, sub, ClosedSub;
-    (D1, U1), (D2, U1) -> (D1) for D1: DimName, D2: Dim;
-    self: PointBase<N, D1, SA>, right: &'b ColumnVector<N, D2, SB>, Output = OwnedPoint<N, D1, SA::Alloc>;
+    (D1, U1), (D2, U1) -> (D1) for D1: DimName, D2: Dim, SB: Storage<N, D2>;
+    self: Point<N, D1>, right: &'b Vector<N, D2, SB>, Output = Point<N, D1>;
     Self::Output::from_coordinates(self.coords - right); 'b);
 
 add_sub_impl!(Sub, sub, ClosedSub;
-    (D1, U1), (D2, U1) -> (D1) for D1: DimName, D2: Dim;
-    self: PointBase<N, D1, SA>, right: ColumnVector<N, D2, SB>, Output = OwnedPoint<N, D1, SA::Alloc>;
+    (D1, U1), (D2, U1) -> (D1) for D1: DimName, D2: Dim, SB: Storage<N, D2>;
+    self: Point<N, D1>, right: Vector<N, D2, SB>, Output = Point<N, D1>;
     Self::Output::from_coordinates(self.coords - right); );
 
 
-// PointBase + Vector
+// Point + Vector
 add_sub_impl!(Add, add, ClosedAdd;
-    (D1, U1), (D2, U1) -> (D1) for D1: DimName, D2: Dim;
-    self: &'a PointBase<N, D1, SA>, right: &'b ColumnVector<N, D2, SB>, Output = OwnedPoint<N, D1, SA::Alloc>;
+    (D1, U1), (D2, U1) -> (D1) for D1: DimName, D2: Dim, SB: Storage<N, D2>;
+    self: &'a Point<N, D1>, right: &'b Vector<N, D2, SB>, Output = Point<N, D1>;
     Self::Output::from_coordinates(&self.coords + right); 'a, 'b);
 
 add_sub_impl!(Add, add, ClosedAdd;
-    (D1, U1), (D2, U1) -> (D1) for D1: DimName, D2: Dim;
-    self: &'a PointBase<N, D1, SA>, right: ColumnVector<N, D2, SB>, Output = OwnedPoint<N, D1, SA::Alloc>;
+    (D1, U1), (D2, U1) -> (D1) for D1: DimName, D2: Dim, SB: Storage<N, D2>;
+    self: &'a Point<N, D1>, right: Vector<N, D2, SB>, Output = Point<N, D1>;
     Self::Output::from_coordinates(&self.coords + &right); 'a); // FIXME: should not be a ref to `right`.
 
 add_sub_impl!(Add, add, ClosedAdd;
-    (D1, U1), (D2, U1) -> (D1) for D1: DimName, D2: Dim;
-    self: PointBase<N, D1, SA>, right: &'b ColumnVector<N, D2, SB>, Output = OwnedPoint<N, D1, SA::Alloc>;
+    (D1, U1), (D2, U1) -> (D1) for D1: DimName, D2: Dim, SB: Storage<N, D2>;
+    self: Point<N, D1>, right: &'b Vector<N, D2, SB>, Output = Point<N, D1>;
     Self::Output::from_coordinates(self.coords + right); 'b);
 
 add_sub_impl!(Add, add, ClosedAdd;
-    (D1, U1), (D2, U1) -> (D1) for D1: DimName, D2: Dim;
-    self: PointBase<N, D1, SA>, right: ColumnVector<N, D2, SB>, Output = OwnedPoint<N, D1, SA::Alloc>;
+    (D1, U1), (D2, U1) -> (D1) for D1: DimName, D2: Dim, SB: Storage<N, D2>;
+    self: Point<N, D1>, right: Vector<N, D2, SB>, Output = Point<N, D1>;
     Self::Output::from_coordinates(self.coords + right); );
 
 
 // XXX: replace by the shared macro: add_sub_assign_impl
 macro_rules! op_assign_impl(
     ($($TraitAssign: ident, $method_assign: ident, $bound: ident);* $(;)*) => {$(
-        impl<'b, N, D1: DimName, D2: Dim, SA, SB> $TraitAssign<&'b ColumnVector<N, D2, SB>> for PointBase<N, D1, SA>
+        impl<'b, N, D1: DimName, D2: Dim, SB> $TraitAssign<&'b Vector<N, D2, SB>> for Point<N, D1>
             where N:  Scalar + $bound,
-                  SA: StorageMut<N, D1, U1>,
-                  SB: Storage<N, D2, U1>,
+                  SB: Storage<N, D2>,
+                  DefaultAllocator: Allocator<N, D1>,
                   ShapeConstraint: SameNumberOfRows<D1, D2> {
 
             #[inline]
-            fn $method_assign(&mut self, right: &'b ColumnVector<N, D2, SB>) {
+            fn $method_assign(&mut self, right: &'b Vector<N, D2, SB>) {
                 self.coords.$method_assign(right)
             }
         }
 
-        impl<N, D1: DimName, D2: Dim, SA, SB> $TraitAssign<ColumnVector<N, D2, SB>> for PointBase<N, D1, SA>
+        impl<N, D1: DimName, D2: Dim, SB> $TraitAssign<Vector<N, D2, SB>> for Point<N, D1>
             where N:  Scalar + $bound,
-                  SA: StorageMut<N, D1, U1>,
-                  SB: Storage<N, D2, U1>,
+                  SB: Storage<N, D2>,
+                  DefaultAllocator: Allocator<N, D1>,
                   ShapeConstraint: SameNumberOfRows<D1, D2> {
 
             #[inline]
-            fn $method_assign(&mut self, right: ColumnVector<N, D2, SB>) {
+            fn $method_assign(&mut self, right: Vector<N, D2, SB>) {
                 self.coords.$method_assign(right)
             }
         }
@@ -171,56 +168,52 @@ op_assign_impl!(
 
 /*
  *
- * Matrix × PointBase
+ * Matrix × Point
  *
  */
 md_impl_all!(
     Mul, mul;
-    (R1, C1), (D2, U1) for R1: DimName, C1: Dim, D2: DimName
-    where SA::Alloc: Allocator<N, R1, U1>
+    (R1, C1), (D2, U1) for R1: DimName, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>
     where ShapeConstraint: AreMultipliable<R1, C1, D2, U1>;
-    self: Matrix<N, R1, C1, SA>, right: PointBase<N, D2, SB>, Output = PointMul<N, R1, C1, SA>;
-    [val val] => PointBase::from_coordinates(self * right.coords);
-    [ref val] => PointBase::from_coordinates(self * right.coords);
-    [val ref] => PointBase::from_coordinates(self * &right.coords);
-    [ref ref] => PointBase::from_coordinates(self * &right.coords);
+    self: Matrix<N, R1, C1, SA>, right: Point<N, D2>, Output = Point<N, R1>;
+    [val val] => Point::from_coordinates(self * right.coords);
+    [ref val] => Point::from_coordinates(self * right.coords);
+    [val ref] => Point::from_coordinates(self * &right.coords);
+    [ref ref] => Point::from_coordinates(self * &right.coords);
 );
 
 
 
 /*
  *
- * PointBase ×/÷ Scalar
+ * Point ×/÷ Scalar
  *
  */
 macro_rules! componentwise_scalarop_impl(
     ($Trait: ident, $method: ident, $bound: ident;
      $TraitAssign: ident, $method_assign: ident) => {
-        impl<N, D: DimName, S> $Trait<N> for PointBase<N, D, S>
-            where N: Scalar + $bound,
-                  S: Storage<N, D, U1> {
-            type Output = OwnedPoint<N, D, S::Alloc>;
+        impl<N: Scalar + $bound, D: DimName> $Trait<N> for Point<N, D>
+            where DefaultAllocator: Allocator<N, D> {
+            type Output = Point<N, D>;
 
             #[inline]
             fn $method(self, right: N) -> Self::Output {
-                PointBase::from_coordinates(self.coords.$method(right))
+                Point::from_coordinates(self.coords.$method(right))
             }
         }
 
-        impl<'a, N, D: DimName, S> $Trait<N> for &'a PointBase<N, D, S>
-            where N: Scalar + $bound,
-                  S: Storage<N, D, U1> {
-            type Output = OwnedPoint<N, D, S::Alloc>;
+        impl<'a, N: Scalar + $bound, D: DimName> $Trait<N> for &'a Point<N, D>
+            where DefaultAllocator: Allocator<N, D> {
+            type Output = Point<N, D>;
 
             #[inline]
             fn $method(self, right: N) -> Self::Output {
-                PointBase::from_coordinates((&self.coords).$method(right))
+                Point::from_coordinates((&self.coords).$method(right))
             }
         }
 
-        impl<N, D: DimName, S> $TraitAssign<N> for PointBase<N, D, S>
-            where N: Scalar + $bound,
-                  S: StorageMut<N, D, U1> {
+        impl<N: Scalar + $bound, D: DimName> $TraitAssign<N> for Point<N, D>
+            where DefaultAllocator: Allocator<N, D> {
             #[inline]
             fn $method_assign(&mut self, right: N) {
                 self.coords.$method_assign(right)
@@ -234,23 +227,23 @@ componentwise_scalarop_impl!(Div, div, ClosedDiv; DivAssign, div_assign);
 
 macro_rules! left_scalar_mul_impl(
     ($($T: ty),* $(,)*) => {$(
-        impl<D: DimName, S> Mul<PointBase<$T, D, S>> for $T
-            where S: Storage<$T, D, U1> {
-            type Output = OwnedPoint<$T, D, S::Alloc>;
+        impl<D: DimName> Mul<Point<$T, D>> for $T
+            where DefaultAllocator: Allocator<$T, D> {
+            type Output = Point<$T, D>;
 
             #[inline]
-            fn mul(self, right: PointBase<$T, D, S>) -> Self::Output {
-                PointBase::from_coordinates(self * right.coords)
+            fn mul(self, right: Point<$T, D>) -> Self::Output {
+                Point::from_coordinates(self * right.coords)
             }
         }
 
-        impl<'b, D: DimName, S> Mul<&'b PointBase<$T, D, S>> for $T
-            where S: Storage<$T, D, U1> {
-            type Output = OwnedPoint<$T, D, S::Alloc>;
+        impl<'b, D: DimName> Mul<&'b Point<$T, D>> for $T
+            where DefaultAllocator: Allocator<$T, D> {
+            type Output = Point<$T, D>;
 
             #[inline]
-            fn mul(self, right: &'b PointBase<$T, D, S>) -> Self::Output {
-                PointBase::from_coordinates(self * &right.coords)
+            fn mul(self, right: &'b Point<$T, D>) -> Self::Output {
+                Point::from_coordinates(self * &right.coords)
             }
         }
     )*}

src/geometry/quaternion.rs

@@ -1,70 +1,34 @@
 use std::fmt;
+use std::hash;
 use num::Zero;
 use approx::ApproxEq;
 
 #[cfg(feature = "serde-serialize")]
-use serde::{Serialize, Serializer, Deserialize, Deserializer};
+use serde;
+#[cfg(feature = "serde-serialize")]
+use core::storage::Owned;
 
 use alga::general::Real;
 
-use core::{Unit, ColumnVector, OwnedColumnVector, MatrixSlice, MatrixSliceMut, SquareMatrix,
-           OwnedSquareMatrix};
-use core::storage::{Storage, StorageMut};
-use core::allocator::Allocator;
+use core::{Unit, Vector3, Vector4, MatrixSlice, MatrixSliceMut, SquareMatrix, MatrixN};
 use core::dimension::{U1, U3, U4};
+use core::storage::{RStride, CStride};
 
-use geometry::{RotationBase, OwnedRotation};
+use geometry::Rotation;
 
-/// A quaternion with an owned storage allocated by `A`.
-pub type OwnedQuaternionBase<N, A> = QuaternionBase<N, <A as Allocator<N, U4, U1>>::Buffer>;
-
-/// A unit quaternion with an owned storage allocated by `A`.
-pub type OwnedUnitQuaternionBase<N, A> = UnitQuaternionBase<N, <A as Allocator<N, U4, U1>>::Buffer>;
-
-/// A quaternion. See the type alias `UnitQuaternionBase = Unit<QuaternionBase>` for a quaternion
+/// A quaternion. See the type alias `UnitQuaternion = Unit<Quaternion>` for a quaternion
 /// that may be used as a rotation.
 #[repr(C)]
-#[derive(Hash, Debug, Copy, Clone)]
-pub struct QuaternionBase<N: Real, S: Storage<N, U4, U1>> {
+#[derive(Debug)]
+pub struct Quaternion<N: Real> {
     /// This quaternion as a 4D vector of coordinates in the `[ x, y, z, w ]` storage order.
-    pub coords: ColumnVector<N, U4, S>
+    pub coords: Vector4<N>
 }
 
-#[cfg(feature = "serde-serialize")]
-impl<N, S> Serialize for QuaternionBase<N, S>
-    where N: Real,
-          S: Storage<N, U4, U1>,
-          ColumnVector<N, U4, S>: Serialize,
-{
-    fn serialize<T>(&self, serializer: T) -> Result<T::Ok, T::Error>
-        where T: Serializer
-    {
-        self.coords.serialize(serializer)
-    }
+impl<N: Real + Eq> Eq for Quaternion<N> {
 }
 
-#[cfg(feature = "serde-serialize")]
-impl<'de, N, S> Deserialize<'de> for QuaternionBase<N, S>
-    where N: Real,
-          S: Storage<N, U4, U1>,
-          ColumnVector<N, U4, S>: Deserialize<'de>,
-{
-    fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>
-        where D: Deserializer<'de>
-    {
-        ColumnVector::deserialize(deserializer).map(|x| QuaternionBase { coords: x })
-    }
-}
-
-
-impl<N, S> Eq for QuaternionBase<N, S>
-    where N: Real + Eq,
-          S: Storage<N, U4, U1> {
-}
-
-impl<N, S> PartialEq for QuaternionBase<N, S>
-    where N: Real,
-          S: Storage<N, U4, U1> {
+impl<N: Real> PartialEq for Quaternion<N> {
     fn eq(&self, rhs: &Self) -> bool {
         self.coords == rhs.coords ||
         // Account for the double-covering of S², i.e. q = -q
@@ -72,24 +36,91 @@ impl<N, S> PartialEq for QuaternionBase<N, S>
     }
 }
 
-impl<N, S> QuaternionBase<N, S>
-    where N: Real,
-          S: Storage<N, U4, U1> {
-    /// Moves this quaternion into one that owns its data.
-    #[inline]
-    pub fn into_owned(self) -> OwnedQuaternionBase<N, S::Alloc> {
-        QuaternionBase::from_vector(self.coords.into_owned())
+impl<N: Real + hash::Hash> hash::Hash for Quaternion<N> {
+    fn hash<H: hash::Hasher>(&self, state: &mut H) {
+        self.coords.hash(state)
+    }
 }
 
-    /// Clones this quaternion into one that owns its data.
+impl<N: Real> Copy for Quaternion<N> { }
+
+impl<N: Real> Clone for Quaternion<N> {
     #[inline]
-    pub fn clone_owned(&self) -> OwnedQuaternionBase<N, S::Alloc> {
-        QuaternionBase::from_vector(self.coords.clone_owned())
+    fn clone(&self) -> Self {
+        Quaternion::from_vector(self.coords.clone())
+    }
+}
+
+#[cfg(feature = "serde-serialize")]
+impl<N: Real> serde::Serialize for Quaternion<N>
+where Owned<N, U4>: serde::Serialize {
+
+    fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
+        where S: serde::Serializer {
+            self.coords.serialize(serializer)
+        }
+}
+
+#[cfg(feature = "serde-serialize")]
+impl<'a, N: Real> serde::Deserialize<'a> for Quaternion<N>
+where Owned<N, U4>: serde::Deserialize<'a> {
+
+    fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
+        where Des: serde::Deserializer<'a> {
+            let coords = Vector4::<N>::deserialize(deserializer)?;
+
+            Ok(Quaternion::from_vector(coords))
+        }
+}
+
+impl<N: Real> Quaternion<N> {
+    /// Moves this unit quaternion into one that owns its data.
+    #[inline]
+    pub fn into_owned(self) -> Quaternion<N> {
+        self
+    }
+
+    /// Clones this unit quaternion into one that owns its data.
+    #[inline]
+    pub fn clone_owned(&self) -> Quaternion<N> {
+        Quaternion::from_vector(self.coords.clone_owned())
+    }
+
+    /// Normalizes this quaternion.
+    #[inline]
+    pub fn normalize(&self) -> Quaternion<N> {
+        Quaternion::from_vector(self.coords.normalize())
+    }
+
+    /// Compute the conjugate of this quaternion.
+    #[inline]
+    pub fn conjugate(&self) -> Quaternion<N> {
+        let v = Vector4::new(-self.coords[0], -self.coords[1], -self.coords[2], self.coords[3]);
+        Quaternion::from_vector(v)
+    }
+
+    /// Inverts this quaternion if it is not zero.
+    #[inline]
+    pub fn try_inverse(&self) -> Option<Quaternion<N>> {
+        let mut res = Quaternion::from_vector(self.coords.clone_owned());
+
+        if res.try_inverse_mut() {
+            Some(res)
+        }
+        else {
+            None
+        }
+    }
+
+    /// Linear interpolation between two quaternion.
+    #[inline]
+    pub fn lerp(&self, other: &Quaternion<N>, t: N) -> Quaternion<N> {
+        self * (N::one() - t) + other * t
     }
 
     /// The vector part `(i, j, k)` of this quaternion.
     #[inline]
-    pub fn vector(&self) -> MatrixSlice<N, U3, U1, S::RStride, S::CStride, S::Alloc> {
+    pub fn vector(&self) -> MatrixSlice<N, U3, U1, RStride<N, U4, U1>, CStride<N, U4, U1>> {
         self.coords.fixed_rows::<U3>(0)
     }
 
@@ -101,7 +132,7 @@ impl<N, S> QuaternionBase<N, S>
 
     /// Reinterprets this quaternion as a 4D vector.
     #[inline]
-    pub fn as_vector(&self) -> &ColumnVector<N, U4, S> {
+    pub fn as_vector(&self) -> &Vector4<N> {
         &self.coords
     }
 
@@ -117,53 +148,11 @@ impl<N, S> QuaternionBase<N, S>
         self.coords.norm_squared()
     }
 
-    /// Normalizes this quaternion.
-    #[inline]
-    pub fn normalize(&self) -> OwnedQuaternionBase<N, S::Alloc> {
-        QuaternionBase::from_vector(self.coords.normalize())
-    }
-
-    /// Compute the conjugate of this quaternion.
-    #[inline]
-    pub fn conjugate(&self) -> OwnedQuaternionBase<N, S::Alloc> {
-        let v = OwnedColumnVector::<N, U4, S::Alloc>::new(-self.coords[0],
-                                                          -self.coords[1],
-                                                          -self.coords[2],
-                                                          self.coords[3]);
-        QuaternionBase::from_vector(v)
-    }
-
-    /// Inverts this quaternion if it is not zero.
-    #[inline]
-    pub fn try_inverse(&self) -> Option<OwnedQuaternionBase<N, S::Alloc>> {
-        let mut res = QuaternionBase::from_vector(self.coords.clone_owned());
-
-        if res.try_inverse_mut() {
-            Some(res)
-        }
-        else {
-            None
-        }
-    }
-
-    /// Linear interpolation between two quaternion.
-    #[inline]
-    pub fn lerp<S2>(&self, other: &QuaternionBase<N, S2>, t: N) -> OwnedQuaternionBase<N, S::Alloc>
-        where S2: Storage<N, U4, U1> {
-        self * (N::one() - t) + other * t
-    }
-}
-
-
-impl<N, S> QuaternionBase<N, S>
-    where N: Real,
-          S: Storage<N, U4, U1>,
-          S::Alloc: Allocator<N, U3, U1> {
     /// The polar decomposition of this quaternion.
     ///
     /// Returns, from left to right: the quaternion norm, the half rotation angle, the rotation
     /// axis. If the rotation angle is zero, the rotation axis is set to `None`.
-    pub fn polar_decomposition(&self) -> (N, N, Option<Unit<OwnedColumnVector<N, U3, S::Alloc>>>) {
+    pub fn polar_decomposition(&self) -> (N, N, Option<Unit<Vector3<N>>>) {
         if let Some((q, n)) = Unit::try_new_and_get(self.clone_owned(), N::zero()) {
             if let Some(axis) = Unit::try_new(self.vector().clone_owned(), N::zero()) {
                 let angle = q.angle() / ::convert(2.0f64);
@@ -181,51 +170,47 @@ impl<N, S> QuaternionBase<N, S>
 
     /// Compute the exponential of a quaternion.
     #[inline]
-    pub fn exp(&self) -> OwnedQuaternionBase<N, S::Alloc> {
+    pub fn exp(&self) -> Quaternion<N> {
         let v  = self.vector();
         let nn = v.norm_squared();
 
         if relative_eq!(nn, N::zero()) {
-            QuaternionBase::identity()
+            Quaternion::identity()
         }
         else {
             let w_exp = self.scalar().exp();
             let n  = nn.sqrt();
             let nv = v * (w_exp * n.sin() / n);
 
-            QuaternionBase::from_parts(n.cos(), nv)
+            Quaternion::from_parts(n.cos(), nv)
         }
     }
 
     /// Compute the natural logarithm of a quaternion.
     #[inline]
-    pub fn ln(&self) -> OwnedQuaternionBase<N, S::Alloc> {
+    pub fn ln(&self) -> Quaternion<N> {
         let n = self.norm();
         let v = self.vector();
         let s = self.scalar();
 
-        QuaternionBase::from_parts(n.ln(), v.normalize() *  (s / n).acos())
+        Quaternion::from_parts(n.ln(), v.normalize() *  (s / n).acos())
     }
 
     /// Raise the quaternion to a given floating power.
     #[inline]
-    pub fn powf(&self, n: N) -> OwnedQuaternionBase<N, S::Alloc> {
+    pub fn powf(&self, n: N) -> Quaternion<N> {
         (self.ln() * n).exp()
     }
-}
 
-impl<N, S> QuaternionBase<N, S>
-    where N: Real,
-          S: StorageMut<N, U4, U1> {
     /// Transforms this quaternion into its 4D vector form (Vector part, Scalar part).
     #[inline]
-    pub fn as_vector_mut(&mut self) -> &mut ColumnVector<N, U4, S> {
+    pub fn as_vector_mut(&mut self) -> &mut Vector4<N> {
         &mut self.coords
     }
 
     /// The mutable vector part `(i, j, k)` of this quaternion.
     #[inline]
-    pub fn vector_mut(&mut self) -> MatrixSliceMut<N, U3, U1, S::RStride, S::CStride, S::Alloc> {
+    pub fn vector_mut(&mut self) -> MatrixSliceMut<N, U3, U1, RStride<N, U4, U1>, CStride<N, U4, U1>> {
         self.coords.fixed_rows_mut::<U3>(0)
     }
 
@@ -260,9 +245,7 @@ impl<N, S> QuaternionBase<N, S>
     }
 }
 
-impl<N, S> ApproxEq for QuaternionBase<N, S>
-    where N: Real + ApproxEq<Epsilon = N>,
-          S: Storage<N, U4, U1> {
+impl<N: Real + ApproxEq<Epsilon = N>> ApproxEq for Quaternion<N> {
     type Epsilon = N;
 
     #[inline]
@@ -296,9 +279,7 @@ impl<N, S> ApproxEq for QuaternionBase<N, S>
 }
 
 
-impl<N, S> fmt::Display for QuaternionBase<N, S>
-    where N: Real + fmt::Display,
-          S: Storage<N, U4, U1> {
+impl<N: Real + fmt::Display> fmt::Display for Quaternion<N> {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         write!(f, "Quaternion {} − ({}, {}, {})", self[3], self[0], self[1], self[2])
     }
@@ -325,118 +306,115 @@ impl<N, S> fmt::Display for QuaternionBase<N, S>
 /// <code>fn <a class="fnname">angle</a>(&self) -> N</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
-/// <code>fn <a class="fnname">angle_to</a>(&self, other: &UnitQuaternionBase) -> N</code>
+/// <code>fn <a class="fnname">angle_to</a>(&self, other: &UnitQuaternion) -> N</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
-/// <code>fn <a class="fnname">axis</a>(&self) -> Option&lt;Unit&lt;OwnedColumnVector&gt;&gt;</code>
+/// <code>fn <a class="fnname">axis</a>(&self) -> Option&lt;Unit&lt;Vector3&gt;&gt;</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
-/// <code>fn <a class="fnname">clone_owned</a>(&self) -> OwnedUnitQuaternionBase</code>
+/// <code>fn <a class="fnname">clone_owned</a>(&self) -> UnitQuaternion</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
 /// <code>fn <a class="fnname">conjugate_mut</a>(&mut self)</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
-/// <code>fn <a class="fnname">conjugate</a>(&self) -> OwnedUnitQuaternionBase</code>
+/// <code>fn <a class="fnname">conjugate</a>(&self) -> UnitQuaternion</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
-/// <code>fn <a class="fnname">exp</a>(&self) -> OwnedQuaternionBase</code>
+/// <code>fn <a class="fnname">exp</a>(&self) -> Quaternion</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
-/// <code>fn <a class="fnname">from_axis_angle</a>(axis: &Unit&lt;ColumnVector&gt;, angle: N) -> Self</code>
+/// <code>fn <a class="fnname">from_axis_angle</a>(axis: &Unit&lt;Vector&gt;, angle: N) -> Self</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
 /// <code>fn <a class="fnname">from_euler_angles</a>(roll: N, pitch: N, yaw: N) -> Self</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
-/// <code>fn <a class="fnname">from_quaternion</a>(q: QuaternionBase) -> Self</code>
+/// <code>fn <a class="fnname">from_quaternion</a>(q: Quaternion) -> Self</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
-/// <code>fn <a class="fnname">from_rotation_matrix</a>(rotmat: &RotationBase) -> Self</code>
+/// <code>fn <a class="fnname">from_rotation_matrix</a>(rotmat: &Rotation) -> Self</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
-/// <code>fn <a class="fnname">from_scaled_axis</a>(axisangle: ColumnVector) -> Self</code>
+/// <code>fn <a class="fnname">from_scaled_axis</a>(axisangle: Vector) -> Self</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
 /// <code>fn <a class="fnname">identity</a>() -> Self</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
-/// <code>fn <a class="fnname">into_owned</a>(self) -> OwnedUnitQuaternionBase</code>
+/// <code>fn <a class="fnname">into_owned</a>(self) -> UnitQuaternion</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
 /// <code>fn <a class="fnname">inverse_mut</a>(&mut self)</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
-/// <code>fn <a class="fnname">inverse</a>(&self) -> OwnedUnitQuaternionBase</code>
+/// <code>fn <a class="fnname">inverse</a>(&self) -> UnitQuaternion</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
-/// <code>fn <a class="fnname">lerp</a>(&self, other: &UnitQuaternionBase, t: N) -> OwnedQuaternionBase</code>
+/// <code>fn <a class="fnname">lerp</a>(&self, other: &UnitQuaternion, t: N) -> Quaternion</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
-/// <code>fn <a class="fnname">ln</a>(&self) -> OwnedQuaternionBase</code>
+/// <code>fn <a class="fnname">ln</a>(&self) -> Quaternion</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
-/// <code>fn <a class="fnname">look_at_lh</a>(dir: &ColumnVector, up: &ColumnVector) -> Self</code>
+/// <code>fn <a class="fnname">look_at_lh</a>(dir: &Vector, up: &Vector) -> Self</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
-/// <code>fn <a class="fnname">look_at_rh</a>(dir: &ColumnVector, up: &ColumnVector) -> Self</code>
+/// <code>fn <a class="fnname">look_at_rh</a>(dir: &Vector, up: &Vector) -> Self</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
-/// <code>fn <a class="fnname">new</a>(axisangle: ColumnVector) -> Self</code>
+/// <code>fn <a class="fnname">new</a>(axisangle: Vector) -> Self</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
-/// <code>fn <a class="fnname">new_observer_frame</a>(dir: &ColumnVector, up: &ColumnVector) -> Self</code>
+/// <code>fn <a class="fnname">new_observer_frame</a>(dir: &Vector, up: &Vector) -> Self</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
-/// <code>fn <a class="fnname">nlerp</a>(&self, other: &UnitQuaternionBase, t: N) -> OwnedUnitQuaternionBase</code>
+/// <code>fn <a class="fnname">nlerp</a>(&self, other: &UnitQuaternion, t: N) -> UnitQuaternion</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
-/// <code>fn <a class="fnname">powf</a>(&self, n: N) -> OwnedUnitQuaternionBase</code>
+/// <code>fn <a class="fnname">powf</a>(&self, n: N) -> UnitQuaternion</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
-/// <code>fn <a class="fnname">quaternion</a>(&self) -> &QuaternionBase</code>
+/// <code>fn <a class="fnname">quaternion</a>(&self) -> &Quaternion</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
-/// <code>fn <a class="fnname">rotation_between</a>(a: &ColumnVector, b: &ColumnVector) -> Option&lt;Self&gt;</code>
+/// <code>fn <a class="fnname">rotation_between</a>(a: &Vector, b: &Vector) -> Option&lt;Self&gt;</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
-/// <code>fn <a class="fnname">rotation_to</a>(&self, other: &UnitQuaternionBase) -> OwnedUnitQuaternionBase</code>
+/// <code>fn <a class="fnname">rotation_to</a>(&self, other: &UnitQuaternion) -> UnitQuaternion</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
-/// <code>fn <a class="fnname">scaled_axis</a>(&self) -> OwnedColumnVector</code>
+/// <code>fn <a class="fnname">scaled_axis</a>(&self) -> Vector3</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
-/// <code>fn <a class="fnname">scaled_rotation_between</a>(a: &ColumnVector, b: &ColumnVector, s: N) -> Option&lt;Self&gt;</code>
+/// <code>fn <a class="fnname">scaled_rotation_between</a>(a: &Vector, b: &Vector, s: N) -> Option&lt;Self&gt;</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
-/// <code>fn <a class="fnname">slerp</a>(&self, other: &UnitQuaternionBase, t: N) -> OwnedUnitQuaternionBase</code>
+/// <code>fn <a class="fnname">slerp</a>(&self, other: &UnitQuaternion, t: N) -> UnitQuaternion</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
-/// <code>fn <a class="fnname">to_homogeneous</a>(&self) -> OwnedSquareMatrix</code>
+/// <code>fn <a class="fnname">to_homogeneous</a>(&self) -> MatrixN</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
-/// <code>fn <a class="fnname">to_rotation_matrix</a>(&self) -> OwnedRotation</code>
+/// <code>fn <a class="fnname">to_rotation_matrix</a>(&self) -> Rotation</code>
 /// </h4>
 /// <h4 class="method"><span class="invisible">
-/// <code>fn <a class="fnname">try_slerp</a>(&self, other: &UnitQuaternionBase, t: N, epsilon: N) -> Option&lt;OwnedUnitQuaternionBase&gt;</code>
+/// <code>fn <a class="fnname">try_slerp</a>(&self, other: &UnitQuaternion, t: N, epsilon: N) -> Option&lt;UnitQuaternion&gt;</code>
 /// </h4>
-pub type UnitQuaternionBase<N, S> = Unit<QuaternionBase<N, S>>;
+pub type UnitQuaternion<N> = Unit<Quaternion<N>>;
 
 
-
-impl<N, S> UnitQuaternionBase<N, S>
-    where N: Real,
-          S: Storage<N, U4, U1> {
+impl<N: Real> UnitQuaternion<N> {
     /// Moves this unit quaternion into one that owns its data.
     #[inline]
-    pub fn into_owned(self) -> OwnedUnitQuaternionBase<N, S::Alloc> {
-        UnitQuaternionBase::new_unchecked(self.unwrap().into_owned())
+    pub fn into_owned(self) -> UnitQuaternion<N> {
+        self
     }
 
     /// Clones this unit quaternion into one that owns its data.
     #[inline]
-    pub fn clone_owned(&self) -> OwnedUnitQuaternionBase<N, S::Alloc> {
-        UnitQuaternionBase::new_unchecked(self.as_ref().clone_owned())
+    pub fn clone_owned(&self) -> UnitQuaternion<N> {
+        UnitQuaternion::new_unchecked(self.as_ref().clone_owned())
     }
 
     /// The rotation angle in [0; pi] of this unit quaternion.
@@ -457,26 +435,25 @@ impl<N, S> UnitQuaternionBase<N, S>
     ///
     /// Same as `self.as_ref()`.
     #[inline]
-    pub fn quaternion(&self) -> &QuaternionBase<N, S> {
+    pub fn quaternion(&self) -> &Quaternion<N> {
         self.as_ref()
     }
 
     /// Compute the conjugate of this unit quaternion.
     #[inline]
-    pub fn conjugate(&self) -> OwnedUnitQuaternionBase<N, S::Alloc> {
-        UnitQuaternionBase::new_unchecked(self.as_ref().conjugate())
+    pub fn conjugate(&self) -> UnitQuaternion<N> {
+        UnitQuaternion::new_unchecked(self.as_ref().conjugate())
     }
 
     /// Inverts this quaternion if it is not zero.
     #[inline]
-    pub fn inverse(&self) -> OwnedUnitQuaternionBase<N, S::Alloc> {
+    pub fn inverse(&self) -> UnitQuaternion<N> {
         self.conjugate()
     }
 
     /// The rotation angle needed to make `self` and `other` coincide.
     #[inline]
-    pub fn angle_to<S2>(&self, other: &UnitQuaternionBase<N, S2>) -> N
-        where S2: Storage<N, U4, U1> {
+    pub fn angle_to(&self, other: &UnitQuaternion<N>) -> N {
         let delta = self.rotation_to(other);
         delta.angle()
     }
@@ -485,8 +462,7 @@ impl<N, S> UnitQuaternionBase<N, S>
     ///
     /// The result is such that: `self.rotation_to(other) * self == other`.
     #[inline]
-    pub fn rotation_to<S2>(&self, other: &UnitQuaternionBase<N, S2>) -> OwnedUnitQuaternionBase<N, S2::Alloc>
-        where S2: Storage<N, U4, U1> {
+    pub fn rotation_to(&self, other: &UnitQuaternion<N>) -> UnitQuaternion<N> {
         other / self
     }
 
@@ -494,19 +470,17 @@ impl<N, S> UnitQuaternionBase<N, S>
     ///
     /// The result is not normalized.
     #[inline]
-    pub fn lerp<S2>(&self, other: &UnitQuaternionBase<N, S2>, t: N) -> OwnedQuaternionBase<N, S::Alloc>
-        where S2: Storage<N, U4, U1> {
+    pub fn lerp(&self, other: &UnitQuaternion<N>, t: N) -> Quaternion<N> {
         self.as_ref().lerp(other.as_ref(), t)
     }
 
     /// Normalized linear interpolation between two unit quaternions.
     #[inline]
-    pub fn nlerp<S2>(&self, other: &UnitQuaternionBase<N, S2>, t: N) -> OwnedUnitQuaternionBase<N, S::Alloc>
-        where S2: Storage<N, U4, U1> {
+    pub fn nlerp(&self, other: &UnitQuaternion<N>, t: N) -> UnitQuaternion<N> {
         let mut res = self.lerp(other, t);
         let _ = res.normalize_mut();
 
-        UnitQuaternionBase::new_unchecked(res)
+        UnitQuaternion::new_unchecked(res)
     }
 
     /// Spherical linear interpolation between two unit quaternions.
@@ -514,8 +488,7 @@ impl<N, S> UnitQuaternionBase<N, S>
     /// Panics if the angle between both quaternion is 180 degrees (in which case the interpolation
     /// is not well-defined).
     #[inline]
-    pub fn slerp<S2>(&self, other: &UnitQuaternionBase<N, S2>, t: N) -> OwnedUnitQuaternionBase<N, S::Alloc>
-        where S2: Storage<N, U4, U1, Alloc = S::Alloc> {
+    pub fn slerp(&self, other: &UnitQuaternion<N>, t: N) -> UnitQuaternion<N> {
         self.try_slerp(other, t, N::zero()).expect(
             "Unable to perform a spherical quaternion interpolation when they \
              are 180 degree apart (the result is not unique).")
@@ -532,9 +505,7 @@ impl<N, S> UnitQuaternionBase<N, S>
     /// * `epsilon`: the value bellow which the sinus of the angle separating both quaternion
     /// must be to return `None`.
     #[inline]
-    pub fn try_slerp<S2>(&self, other: &UnitQuaternionBase<N, S2>, t: N, epsilon: N)
-                         -> Option<OwnedUnitQuaternionBase<N, S::Alloc>>
-        where S2: Storage<N, U4, U1, Alloc = S::Alloc> {
+    pub fn try_slerp(&self, other: &UnitQuaternion<N>, t: N, epsilon: N) -> Option<UnitQuaternion<N>> {
 
         let c_hang = self.coords.dot(&other.coords);
 
@@ -555,14 +526,10 @@ impl<N, S> UnitQuaternionBase<N, S>
             let tb = (t * hang).sin() / s_hang; 
             let res = self.as_ref() * ta + other.as_ref() * tb;
 
-            Some(UnitQuaternionBase::new_unchecked(res))
-        }
+            Some(UnitQuaternion::new_unchecked(res))
         }
     }
 
-impl<N, S> UnitQuaternionBase<N, S>
-    where N: Real,
-          S: StorageMut<N, U4, U1> {
     /// Compute the conjugate of this unit quaternion in-place.
     #[inline]
     pub fn conjugate_mut(&mut self) {
@@ -574,15 +541,10 @@ impl<N, S> UnitQuaternionBase<N, S>
     pub fn inverse_mut(&mut self) {
         self.as_mut_unchecked().conjugate_mut()
     }
-}
 
-impl<N, S> UnitQuaternionBase<N, S>
-    where N: Real,
-          S: Storage<N, U4, U1>,
-          S::Alloc: Allocator<N, U3, U1> {
     /// The rotation axis of this unit quaternion or `None` if the rotation is zero.
     #[inline]
-    pub fn axis(&self) -> Option<Unit<OwnedColumnVector<N, U3, S::Alloc>>> {
+    pub fn axis(&self) -> Option<Unit<Vector3<N>>> {
         let v =
             if self.quaternion().scalar() >= N::zero() {
                 self.as_ref().vector().clone_owned()
@@ -597,35 +559,35 @@ impl<N, S> UnitQuaternionBase<N, S>
 
     /// The rotation axis of this unit quaternion multiplied by the rotation agle.
     #[inline]
-    pub fn scaled_axis(&self) -> OwnedColumnVector<N, U3, S::Alloc> {
+    pub fn scaled_axis(&self) -> Vector3<N> {
         if let Some(axis) = self.axis() {
             axis.unwrap() * self.angle()
         }
         else {
-            ColumnVector::zero()
+            Vector3::zero()
         }
     }
 
     /// Compute the exponential of a quaternion.
     ///
-    /// Note that this function yields a `QuaternionBase<N>` because it looses the unit property.
+    /// Note that this function yields a `Quaternion<N>` because it looses the unit property.
     #[inline]
-    pub fn exp(&self) -> OwnedQuaternionBase<N, S::Alloc> {
+    pub fn exp(&self) -> Quaternion<N> {
         self.as_ref().exp()
     }
 
     /// Compute the natural logarithm of a quaternion.
     ///
-    /// Note that this function yields a `QuaternionBase<N>` because it looses the unit property.
+    /// Note that this function yields a `Quaternion<N>` because it looses the unit property.
     /// The vector part of the return value corresponds to the axis-angle representation (divided
     /// by 2.0) of this unit quaternion.
     #[inline]
-    pub fn ln(&self) -> OwnedQuaternionBase<N, S::Alloc> {
+    pub fn ln(&self) -> Quaternion<N> {
         if let Some(v) = self.axis() {
-            QuaternionBase::from_parts(N::zero(), v.unwrap() * self.angle())
+            Quaternion::from_parts(N::zero(), v.unwrap() * self.angle())
         }
         else {
-            QuaternionBase::zero()
+            Quaternion::zero()
         }
     }
 
@@ -634,23 +596,18 @@ impl<N, S> UnitQuaternionBase<N, S>
     /// This returns the unit quaternion that identifies a rotation with axis `self.axis()` and
     /// angle `self.angle() × n`.
     #[inline]
-    pub fn powf(&self, n: N) -> OwnedUnitQuaternionBase<N, S::Alloc> {
+    pub fn powf(&self, n: N) -> UnitQuaternion<N> {
         if let Some(v) = self.axis() {
-            UnitQuaternionBase::from_axis_angle(&v, self.angle() * n)
+            UnitQuaternion::from_axis_angle(&v, self.angle() * n)
         }
         else {
-            UnitQuaternionBase::identity()
-        }
+            UnitQuaternion::identity()
         }
     }
 
-impl<N, S> UnitQuaternionBase<N, S>
-    where N: Real,
-          S: Storage<N, U4, U1>,
-          S::Alloc: Allocator<N, U3, U3> {
     /// Builds a rotation matrix from this unit quaternion.
     #[inline]
-    pub fn to_rotation_matrix(&self) -> OwnedRotation<N, U3, S::Alloc> {
+    pub fn to_rotation_matrix(&self) -> Rotation<N, U3> {
         let i = self.as_ref()[0];
         let j = self.as_ref()[1];
         let k = self.as_ref()[2];
@@ -667,7 +624,7 @@ impl<N, S> UnitQuaternionBase<N, S>
         let jk = j * k * ::convert(2.0f64);
         let wi = w * i * ::convert(2.0f64);
 
-        RotationBase::from_matrix_unchecked(
+        Rotation::from_matrix_unchecked(
             SquareMatrix::<_, U3, _>::new(
                 ww + ii - jj - kk, ij - wk,           wj + ik,
                 wk + ij,           ww - ii + jj - kk, jk - wi,
@@ -678,17 +635,13 @@ impl<N, S> UnitQuaternionBase<N, S>
 
     /// Converts this unit quaternion into its equivalent homogeneous transformation matrix.
     #[inline]
-    pub fn to_homogeneous(&self) -> OwnedSquareMatrix<N, U4, S::Alloc>
-        where S::Alloc: Allocator<N, U4, U4> {
+    pub fn to_homogeneous(&self) -> MatrixN<N, U4> {
         self.to_rotation_matrix().to_homogeneous()
     }
 }
 
 
-impl<N, S> fmt::Display for UnitQuaternionBase<N, S>
-    where N: Real + fmt::Display,
-          S: Storage<N, U4, U1>,
-          S::Alloc: Allocator<N, U3, U1> {
+impl<N: Real + fmt::Display> fmt::Display for UnitQuaternion<N> {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         if let Some(axis) = self.axis() {
             let axis = axis.unwrap();
@@ -700,9 +653,7 @@ impl<N, S> fmt::Display for UnitQuaternionBase<N, S>
     }
 }
 
-impl<N, S> ApproxEq for UnitQuaternionBase<N, S>
-    where N: Real + ApproxEq<Epsilon = N>,
-          S: Storage<N, U4, U1> {
+impl<N: Real + ApproxEq<Epsilon = N>> ApproxEq for UnitQuaternion<N> {
     type Epsilon = N;
 
     #[inline]

src/geometry/quaternion_alga.rs

@@ -7,57 +7,39 @@ use alga::linear::{Transformation, AffineTransformation, Similarity, Isometry, D
                    OrthogonalTransformation, VectorSpace, FiniteDimVectorSpace, NormedSpace,
                    Rotation, ProjectiveTransformation};
 
-use core::ColumnVector;
-use core::storage::OwnedStorage;
-use core::allocator::{Allocator, OwnedAllocator};
-use core::dimension::{U1, U3, U4};
-use geometry::{PointBase, QuaternionBase, UnitQuaternionBase};
+use core::{Vector3, Vector4};
+use geometry::{Point3, Quaternion, UnitQuaternion};
 
 
-impl<N, S> Identity<Multiplicative> for QuaternionBase<N, S>
-    where N: Real,
-          S: OwnedStorage<N, U4, U1>,
-          S::Alloc: OwnedAllocator<N, U4, U1, S> {
+impl<N: Real> Identity<Multiplicative> for Quaternion<N> {
     #[inline]
     fn identity() -> Self {
         Self::identity()
     }
 }
 
-impl<N, S> Identity<Additive> for QuaternionBase<N, S>
-    where N: Real,
-          S: OwnedStorage<N, U4, U1>,
-          S::Alloc: OwnedAllocator<N, U4, U1, S> {
+impl<N: Real> Identity<Additive> for Quaternion<N> {
     #[inline]
     fn identity() -> Self {
         Self::zero()
     }
 }
 
-impl<N, S> AbstractMagma<Multiplicative> for QuaternionBase<N, S>
-    where N: Real,
-          S: OwnedStorage<N, U4, U1>,
-          S::Alloc: OwnedAllocator<N, U4, U1, S> {
+impl<N: Real> AbstractMagma<Multiplicative> for Quaternion<N> {
     #[inline]
     fn operate(&self, rhs: &Self) -> Self {
         self * rhs
     }
 }
 
-impl<N, S> AbstractMagma<Additive> for QuaternionBase<N, S>
-    where N: Real,
-          S: OwnedStorage<N, U4, U1>,
-          S::Alloc: OwnedAllocator<N, U4, U1, S> {
+impl<N: Real> AbstractMagma<Additive> for Quaternion<N> {
     #[inline]
     fn operate(&self, rhs: &Self) -> Self {
         self + rhs
     }
 }
 
-impl<N, S> Inverse<Additive> for QuaternionBase<N, S>
-    where N: Real,
-          S: OwnedStorage<N, U4, U1>,
-          S::Alloc: OwnedAllocator<N, U4, U1, S> {
+impl<N: Real> Inverse<Additive> for Quaternion<N> {
     #[inline]
     fn inverse(&self) -> Self {
         -self
@@ -66,15 +48,12 @@ impl<N, S> Inverse<Additive> for QuaternionBase<N, S>
 
 macro_rules! impl_structures(
     ($Quaternion: ident; $($marker: ident<$operator: ident>),* $(,)*) => {$(
-        impl<N, S> $marker<$operator> for $Quaternion<N, S>
-            where N: Real,
-                  S: OwnedStorage<N, U4, U1>,
-                  S::Alloc: OwnedAllocator<N, U4, U1, S> { }
+        impl<N: Real> $marker<$operator> for $Quaternion<N> { }
     )*}
 );
 
 impl_structures!(
-    QuaternionBase;
+    Quaternion;
     AbstractSemigroup<Multiplicative>,
     AbstractMonoid<Multiplicative>,
 
@@ -92,10 +71,7 @@ impl_structures!(
  * Vector space.
  *
  */
-impl<N, S> AbstractModule for QuaternionBase<N, S>
-    where N: Real,
-          S: OwnedStorage<N, U4, U1>,
-          S::Alloc: OwnedAllocator<N, U4, U1, S> {
+impl<N: Real> AbstractModule for Quaternion<N> {
     type AbstractRing = N;
 
     #[inline]
@@ -104,24 +80,15 @@ impl<N, S> AbstractModule for QuaternionBase<N, S>
     }
 }
 
-impl<N, S> Module for QuaternionBase<N, S>
-    where N: Real,
-          S: OwnedStorage<N, U4, U1>,
-          S::Alloc: OwnedAllocator<N, U4, U1, S> {
+impl<N: Real> Module for Quaternion<N> {
     type Ring = N;
 }
 
-impl<N, S> VectorSpace for QuaternionBase<N, S>
-    where N: Real,
-          S: OwnedStorage<N, U4, U1>,
-          S::Alloc: OwnedAllocator<N, U4, U1, S> {
+impl<N: Real> VectorSpace for Quaternion<N> {
     type Field = N;
 }
 
-impl<N, S> FiniteDimVectorSpace for QuaternionBase<N, S>
-    where N: Real,
-          S: OwnedStorage<N, U4, U1>,
-          S::Alloc: OwnedAllocator<N, U4, U1, S> {
+impl<N: Real> FiniteDimVectorSpace for Quaternion<N> {
     #[inline]
     fn dimension() -> usize {
         4
@@ -129,7 +96,7 @@ impl<N, S> FiniteDimVectorSpace for QuaternionBase<N, S>
 
     #[inline]
     fn canonical_basis_element(i: usize) -> Self {
-        Self::from_vector(ColumnVector::canonical_basis_element(i))
+        Self::from_vector(Vector4::canonical_basis_element(i))
     }
 
     #[inline]
@@ -148,10 +115,7 @@ impl<N, S> FiniteDimVectorSpace for QuaternionBase<N, S>
     }
 }
 
-impl<N, S> NormedSpace for QuaternionBase<N, S>
-    where N: Real,
-          S: OwnedStorage<N, U4, U1>,
-          S::Alloc: OwnedAllocator<N, U4, U1, S> {
+impl<N: Real> NormedSpace for Quaternion<N> {
     #[inline]
     fn norm_squared(&self) -> N {
         self.coords.norm_squared()
@@ -191,33 +155,24 @@ impl<N, S> NormedSpace for QuaternionBase<N, S>
 
 /*
  *
- * Implementations for UnitQuaternionBase.
+ * Implementations for UnitQuaternion.
  *
  */
-impl<N, S> Identity<Multiplicative> for UnitQuaternionBase<N, S>
-    where N: Real,
-          S: OwnedStorage<N, U4, U1>,
-          S::Alloc: OwnedAllocator<N, U4, U1, S> {
+impl<N: Real> Identity<Multiplicative> for UnitQuaternion<N> {
     #[inline]
     fn identity() -> Self {
         Self::identity()
     }
 }
 
-impl<N, S> AbstractMagma<Multiplicative> for UnitQuaternionBase<N, S>
-    where N: Real,
-          S: OwnedStorage<N, U4, U1>,
-          S::Alloc: OwnedAllocator<N, U4, U1, S> {
+impl<N: Real> AbstractMagma<Multiplicative> for UnitQuaternion<N> {
     #[inline]
     fn operate(&self, rhs: &Self) -> Self {
         self * rhs
     }
 }
 
-impl<N, S> Inverse<Multiplicative> for UnitQuaternionBase<N, S>
-    where N: Real,
-          S: OwnedStorage<N, U4, U1>,
-          S::Alloc: OwnedAllocator<N, U4, U1, S> {
+impl<N: Real> Inverse<Multiplicative> for UnitQuaternion<N> {
     #[inline]
     fn inverse(&self) -> Self {
         self.inverse()
@@ -230,7 +185,7 @@ impl<N, S> Inverse<Multiplicative> for UnitQuaternionBase<N, S>
 }
 
 impl_structures!(
-    UnitQuaternionBase;
+    UnitQuaternion;
     AbstractSemigroup<Multiplicative>,
     AbstractQuasigroup<Multiplicative>,
     AbstractMonoid<Multiplicative>,
@@ -238,48 +193,33 @@ impl_structures!(
     AbstractGroup<Multiplicative>
 );
 
-impl<N, SA, SB> Transformation<PointBase<N, U3, SB>> for UnitQuaternionBase<N, SA>
-    where N: Real,
-          SA: OwnedStorage<N, U4, U1>,
-          SB: OwnedStorage<N, U3, U1, Alloc = SA::Alloc>,
-          SA::Alloc: OwnedAllocator<N, U4, U1, SA>,
-          SB::Alloc: OwnedAllocator<N, U3, U1, SB> {
+impl<N: Real> Transformation<Point3<N>> for UnitQuaternion<N> {
     #[inline]
-    fn transform_point(&self, pt: &PointBase<N, U3, SB>) -> PointBase<N, U3, SB> {
+    fn transform_point(&self, pt: &Point3<N>) -> Point3<N> {
         self * pt
     }
 
     #[inline]
-    fn transform_vector(&self, v: &ColumnVector<N, U3, SB>) -> ColumnVector<N, U3, SB> {
+    fn transform_vector(&self, v: &Vector3<N>) -> Vector3<N> {
         self * v
     }
 }
 
-impl<N, SA, SB> ProjectiveTransformation<PointBase<N, U3, SB>> for UnitQuaternionBase<N, SA>
-    where N: Real,
-          SA: OwnedStorage<N, U4, U1>,
-          SB: OwnedStorage<N, U3, U1, Alloc = SA::Alloc>,
-          SA::Alloc: OwnedAllocator<N, U4, U1, SA>,
-          SB::Alloc: OwnedAllocator<N, U3, U1, SB> {
+impl<N: Real> ProjectiveTransformation<Point3<N>> for UnitQuaternion<N> {
     #[inline]
-    fn inverse_transform_point(&self, pt: &PointBase<N, U3, SB>) -> PointBase<N, U3, SB> {
+    fn inverse_transform_point(&self, pt: &Point3<N>) -> Point3<N> {
         // FIXME: would it be useful performancewise not to call inverse explicitly (i-e. implement
         // the inverse transformation explicitly here) ?
         self.inverse() * pt
     }
 
     #[inline]
-    fn inverse_transform_vector(&self, v: &ColumnVector<N, U3, SB>) -> ColumnVector<N, U3, SB> {
+    fn inverse_transform_vector(&self, v: &Vector3<N>) -> Vector3<N> {
         self.inverse() * v
     }
 }
 
-impl<N, SA, SB> AffineTransformation<PointBase<N, U3, SB>> for UnitQuaternionBase<N, SA>
-    where N: Real,
-          SA: OwnedStorage<N, U4, U1>,
-          SB: OwnedStorage<N, U3, U1, Alloc = SA::Alloc>,
-          SA::Alloc: OwnedAllocator<N, U4, U1, SA>,
-          SB::Alloc: OwnedAllocator<N, U3, U1, SB> {
+impl<N: Real> AffineTransformation<Point3<N>> for UnitQuaternion<N> {
     type Rotation          = Self;
     type NonUniformScaling = Id;
     type Translation       = Id;
@@ -320,12 +260,7 @@ impl<N, SA, SB> AffineTransformation<PointBase<N, U3, SB>> for UnitQuaternionBas
     }
 }
 
-impl<N, SA, SB> Similarity<PointBase<N, U3, SB>> for UnitQuaternionBase<N, SA>
-    where N: Real,
-          SA: OwnedStorage<N, U4, U1>,
-          SB: OwnedStorage<N, U3, U1, Alloc = SA::Alloc>,
-          SA::Alloc: OwnedAllocator<N, U4, U1, SA>,
-          SB::Alloc: OwnedAllocator<N, U3, U1, SB> {
+impl<N: Real> Similarity<Point3<N>> for UnitQuaternion<N> {
     type Scaling  = Id;
 
     #[inline]
@@ -346,12 +281,7 @@ impl<N, SA, SB> Similarity<PointBase<N, U3, SB>> for UnitQuaternionBase<N, SA>
 
 macro_rules! marker_impl(
     ($($Trait: ident),*) => {$(
-        impl<N, SA, SB> $Trait<PointBase<N, U3, SB>> for UnitQuaternionBase<N, SA>
-        where N: Real,
-              SA: OwnedStorage<N, U4, U1>,
-              SB: OwnedStorage<N, U3, U1, Alloc = SA::Alloc>,
-              SA::Alloc: OwnedAllocator<N, U4, U1, SA>,
-              SB::Alloc: OwnedAllocator<N, U3, U1, SB> { }
+        impl<N: Real> $Trait<Point3<N>> for UnitQuaternion<N> { }
     )*}
 );
 
@@ -359,24 +289,19 @@ marker_impl!(Isometry, DirectIsometry, OrthogonalTransformation);
 
 
 
-impl<N, SA, SB> Rotation<PointBase<N, U3, SB>> for UnitQuaternionBase<N, SA>
-    where N:  Real,
-          SA: OwnedStorage<N, U4, U1>,
-          SB: OwnedStorage<N, U3, U1, Alloc = SA::Alloc>,
-          SA::Alloc: OwnedAllocator<N, U4, U1, SA> + Allocator<N, U3, U1>,
-          SB::Alloc: OwnedAllocator<N, U3, U1, SB> {
+impl<N: Real> Rotation<Point3<N>> for UnitQuaternion<N> {
     #[inline]
     fn powf(&self, n: N) -> Option<Self> {
         Some(self.powf(n))
     }
 
     #[inline]
-    fn rotation_between(a: &ColumnVector<N, U3, SB>, b: &ColumnVector<N, U3, SB>) -> Option<Self> {
+    fn rotation_between(a: &Vector3<N>, b: &Vector3<N>) -> Option<Self> {
         Self::rotation_between(a, b)
     }
 
     #[inline]
-    fn scaled_rotation_between(a: &ColumnVector<N, U3, SB>, b: &ColumnVector<N, U3, SB>, s: N) -> Option<Self> {
+    fn scaled_rotation_between(a: &Vector3<N>, b: &Vector3<N>, s: N) -> Option<Self> {
         Self::scaled_rotation_between(a, b, s)
     }
 }

src/geometry/quaternion_alias.rs

@@ -1,10 +0,0 @@
-use core::MatrixArray;
-use core::dimension::{U1, U4};
-
-use geometry::{QuaternionBase, UnitQuaternionBase};
-
-/// A statically-allocated quaternion.
-pub type Quaternion<N> = QuaternionBase<N, MatrixArray<N, U4, U1>>;
-
-/// A statically-allocated unit quaternion.
-pub type UnitQuaternion<N> = UnitQuaternionBase<N, MatrixArray<N, U4, U1>>;

src/geometry/quaternion_construction.rs

@@ -1,42 +1,38 @@
 #[cfg(feature = "arbitrary")]
 use quickcheck::{Arbitrary, Gen};
+#[cfg(feature = "arbitrary")]
+use core::storage::Owned;
+#[cfg(feature = "arbitrary")]
+use core::dimension::U4;
 
 use rand::{Rand, Rng};
 use num::{Zero, One};
 
 use alga::general::Real;
 
-use core::{Unit, ColumnVector, Vector3};
-use core::storage::{Storage, OwnedStorage};
-use core::allocator::{Allocator, OwnedAllocator};
-use core::dimension::{U1, U3, U4};
+use core::{Unit, Vector, Vector4, Vector3};
+use core::storage::Storage;
+use core::dimension::U3;
 
-use geometry::{QuaternionBase, UnitQuaternionBase, RotationBase, OwnedRotation};
+use geometry::{Quaternion, UnitQuaternion, Rotation};
 
-impl<N, S> QuaternionBase<N, S>
-    where N: Real,
-          S: Storage<N, U4, U1> {
+impl<N: Real> Quaternion<N> {
     /// Creates a quaternion from a 4D vector. The quaternion scalar part corresponds to the `w`
     /// vector component.
     #[inline]
-    pub fn from_vector(vector: ColumnVector<N, U4, S>) -> Self {
-        QuaternionBase {
+    pub fn from_vector(vector: Vector4<N>) -> Self {
+        Quaternion {
             coords: vector
         }
     }
-}
 
-impl<N, S> QuaternionBase<N, S>
-    where N: Real,
-          S: OwnedStorage<N, U4, U1>,
-          S::Alloc: OwnedAllocator<N, U4, U1, S> {
     /// Creates a new quaternion from its individual components. Note that the arguments order does
     /// **not** follow the storage order.
     ///
     /// The storage order is `[ x, y, z, w ]`.
     #[inline]
     pub fn new(w: N, x: N, y: N, z: N) -> Self {
-        let v = ColumnVector::<N, U4, S>::new(x, y, z, w);
+        let v = Vector4::<N>::new(x, y, z, w);
         Self::from_vector(v)
     }
 
@@ -46,8 +42,8 @@ impl<N, S> QuaternionBase<N, S>
     /// The storage order is [ vector, scalar ].
     #[inline]
     // FIXME: take a reference to `vector`?
-    pub fn from_parts<SB>(scalar: N, vector: ColumnVector<N, U3, SB>) -> Self
-        where SB: Storage<N, U3, U1> {
+    pub fn from_parts<SB>(scalar: N, vector: Vector<N, U3, SB>) -> Self
+        where SB: Storage<N, U3> {
 
         Self::new(scalar, vector[0], vector[1], vector[2])
     }
@@ -56,9 +52,9 @@ impl<N, S> QuaternionBase<N, S>
     ///
     /// Note that `axis` is assumed to be a unit vector.
     // FIXME: take a reference to `axis`?
-    pub fn from_polar_decomposition<SB>(scale: N, theta: N, axis: Unit<ColumnVector<N, U3, SB>>) -> Self
-        where SB: Storage<N, U3, U1> {
-        let rot = UnitQuaternionBase::<N, S>::from_axis_angle(&axis, theta * ::convert(2.0f64));
+    pub fn from_polar_decomposition<SB>(scale: N, theta: N, axis: Unit<Vector<N, U3, SB>>) -> Self
+        where SB: Storage<N, U3> {
+        let rot = UnitQuaternion::<N>::from_axis_angle(&axis, theta * ::convert(2.0f64));
 
         rot.unwrap() * scale
     }
@@ -70,20 +66,14 @@ impl<N, S> QuaternionBase<N, S>
     }
 }
 
-impl<N, S> One for QuaternionBase<N, S>
-    where N: Real,
-          S: OwnedStorage<N, U4, U1>,
-          S::Alloc: OwnedAllocator<N, U4, U1, S> {
+impl<N: Real> One for Quaternion<N> {
     #[inline]
     fn one() -> Self {
         Self::identity()
     }
 }
 
-impl<N, S> Zero for QuaternionBase<N, S>
-    where N: Real,
-          S: OwnedStorage<N, U4, U1>,
-          S::Alloc: OwnedAllocator<N, U4, U1, S> {
+impl<N: Real> Zero for Quaternion<N> {
     #[inline]
     fn zero() -> Self {
         Self::new(N::zero(), N::zero(), N::zero(), N::zero())
@@ -95,46 +85,38 @@ impl<N, S> Zero for QuaternionBase<N, S>
     }
 }
 
-impl<N, S> Rand for QuaternionBase<N, S>
-    where N: Real + Rand,
-          S: OwnedStorage<N, U4, U1>,
-          S::Alloc: OwnedAllocator<N, U4, U1, S> {
+impl<N: Real + Rand> Rand for Quaternion<N> {
     #[inline]
     fn rand<R: Rng>(rng: &mut R) -> Self {
-        QuaternionBase::new(rng.gen(), rng.gen(), rng.gen(), rng.gen())
+        Quaternion::new(rng.gen(), rng.gen(), rng.gen(), rng.gen())
     }
 }
 
 #[cfg(feature="arbitrary")]
-impl<N, S> Arbitrary for QuaternionBase<N, S>
-    where N: Real + Arbitrary,
-          S: OwnedStorage<N, U4, U1> + Send,
-          S::Alloc: OwnedAllocator<N, U4, U1, S> {
+impl<N: Real + Arbitrary> Arbitrary for Quaternion<N>
+    where Owned<N, U4>: Send {
     #[inline]
     fn arbitrary<G: Gen>(g: &mut G) -> Self {
-        QuaternionBase::new(N::arbitrary(g), N::arbitrary(g),
+        Quaternion::new(N::arbitrary(g), N::arbitrary(g),
                             N::arbitrary(g), N::arbitrary(g))
     }
 }
 
-impl<N, S> UnitQuaternionBase<N, S>
-    where N: Real,
-          S: OwnedStorage<N, U4, U1>,
-          S::Alloc: OwnedAllocator<N, U4, U1, S> {
+impl<N: Real> UnitQuaternion<N> {
     /// The quaternion multiplicative identity.
     #[inline]
     pub fn identity() -> Self {
-        Self::new_unchecked(QuaternionBase::identity())
+        Self::new_unchecked(Quaternion::identity())
     }
 
     /// Creates a new quaternion from a unit vector (the rotation axis) and an angle
     /// (the rotation angle).
     #[inline]
-    pub fn from_axis_angle<SB>(axis: &Unit<ColumnVector<N, U3, SB>>, angle: N) -> Self
-        where SB: Storage<N, U3, U1> {
+    pub fn from_axis_angle<SB>(axis: &Unit<Vector<N, U3, SB>>, angle: N) -> Self
+        where SB: Storage<N, U3> {
         let (sang, cang) = (angle / ::convert(2.0f64)).sin_cos();
 
-        let q = QuaternionBase::from_parts(cang, axis.as_ref() * sang);
+        let q = Quaternion::from_parts(cang, axis.as_ref() * sang);
         Self::new_unchecked(q)
     }
 
@@ -142,7 +124,7 @@ impl<N, S> UnitQuaternionBase<N, S>
     ///
     /// The input quaternion will be normalized.
     #[inline]
-    pub fn from_quaternion(q: QuaternionBase<N, S>) -> Self {
+    pub fn from_quaternion(q: Quaternion<N>) -> Self {
         Self::new_normalize(q)
     }
 
@@ -155,7 +137,7 @@ impl<N, S> UnitQuaternionBase<N, S>
         let (sp, cp) = (pitch * ::convert(0.5f64)).sin_cos();
         let (sy, cy) = (yaw   * ::convert(0.5f64)).sin_cos();
 
-        let q = QuaternionBase::new(
+        let q = Quaternion::new(
                     cr * cp * cy + sr * sp * sy,
                     sr * cp * cy - cr * sp * sy,
                     cr * sp * cy + sr * cp * sy,
@@ -166,10 +148,7 @@ impl<N, S> UnitQuaternionBase<N, S>
 
     /// Builds an unit quaternion from a rotation matrix.
     #[inline]
-    pub fn from_rotation_matrix<SB>(rotmat: &RotationBase<N, U3, SB>) -> Self
-        where SB: Storage<N, U3, U3>,
-              SB::Alloc: Allocator<N, U3, U1> {
-
+    pub fn from_rotation_matrix(rotmat: &Rotation<N, U3>) -> Self {
         // Robust matrix to quaternion transformation.
         // See http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion
         let tr = rotmat[(0, 0)] + rotmat[(1, 1)] + rotmat[(2, 2)];
@@ -179,28 +158,28 @@ impl<N, S> UnitQuaternionBase<N, S>
 
         if tr > N::zero() {
           let denom = (tr + N::one()).sqrt() * ::convert(2.0);
-          res = QuaternionBase::new(_0_25 * denom,
+          res = Quaternion::new(_0_25 * denom,
                                     (rotmat[(2, 1)] - rotmat[(1, 2)]) / denom,
                                     (rotmat[(0, 2)] - rotmat[(2, 0)]) / denom,
                                     (rotmat[(1, 0)] - rotmat[(0, 1)]) / denom);
         }
         else if rotmat[(0, 0)] > rotmat[(1, 1)] && rotmat[(0, 0)] > rotmat[(2, 2)] {
           let denom = (N::one() + rotmat[(0, 0)] - rotmat[(1, 1)] - rotmat[(2, 2)]).sqrt() * ::convert(2.0);
-          res = QuaternionBase::new((rotmat[(2, 1)] - rotmat[(1, 2)]) / denom,
+          res = Quaternion::new((rotmat[(2, 1)] - rotmat[(1, 2)]) / denom,
                                     _0_25 * denom,
                                     (rotmat[(0, 1)] + rotmat[(1, 0)]) / denom,
                                     (rotmat[(0, 2)] + rotmat[(2, 0)]) / denom);
         }
         else if rotmat[(1, 1)] > rotmat[(2, 2)] {
           let denom = (N::one() + rotmat[(1, 1)] - rotmat[(0, 0)] - rotmat[(2, 2)]).sqrt() * ::convert(2.0);
-          res = QuaternionBase::new((rotmat[(0, 2)] - rotmat[(2, 0)]) / denom,
+          res = Quaternion::new((rotmat[(0, 2)] - rotmat[(2, 0)]) / denom,
                                     (rotmat[(0, 1)] + rotmat[(1, 0)]) / denom,
                                     _0_25 * denom,
                                     (rotmat[(1, 2)] + rotmat[(2, 1)]) / denom);
         }
         else {
           let denom = (N::one() + rotmat[(2, 2)] - rotmat[(0, 0)] - rotmat[(1, 1)]).sqrt() * ::convert(2.0);
-          res = QuaternionBase::new((rotmat[(1, 0)] - rotmat[(0, 1)]) / denom,
+          res = Quaternion::new((rotmat[(1, 0)] - rotmat[(0, 1)]) / denom,
                                     (rotmat[(0, 2)] + rotmat[(2, 0)]) / denom,
                                     (rotmat[(1, 2)] + rotmat[(2, 1)]) / denom,
                                     _0_25 * denom);
@@ -212,19 +191,22 @@ impl<N, S> UnitQuaternionBase<N, S>
     /// The unit quaternion needed to make `a` and `b` be collinear and point toward the same
     /// direction.
     #[inline]
-    pub fn rotation_between<SB, SC>(a: &ColumnVector<N, U3, SB>, b: &ColumnVector<N, U3, SC>) -> Option<Self>
-        where SB: Storage<N, U3, U1>,
-              SC: Storage<N, U3, U1> {
+    pub fn rotation_between<SB, SC>(a: &Vector<N, U3, SB>, b: &Vector<N, U3, SC>) -> Option<Self>
+        where SB: Storage<N, U3>,
+              SC: Storage<N, U3> {
         Self::scaled_rotation_between(a, b, N::one())
     }
 
     /// The smallest rotation needed to make `a` and `b` collinear and point toward the same
     /// direction, raised to the power `s`.
     #[inline]
-    pub fn scaled_rotation_between<SB, SC>(a: &ColumnVector<N, U3, SB>, b: &ColumnVector<N, U3, SC>, s: N) -> Option<Self>
-        where SB: Storage<N, U3, U1>,
-              SC: Storage<N, U3, U1> {
-        // FIXME: code duplication with RotationBase.
+    pub fn scaled_rotation_between<SB, SC>(a: &Vector<N, U3, SB>,
+                                           b: &Vector<N, U3, SC>,
+                                           s: N)
+                                           -> Option<Self>
+        where SB: Storage<N, U3>,
+              SC: Storage<N, U3> {
+        // FIXME: code duplication with Rotation.
         if let (Some(na), Some(nb)) = (a.try_normalize(N::zero()), b.try_normalize(N::zero())) {
             let c = na.cross(&nb);
 
@@ -257,12 +239,10 @@ impl<N, S> UnitQuaternionBase<N, S>
     ///   collinear
     ///   to `dir`. Non-collinearity is not checked.
     #[inline]
-    pub fn new_observer_frame<SB, SC>(dir: &ColumnVector<N, U3, SB>, up: &ColumnVector<N, U3, SC>) -> Self
-    where SB: Storage<N, U3, U1>,
-          SC: Storage<N, U3, U1>,
-          S::Alloc: Allocator<N, U3, U3> +
-                    Allocator<N, U3, U1> {
-        Self::from_rotation_matrix(&OwnedRotation::<N, U3, S::Alloc>::new_observer_frame(dir, up))
+    pub fn new_observer_frame<SB, SC>(dir: &Vector<N, U3, SB>, up: &Vector<N, U3, SC>) -> Self
+    where SB: Storage<N, U3>,
+          SC: Storage<N, U3> {
+        Self::from_rotation_matrix(&Rotation::<N, U3>::new_observer_frame(dir, up))
     }
 
 
@@ -277,11 +257,9 @@ impl<N, S> UnitQuaternionBase<N, S>
     ///   * up - A vector approximately aligned with required the vertical axis. The only
     ///   requirement of this parameter is to not be collinear to `target - eye`.
     #[inline]
-    pub fn look_at_rh<SB, SC>(dir: &ColumnVector<N, U3, SB>, up: &ColumnVector<N, U3, SC>) -> Self
-    where SB: Storage<N, U3, U1>,
-          SC: Storage<N, U3, U1>,
-          S::Alloc: Allocator<N, U3, U3> +
-                    Allocator<N, U3, U1> {
+    pub fn look_at_rh<SB, SC>(dir: &Vector<N, U3, SB>, up: &Vector<N, U3, SC>) -> Self
+    where SB: Storage<N, U3>,
+          SC: Storage<N, U3> {
         Self::new_observer_frame(&-dir, up).inverse()
     }
 
@@ -296,28 +274,20 @@ impl<N, S> UnitQuaternionBase<N, S>
     ///   * up - A vector approximately aligned with required the vertical axis. The only
     ///   requirement of this parameter is to not be collinear to `target - eye`.
     #[inline]
-    pub fn look_at_lh<SB, SC>(dir: &ColumnVector<N, U3, SB>, up: &ColumnVector<N, U3, SC>) -> Self
-    where SB: Storage<N, U3, U1>,
-          SC: Storage<N, U3, U1>,
-          S::Alloc: Allocator<N, U3, U3> +
-                    Allocator<N, U3, U1> {
+    pub fn look_at_lh<SB, SC>(dir: &Vector<N, U3, SB>, up: &Vector<N, U3, SC>) -> Self
+    where SB: Storage<N, U3>,
+          SC: Storage<N, U3> {
             Self::new_observer_frame(dir, up).inverse()
     }
-}
 
-impl<N, S> UnitQuaternionBase<N, S>
-    where N: Real,
-          S: OwnedStorage<N, U4, U1>,
-          S::Alloc: OwnedAllocator<N, U4, U1, S> +
-                    Allocator<N, U3, U1> {
     /// Creates a new unit quaternion rotation from a rotation axis scaled by the rotation angle.
     ///
     /// If `axisangle` is zero, this returns the indentity rotation.
     #[inline]
-    pub fn new<SB>(axisangle: ColumnVector<N, U3, SB>) -> Self
-        where SB: Storage<N, U3, U1> {
+    pub fn new<SB>(axisangle: Vector<N, U3, SB>) -> Self
+        where SB: Storage<N, U3> {
         let two: N = ::convert(2.0f64);
-        let q = QuaternionBase::<N, S>::from_parts(N::zero(), axisangle / two).exp();
+        let q = Quaternion::<N>::from_parts(N::zero(), axisangle / two).exp();
         Self::new_unchecked(q)
     }
 
@@ -326,44 +296,35 @@ impl<N, S> UnitQuaternionBase<N, S>
     /// If `axisangle` is zero, this returns the indentity rotation.
     /// Same as `Self::new(axisangle)`.
     #[inline]
-    pub fn from_scaled_axis<SB>(axisangle: ColumnVector<N, U3, SB>) -> Self
-        where SB: Storage<N, U3, U1> {
+    pub fn from_scaled_axis<SB>(axisangle: Vector<N, U3, SB>) -> Self
+        where SB: Storage<N, U3> {
         Self::new(axisangle)
     }
 }
 
-impl<N, S> One for UnitQuaternionBase<N, S>
-    where N: Real,
-          S: OwnedStorage<N, U4, U1>,
-          S::Alloc: OwnedAllocator<N, U4, U1, S> {
+impl<N: Real> One for UnitQuaternion<N> {
     #[inline]
     fn one() -> Self {
         Self::identity()
     }
 }
 
-impl<N, S> Rand for UnitQuaternionBase<N, S>
-    where N: Real + Rand,
-          S: OwnedStorage<N, U4, U1>,
-          S::Alloc: OwnedAllocator<N, U4, U1, S> +
-                    Allocator<N, U3, U1> {
+impl<N: Real + Rand> Rand for UnitQuaternion<N> {
     #[inline]
     fn rand<R: Rng>(rng: &mut R) -> Self {
         let axisangle = Vector3::rand(rng);
-        UnitQuaternionBase::from_scaled_axis(axisangle)
+        UnitQuaternion::from_scaled_axis(axisangle)
     }
 }
 
 #[cfg(feature="arbitrary")]
-impl<N, S> Arbitrary for UnitQuaternionBase<N, S>
-    where N: Real + Arbitrary,
-          S: OwnedStorage<N, U4, U1> + Send,
-          S::Alloc: OwnedAllocator<N, U4, U1, S> +
-                    Allocator<N, U3, U1> {
+impl<N: Real + Arbitrary> Arbitrary for UnitQuaternion<N>
+    where Owned<N, U4>: Send,
+          Owned<N, U3>: Send {
     #[inline]
     fn arbitrary<G: Gen>(g: &mut G) -> Self {
         let axisangle = Vector3::arbitrary(g);
-        UnitQuaternionBase::from_scaled_axis(axisangle)
+        UnitQuaternion::from_scaled_axis(axisangle)
 
     }
 }

src/geometry/quaternion_conversion.rs

@@ -3,12 +3,11 @@ use num::Zero;
 use alga::general::{SubsetOf, SupersetOf, Real};
 use alga::linear::Rotation as AlgaRotation;
 
-use core::{ColumnVector, SquareMatrix};
-use core::dimension::{U1, U3, U4};
-use core::storage::OwnedStorage;
-use core::allocator::{Allocator, OwnedAllocator};
-use geometry::{PointBase, QuaternionBase, UnitQuaternionBase, OwnedUnitQuaternionBase, RotationBase,
-               OwnedRotation, IsometryBase, SimilarityBase, TransformBase, SuperTCategoryOf, TAffine, TranslationBase};
+use core::{Vector4, Matrix4};
+use core::dimension::U3;
+use geometry::{Quaternion, UnitQuaternion, Rotation, Isometry, Similarity,
+               Transform, SuperTCategoryOf, TAffine, Translation,
+               Rotation3, Point3};
 
 /*
  * This file provides the following conversions:
@@ -16,197 +15,154 @@ use geometry::{PointBase, QuaternionBase, UnitQuaternionBase, OwnedUnitQuaternio
  *
  * Quaternion     -> Quaternion
  * UnitQuaternion -> UnitQuaternion
- * UnitQuaternion -> RotationBase<U3>
- * UnitQuaternion -> IsometryBase<U3>
- * UnitQuaternion -> SimilarityBase<U3>
- * UnitQuaternion -> TransformBase<U3>
+ * UnitQuaternion -> Rotation<U3>
+ * UnitQuaternion -> Isometry<U3>
+ * UnitQuaternion -> Similarity<U3>
+ * UnitQuaternion -> Transform<U3>
  * UnitQuaternion -> Matrix<U4> (homogeneous)
  *
  * NOTE:
  * UnitQuaternion -> Quaternion is already provided by: Unit<T> -> T
  */
 
-impl<N1, N2, SA, SB> SubsetOf<QuaternionBase<N2, SB>> for QuaternionBase<N1, SA>
+impl<N1, N2> SubsetOf<Quaternion<N2>> for Quaternion<N1>
     where N1: Real,
-          N2: Real + SupersetOf<N1>,
-          SA: OwnedStorage<N1, U4, U1>,
-          SB: OwnedStorage<N2, U4, U1>,
-          SA::Alloc: OwnedAllocator<N1, U4, U1, SA>,
-          SB::Alloc: OwnedAllocator<N2, U4, U1, SB> {
+          N2: Real + SupersetOf<N1> {
     #[inline]
-    fn to_superset(&self) -> QuaternionBase<N2, SB> {
-        QuaternionBase::from_vector(self.coords.to_superset())
+    fn to_superset(&self) -> Quaternion<N2> {
+        Quaternion::from_vector(self.coords.to_superset())
     }
 
     #[inline]
-    fn is_in_subset(q: &QuaternionBase<N2, SB>) -> bool {
-        ::is_convertible::<_, ColumnVector<N1, U4, SA>>(&q.coords)
+    fn is_in_subset(q: &Quaternion<N2>) -> bool {
+        ::is_convertible::<_, Vector4<N1>>(&q.coords)
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(q: &QuaternionBase<N2, SB>) -> Self {
+    unsafe fn from_superset_unchecked(q: &Quaternion<N2>) -> Self {
         Self::from_vector(q.coords.to_subset_unchecked())
     }
 }
 
-impl<N1, N2, SA, SB> SubsetOf<UnitQuaternionBase<N2, SB>> for UnitQuaternionBase<N1, SA>
+impl<N1, N2> SubsetOf<UnitQuaternion<N2>> for UnitQuaternion<N1>
     where N1: Real,
-          N2: Real + SupersetOf<N1>,
-          SA: OwnedStorage<N1, U4, U1>,
-          SB: OwnedStorage<N2, U4, U1>,
-          SA::Alloc: OwnedAllocator<N1, U4, U1, SA>,
-          SB::Alloc: OwnedAllocator<N2, U4, U1, SB> {
+          N2: Real + SupersetOf<N1> {
     #[inline]
-    fn to_superset(&self) -> UnitQuaternionBase<N2, SB> {
-        UnitQuaternionBase::new_unchecked(self.as_ref().to_superset())
+    fn to_superset(&self) -> UnitQuaternion<N2> {
+        UnitQuaternion::new_unchecked(self.as_ref().to_superset())
     }
 
     #[inline]
-    fn is_in_subset(uq: &UnitQuaternionBase<N2, SB>) -> bool {
-        ::is_convertible::<_, QuaternionBase<N1, SA>>(uq.as_ref())
+    fn is_in_subset(uq: &UnitQuaternion<N2>) -> bool {
+        ::is_convertible::<_, Quaternion<N1>>(uq.as_ref())
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(uq: &UnitQuaternionBase<N2, SB>) -> Self {
+    unsafe fn from_superset_unchecked(uq: &UnitQuaternion<N2>) -> Self {
         Self::new_unchecked(::convert_ref_unchecked(uq.as_ref()))
     }
 }
 
-impl<N1, N2, SA, SB> SubsetOf<RotationBase<N2, U3, SB>> for UnitQuaternionBase<N1, SA>
+impl<N1, N2> SubsetOf<Rotation<N2, U3>> for UnitQuaternion<N1>
     where N1: Real,
-          N2: Real + SupersetOf<N1>,
-          SA: OwnedStorage<N1, U4, U1>,
-          SB: OwnedStorage<N2, U3, U3>,
-          SA::Alloc: OwnedAllocator<N1, U4, U1, SA> +
-                     Allocator<N1, U3, U3>,
-          SB::Alloc: OwnedAllocator<N2, U3, U3, SB> +
-                     Allocator<N2, U4, U1> +
-                     Allocator<N2, U3, U1> {
+          N2: Real + SupersetOf<N1> {
     #[inline]
-    fn to_superset(&self) -> RotationBase<N2, U3, SB> {
-        let q: OwnedUnitQuaternionBase<N2, SB::Alloc> = self.to_superset();
+    fn to_superset(&self) -> Rotation3<N2> {
+        let q: UnitQuaternion<N2> = self.to_superset();
         q.to_rotation_matrix()
     }
 
     #[inline]
-    fn is_in_subset(rot: &RotationBase<N2, U3, SB>) -> bool {
-        ::is_convertible::<_, OwnedRotation<N1, U3, SA::Alloc>>(rot)
+    fn is_in_subset(rot: &Rotation3<N2>) -> bool {
+        ::is_convertible::<_, Rotation3<N1>>(rot)
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(rot: &RotationBase<N2, U3, SB>) -> Self {
-        let q = OwnedUnitQuaternionBase::<N2, SB::Alloc>::from_rotation_matrix(rot);
+    unsafe fn from_superset_unchecked(rot: &Rotation3<N2>) -> Self {
+        let q = UnitQuaternion::<N2>::from_rotation_matrix(rot);
         ::convert_unchecked(q)
     }
 }
 
 
-impl<N1, N2, SA, SB, R> SubsetOf<IsometryBase<N2, U3, SB, R>> for UnitQuaternionBase<N1, SA>
+impl<N1, N2, R> SubsetOf<Isometry<N2, U3, R>> for UnitQuaternion<N1>
     where N1: Real,
           N2: Real + SupersetOf<N1>,
-          SA: OwnedStorage<N1, U4, U1>,
-          SB: OwnedStorage<N2, U3, U1>,
-          R:  AlgaRotation<PointBase<N2, U3, SB>> + SupersetOf<UnitQuaternionBase<N1, SA>>,
-          SA::Alloc: OwnedAllocator<N1, U4, U1, SA>,
-          SB::Alloc: OwnedAllocator<N2, U3, U1, SB> {
+          R:  AlgaRotation<Point3<N2>> + SupersetOf<UnitQuaternion<N1>> {
     #[inline]
-    fn to_superset(&self) -> IsometryBase<N2, U3, SB, R> {
-        IsometryBase::from_parts(TranslationBase::identity(), ::convert_ref(self))
+    fn to_superset(&self) -> Isometry<N2, U3, R> {
+        Isometry::from_parts(Translation::identity(), ::convert_ref(self))
     }
 
     #[inline]
-    fn is_in_subset(iso: &IsometryBase<N2, U3, SB, R>) -> bool {
+    fn is_in_subset(iso: &Isometry<N2, U3, R>) -> bool {
         iso.translation.vector.is_zero()
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(iso: &IsometryBase<N2, U3, SB, R>) -> Self {
+    unsafe fn from_superset_unchecked(iso: &Isometry<N2, U3, R>) -> Self {
         ::convert_ref_unchecked(&iso.rotation)
     }
 }
 
 
-impl<N1, N2, SA, SB, R> SubsetOf<SimilarityBase<N2, U3, SB, R>> for UnitQuaternionBase<N1, SA>
+impl<N1, N2, R> SubsetOf<Similarity<N2, U3, R>> for UnitQuaternion<N1>
     where N1: Real,
           N2: Real + SupersetOf<N1>,
-          SA: OwnedStorage<N1, U4, U1>,
-          SB: OwnedStorage<N2, U3, U1>,
-          R:  AlgaRotation<PointBase<N2, U3, SB>> + SupersetOf<UnitQuaternionBase<N1, SA>>,
-          SA::Alloc: OwnedAllocator<N1, U4, U1, SA>,
-          SB::Alloc: OwnedAllocator<N2, U3, U1, SB> {
+          R:  AlgaRotation<Point3<N2>> + SupersetOf<UnitQuaternion<N1>> {
     #[inline]
-    fn to_superset(&self) -> SimilarityBase<N2, U3, SB, R> {
-        SimilarityBase::from_isometry(::convert_ref(self), N2::one())
+    fn to_superset(&self) -> Similarity<N2, U3, R> {
+        Similarity::from_isometry(::convert_ref(self), N2::one())
     }
 
     #[inline]
-    fn is_in_subset(sim: &SimilarityBase<N2, U3, SB, R>) -> bool {
+    fn is_in_subset(sim: &Similarity<N2, U3, R>) -> bool {
         sim.isometry.translation.vector.is_zero() &&
         sim.scaling() == N2::one()
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(sim: &SimilarityBase<N2, U3, SB, R>) -> Self {
+    unsafe fn from_superset_unchecked(sim: &Similarity<N2, U3, R>) -> Self {
         ::convert_ref_unchecked(&sim.isometry)
     }
 }
 
 
-impl<N1, N2, SA, SB, C> SubsetOf<TransformBase<N2, U3, SB, C>> for UnitQuaternionBase<N1, SA>
+impl<N1, N2, C> SubsetOf<Transform<N2, U3, C>> for UnitQuaternion<N1>
     where N1: Real,
           N2: Real + SupersetOf<N1>,
-          SA: OwnedStorage<N1, U4, U1>,
-          SB: OwnedStorage<N2, U4, U4>,
-          C:  SuperTCategoryOf<TAffine>,
-          SA::Alloc: OwnedAllocator<N1, U4, U1, SA> +
-                     Allocator<N1, U3, U3> +
-                     Allocator<N1, U3, U1> +
-                     Allocator<N1, U4, U4>,
-          SB::Alloc: OwnedAllocator<N2, U4, U4, SB> +
-                     Allocator<N2, U3, U3> +
-                     Allocator<N2, U1, U3> {
+          C:  SuperTCategoryOf<TAffine> {
     #[inline]
-    fn to_superset(&self) -> TransformBase<N2, U3, SB, C> {
-        TransformBase::from_matrix_unchecked(self.to_homogeneous().to_superset())
+    fn to_superset(&self) -> Transform<N2, U3, C> {
+        Transform::from_matrix_unchecked(self.to_homogeneous().to_superset())
     }
 
     #[inline]
-    fn is_in_subset(t: &TransformBase<N2, U3, SB, C>) -> bool {
+    fn is_in_subset(t: &Transform<N2, U3, C>) -> bool {
         <Self as SubsetOf<_>>::is_in_subset(t.matrix())
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(t: &TransformBase<N2, U3, SB, C>) -> Self {
+    unsafe fn from_superset_unchecked(t: &Transform<N2, U3, C>) -> Self {
         Self::from_superset_unchecked(t.matrix())
     }
 }
 
 
-impl<N1, N2, SA, SB> SubsetOf<SquareMatrix<N2, U4, SB>> for UnitQuaternionBase<N1, SA>
-    where N1: Real,
-          N2: Real + SupersetOf<N1>,
-          SA: OwnedStorage<N1, U4, U1>,
-          SB: OwnedStorage<N2, U4, U4>,
-          SA::Alloc: OwnedAllocator<N1, U4, U1, SA> +
-                     Allocator<N1, U3, U3> +
-                     Allocator<N1, U3, U1> +
-                     Allocator<N1, U4, U4>,
-          SB::Alloc: OwnedAllocator<N2, U4, U4, SB> +
-                     Allocator<N2, U3, U3> +
-                     Allocator<N2, U1, U3> {
+impl<N1: Real, N2: Real + SupersetOf<N1>> SubsetOf<Matrix4<N2>> for UnitQuaternion<N1> {
     #[inline]
-    fn to_superset(&self) -> SquareMatrix<N2, U4, SB> {
+    fn to_superset(&self) -> Matrix4<N2> {
         self.to_homogeneous().to_superset()
     }
 
     #[inline]
-    fn is_in_subset(m: &SquareMatrix<N2, U4, SB>) -> bool {
-        ::is_convertible::<_, OwnedRotation<N1, U3, SA::Alloc>>(m)
+    fn is_in_subset(m: &Matrix4<N2>) -> bool {
+        ::is_convertible::<_, Rotation3<N1>>(m)
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(m: &SquareMatrix<N2, U4, SB>) -> Self {
-        let rot: OwnedRotation<N1, U3, SA::Alloc> = ::convert_ref_unchecked(m);
+    unsafe fn from_superset_unchecked(m: &Matrix4<N2>) -> Self {
+        let rot: Rotation3<N1> = ::convert_ref_unchecked(m);
         Self::from_rotation_matrix(&rot)
     }
 }

src/geometry/quaternion_coordinates.rs

@@ -4,17 +4,11 @@ use std::ops::{Deref, DerefMut};
 use alga::general::Real;
 
 use core::coordinates::IJKW;
-use core::storage::OwnedStorage;
-use core::allocator::OwnedAllocator;
-use core::dimension::{U1, U4};
 
-use geometry::QuaternionBase;
+use geometry::Quaternion;
 
 
-impl<N, S> Deref for QuaternionBase<N, S>
-    where N: Real,
-          S: OwnedStorage<N, U4, U1>,
-          S::Alloc: OwnedAllocator<N, U4, U1, S> {
+impl<N: Real> Deref for Quaternion<N> {
     type Target = IJKW<N>;
 
     #[inline]
@@ -23,10 +17,7 @@ impl<N, S> Deref for QuaternionBase<N, S>
     }
 }
 
-impl<N, S> DerefMut for QuaternionBase<N, S>
-    where N: Real,
-          S: OwnedStorage<N, U4, U1>,
-          S::Alloc: OwnedAllocator<N, U4, U1, S> {
+impl<N: Real> DerefMut for Quaternion<N> {
     #[inline]
     fn deref_mut(&mut self) -> &mut Self::Target {
         unsafe { mem::transmute(self) }

src/geometry/quaternion_ops.rs

@@ -17,17 +17,17 @@
  *
  * (Unit Quaternion)
  * UnitQuaternion × UnitQuaternion
- * UnitQuaternion × RotationBase   -> UnitQuaternion
- * RotationBase   × UnitQuaternion -> UnitQuaternion
+ * UnitQuaternion × Rotation       -> UnitQuaternion
+ * Rotation       × UnitQuaternion -> UnitQuaternion
  *
  * UnitQuaternion ÷ UnitQuaternion
- * UnitQuaternion ÷ RotationBase   -> UnitQuaternion
- * RotationBase   ÷ UnitQuaternion -> UnitQuaternion
+ * UnitQuaternion ÷ Rotation       -> UnitQuaternion
+ * Rotation       ÷ UnitQuaternion -> UnitQuaternion
  *
  *
- * UnitQuaternion × PointBase
- * UnitQuaternion × ColumnVector
- * UnitQuaternion × Unit<ColumnVector>
+ * UnitQuaternion × Point
+ * UnitQuaternion × Vector
+ * UnitQuaternion × Unit<Vector>
  *
  * NOTE: -UnitQuaternion is already provided by `Unit<T>`.
  *
@@ -40,31 +40,28 @@
  * Quaternion -= Quaternion
  *
  * UnitQuaternion ×= UnitQuaternion
- * UnitQuaternion ×= RotationBase
+ * UnitQuaternion ×= Rotation
  *
  * UnitQuaternion ÷= UnitQuaternion
- * UnitQuaternion ÷= RotationBase
+ * UnitQuaternion ÷= Rotation
  *
- * FIXME: RotationBase ×= UnitQuaternion
- * FIXME: RotationBase ÷= UnitQuaternion
+ * FIXME: Rotation ×= UnitQuaternion
+ * FIXME: Rotation ÷= UnitQuaternion
  *
  */
 
-use std::ops::{Index, IndexMut, Neg, Add, AddAssign, Mul, MulAssign, Div, DivAssign, Sub, SubAssign};
+use std::ops::{Index, IndexMut, Neg, Add, AddAssign, Mul, MulAssign, Sub, SubAssign, Div, DivAssign};
 
 use alga::general::Real;
 
-use core::{ColumnVector, OwnedColumnVector, Unit};
-use core::storage::{Storage, StorageMut};
+use core::{DefaultAllocator, Vector, Vector3, Unit};
+use core::storage::Storage;
 use core::allocator::Allocator;
 use core::dimension::{U1, U3, U4};
 
-use geometry::{QuaternionBase, OwnedQuaternionBase, UnitQuaternionBase, OwnedUnitQuaternionBase,
-               PointBase, OwnedPoint, RotationBase};
+use geometry::{Quaternion, UnitQuaternion, Point3, Rotation};
 
-impl<N, S> Index<usize> for QuaternionBase<N, S>
-    where N: Real,
-          S: Storage<N, U4, U1> {
+impl<N: Real> Index<usize> for Quaternion<N> {
     type Output = N;
 
     #[inline]
@@ -73,10 +70,7 @@ impl<N, S> Index<usize> for QuaternionBase<N, S>
     }
 }
 
-impl<N, S> IndexMut<usize> for QuaternionBase<N, S>
-    where N: Real,
-          S: StorageMut<N, U4, U1> {
-
+impl<N: Real> IndexMut<usize> for Quaternion<N> {
     #[inline]
     fn index_mut(&mut self, i: usize) -> &mut N {
         &mut self.coords[i]
@@ -85,15 +79,13 @@ impl<N, S> IndexMut<usize> for QuaternionBase<N, S>
 
 macro_rules! quaternion_op_impl(
     ($Op: ident, $op: ident;
-     ($LhsRDim: ident, $LhsCDim: ident), ($RhsRDim: ident, $RhsCDim: ident);
+     ($LhsRDim: ident, $LhsCDim: ident), ($RhsRDim: ident, $RhsCDim: ident)
+     $(for $Storage: ident: $StoragesBound: ident $(<$($BoundParam: ty),*>)*),*;
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Result: ty $(=> $VDimA: ty, $VDimB: ty)*;
      $action: expr; $($lives: tt),*) => {
-        impl<$($lives ,)* N, SA, SB> $Op<$Rhs> for $Lhs
-            where N: Real,
-                  SA: Storage<N, $LhsRDim, $LhsCDim>,
-                  SB: Storage<N, $RhsRDim, $RhsCDim>,
-                  $(SA::Alloc: Allocator<N, $VDimA, U1>,
-                    SB::Alloc: Allocator<N, $VDimB, U1>)* {
+        impl<$($lives ,)* N: Real $(, $Storage: $StoragesBound $(<$($BoundParam),*>)*)*> $Op<$Rhs> for $Lhs
+            where DefaultAllocator: Allocator<N, $LhsRDim, $LhsCDim> +
+                                    Allocator<N, $RhsRDim, $RhsCDim> {
             type Output = $Result;
 
             #[inline]
@@ -109,29 +101,29 @@ macro_rules! quaternion_op_impl(
 quaternion_op_impl!(
     Add, add;
     (U4, U1), (U4, U1);
-    self: &'a QuaternionBase<N, SA>, rhs: &'b QuaternionBase<N, SB>, Output = OwnedQuaternionBase<N, SA::Alloc>;
-    QuaternionBase::from_vector(&self.coords + &rhs.coords);
+    self: &'a Quaternion<N>, rhs: &'b Quaternion<N>, Output = Quaternion<N>;
+    Quaternion::from_vector(&self.coords + &rhs.coords);
     'a, 'b);
 
 quaternion_op_impl!(
     Add, add;
     (U4, U1), (U4, U1);
-    self: &'a QuaternionBase<N, SA>, rhs: QuaternionBase<N, SB>, Output = OwnedQuaternionBase<N, SB::Alloc>;
-    QuaternionBase::from_vector(&self.coords + rhs.coords);
+    self: &'a Quaternion<N>, rhs: Quaternion<N>, Output = Quaternion<N>;
+    Quaternion::from_vector(&self.coords + rhs.coords);
     'a);
 
 quaternion_op_impl!(
     Add, add;
     (U4, U1), (U4, U1);
-    self: QuaternionBase<N, SA>, rhs: &'b QuaternionBase<N, SB>, Output = OwnedQuaternionBase<N, SA::Alloc>;
-    QuaternionBase::from_vector(self.coords + &rhs.coords);
+    self: Quaternion<N>, rhs: &'b Quaternion<N>, Output = Quaternion<N>;
+    Quaternion::from_vector(self.coords + &rhs.coords);
     'b);
 
 quaternion_op_impl!(
     Add, add;
     (U4, U1), (U4, U1);
-    self: QuaternionBase<N, SA>, rhs: QuaternionBase<N, SB>, Output = OwnedQuaternionBase<N, SA::Alloc>;
-    QuaternionBase::from_vector(self.coords + rhs.coords);
+    self: Quaternion<N>, rhs: Quaternion<N>, Output = Quaternion<N>;
+    Quaternion::from_vector(self.coords + rhs.coords);
     );
 
 
@@ -139,29 +131,29 @@ quaternion_op_impl!(
 quaternion_op_impl!(
     Sub, sub;
     (U4, U1), (U4, U1);
-    self: &'a QuaternionBase<N, SA>, rhs: &'b QuaternionBase<N, SB>, Output = OwnedQuaternionBase<N, SA::Alloc>;
-    QuaternionBase::from_vector(&self.coords - &rhs.coords);
+    self: &'a Quaternion<N>, rhs: &'b Quaternion<N>, Output = Quaternion<N>;
+    Quaternion::from_vector(&self.coords - &rhs.coords);
     'a, 'b);
 
 quaternion_op_impl!(
     Sub, sub;
     (U4, U1), (U4, U1);
-    self: &'a QuaternionBase<N, SA>, rhs: QuaternionBase<N, SB>, Output = OwnedQuaternionBase<N, SB::Alloc>;
-    QuaternionBase::from_vector(&self.coords - rhs.coords);
+    self: &'a Quaternion<N>, rhs: Quaternion<N>, Output = Quaternion<N>;
+    Quaternion::from_vector(&self.coords - rhs.coords);
     'a);
 
 quaternion_op_impl!(
     Sub, sub;
     (U4, U1), (U4, U1);
-    self: QuaternionBase<N, SA>, rhs: &'b QuaternionBase<N, SB>, Output = OwnedQuaternionBase<N, SA::Alloc>;
-    QuaternionBase::from_vector(self.coords - &rhs.coords);
+    self: Quaternion<N>, rhs: &'b Quaternion<N>, Output = Quaternion<N>;
+    Quaternion::from_vector(self.coords - &rhs.coords);
     'b);
 
 quaternion_op_impl!(
     Sub, sub;
     (U4, U1), (U4, U1);
-    self: QuaternionBase<N, SA>, rhs: QuaternionBase<N, SB>, Output = OwnedQuaternionBase<N, SA::Alloc>;
-    QuaternionBase::from_vector(self.coords - rhs.coords);
+    self: Quaternion<N>, rhs: Quaternion<N>, Output = Quaternion<N>;
+    Quaternion::from_vector(self.coords - rhs.coords);
     );
 
 
@@ -169,8 +161,8 @@ quaternion_op_impl!(
 quaternion_op_impl!(
     Mul, mul;
     (U4, U1), (U4, U1);
-    self: &'a QuaternionBase<N, SA>, rhs: &'b QuaternionBase<N, SB>, Output = OwnedQuaternionBase<N, SA::Alloc>;
-    QuaternionBase::new(
+    self: &'a Quaternion<N>, rhs: &'b Quaternion<N>, Output = Quaternion<N>;
+    Quaternion::new(
         self[3] * rhs[3] - self[0] * rhs[0] - self[1] * rhs[1] - self[2] * rhs[2],
         self[3] * rhs[0] + self[0] * rhs[3] + self[1] * rhs[2] - self[2] * rhs[1],
         self[3] * rhs[1] - self[0] * rhs[2] + self[1] * rhs[3] + self[2] * rhs[0],
@@ -180,21 +172,21 @@ quaternion_op_impl!(
 quaternion_op_impl!(
     Mul, mul;
     (U4, U1), (U4, U1);
-    self: &'a QuaternionBase<N, SA>, rhs: QuaternionBase<N, SB>, Output = OwnedQuaternionBase<N, SA::Alloc>;
+    self: &'a Quaternion<N>, rhs: Quaternion<N>, Output = Quaternion<N>;
     self * &rhs;
     'a);
 
 quaternion_op_impl!(
     Mul, mul;
     (U4, U1), (U4, U1);
-    self: QuaternionBase<N, SA>, rhs: &'b QuaternionBase<N, SB>, Output = OwnedQuaternionBase<N, SA::Alloc>;
+    self: Quaternion<N>, rhs: &'b Quaternion<N>, Output = Quaternion<N>;
     &self * rhs;
     'b);
 
 quaternion_op_impl!(
     Mul, mul;
     (U4, U1), (U4, U1);
-    self: QuaternionBase<N, SA>, rhs: QuaternionBase<N, SB>, Output = OwnedQuaternionBase<N, SA::Alloc>;
+    self: Quaternion<N>, rhs: Quaternion<N>, Output = Quaternion<N>;
     &self * &rhs;
     );
 
@@ -202,28 +194,28 @@ quaternion_op_impl!(
 quaternion_op_impl!(
     Mul, mul;
     (U4, U1), (U4, U1);
-    self: &'a UnitQuaternionBase<N, SA>, rhs: &'b UnitQuaternionBase<N, SB>, Output = OwnedUnitQuaternionBase<N, SA::Alloc>;
-    UnitQuaternionBase::new_unchecked(self.quaternion() * rhs.quaternion());
+    self: &'a UnitQuaternion<N>, rhs: &'b UnitQuaternion<N>, Output = UnitQuaternion<N>;
+    UnitQuaternion::new_unchecked(self.quaternion() * rhs.quaternion());
     'a, 'b);
 
 quaternion_op_impl!(
     Mul, mul;
     (U4, U1), (U4, U1);
-    self: &'a UnitQuaternionBase<N, SA>, rhs: UnitQuaternionBase<N, SB>, Output = OwnedUnitQuaternionBase<N, SA::Alloc>;
+    self: &'a UnitQuaternion<N>, rhs: UnitQuaternion<N>, Output = UnitQuaternion<N>;
     self * &rhs;
     'a);
 
 quaternion_op_impl!(
     Mul, mul;
     (U4, U1), (U4, U1);
-    self: UnitQuaternionBase<N, SA>, rhs: &'b UnitQuaternionBase<N, SB>, Output = OwnedUnitQuaternionBase<N, SA::Alloc>;
+    self: UnitQuaternion<N>, rhs: &'b UnitQuaternion<N>, Output = UnitQuaternion<N>;
     &self * rhs;
     'b);
 
 quaternion_op_impl!(
     Mul, mul;
     (U4, U1), (U4, U1);
-    self: UnitQuaternionBase<N, SA>, rhs: UnitQuaternionBase<N, SB>, Output = OwnedUnitQuaternionBase<N, SA::Alloc>;
+    self: UnitQuaternion<N>, rhs: UnitQuaternion<N>, Output = UnitQuaternion<N>;
     &self * &rhs;
     );
 
@@ -231,173 +223,173 @@ quaternion_op_impl!(
 quaternion_op_impl!(
     Div, div;
     (U4, U1), (U4, U1);
-    self: &'a UnitQuaternionBase<N, SA>, rhs: &'b UnitQuaternionBase<N, SB>, Output = OwnedUnitQuaternionBase<N, SA::Alloc>;
+    self: &'a UnitQuaternion<N>, rhs: &'b UnitQuaternion<N>, Output = UnitQuaternion<N>;
     self * rhs.inverse();
     'a, 'b);
 
 quaternion_op_impl!(
     Div, div;
     (U4, U1), (U4, U1);
-    self: &'a UnitQuaternionBase<N, SA>, rhs: UnitQuaternionBase<N, SB>, Output = OwnedUnitQuaternionBase<N, SA::Alloc>;
+    self: &'a UnitQuaternion<N>, rhs: UnitQuaternion<N>, Output = UnitQuaternion<N>;
     self / &rhs;
     'a);
 
 quaternion_op_impl!(
     Div, div;
     (U4, U1), (U4, U1);
-    self: UnitQuaternionBase<N, SA>, rhs: &'b UnitQuaternionBase<N, SB>, Output = OwnedUnitQuaternionBase<N, SA::Alloc>;
+    self: UnitQuaternion<N>, rhs: &'b UnitQuaternion<N>, Output = UnitQuaternion<N>;
     &self / rhs;
     'b);
 
 quaternion_op_impl!(
     Div, div;
     (U4, U1), (U4, U1);
-    self: UnitQuaternionBase<N, SA>, rhs: UnitQuaternionBase<N, SB>, Output = OwnedUnitQuaternionBase<N, SA::Alloc>;
+    self: UnitQuaternion<N>, rhs: UnitQuaternion<N>, Output = UnitQuaternion<N>;
     &self / &rhs;
     );
 
-// UnitQuaternion × RotationBase
+// UnitQuaternion × Rotation
 quaternion_op_impl!(
     Mul, mul;
     (U4, U1), (U3, U3);
-    self: &'a UnitQuaternionBase<N, SA>, rhs: &'b RotationBase<N, U3, SB>,
-    Output = OwnedUnitQuaternionBase<N, SA::Alloc> => U3, U3;
+    self: &'a UnitQuaternion<N>, rhs: &'b Rotation<N, U3>,
+    Output = UnitQuaternion<N> => U3, U3;
     // FIXME: can we avoid the conversion from a rotation matrix?
-    self * OwnedUnitQuaternionBase::<N, SA::Alloc>::from_rotation_matrix(rhs);
+    self * UnitQuaternion::<N>::from_rotation_matrix(rhs);
     'a, 'b);
 
 quaternion_op_impl!(
     Mul, mul;
     (U4, U1), (U3, U3);
-    self: &'a UnitQuaternionBase<N, SA>, rhs: RotationBase<N, U3, SB>,
-    Output = OwnedUnitQuaternionBase<N, SA::Alloc> => U3, U3;
-    self * OwnedUnitQuaternionBase::<N, SA::Alloc>::from_rotation_matrix(&rhs);
+    self: &'a UnitQuaternion<N>, rhs: Rotation<N, U3>,
+    Output = UnitQuaternion<N> => U3, U3;
+    self * UnitQuaternion::<N>::from_rotation_matrix(&rhs);
     'a);
 
 quaternion_op_impl!(
     Mul, mul;
     (U4, U1), (U3, U3);
-    self: UnitQuaternionBase<N, SA>, rhs: &'b RotationBase<N, U3, SB>,
-    Output = OwnedUnitQuaternionBase<N, SA::Alloc> => U3, U3;
-    self * OwnedUnitQuaternionBase::<N, SA::Alloc>::from_rotation_matrix(rhs);
+    self: UnitQuaternion<N>, rhs: &'b Rotation<N, U3>,
+    Output = UnitQuaternion<N> => U3, U3;
+    self * UnitQuaternion::<N>::from_rotation_matrix(rhs);
     'b);
 
 quaternion_op_impl!(
     Mul, mul;
     (U4, U1), (U3, U3);
-    self: UnitQuaternionBase<N, SA>, rhs: RotationBase<N, U3, SB>,
-    Output = OwnedUnitQuaternionBase<N, SA::Alloc> => U3, U3;
-    self * OwnedUnitQuaternionBase::<N, SA::Alloc>::from_rotation_matrix(&rhs);
+    self: UnitQuaternion<N>, rhs: Rotation<N, U3>,
+    Output = UnitQuaternion<N> => U3, U3;
+    self * UnitQuaternion::<N>::from_rotation_matrix(&rhs);
     );
 
-// UnitQuaternion ÷ RotationBase
+// UnitQuaternion ÷ Rotation
 quaternion_op_impl!(
     Div, div;
     (U4, U1), (U3, U3);
-    self: &'a UnitQuaternionBase<N, SA>, rhs: &'b RotationBase<N, U3, SB>,
-    Output = OwnedUnitQuaternionBase<N, SA::Alloc> => U3, U3;
+    self: &'a UnitQuaternion<N>, rhs: &'b Rotation<N, U3>,
+    Output = UnitQuaternion<N> => U3, U3;
     // FIXME: can we avoid the conversion to a rotation matrix?
-    self / OwnedUnitQuaternionBase::<N, SA::Alloc>::from_rotation_matrix(rhs);
+    self / UnitQuaternion::<N>::from_rotation_matrix(rhs);
     'a, 'b);
 
 quaternion_op_impl!(
     Div, div;
     (U4, U1), (U3, U3);
-    self: &'a UnitQuaternionBase<N, SA>, rhs: RotationBase<N, U3, SB>,
-    Output = OwnedUnitQuaternionBase<N, SA::Alloc> => U3, U3;
-    self / OwnedUnitQuaternionBase::<N, SA::Alloc>::from_rotation_matrix(&rhs);
+    self: &'a UnitQuaternion<N>, rhs: Rotation<N, U3>,
+    Output = UnitQuaternion<N> => U3, U3;
+    self / UnitQuaternion::<N>::from_rotation_matrix(&rhs);
     'a);
 
 quaternion_op_impl!(
     Div, div;
     (U4, U1), (U3, U3);
-    self: UnitQuaternionBase<N, SA>, rhs: &'b RotationBase<N, U3, SB>,
-    Output = OwnedUnitQuaternionBase<N, SA::Alloc> => U3, U3;
-    self / OwnedUnitQuaternionBase::<N, SA::Alloc>::from_rotation_matrix(rhs);
+    self: UnitQuaternion<N>, rhs: &'b Rotation<N, U3>,
+    Output = UnitQuaternion<N> => U3, U3;
+    self / UnitQuaternion::<N>::from_rotation_matrix(rhs);
     'b);
 
 quaternion_op_impl!(
     Div, div;
     (U4, U1), (U3, U3);
-    self: UnitQuaternionBase<N, SA>, rhs: RotationBase<N, U3, SB>,
-    Output = OwnedUnitQuaternionBase<N, SA::Alloc> => U3, U3;
-    self / OwnedUnitQuaternionBase::<N, SA::Alloc>::from_rotation_matrix(&rhs);
+    self: UnitQuaternion<N>, rhs: Rotation<N, U3>,
+    Output = UnitQuaternion<N> => U3, U3;
+    self / UnitQuaternion::<N>::from_rotation_matrix(&rhs);
     );
 
-// RotationBase × UnitQuaternion
+// Rotation × UnitQuaternion
 quaternion_op_impl!(
     Mul, mul;
     (U3, U3), (U4, U1);
-    self: &'a RotationBase<N, U3, SA>, rhs: &'b UnitQuaternionBase<N, SB>,
-    Output = OwnedUnitQuaternionBase<N, SB::Alloc> => U3, U3;
+    self: &'a Rotation<N, U3>, rhs: &'b UnitQuaternion<N>,
+    Output = UnitQuaternion<N> => U3, U3;
     // FIXME: can we avoid the conversion from a rotation matrix?
-    OwnedUnitQuaternionBase::<N, SB::Alloc>::from_rotation_matrix(self) * rhs;
+    UnitQuaternion::<N>::from_rotation_matrix(self) * rhs;
     'a, 'b);
 
 quaternion_op_impl!(
     Mul, mul;
     (U3, U3), (U4, U1);
-    self: &'a RotationBase<N, U3, SA>, rhs: UnitQuaternionBase<N, SB>,
-    Output = OwnedUnitQuaternionBase<N, SB::Alloc> => U3, U3;
-    OwnedUnitQuaternionBase::<N, SB::Alloc>::from_rotation_matrix(self) * rhs;
+    self: &'a Rotation<N, U3>, rhs: UnitQuaternion<N>,
+    Output = UnitQuaternion<N> => U3, U3;
+    UnitQuaternion::<N>::from_rotation_matrix(self) * rhs;
     'a);
 
 quaternion_op_impl!(
     Mul, mul;
     (U3, U3), (U4, U1);
-    self: RotationBase<N, U3, SA>, rhs: &'b UnitQuaternionBase<N, SB>,
-    Output = OwnedUnitQuaternionBase<N, SB::Alloc> => U3, U3;
-    OwnedUnitQuaternionBase::<N, SB::Alloc>::from_rotation_matrix(&self) * rhs;
+    self: Rotation<N, U3>, rhs: &'b UnitQuaternion<N>,
+    Output = UnitQuaternion<N> => U3, U3;
+    UnitQuaternion::<N>::from_rotation_matrix(&self) * rhs;
     'b);
 
 quaternion_op_impl!(
     Mul, mul;
     (U3, U3), (U4, U1);
-    self: RotationBase<N, U3, SA>, rhs: UnitQuaternionBase<N, SB>,
-    Output = OwnedUnitQuaternionBase<N, SB::Alloc> => U3, U3;
-    OwnedUnitQuaternionBase::<N, SB::Alloc>::from_rotation_matrix(&self) * rhs;
+    self: Rotation<N, U3>, rhs: UnitQuaternion<N>,
+    Output = UnitQuaternion<N> => U3, U3;
+    UnitQuaternion::<N>::from_rotation_matrix(&self) * rhs;
     );
 
-// RotationBase ÷ UnitQuaternion
+// Rotation ÷ UnitQuaternion
 quaternion_op_impl!(
     Div, div;
     (U3, U3), (U4, U1);
-    self: &'a RotationBase<N, U3, SA>, rhs: &'b UnitQuaternionBase<N, SB>,
-    Output = OwnedUnitQuaternionBase<N, SB::Alloc> => U3, U3;
+    self: &'a Rotation<N, U3>, rhs: &'b UnitQuaternion<N>,
+    Output = UnitQuaternion<N> => U3, U3;
     // FIXME: can we avoid the conversion from a rotation matrix?
-    OwnedUnitQuaternionBase::<N, SB::Alloc>::from_rotation_matrix(self) / rhs;
+    UnitQuaternion::<N>::from_rotation_matrix(self) / rhs;
     'a, 'b);
 
 quaternion_op_impl!(
     Div, div;
     (U3, U3), (U4, U1);
-    self: &'a RotationBase<N, U3, SA>, rhs: UnitQuaternionBase<N, SB>,
-    Output = OwnedUnitQuaternionBase<N, SB::Alloc> => U3, U3;
-    OwnedUnitQuaternionBase::<N, SB::Alloc>::from_rotation_matrix(self) / rhs;
+    self: &'a Rotation<N, U3>, rhs: UnitQuaternion<N>,
+    Output = UnitQuaternion<N> => U3, U3;
+    UnitQuaternion::<N>::from_rotation_matrix(self) / rhs;
     'a);
 
 quaternion_op_impl!(
     Div, div;
     (U3, U3), (U4, U1);
-    self: RotationBase<N, U3, SA>, rhs: &'b UnitQuaternionBase<N, SB>,
-    Output = OwnedUnitQuaternionBase<N, SB::Alloc> => U3, U3;
-    OwnedUnitQuaternionBase::<N, SB::Alloc>::from_rotation_matrix(&self) / rhs;
+    self: Rotation<N, U3>, rhs: &'b UnitQuaternion<N>,
+    Output = UnitQuaternion<N> => U3, U3;
+    UnitQuaternion::<N>::from_rotation_matrix(&self) / rhs;
     'b);
 
 quaternion_op_impl!(
     Div, div;
     (U3, U3), (U4, U1);
-    self: RotationBase<N, U3, SA>, rhs: UnitQuaternionBase<N, SB>,
-    Output = OwnedUnitQuaternionBase<N, SB::Alloc> => U3, U3;
-    OwnedUnitQuaternionBase::<N, SB::Alloc>::from_rotation_matrix(&self) / rhs;
+    self: Rotation<N, U3>, rhs: UnitQuaternion<N>,
+    Output = UnitQuaternion<N> => U3, U3;
+    UnitQuaternion::<N>::from_rotation_matrix(&self) / rhs;
     );
 
 // UnitQuaternion × Vector
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U3, U1);
-    self: &'a UnitQuaternionBase<N, SA>, rhs: &'b ColumnVector<N, U3, SB>,
-    Output = OwnedColumnVector<N, U3, SA::Alloc> => U3, U4;
+    (U4, U1), (U3, U1) for SB: Storage<N, U3> ;
+    self: &'a UnitQuaternion<N>, rhs: &'b Vector<N, U3, SB>,
+    Output = Vector3<N> => U3, U4;
     {
         let two: N = ::convert(2.0f64);
         let t = self.as_ref().vector().cross(rhs) * two;
@@ -409,91 +401,91 @@ quaternion_op_impl!(
 
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U3, U1);
-    self: &'a UnitQuaternionBase<N, SA>, rhs: ColumnVector<N, U3, SB>,
-    Output = OwnedColumnVector<N, U3, SA::Alloc> => U3, U4;
+    (U4, U1), (U3, U1) for SB: Storage<N, U3> ;
+    self: &'a UnitQuaternion<N>, rhs: Vector<N, U3, SB>,
+    Output = Vector3<N> => U3, U4;
     self * &rhs;
     'a);
 
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U3, U1);
-    self: UnitQuaternionBase<N, SA>, rhs: &'b ColumnVector<N, U3, SB>,
-    Output = OwnedColumnVector<N, U3, SA::Alloc> => U3, U4;
+    (U4, U1), (U3, U1) for SB: Storage<N, U3> ;
+    self: UnitQuaternion<N>, rhs: &'b Vector<N, U3, SB>,
+    Output = Vector3<N> => U3, U4;
     &self * rhs;
     'b);
 
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U3, U1);
-    self: UnitQuaternionBase<N, SA>, rhs: ColumnVector<N, U3, SB>,
-    Output = OwnedColumnVector<N, U3, SA::Alloc> => U3, U4;
+    (U4, U1), (U3, U1) for SB: Storage<N, U3> ;
+    self: UnitQuaternion<N>, rhs: Vector<N, U3, SB>,
+    Output = Vector3<N> => U3, U4;
     &self * &rhs;
     );
 
-// UnitQuaternion × PointBase
+// UnitQuaternion × Point
 quaternion_op_impl!(
     Mul, mul;
     (U4, U1), (U3, U1);
-    self: &'a UnitQuaternionBase<N, SA>, rhs: &'b PointBase<N, U3, SB>,
-    Output = OwnedPoint<N, U3, SA::Alloc> => U3, U4;
-    PointBase::from_coordinates(self * &rhs.coords);
+    self: &'a UnitQuaternion<N>, rhs: &'b Point3<N>,
+    Output = Point3<N> => U3, U4;
+    Point3::from_coordinates(self * &rhs.coords);
     'a, 'b);
 
 quaternion_op_impl!(
     Mul, mul;
     (U4, U1), (U3, U1);
-    self: &'a UnitQuaternionBase<N, SA>, rhs: PointBase<N, U3, SB>,
-    Output = OwnedPoint<N, U3, SA::Alloc> => U3, U4;
-    PointBase::from_coordinates(self * rhs.coords);
+    self: &'a UnitQuaternion<N>, rhs: Point3<N>,
+    Output = Point3<N> => U3, U4;
+    Point3::from_coordinates(self * rhs.coords);
     'a);
 
 quaternion_op_impl!(
     Mul, mul;
     (U4, U1), (U3, U1);
-    self: UnitQuaternionBase<N, SA>, rhs: &'b PointBase<N, U3, SB>,
-    Output = OwnedPoint<N, U3, SA::Alloc> => U3, U4;
-    PointBase::from_coordinates(self * &rhs.coords);
+    self: UnitQuaternion<N>, rhs: &'b Point3<N>,
+    Output = Point3<N> => U3, U4;
+    Point3::from_coordinates(self * &rhs.coords);
     'b);
 
 quaternion_op_impl!(
     Mul, mul;
     (U4, U1), (U3, U1);
-    self: UnitQuaternionBase<N, SA>, rhs: PointBase<N, U3, SB>,
-    Output = OwnedPoint<N, U3, SA::Alloc> => U3, U4;
-    PointBase::from_coordinates(self * rhs.coords);
+    self: UnitQuaternion<N>, rhs: Point3<N>,
+    Output = Point3<N> => U3, U4;
+    Point3::from_coordinates(self * rhs.coords);
     );
 
 // UnitQuaternion × Unit<Vector>
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U3, U1);
-    self: &'a UnitQuaternionBase<N, SA>, rhs: &'b Unit<ColumnVector<N, U3, SB>>,
-    Output = Unit<OwnedColumnVector<N, U3, SA::Alloc>> => U3, U4;
+    (U4, U1), (U3, U1) for SB: Storage<N, U3> ;
+    self: &'a UnitQuaternion<N>, rhs: &'b Unit<Vector<N, U3, SB>>,
+    Output = Unit<Vector3<N>> => U3, U4;
     Unit::new_unchecked(self * rhs.as_ref());
     'a, 'b);
 
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U3, U1);
-    self: &'a UnitQuaternionBase<N, SA>, rhs: Unit<ColumnVector<N, U3, SB>>,
-    Output = Unit<OwnedColumnVector<N, U3, SA::Alloc>> => U3, U4;
+    (U4, U1), (U3, U1) for SB: Storage<N, U3> ;
+    self: &'a UnitQuaternion<N>, rhs: Unit<Vector<N, U3, SB>>,
+    Output = Unit<Vector3<N>> => U3, U4;
     Unit::new_unchecked(self * rhs.unwrap());
     'a);
 
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U3, U1);
-    self: UnitQuaternionBase<N, SA>, rhs: &'b Unit<ColumnVector<N, U3, SB>>,
-    Output = Unit<OwnedColumnVector<N, U3, SA::Alloc>> => U3, U4;
+    (U4, U1), (U3, U1) for SB: Storage<N, U3> ;
+    self: UnitQuaternion<N>, rhs: &'b Unit<Vector<N, U3, SB>>,
+    Output = Unit<Vector3<N>> => U3, U4;
     Unit::new_unchecked(self * rhs.as_ref());
     'b);
 
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U3, U1);
-    self: UnitQuaternionBase<N, SA>, rhs: Unit<ColumnVector<N, U3, SB>>,
-    Output = Unit<OwnedColumnVector<N, U3, SA::Alloc>> => U3, U4;
+    (U4, U1), (U3, U1) for SB: Storage<N, U3> ;
+    self: UnitQuaternion<N>, rhs: Unit<Vector<N, U3, SB>>,
+    Output = Unit<Vector3<N>> => U3, U4;
     Unit::new_unchecked(self * rhs.unwrap());
     );
 
@@ -501,31 +493,25 @@ quaternion_op_impl!(
 
 macro_rules! scalar_op_impl(
     ($($Op: ident, $op: ident, $OpAssign: ident, $op_assign: ident);* $(;)*) => {$(
-        impl<N, S> $Op<N> for QuaternionBase<N, S>
-            where N: Real,
-                  S: Storage<N, U4, U1> {
-            type Output = OwnedQuaternionBase<N, S::Alloc>;
+        impl<N: Real> $Op<N> for Quaternion<N> {
+            type Output = Quaternion<N>;
 
             #[inline]
             fn $op(self, n: N) -> Self::Output {
-                QuaternionBase::from_vector(self.coords.$op(n))
+                Quaternion::from_vector(self.coords.$op(n))
             }
         }
 
-        impl<'a, N, S> $Op<N> for &'a QuaternionBase<N, S>
-            where N: Real,
-                  S: Storage<N, U4, U1> {
-            type Output = OwnedQuaternionBase<N, S::Alloc>;
+        impl<'a, N: Real> $Op<N> for &'a Quaternion<N> {
+            type Output = Quaternion<N>;
 
             #[inline]
             fn $op(self, n: N) -> Self::Output {
-                QuaternionBase::from_vector((&self.coords).$op(n))
+                Quaternion::from_vector((&self.coords).$op(n))
             }
         }
 
-        impl<N, S> $OpAssign<N> for QuaternionBase<N, S>
-            where N: Real,
-                  S: StorageMut<N, U4, U1> {
+        impl<N: Real> $OpAssign<N> for Quaternion<N> {
 
             #[inline]
             fn $op_assign(&mut self, n: N) {
@@ -542,23 +528,21 @@ scalar_op_impl!(
 
 macro_rules! left_scalar_mul_impl(
     ($($T: ty),* $(,)*) => {$(
-        impl<S> Mul<QuaternionBase<$T, S>> for $T
-            where S: Storage<$T, U4, U1> {
-            type Output = OwnedQuaternionBase<$T, S::Alloc>;
+        impl Mul<Quaternion<$T>> for $T {
+            type Output = Quaternion<$T>;
 
             #[inline]
-            fn mul(self, right: QuaternionBase<$T, S>) -> Self::Output {
-                QuaternionBase::from_vector(self * right.coords)
+            fn mul(self, right: Quaternion<$T>) -> Self::Output {
+                Quaternion::from_vector(self * right.coords)
             }
         }
 
-        impl<'b, S> Mul<&'b QuaternionBase<$T, S>> for $T
-            where S: Storage<$T, U4, U1> {
-            type Output = OwnedQuaternionBase<$T, S::Alloc>;
+        impl<'b> Mul<&'b Quaternion<$T>> for $T {
+            type Output = Quaternion<$T>;
 
             #[inline]
-            fn mul(self, right: &'b QuaternionBase<$T, S>) -> Self::Output {
-                QuaternionBase::from_vector(self * &right.coords)
+            fn mul(self, right: &'b Quaternion<$T>) -> Self::Output {
+                Quaternion::from_vector(self * &right.coords)
             }
         }
     )*}
@@ -566,25 +550,21 @@ macro_rules! left_scalar_mul_impl(
 
 left_scalar_mul_impl!(f32, f64);
 
-impl<N, S> Neg for QuaternionBase<N, S>
-    where N: Real,
-          S: Storage<N, U4, U1> {
-    type Output = OwnedQuaternionBase<N, S::Alloc>;
+impl<N: Real> Neg for Quaternion<N> {
+    type Output = Quaternion<N>;
 
     #[inline]
     fn neg(self) -> Self::Output {
-        QuaternionBase::from_vector(-self.coords)
+        Quaternion::from_vector(-self.coords)
     }
 }
 
-impl<'a, N, S> Neg for &'a QuaternionBase<N, S>
-    where N: Real,
-          S: Storage<N, U4, U1> {
-    type Output = OwnedQuaternionBase<N, S::Alloc>;
+impl<'a, N: Real> Neg for &'a Quaternion<N> {
+    type Output = Quaternion<N>;
 
     #[inline]
     fn neg(self) -> Self::Output {
-        QuaternionBase::from_vector(-&self.coords)
+        Quaternion::from_vector(-&self.coords)
     }
 }
 
@@ -593,17 +573,9 @@ macro_rules! quaternion_op_impl(
      ($LhsRDim: ident, $LhsCDim: ident), ($RhsRDim: ident, $RhsCDim: ident);
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty $(=> $VDimA: ty, $VDimB: ty)*;
      $action: expr; $($lives: tt),*) => {
-        impl<$($lives ,)* N, SA, SB> $OpAssign<$Rhs> for $Lhs
-            where N: Real,
-                  SA: StorageMut<N, $LhsRDim, $LhsCDim>,
-                  SB: Storage<N, $RhsRDim, $RhsCDim>,
-                  $(SA::Alloc: Allocator<N, $VDimA, U1> + Allocator<N, U4, U1>,
-                    //                                    ^^^^^^^^^^^^^^^^^^^^
-                    //                                    XXX: For some reasons, the compiler needs
-                    //                                    this bound to compile UnitQuat *= RotationBase.
-                    //                                    Though in theory this bound is already
-                    //                                    inherited from `SA: StorageMut`…
-                    SB::Alloc: Allocator<N, $VDimB, U1>)* {
+        impl<$($lives ,)* N: Real> $OpAssign<$Rhs> for $Lhs
+            where DefaultAllocator: Allocator<N, $LhsRDim, $LhsCDim> +
+                                    Allocator<N, $RhsRDim, $RhsCDim> {
 
             #[inline]
             fn $op_assign(&mut $lhs, $rhs: $Rhs) {
@@ -617,14 +589,14 @@ macro_rules! quaternion_op_impl(
 quaternion_op_impl!(
     AddAssign, add_assign;
     (U4, U1), (U4, U1);
-    self: QuaternionBase<N, SA>, rhs: &'b QuaternionBase<N, SB>;
+    self: Quaternion<N>, rhs: &'b Quaternion<N>;
     self.coords += &rhs.coords;
     'b);
 
 quaternion_op_impl!(
     AddAssign, add_assign;
     (U4, U1), (U4, U1);
-    self: QuaternionBase<N, SA>, rhs: QuaternionBase<N, SB>;
+    self: Quaternion<N>, rhs: Quaternion<N>;
     self.coords += rhs.coords; );
 
 
@@ -632,21 +604,21 @@ quaternion_op_impl!(
 quaternion_op_impl!(
     SubAssign, sub_assign;
     (U4, U1), (U4, U1);
-    self: QuaternionBase<N, SA>, rhs: &'b QuaternionBase<N, SB>;
+    self: Quaternion<N>, rhs: &'b Quaternion<N>;
     self.coords -= &rhs.coords;
     'b);
 
 quaternion_op_impl!(
     SubAssign, sub_assign;
     (U4, U1), (U4, U1);
-    self: QuaternionBase<N, SA>, rhs: QuaternionBase<N, SB>;
+    self: Quaternion<N>, rhs: Quaternion<N>;
     self.coords -= rhs.coords; );
 
 // Quaternion ×= Quaternion
 quaternion_op_impl!(
     MulAssign, mul_assign;
     (U4, U1), (U4, U1);
-    self: QuaternionBase<N, SA>, rhs: &'b QuaternionBase<N, SB>;
+    self: Quaternion<N>, rhs: &'b Quaternion<N>;
     {
         let res = &*self * rhs;
         // FIXME: will this be optimized away?
@@ -657,14 +629,14 @@ quaternion_op_impl!(
 quaternion_op_impl!(
     MulAssign, mul_assign;
     (U4, U1), (U4, U1);
-    self: QuaternionBase<N, SA>, rhs: QuaternionBase<N, SB>;
+    self: Quaternion<N>, rhs: Quaternion<N>;
     *self *= &rhs; );
 
 // UnitQuaternion ×= UnitQuaternion
 quaternion_op_impl!(
     MulAssign, mul_assign;
     (U4, U1), (U4, U1);
-    self: UnitQuaternionBase<N, SA>, rhs: &'b UnitQuaternionBase<N, SB>;
+    self: UnitQuaternion<N>, rhs: &'b UnitQuaternion<N>;
     {
         let res = &*self * rhs;
         self.as_mut_unchecked().coords.copy_from(&res.as_ref().coords);
@@ -674,14 +646,14 @@ quaternion_op_impl!(
 quaternion_op_impl!(
     MulAssign, mul_assign;
     (U4, U1), (U4, U1);
-    self: UnitQuaternionBase<N, SA>, rhs: UnitQuaternionBase<N, SB>;
+    self: UnitQuaternion<N>, rhs: UnitQuaternion<N>;
     *self *= &rhs; );
 
 // UnitQuaternion ÷= UnitQuaternion
 quaternion_op_impl!(
     DivAssign, div_assign;
     (U4, U1), (U4, U1);
-    self: UnitQuaternionBase<N, SA>, rhs: &'b UnitQuaternionBase<N, SB>;
+    self: UnitQuaternion<N>, rhs: &'b UnitQuaternion<N>;
     {
         let res = &*self / rhs;
         self.as_mut_unchecked().coords.copy_from(&res.as_ref().coords);
@@ -691,14 +663,14 @@ quaternion_op_impl!(
 quaternion_op_impl!(
     DivAssign, div_assign;
     (U4, U1), (U4, U1);
-    self: UnitQuaternionBase<N, SA>, rhs: UnitQuaternionBase<N, SB>;
+    self: UnitQuaternion<N>, rhs: UnitQuaternion<N>;
     *self /= &rhs; );
 
-// UnitQuaternion ×= RotationBase
+// UnitQuaternion ×= Rotation
 quaternion_op_impl!(
     MulAssign, mul_assign;
     (U4, U1), (U3, U3);
-    self: UnitQuaternionBase<N, SA>, rhs: &'b RotationBase<N, U3, SB> => U3, U3;
+    self: UnitQuaternion<N>, rhs: &'b Rotation<N, U3> => U3, U3;
     {
         let res = &*self * rhs;
         self.as_mut_unchecked().coords.copy_from(&res.as_ref().coords);
@@ -708,14 +680,14 @@ quaternion_op_impl!(
 quaternion_op_impl!(
     MulAssign, mul_assign;
     (U4, U1), (U3, U3);
-    self: UnitQuaternionBase<N, SA>, rhs: RotationBase<N, U3, SB> => U3, U3;
+    self: UnitQuaternion<N>, rhs: Rotation<N, U3> => U3, U3;
     *self *= &rhs; );
 
-// UnitQuaternion ÷= RotationBase
+// UnitQuaternion ÷= Rotation
 quaternion_op_impl!(
     DivAssign, div_assign;
     (U4, U1), (U3, U3);
-    self: UnitQuaternionBase<N, SA>, rhs: &'b RotationBase<N, U3, SB> => U3, U3;
+    self: UnitQuaternion<N>, rhs: &'b Rotation<N, U3> => U3, U3;
     {
         let res = &*self / rhs;
         self.as_mut_unchecked().coords.copy_from(&res.as_ref().coords);
@@ -725,5 +697,5 @@ quaternion_op_impl!(
 quaternion_op_impl!(
     DivAssign, div_assign;
     (U4, U1), (U3, U3);
-    self: UnitQuaternionBase<N, SA>, rhs: RotationBase<N, U3, SB> => U3, U3;
+    self: UnitQuaternion<N>, rhs: Rotation<N, U3> => U3, U3;
     *self /= &rhs; );

src/geometry/reflection.rs

@@ -0,0 +1,72 @@
+use alga::general::Real;
+use core::{DefaultAllocator, Scalar, Unit, Matrix, Vector};
+use core::constraint::{ShapeConstraint, SameNumberOfRows, DimEq, AreMultipliable};
+use core::allocator::Allocator;
+use dimension::{Dim, DimName, U1};
+use storage::{Storage, StorageMut};
+
+use geometry::Point;
+
+/// A reflection wrt. a plane.
+pub struct Reflection<N: Scalar, D: Dim, S: Storage<N, D>> {
+    axis:  Vector<N, D, S>,
+    bias:  N
+}
+
+impl<N: Real, D: Dim, S: Storage<N, D>> Reflection<N, D, S> {
+    /// Creates a new reflection wrt the plane orthogonal to the given axis and bias.
+    ///
+    /// The bias is the position of the plane on the axis. In particular, a bias equal to zero
+    /// represents a plane that passes through the origin.
+    pub fn new(axis: Unit<Vector<N, D, S>>, bias: N) -> Reflection<N, D, S> {
+        Reflection { axis: axis.unwrap(), bias: bias }
+    }
+
+    /// Creates a new reflection wrt. the plane orthogonal to the given axis and that contains the
+    /// point `pt`.
+    pub fn new_containing_point(axis: Unit<Vector<N, D, S>>, pt: &Point<N, D>) -> Reflection<N, D, S>
+        where D: DimName,
+              DefaultAllocator: Allocator<N, D> {
+        let bias = pt.coords.dot(axis.as_ref());
+        Self::new(axis, bias)
+    }
+
+    /// The reflexion axis.
+    pub fn axis(&self) -> &Vector<N, D, S> {
+        &self.axis
+    }
+
+    // FIXME: naming convension: reflect_to, reflect_assign ?
+    /// Applies the reflection to the columns of `rhs`.
+    pub fn reflect<R2: Dim, C2: Dim, S2>(&self, rhs: &mut Matrix<N, R2, C2, S2>)
+        where S2: StorageMut<N, R2, C2>,
+              ShapeConstraint: SameNumberOfRows<R2, D> {
+
+        for i in 0 .. rhs.ncols() {
+            // NOTE: we borrow the column twice here. First it is borrowed immutably for the
+            // dot product, and then mutably. Somehow, this allows significantly
+            // better optimizations of the dot product from the compiler.
+            let m_two: N = ::convert(-2.0f64);
+            let factor  = (rhs.column(i).dot(&self.axis) - self.bias) * m_two;
+            rhs.column_mut(i).axpy(factor, &self.axis, N::one());
+        }
+    }
+
+    /// Applies the reflection to the rows of `rhs`.
+    pub fn reflect_rows<R2: Dim, C2: Dim, S2, S3>(&self,
+                                                  rhs:  &mut Matrix<N, R2, C2, S2>,
+                                                  work: &mut Vector<N, R2, S3>)
+        where S2: StorageMut<N, R2, C2>,
+              S3: StorageMut<N, R2>,
+              ShapeConstraint: DimEq<C2, D> + AreMultipliable<R2, C2, D, U1> {
+
+        rhs.mul_to(&self.axis, work);
+
+        if !self.bias.is_zero() {
+            work.add_scalar_mut(-self.bias);
+        }
+
+        let m_two: N = ::convert(-2.0f64);
+        rhs.ger(m_two, &work, &self.axis, N::one());
+    }
+}

src/geometry/rotation.rs

@@ -1,60 +1,79 @@
 use num::{Zero, One};
+use std::hash;
 use std::fmt;
 use approx::ApproxEq;
 
 #[cfg(feature = "serde-serialize")]
-use serde::{Serialize, Serializer, Deserialize, Deserializer};
+use serde;
+
+#[cfg(feature = "serde-serialize")]
+use core::storage::Owned;
 
 use alga::general::Real;
 
-use core::{SquareMatrix, Scalar, OwnedSquareMatrix};
+use core::{DefaultAllocator, Scalar, MatrixN};
 use core::dimension::{DimName, DimNameSum, DimNameAdd, U1};
-use core::storage::{Storage, StorageMut};
 use core::allocator::Allocator;
 
 
-/// A rotation matrix with an owned storage.
-pub type OwnedRotation<N, D, A> = RotationBase<N, D, <A as Allocator<N, D, D>>::Buffer>;
-
 /// A rotation matrix.
 #[repr(C)]
-#[derive(Hash, Debug, Clone, Copy)]
-pub struct RotationBase<N: Scalar, D: DimName, S> {
-    matrix: SquareMatrix<N, D, S>
+#[derive(Debug)]
+pub struct Rotation<N: Scalar, D: DimName>
+    where DefaultAllocator: Allocator<N, D, D> {
+    matrix: MatrixN<N, D>
+}
+
+impl<N: Scalar + hash::Hash, D: DimName + hash::Hash> hash::Hash for Rotation<N, D>
+    where DefaultAllocator: Allocator<N, D, D>,
+          <DefaultAllocator as Allocator<N, D, D>>::Buffer: hash::Hash {
+    fn hash<H: hash::Hasher>(&self, state: &mut H) {
+        self.matrix.hash(state)
+    }
+}
+
+impl<N: Scalar, D: DimName> Copy for Rotation<N, D>
+    where DefaultAllocator: Allocator<N, D, D>,
+          <DefaultAllocator as Allocator<N, D, D>>::Buffer: Copy { }
+
+impl<N: Scalar, D: DimName> Clone for Rotation<N, D>
+    where DefaultAllocator: Allocator<N, D, D>,
+          <DefaultAllocator as Allocator<N, D, D>>::Buffer: Clone {
+    #[inline]
+    fn clone(&self) -> Self {
+        Rotation::from_matrix_unchecked(self.matrix.clone())
+    }
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<N, D, S> Serialize for RotationBase<N, D, S>
-    where N: Scalar,
-          D: DimName,
-          SquareMatrix<N, D, S>: Serialize,
-{
-    fn serialize<T>(&self, serializer: T) -> Result<T::Ok, T::Error>
-        where T: Serializer
-    {
+impl<N: Scalar, D: DimName> serde::Serialize for Rotation<N, D>
+where DefaultAllocator: Allocator<N, D, D>,
+      Owned<N, D, D>: serde::Serialize {
+
+    fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
+        where S: serde::Serializer {
             self.matrix.serialize(serializer)
         }
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<'de, N, D, S> Deserialize<'de> for RotationBase<N, D, S>
-    where N: Scalar,
-          D: DimName,
-          SquareMatrix<N, D, S>: Deserialize<'de>,
-{
-    fn deserialize<T>(deserializer: T) -> Result<Self, T::Error>
-        where T: Deserializer<'de>
-    {
-        SquareMatrix::deserialize(deserializer).map(|x| RotationBase { matrix: x })
+impl<'a, N: Scalar, D: DimName> serde::Deserialize<'a> for Rotation<N, D>
+where DefaultAllocator: Allocator<N, D, D>,
+      Owned<N, D, D>: serde::Deserialize<'a> {
+
+    fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
+        where Des: serde::Deserializer<'a> {
+            let matrix = MatrixN::<N, D>::deserialize(deserializer)?;
+
+            Ok(Rotation::from_matrix_unchecked(matrix))
         }
 }
 
-impl<N: Scalar, D: DimName, S: Storage<N, D, D>> RotationBase<N, D, S>
-    where N: Scalar,
-          S: Storage<N, D, D> {
+impl<N: Scalar, D: DimName> Rotation<N, D>
+    where DefaultAllocator: Allocator<N, D, D> {
     /// A reference to the underlying matrix representation of this rotation.
     #[inline]
-    pub fn matrix(&self) -> &SquareMatrix<N, D, S> {
+    pub fn matrix(&self) -> &MatrixN<N, D> {
         &self.matrix
     }
 
@@ -64,57 +83,52 @@ impl<N: Scalar, D: DimName, S: Storage<N, D, D>> RotationBase<N, D, S>
     /// non-square, non-inversible, or non-orthonormal. If one of those properties is broken,
     /// subsequent method calls may be UB.
     #[inline]
-    pub unsafe fn matrix_mut(&mut self) -> &mut SquareMatrix<N, D, S> {
+    pub unsafe fn matrix_mut(&mut self) -> &mut MatrixN<N, D> {
         &mut self.matrix
     }
 
     /// Unwraps the underlying matrix.
     #[inline]
-    pub fn unwrap(self) -> SquareMatrix<N, D, S> {
+    pub fn unwrap(self) -> MatrixN<N, D> {
         self.matrix
     }
 
     /// Converts this rotation into its equivalent homogeneous transformation matrix.
     #[inline]
-    pub fn to_homogeneous(&self) -> OwnedSquareMatrix<N, DimNameSum<D, U1>, S::Alloc>
+    pub fn to_homogeneous(&self) -> MatrixN<N, DimNameSum<D, U1>>
         where N: Zero + One,
               D: DimNameAdd<U1>,
-              S::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
-        let mut res = OwnedSquareMatrix::<N, _, S::Alloc>::identity();
+              DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
+        let mut res = MatrixN::<N, DimNameSum<D, U1>>::identity();
         res.fixed_slice_mut::<D, D>(0, 0).copy_from(&self.matrix);
 
         res
     }
-}
 
-impl<N: Scalar, D: DimName, S: Storage<N, D, D>> RotationBase<N, D, S> {
     /// Creates a new rotation from the given square matrix.
     ///
     /// The matrix squareness is checked but not its orthonormality.
     #[inline]
-    pub fn from_matrix_unchecked(matrix: SquareMatrix<N, D, S>) -> RotationBase<N, D, S> {
+    pub fn from_matrix_unchecked(matrix: MatrixN<N, D>) -> Rotation<N, D> {
         assert!(matrix.is_square(), "Unable to create a rotation from a non-square matrix.");
 
-        RotationBase {
+        Rotation {
             matrix: matrix
         }
     }
 
     /// Transposes `self`.
     #[inline]
-    pub fn transpose(&self) -> OwnedRotation<N, D, S::Alloc> {
-        RotationBase::from_matrix_unchecked(self.matrix.transpose())
+    pub fn transpose(&self) -> Rotation<N, D> {
+        Rotation::from_matrix_unchecked(self.matrix.transpose())
     }
 
     /// Inverts `self`.
     #[inline]
-    pub fn inverse(&self) -> OwnedRotation<N, D, S::Alloc> {
+    pub fn inverse(&self) -> Rotation<N, D> {
         self.transpose()
     }
-}
 
-
-impl<N: Scalar, D: DimName, S: StorageMut<N, D, D>> RotationBase<N, D, S> {
     /// Transposes `self` in-place.
     #[inline]
     pub fn transpose_mut(&mut self) {
@@ -128,18 +142,20 @@ impl<N: Scalar, D: DimName, S: StorageMut<N, D, D>> RotationBase<N, D, S> {
     }
 }
 
-impl<N: Scalar + Eq, D: DimName, S: Storage<N, D, D>> Eq for RotationBase<N, D, S> { }
+impl<N: Scalar + Eq, D: DimName> Eq for Rotation<N, D>
+    where DefaultAllocator: Allocator<N, D, D> { }
 
-impl<N: Scalar + PartialEq, D: DimName, S: Storage<N, D, D>> PartialEq for RotationBase<N, D, S> {
+impl<N: Scalar + PartialEq, D: DimName> PartialEq for Rotation<N, D>
+    where DefaultAllocator: Allocator<N, D, D> {
     #[inline]
-    fn eq(&self, right: &RotationBase<N, D, S>) -> bool {
+    fn eq(&self, right: &Rotation<N, D>) -> bool {
         self.matrix == right.matrix
     }
 }
 
-impl<N, D: DimName, S> ApproxEq for RotationBase<N, D, S>
+impl<N, D: DimName> ApproxEq for Rotation<N, D>
     where N: Scalar + ApproxEq,
-          S: Storage<N, D, D>,
+          DefaultAllocator: Allocator<N, D, D>,
           N::Epsilon: Copy {
     type Epsilon = N::Epsilon;
 
@@ -174,14 +190,14 @@ impl<N, D: DimName, S> ApproxEq for RotationBase<N, D, S>
  * Display
  *
  */
-impl<N, D: DimName, S> fmt::Display for RotationBase<N, D, S>
+impl<N, D: DimName> fmt::Display for Rotation<N, D>
     where N: Real + fmt::Display,
-          S: Storage<N, D, D>,
-          S::Alloc: Allocator<usize, D, D> {
+          DefaultAllocator: Allocator<N, D, D> +
+                            Allocator<usize, D, D> {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         let precision = f.precision().unwrap_or(3);
 
-        try!(writeln!(f, "RotationBase matrix {{"));
+        try!(writeln!(f, "Rotation matrix {{"));
         try!(write!(f, "{:.*}", precision, self.matrix));
         writeln!(f, "}}")
     }

src/geometry/rotation_alga.rs

@@ -1,14 +1,13 @@
 use alga::general::{AbstractMagma, AbstractGroup, AbstractLoop, AbstractMonoid, AbstractQuasigroup,
                     AbstractSemigroup, Real, Inverse, Multiplicative, Identity, Id};
-use alga::linear::{Transformation, Similarity, AffineTransformation, Isometry, DirectIsometry,
-                   OrthogonalTransformation, ProjectiveTransformation, Rotation};
+use alga::linear::{self, Transformation, Similarity, AffineTransformation, Isometry,
+                   DirectIsometry, OrthogonalTransformation, ProjectiveTransformation};
 
-use core::ColumnVector;
-use core::dimension::{DimName, U1};
-use core::storage::OwnedStorage;
-use core::allocator::OwnedAllocator;
+use core::{DefaultAllocator, VectorN};
+use core::dimension::DimName;
+use core::allocator::Allocator;
 
-use geometry::{RotationBase, PointBase};
+use geometry::{Rotation, Point};
 
 
 
@@ -17,20 +16,16 @@ use geometry::{RotationBase, PointBase};
  * Algebraic structures.
  *
  */
-impl<N, D: DimName, S> Identity<Multiplicative> for RotationBase<N, D, S>
-    where N: Real,
-          S: OwnedStorage<N, D, D>,
-          S::Alloc: OwnedAllocator<N, D, D, S> {
+impl<N: Real, D: DimName> Identity<Multiplicative> for Rotation<N, D>
+    where DefaultAllocator: Allocator<N, D, D> {
     #[inline]
     fn identity() -> Self {
         Self::identity()
     }
 }
 
-impl<N, D: DimName, S> Inverse<Multiplicative> for RotationBase<N, D, S>
-    where N: Real,
-          S: OwnedStorage<N, D, D>,
-          S::Alloc: OwnedAllocator<N, D, D, S> {
+impl<N: Real, D: DimName> Inverse<Multiplicative> for Rotation<N, D>
+    where DefaultAllocator: Allocator<N, D, D> {
     #[inline]
     fn inverse(&self) -> Self {
         self.transpose()
@@ -42,10 +37,8 @@ impl<N, D: DimName, S> Inverse<Multiplicative> for RotationBase<N, D, S>
     }
 }
 
-impl<N, D: DimName, S> AbstractMagma<Multiplicative> for RotationBase<N, D, S>
-    where N: Real,
-          S: OwnedStorage<N, D, D>,
-          S::Alloc: OwnedAllocator<N, D, D, S> {
+impl<N: Real, D: DimName> AbstractMagma<Multiplicative> for Rotation<N, D>
+    where DefaultAllocator: Allocator<N, D, D> {
     #[inline]
     fn operate(&self, rhs: &Self) -> Self {
         self * rhs
@@ -54,10 +47,8 @@ impl<N, D: DimName, S> AbstractMagma<Multiplicative> for RotationBase<N, D, S>
 
 macro_rules! impl_multiplicative_structures(
     ($($marker: ident<$operator: ident>),* $(,)*) => {$(
-        impl<N, D: DimName, S> $marker<$operator> for RotationBase<N, D, S>
-            where N: Real,
-                  S: OwnedStorage<N, D, D>,
-                  S::Alloc: OwnedAllocator<N, D, D, S> { }
+        impl<N: Real, D: DimName> $marker<$operator> for Rotation<N, D>
+            where DefaultAllocator: Allocator<N, D, D> { }
     )*}
 );
 
@@ -74,46 +65,37 @@ impl_multiplicative_structures!(
  * Transformation groups.
  *
  */
-impl<N, D: DimName, SA, SB> Transformation<PointBase<N, D, SB>> for RotationBase<N, D, SA>
-    where N:  Real,
-          SA: OwnedStorage<N, D, D>,
-          SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
-          SA::Alloc: OwnedAllocator<N, D, D, SA>,
-          SB::Alloc: OwnedAllocator<N, D, U1, SB> {
+impl<N: Real, D: DimName> Transformation<Point<N, D>> for Rotation<N, D>
+    where DefaultAllocator: Allocator<N, D, D> +
+                            Allocator<N, D> {
     #[inline]
-    fn transform_point(&self, pt: &PointBase<N, D, SB>) -> PointBase<N, D, SB> {
+    fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
         self * pt
     }
 
     #[inline]
-    fn transform_vector(&self, v: &ColumnVector<N, D, SB>) -> ColumnVector<N, D, SB> {
+    fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
         self * v
     }
 }
 
-impl<N, D: DimName, SA, SB> ProjectiveTransformation<PointBase<N, D, SB>> for RotationBase<N, D, SA>
-    where N:  Real,
-          SA: OwnedStorage<N, D, D>,
-          SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
-          SA::Alloc: OwnedAllocator<N, D, D, SA>,
-          SB::Alloc: OwnedAllocator<N, D, U1, SB> {
+impl<N: Real, D: DimName> ProjectiveTransformation<Point<N, D>> for Rotation<N, D>
+    where DefaultAllocator: Allocator<N, D, D> +
+                            Allocator<N, D> {
     #[inline]
-    fn inverse_transform_point(&self, pt: &PointBase<N, D, SB>) -> PointBase<N, D, SB> {
-        PointBase::from_coordinates(self.inverse_transform_vector(&pt.coords))
+    fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
+        Point::from_coordinates(self.inverse_transform_vector(&pt.coords))
     }
 
     #[inline]
-    fn inverse_transform_vector(&self, v: &ColumnVector<N, D, SB>) -> ColumnVector<N, D, SB> {
+    fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
         self.matrix().tr_mul(v)
     }
 }
 
-impl<N, D: DimName, SA, SB> AffineTransformation<PointBase<N, D, SB>> for RotationBase<N, D, SA>
-    where N:  Real,
-          SA: OwnedStorage<N, D, D>,
-          SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
-          SA::Alloc: OwnedAllocator<N, D, D, SA>,
-          SB::Alloc: OwnedAllocator<N, D, U1, SB> {
+impl<N: Real, D: DimName> AffineTransformation<Point<N, D>> for Rotation<N, D>
+    where DefaultAllocator: Allocator<N, D, D> +
+                            Allocator<N, D> {
     type Rotation          = Self;
     type NonUniformScaling = Id;
     type Translation       = Id;
@@ -155,12 +137,9 @@ impl<N, D: DimName, SA, SB> AffineTransformation<PointBase<N, D, SB>> for Rotati
 }
 
 
-impl<N, D: DimName, SA, SB> Similarity<PointBase<N, D, SB>> for RotationBase<N, D, SA>
-    where N:  Real,
-          SA: OwnedStorage<N, D, D>,
-          SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
-          SA::Alloc: OwnedAllocator<N, D, D, SA>,
-          SB::Alloc: OwnedAllocator<N, D, U1, SB> {
+impl<N: Real, D: DimName> Similarity<Point<N, D>> for Rotation<N, D>
+    where DefaultAllocator: Allocator<N, D, D> +
+                            Allocator<N, D> {
     type Scaling  = Id;
 
     #[inline]
@@ -181,12 +160,9 @@ impl<N, D: DimName, SA, SB> Similarity<PointBase<N, D, SB>> for RotationBase<N,
 
 macro_rules! marker_impl(
     ($($Trait: ident),*) => {$(
-        impl<N, D: DimName, SA, SB> $Trait<PointBase<N, D, SB>> for RotationBase<N, D, SA>
-        where N:  Real,
-              SA: OwnedStorage<N, D, D>,
-              SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
-              SA::Alloc: OwnedAllocator<N, D, D, SA>,
-              SB::Alloc: OwnedAllocator<N, D, U1, SB> { }
+        impl<N: Real, D: DimName> $Trait<Point<N, D>> for Rotation<N, D>
+        where DefaultAllocator: Allocator<N, D, D> +
+                                Allocator<N, D> { }
     )*}
 );
 
@@ -194,12 +170,9 @@ marker_impl!(Isometry, DirectIsometry, OrthogonalTransformation);
 
 
 /// Subgroups of the n-dimensional rotation group `SO(n)`.
-impl<N, D: DimName, SA, SB> Rotation<PointBase<N, D, SB>> for RotationBase<N, D, SA>
-    where N:  Real,
-          SA: OwnedStorage<N, D, D>,
-          SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
-          SA::Alloc: OwnedAllocator<N, D, D, SA>,
-          SB::Alloc: OwnedAllocator<N, D, U1, SB> {
+impl<N: Real, D: DimName> linear::Rotation<Point<N, D>> for Rotation<N, D>
+    where DefaultAllocator: Allocator<N, D, D> +
+                            Allocator<N, D> {
     #[inline]
     fn powf(&self, _: N) -> Option<Self> {
         // XXX: Add the general case.
@@ -208,14 +181,14 @@ impl<N, D: DimName, SA, SB> Rotation<PointBase<N, D, SB>> for RotationBase<N, D,
     }
 
     #[inline]
-    fn rotation_between(_: &ColumnVector<N, D, SB>, _: &ColumnVector<N, D, SB>) -> Option<Self> {
+    fn rotation_between(_: &VectorN<N, D>, _: &VectorN<N, D>) -> Option<Self> {
         // XXX: Add the general case.
         // XXX: Use specialization for 2D and 3D.
         unimplemented!()
     }
 
     #[inline]
-    fn scaled_rotation_between(_: &ColumnVector<N, D, SB>, _: &ColumnVector<N, D, SB>, _: N) -> Option<Self> {
+    fn scaled_rotation_between(_: &VectorN<N, D>, _: &VectorN<N, D>, _: N) -> Option<Self> {
         // XXX: Add the general case.
         // XXX: Use specialization for 2D and 3D.
         unimplemented!()
@@ -223,7 +196,7 @@ impl<N, D: DimName, SA, SB> Rotation<PointBase<N, D, SB>> for RotationBase<N, D,
 }
 
 /*
-impl<N: Real> Matrix for RotationBase<N> {
+impl<N: Real> Matrix for Rotation<N> {
     type Field     = N;
     type Row       = Matrix<N>;
     type Column    = Matrix<N>;
@@ -261,11 +234,11 @@ impl<N: Real> Matrix for RotationBase<N> {
 
     #[inline]
     fn transpose(&self) -> Self::Transpose {
-        RotationBase::from_matrix_unchecked(self.submatrix.transpose())
+        Rotation::from_matrix_unchecked(self.submatrix.transpose())
     }
 }
 
-impl<N: Real> SquareMatrix for RotationBase<N> {
+impl<N: Real> SquareMatrix for Rotation<N> {
     type Vector = Matrix<N>;
 
     #[inline]
@@ -295,7 +268,7 @@ impl<N: Real> SquareMatrix for RotationBase<N> {
     }
 }
 
-impl<N: Real> InversibleSquareMatrix for RotationBase<N> { }
+impl<N: Real> InversibleSquareMatrix for Rotation<N> { }
 */
 
 

src/geometry/rotation_alias.rs

@@ -1,10 +1,6 @@
-use core::MatrixArray;
 use core::dimension::{U2, U3};
 
-use geometry::RotationBase;
-
-/// A D-dimensional rotation matrix.
-pub type Rotation<N, D> = RotationBase<N, D, MatrixArray<N, D, D>>;
+use geometry::Rotation;
 
 /// A 2-dimensional rotation matrix.
 pub type Rotation2<N> = Rotation<N, U2>;

src/geometry/rotation_construction.rs

@@ -2,28 +2,25 @@ use num::{Zero, One};
 
 use alga::general::{ClosedAdd, ClosedMul};
 
-use core::{SquareMatrix, Scalar};
+use core::{DefaultAllocator, MatrixN, Scalar};
 use core::dimension::DimName;
-use core::storage::OwnedStorage;
-use core::allocator::OwnedAllocator;
+use core::allocator::Allocator;
 
-use geometry::RotationBase;
+use geometry::Rotation;
 
-impl<N, D: DimName, S> RotationBase<N, D, S>
+impl<N, D: DimName> Rotation<N, D>
     where N: Scalar + Zero + One,
-          S: OwnedStorage<N, D, D>,
-          S::Alloc: OwnedAllocator<N, D, D, S> {
+          DefaultAllocator: Allocator<N, D, D> {
     /// Creates a new square identity rotation of the given `dimension`.
     #[inline]
-    pub fn identity() -> RotationBase<N, D, S> {
-        Self::from_matrix_unchecked(SquareMatrix::<N, D, S>::identity())
+    pub fn identity() -> Rotation<N, D> {
+        Self::from_matrix_unchecked(MatrixN::<N, D>::identity())
     }
 }
 
-impl<N, D: DimName, S> One for RotationBase<N, D, S>
+impl<N, D: DimName> One for Rotation<N, D>
     where N: Scalar + Zero + One + ClosedAdd + ClosedMul,
-          S: OwnedStorage<N, D, D>,
-          S::Alloc: OwnedAllocator<N, D, D, S> {
+          DefaultAllocator: Allocator<N, D, D> {
     #[inline]
     fn one() -> Self {
         Self::identity()

src/geometry/rotation_conversion.rs

@@ -3,178 +3,186 @@ use num::Zero;
 use alga::general::{Real, SubsetOf, SupersetOf};
 use alga::linear::Rotation as AlgaRotation;
 
-use core::{Matrix, SquareMatrix};
-use core::dimension::{DimName, DimNameSum, DimNameAdd, U1, U3, U4};
-use core::storage::OwnedStorage;
-use core::allocator::{OwnedAllocator, Allocator};
+use core::{DefaultAllocator, MatrixN};
+use core::dimension::{DimName, DimNameSum, DimNameAdd, DimMin, U1};
+use core::allocator::Allocator;
 
-use geometry::{PointBase, TranslationBase, RotationBase, UnitQuaternionBase, OwnedUnitQuaternionBase, IsometryBase,
-               SimilarityBase, TransformBase, SuperTCategoryOf, TAffine};
+use geometry::{Point, Translation, Rotation, UnitQuaternion, UnitComplex, Isometry,
+               Similarity, Transform, SuperTCategoryOf, TAffine,
+               Rotation2, Rotation3};
 
 /*
  * This file provides the following conversions:
  * =============================================
  *
- * RotationBase  -> RotationBase
+ * Rotation  -> Rotation
  * Rotation3 -> UnitQuaternion
- * RotationBase  -> IsometryBase
- * RotationBase  -> SimilarityBase
- * RotationBase  -> TransformBase
- * RotationBase  -> Matrix (homogeneous)
+ * Rotation2 -> UnitComplex
+ * Rotation  -> Isometry
+ * Rotation  -> Similarity
+ * Rotation  -> Transform
+ * Rotation  -> Matrix (homogeneous)
  */
 
 
-impl<N1, N2, D: DimName, SA, SB> SubsetOf<RotationBase<N2, D, SB>> for RotationBase<N1, D, SA>
+impl<N1, N2, D: DimName> SubsetOf<Rotation<N2, D>> for Rotation<N1, D>
     where N1: Real,
           N2: Real + SupersetOf<N1>,
-          SA: OwnedStorage<N1, D, D>,
-          SB: OwnedStorage<N2, D, D>,
-          SA::Alloc: OwnedAllocator<N1, D, D, SA>,
-          SB::Alloc: OwnedAllocator<N2, D, D, SB> {
+          DefaultAllocator: Allocator<N1, D, D> +
+                            Allocator<N2, D, D> {
     #[inline]
-    fn to_superset(&self) -> RotationBase<N2, D, SB> {
-        RotationBase::from_matrix_unchecked(self.matrix().to_superset())
+    fn to_superset(&self) -> Rotation<N2, D> {
+        Rotation::from_matrix_unchecked(self.matrix().to_superset())
     }
 
     #[inline]
-    fn is_in_subset(rot: &RotationBase<N2, D, SB>) -> bool {
-        ::is_convertible::<_, Matrix<N1, D, D, SA>>(rot.matrix())
+    fn is_in_subset(rot: &Rotation<N2, D>) -> bool {
+        ::is_convertible::<_, MatrixN<N1, D>>(rot.matrix())
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(rot: &RotationBase<N2, D, SB>) -> Self {
-        RotationBase::from_matrix_unchecked(rot.matrix().to_subset_unchecked())
+    unsafe fn from_superset_unchecked(rot: &Rotation<N2, D>) -> Self {
+        Rotation::from_matrix_unchecked(rot.matrix().to_subset_unchecked())
     }
 }
 
 
-impl<N1, N2, SA, SB> SubsetOf<UnitQuaternionBase<N2, SB>> for RotationBase<N1, U3, SA>
+impl<N1, N2> SubsetOf<UnitQuaternion<N2>> for Rotation3<N1>
     where N1: Real,
-          N2: Real + SupersetOf<N1>,
-          SA: OwnedStorage<N1, U3, U3>,
-          SB: OwnedStorage<N2, U4, U1>,
-          SA::Alloc: OwnedAllocator<N1, U3, U3, SA> +
-                     Allocator<N1, U4, U1> +
-                     Allocator<N1, U3, U1>,
-          SB::Alloc: OwnedAllocator<N2, U4, U1, SB> +
-                     Allocator<N2, U3, U3> {
+          N2: Real + SupersetOf<N1> {
     #[inline]
-    fn to_superset(&self) -> UnitQuaternionBase<N2, SB> {
-        let q = OwnedUnitQuaternionBase::<N1, SA::Alloc>::from_rotation_matrix(self);
+    fn to_superset(&self) -> UnitQuaternion<N2> {
+        let q = UnitQuaternion::<N1>::from_rotation_matrix(self);
         q.to_superset()
     }
 
     #[inline]
-    fn is_in_subset(q: &UnitQuaternionBase<N2, SB>) -> bool {
-        ::is_convertible::<_, OwnedUnitQuaternionBase<N1, SA::Alloc>>(q)
+    fn is_in_subset(q: &UnitQuaternion<N2>) -> bool {
+        ::is_convertible::<_, UnitQuaternion<N1>>(q)
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(q: &UnitQuaternionBase<N2, SB>) -> Self {
-        let q: OwnedUnitQuaternionBase<N1, SA::Alloc> = ::convert_ref_unchecked(q);
+    unsafe fn from_superset_unchecked(q: &UnitQuaternion<N2>) -> Self {
+        let q: UnitQuaternion<N1> = ::convert_ref_unchecked(q);
+        q.to_rotation_matrix()
+    }
+}
+
+impl<N1, N2> SubsetOf<UnitComplex<N2>> for Rotation2<N1>
+    where N1: Real,
+          N2: Real + SupersetOf<N1> {
+    #[inline]
+    fn to_superset(&self) -> UnitComplex<N2> {
+        let q = UnitComplex::<N1>::from_rotation_matrix(self);
+        q.to_superset()
+    }
+
+    #[inline]
+    fn is_in_subset(q: &UnitComplex<N2>) -> bool {
+        ::is_convertible::<_, UnitComplex<N1>>(q)
+    }
+
+    #[inline]
+    unsafe fn from_superset_unchecked(q: &UnitComplex<N2>) -> Self {
+        let q: UnitComplex<N1> = ::convert_ref_unchecked(q);
         q.to_rotation_matrix()
     }
 }
 
 
-impl<N1, N2, D: DimName, SA, SB, R> SubsetOf<IsometryBase<N2, D, SB, R>> for RotationBase<N1, D, SA>
+
+impl<N1, N2, D: DimName, R> SubsetOf<Isometry<N2, D, R>> for Rotation<N1, D>
     where N1: Real,
           N2: Real + SupersetOf<N1>,
-          SA: OwnedStorage<N1, D, D>,
-          SB: OwnedStorage<N2, D, U1>,
-          R:  AlgaRotation<PointBase<N2, D, SB>> + SupersetOf<RotationBase<N1, D, SA>>,
-          SA::Alloc: OwnedAllocator<N1, D, D, SA>,
-          SB::Alloc: OwnedAllocator<N2, D, U1, SB> {
+          R:  AlgaRotation<Point<N2, D>> + SupersetOf<Rotation<N1, D>>,
+          DefaultAllocator: Allocator<N1, D, D> +
+                            Allocator<N2, D> {
     #[inline]
-    fn to_superset(&self) -> IsometryBase<N2, D, SB, R> {
-        IsometryBase::from_parts(TranslationBase::identity(), ::convert_ref(self))
+    fn to_superset(&self) -> Isometry<N2, D, R> {
+        Isometry::from_parts(Translation::identity(), ::convert_ref(self))
     }
 
     #[inline]
-    fn is_in_subset(iso: &IsometryBase<N2, D, SB, R>) -> bool {
+    fn is_in_subset(iso: &Isometry<N2, D, R>) -> bool {
         iso.translation.vector.is_zero()
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(iso: &IsometryBase<N2, D, SB, R>) -> Self {
+    unsafe fn from_superset_unchecked(iso: &Isometry<N2, D, R>) -> Self {
         ::convert_ref_unchecked(&iso.rotation)
     }
 }
 
 
-impl<N1, N2, D: DimName, SA, SB, R> SubsetOf<SimilarityBase<N2, D, SB, R>> for RotationBase<N1, D, SA>
+impl<N1, N2, D: DimName, R> SubsetOf<Similarity<N2, D, R>> for Rotation<N1, D>
     where N1: Real,
           N2: Real + SupersetOf<N1>,
-          SA: OwnedStorage<N1, D, D>,
-          SB: OwnedStorage<N2, D, U1>,
-          R:  AlgaRotation<PointBase<N2, D, SB>> + SupersetOf<RotationBase<N1, D, SA>>,
-          SA::Alloc: OwnedAllocator<N1, D, D, SA>,
-          SB::Alloc: OwnedAllocator<N2, D, U1, SB> {
+          R:  AlgaRotation<Point<N2, D>> + SupersetOf<Rotation<N1, D>>,
+          DefaultAllocator: Allocator<N1, D, D> +
+                            Allocator<N2, D> {
     #[inline]
-    fn to_superset(&self) -> SimilarityBase<N2, D, SB, R> {
-        SimilarityBase::from_parts(TranslationBase::identity(), ::convert_ref(self), N2::one())
+    fn to_superset(&self) -> Similarity<N2, D, R> {
+        Similarity::from_parts(Translation::identity(), ::convert_ref(self), N2::one())
     }
 
     #[inline]
-    fn is_in_subset(sim: &SimilarityBase<N2, D, SB, R>) -> bool {
+    fn is_in_subset(sim: &Similarity<N2, D, R>) -> bool {
         sim.isometry.translation.vector.is_zero() &&
         sim.scaling() == N2::one()
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(sim: &SimilarityBase<N2, D, SB, R>) -> Self {
+    unsafe fn from_superset_unchecked(sim: &Similarity<N2, D, R>) -> Self {
         ::convert_ref_unchecked(&sim.isometry.rotation)
     }
 }
 
 
-impl<N1, N2, D, SA, SB, C> SubsetOf<TransformBase<N2, D, SB, C>> for RotationBase<N1, D, SA>
+impl<N1, N2, D, C> SubsetOf<Transform<N2, D, C>> for Rotation<N1, D>
     where N1: Real,
           N2: Real + SupersetOf<N1>,
-          SA: OwnedStorage<N1, D, D>,
-          SB: OwnedStorage<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>,
           C:  SuperTCategoryOf<TAffine>,
-          D:  DimNameAdd<U1>,
-          SA::Alloc: OwnedAllocator<N1, D, D, SA> +
-                     Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>>,
-          SB::Alloc: OwnedAllocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>, SB> +
+          D:  DimNameAdd<U1> +
+              DimMin<D, Output = D>, // needed by .is_special_orthogonal()
+          DefaultAllocator: Allocator<N1, D, D> +
                             Allocator<N2, D, D> +
-                     Allocator<N2, U1, D> {
+                            Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>> +
+                            Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>> +
+                            Allocator<(usize, usize), D> { // needed by .is_special_orthogonal()
     #[inline]
-    fn to_superset(&self) -> TransformBase<N2, D, SB, C> {
-        TransformBase::from_matrix_unchecked(self.to_homogeneous().to_superset())
+    fn to_superset(&self) -> Transform<N2, D, C> {
+        Transform::from_matrix_unchecked(self.to_homogeneous().to_superset())
     }
 
     #[inline]
-    fn is_in_subset(t: &TransformBase<N2, D, SB, C>) -> bool {
+    fn is_in_subset(t: &Transform<N2, D, C>) -> bool {
         <Self as SubsetOf<_>>::is_in_subset(t.matrix())
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(t: &TransformBase<N2, D, SB, C>) -> Self {
+    unsafe fn from_superset_unchecked(t: &Transform<N2, D, C>) -> Self {
         Self::from_superset_unchecked(t.matrix())
     }
 }
 
 
-impl<N1, N2, D, SA, SB> SubsetOf<SquareMatrix<N2, DimNameSum<D, U1>, SB>> for RotationBase<N1, D, SA>
+impl<N1, N2, D> SubsetOf<MatrixN<N2, DimNameSum<D, U1>>> for Rotation<N1, D>
     where N1: Real,
           N2: Real + SupersetOf<N1>,
-          SA: OwnedStorage<N1, D, D>,
-          SB: OwnedStorage<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>,
-          D:  DimNameAdd<U1>,
-          SA::Alloc: OwnedAllocator<N1, D, D, SA> +
-                     Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>>,
-          SB::Alloc: OwnedAllocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>, SB> +
+          D:  DimNameAdd<U1> +
+              DimMin<D, Output = D>, // needed by .is_special_orthogonal()
+          DefaultAllocator: Allocator<N1, D, D> +
                             Allocator<N2, D, D> +
-                     Allocator<N2, U1, D> {
+                            Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>> +
+                            Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>> +
+                            Allocator<(usize, usize), D> { // needed by .is_special_orthogonal()
     #[inline]
-    fn to_superset(&self) -> SquareMatrix<N2, DimNameSum<D, U1>, SB> {
+    fn to_superset(&self) -> MatrixN<N2, DimNameSum<D, U1>> {
         self.to_homogeneous().to_superset()
     }
 
     #[inline]
-    fn is_in_subset(m: &SquareMatrix<N2, DimNameSum<D, U1>, SB>) -> bool {
+    fn is_in_subset(m: &MatrixN<N2, DimNameSum<D, U1>>) -> bool {
         let rot    = m.fixed_slice::<D, D>(0, 0);
         let bottom = m.fixed_slice::<U1, D>(D::dim(), 0);
 
@@ -188,7 +196,7 @@ impl<N1, N2, D, SA, SB> SubsetOf<SquareMatrix<N2, DimNameSum<D, U1>, SB>> for Ro
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(m: &SquareMatrix<N2, DimNameSum<D, U1>, SB>) -> Self {
+    unsafe fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self {
         let r = m.fixed_slice::<D, D>(0, 0);
         Self::from_matrix_unchecked(::convert_unchecked(r.into_owned()))
     }

src/geometry/rotation_ops.rs

@@ -4,33 +4,34 @@
  *
  * Index<(usize, usize)>
  *
- * RotationBase × RotationBase
- * RotationBase ÷ RotationBase
- * RotationBase × Matrix
- * Matrix       × RotationBase
- * Matrix       ÷ RotationBase
- * RotationBase × PointBase
+ * Rotation × Rotation
+ * Rotation ÷ Rotation
+ * Rotation × Matrix
+ * Matrix   × Rotation
+ * Matrix   ÷ Rotation
+ * Rotation × Point
  *
  *
- * RotationBase ×= RotationBase
- * Matrix       ×= RotationBase
+ * Rotation ×= Rotation
+ * Matrix   ×= Rotation
  */
 
 
 use std::ops::{Mul, MulAssign, Div, DivAssign, Index};
-use num::Zero;
+use num::{Zero, One};
 
 use alga::general::{ClosedMul, ClosedAdd};
 
-use core::{Scalar, Matrix, MatrixMul};
+use core::{DefaultAllocator, Scalar, Matrix, MatrixMN};
 use core::dimension::{Dim, DimName, U1};
 use core::constraint::{ShapeConstraint, AreMultipliable};
-use core::storage::{OwnedStorage, Storage};
-use core::allocator::{OwnedAllocator, Allocator};
+use core::storage::Storage;
+use core::allocator::Allocator;
 
-use geometry::{PointBase, PointMul, RotationBase, OwnedRotation};
+use geometry::{Point, Rotation};
 
-impl<N: Scalar, D: DimName, S: Storage<N, D, D>> Index<(usize, usize)> for RotationBase<N, D, S> {
+impl<N: Scalar, D: DimName> Index<(usize, usize)> for Rotation<N, D>
+    where DefaultAllocator: Allocator<N, D, D> {
     type Output = N;
 
     #[inline]
@@ -39,62 +40,62 @@ impl<N: Scalar, D: DimName, S: Storage<N, D, D>> Index<(usize, usize)> for Rotat
     }
 }
 
-// RotationBase × RotationBase
+// Rotation × Rotation
 md_impl_all!(
     Mul, mul;
     (D, D), (D, D) for D: DimName;
-    self: RotationBase<N, D, SA>, right: RotationBase<N, D, SB>, Output = OwnedRotation<N, D, SA::Alloc>;
-    [val val] => RotationBase::from_matrix_unchecked(self.unwrap() * right.unwrap());
-    [ref val] => RotationBase::from_matrix_unchecked(self.matrix() * right.unwrap());
-    [val ref] => RotationBase::from_matrix_unchecked(self.unwrap() * right.matrix());
-    [ref ref] => RotationBase::from_matrix_unchecked(self.matrix() * right.matrix());
+    self: Rotation<N, D>, right: Rotation<N, D>, Output = Rotation<N, D>;
+    [val val] => Rotation::from_matrix_unchecked(self.unwrap() * right.unwrap());
+    [ref val] => Rotation::from_matrix_unchecked(self.matrix() * right.unwrap());
+    [val ref] => Rotation::from_matrix_unchecked(self.unwrap() * right.matrix());
+    [ref ref] => Rotation::from_matrix_unchecked(self.matrix() * right.matrix());
 );
 
-// RotationBase ÷ RotationBase
+// Rotation ÷ Rotation
 // FIXME: instead of calling inverse explicitely, could we just add a `mul_tr` or `mul_inv` method?
 md_impl_all!(
     Div, div;
     (D, D), (D, D) for D: DimName;
-    self: RotationBase<N, D, SA>, right: RotationBase<N, D, SB>, Output = OwnedRotation<N, D, SA::Alloc>;
+    self: Rotation<N, D>, right: Rotation<N, D>, Output = Rotation<N, D>;
     [val val] => self * right.inverse();
     [ref val] => self * right.inverse();
     [val ref] => self * right.inverse();
     [ref ref] => self * right.inverse();
 );
 
-// RotationBase × Matrix
+// Rotation × Matrix
 md_impl_all!(
     Mul, mul;
-    (D1, D1), (R2, C2) for D1: DimName, R2: Dim, C2: Dim
-    where SA::Alloc: Allocator<N, D1, C2>
+    (D1, D1), (R2, C2) for D1: DimName, R2: Dim, C2: Dim, SB: Storage<N, R2, C2>
+    where DefaultAllocator: Allocator<N, D1, C2>
     where ShapeConstraint: AreMultipliable<D1, D1, R2, C2>;
-    self: RotationBase<N, D1, SA>, right: Matrix<N, R2, C2, SB>, Output = MatrixMul<N, D1, D1, C2 , SA>;
+    self: Rotation<N, D1>, right: Matrix<N, R2, C2, SB>, Output = MatrixMN<N, D1, C2>;
     [val val] => self.unwrap() * right;
     [ref val] => self.matrix() * right;
     [val ref] => self.unwrap() * right;
     [ref ref] => self.matrix() * right;
 );
 
-// Matrix × RotationBase
+// Matrix × Rotation
 md_impl_all!(
     Mul, mul;
-    (R1, C1), (D2, D2) for R1: Dim, C1: Dim, D2: DimName
-    where SA::Alloc: Allocator<N, R1, D2>
+    (R1, C1), (D2, D2) for R1: Dim, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>
+    where DefaultAllocator: Allocator<N, R1, D2>
     where ShapeConstraint:  AreMultipliable<R1, C1, D2, D2>;
-    self: Matrix<N, R1, C1, SA>, right: RotationBase<N, D2, SB>, Output = MatrixMul<N, R1, C1, D2, SA>;
+    self: Matrix<N, R1, C1, SA>, right: Rotation<N, D2>, Output = MatrixMN<N, R1, D2>;
     [val val] => self * right.unwrap();
     [ref val] => self * right.unwrap();
     [val ref] => self * right.matrix();
     [ref ref] => self * right.matrix();
 );
 
-// Matrix ÷ RotationBase
+// Matrix ÷ Rotation
 md_impl_all!(
     Div, div;
-    (R1, C1), (D2, D2) for R1: Dim, C1: Dim, D2: DimName
-    where SA::Alloc: Allocator<N, R1, D2>
+    (R1, C1), (D2, D2) for R1: Dim, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>
+    where DefaultAllocator: Allocator<N, R1, D2>
     where ShapeConstraint: AreMultipliable<R1, C1, D2, D2>;
-    self: Matrix<N, R1, C1, SA>, right: RotationBase<N, D2, SB>, Output = MatrixMul<N, R1, C1, D2, SA>;
+    self: Matrix<N, R1, C1, SA>, right: Rotation<N, D2>, Output = MatrixMN<N, R1, D2>;
     [val val] => self * right.inverse();
     [ref val] => self * right.inverse();
     [val ref] => self * right.inverse();
@@ -102,15 +103,15 @@ md_impl_all!(
 );
 
 
-// RotationBase × PointBase
+// Rotation × Point
 // FIXME: we don't handle properly non-zero origins here. Do we want this to be the intended
 // behavior?
 md_impl_all!(
     Mul, mul;
     (D, D), (D, U1) for D: DimName
-    where SA::Alloc: Allocator<N, D, U1>
+    where DefaultAllocator: Allocator<N, D>
     where ShapeConstraint:  AreMultipliable<D, D, D, U1>;
-    self: RotationBase<N, D, SA>, right: PointBase<N, D, SB>, Output = PointMul<N, D, D, SA>;
+    self: Rotation<N, D>, right: Point<N, D>, Output = Point<N, D>;
     [val val] => self.unwrap() * right;
     [ref val] => self.matrix() * right;
     [val ref] => self.unwrap() * right;
@@ -118,13 +119,13 @@ md_impl_all!(
 );
 
 
-// RotationBase ×= RotationBase
+// Rotation ×= Rotation
 // FIXME: try not to call `inverse()` explicitly.
 
 md_assign_impl_all!(
     MulAssign, mul_assign;
     (D, D), (D, D) for D: DimName;
-    self: RotationBase<N, D, SA>, right: RotationBase<N, D, SB>;
+    self: Rotation<N, D>, right: Rotation<N, D>;
     [val] => unsafe { self.matrix_mut().mul_assign(right.unwrap()) };
     [ref] => unsafe { self.matrix_mut().mul_assign(right.matrix()) };
 );
@@ -133,12 +134,12 @@ md_assign_impl_all!(
 md_assign_impl_all!(
     DivAssign, div_assign;
     (D, D), (D, D) for D: DimName;
-    self: RotationBase<N, D, SA>, right: RotationBase<N, D, SB>;
+    self: Rotation<N, D>, right: Rotation<N, D>;
     [val] => unsafe { self.matrix_mut().mul_assign(right.inverse().unwrap()) };
     [ref] => unsafe { self.matrix_mut().mul_assign(right.inverse().matrix()) };
 );
 
-// Matrix *= RotationBase
+// Matrix *= Rotation
 // FIXME: try not to call `inverse()` explicitly.
 // FIXME: this shares the same limitations as for the current impl. of MulAssign for matrices.
 // (In particular the number of matrix column must be equal to the number of rotation columns,
@@ -147,7 +148,7 @@ md_assign_impl_all!(
 md_assign_impl_all!(
     MulAssign, mul_assign;
     (R1, C1), (C1, C1) for R1: DimName, C1: DimName;
-    self: Matrix<N, R1, C1, SA>, right: RotationBase<N, C1, SB>;
+    self: MatrixMN<N, R1, C1>, right: Rotation<N, C1>;
     [val] => self.mul_assign(right.unwrap());
     [ref] => self.mul_assign(right.matrix());
 );
@@ -156,7 +157,7 @@ md_assign_impl_all!(
 md_assign_impl_all!(
     DivAssign, div_assign;
     (R1, C1), (C1, C1) for R1: DimName, C1: DimName;
-    self: Matrix<N, R1, C1, SA>, right: RotationBase<N, C1, SB>;
+    self: MatrixMN<N, R1, C1>, right: Rotation<N, C1>;
     [val] => self.mul_assign(right.inverse().unwrap());
     [ref] => self.mul_assign(right.inverse().matrix());
 );

src/geometry/rotation_specialization.rs

@@ -1,39 +1,37 @@
 #[cfg(feature = "arbitrary")]
 use quickcheck::{Arbitrary, Gen};
+#[cfg(feature = "arbitrary")]
+use core::storage::Owned;
 
 use std::ops::Neg;
 use num::Zero;
 use rand::{Rand, Rng};
 use alga::general::Real;
 
-use core::{Unit, ColumnVector, SquareMatrix, OwnedSquareMatrix, OwnedColumnVector, Vector3};
+use core::{Unit, Vector, MatrixN, VectorN, Vector3};
 use core::dimension::{U1, U2, U3};
-use core::storage::{Storage, OwnedStorage};
-use core::allocator::{Allocator, OwnedAllocator};
+use core::storage::Storage;
 
-use geometry::{RotationBase, OwnedRotation, UnitComplex};
+use geometry::{UnitComplex, Rotation2, Rotation3};
 
 
 /*
  *
- * 2D RotationBase matrix.
+ * 2D Rotation matrix.
  *
  */
-impl<N, S> RotationBase<N, U2, S>
-where N: Real,
-      S: OwnedStorage<N, U2, U2>,
-      S::Alloc: OwnedAllocator<N, U2, U2, S> {
+impl<N: Real> Rotation2<N> {
     /// Builds a 2 dimensional rotation matrix from an angle in radian.
     pub fn new(angle: N) -> Self {
         let (sia, coa) = angle.sin_cos();
-        Self::from_matrix_unchecked(SquareMatrix::<N, U2, S>::new(coa, -sia, sia, coa))
+        Self::from_matrix_unchecked(MatrixN::<N, U2>::new(coa, -sia, sia, coa))
     }
 
     /// Builds a 2 dimensional rotation matrix from an angle in radian wrapped in a 1-dimensional vector.
     ///
     /// Equivalent to `Self::new(axisangle[0])`.
     #[inline]
-    pub fn from_scaled_axis<SB: Storage<N, U1, U1>>(axisangle: ColumnVector<N, U1, SB>) -> Self {
+    pub fn from_scaled_axis<SB: Storage<N, U1>>(axisangle: Vector<N, U1, SB>) -> Self {
         Self::new(axisangle[0])
     }
 
@@ -41,25 +39,23 @@ where N: Real,
     ///
     /// This is the rotation `R` such that `(R * a).angle(b) == 0 && (R * a).dot(b).is_positive()`.
     #[inline]
-    pub fn rotation_between<SB, SC>(a: &ColumnVector<N, U2, SB>, b: &ColumnVector<N, U2, SC>) -> Self
-        where SB: Storage<N, U2, U1>,
-              SC: Storage<N, U2, U1> {
+    pub fn rotation_between<SB, SC>(a: &Vector<N, U2, SB>, b: &Vector<N, U2, SC>) -> Self
+        where SB: Storage<N, U2>,
+              SC: Storage<N, U2> {
         ::convert(UnitComplex::rotation_between(a, b).to_rotation_matrix())
     }
 
     /// The smallest rotation needed to make `a` and `b` collinear and point toward the same
     /// direction, raised to the power `s`.
     #[inline]
-    pub fn scaled_rotation_between<SB, SC>(a: &ColumnVector<N, U2, SB>, b: &ColumnVector<N, U2, SC>, s: N) -> Self
-        where SB: Storage<N, U2, U1>,
-              SC: Storage<N, U2, U1> {
+    pub fn scaled_rotation_between<SB, SC>(a: &Vector<N, U2, SB>, b: &Vector<N, U2, SC>, s: N) -> Self
+        where SB: Storage<N, U2>,
+              SC: Storage<N, U2> {
         ::convert(UnitComplex::scaled_rotation_between(a, b, s).to_rotation_matrix())
     }
 }
 
-impl<N, S> RotationBase<N, U2, S>
-where N: Real,
-      S: Storage<N, U2, U2> {
+impl<N: Real> Rotation2<N> {
     /// The rotation angle.
     #[inline]
     pub fn angle(&self) -> N {
@@ -68,7 +64,7 @@ where N: Real,
 
     /// The rotation angle needed to make `self` and `other` coincide.
     #[inline]
-    pub fn angle_to<SB: Storage<N, U2, U2>>(&self, other: &RotationBase<N, U2, SB>) -> N {
+    pub fn angle_to(&self, other: &Rotation2<N>) -> N {
         self.rotation_to(other).angle()
     }
 
@@ -76,30 +72,25 @@ where N: Real,
     ///
     /// The result is such that: `self.rotation_to(other) * self == other`.
     #[inline]
-    pub fn rotation_to<SB>(&self, other: &RotationBase<N, U2, SB>) -> OwnedRotation<N, U2, SB::Alloc>
-        where SB: Storage<N, U2, U2> {
+    pub fn rotation_to(&self, other: &Rotation2<N>) -> Rotation2<N> {
         other * self.inverse()
     }
 
     /// Raise the quaternion to a given floating power, i.e., returns the rotation with the angle
     /// of `self` multiplied by `n`.
     #[inline]
-    pub fn powf(&self, n: N) -> OwnedRotation<N, U2, S::Alloc> {
-        OwnedRotation::<_, _, S::Alloc>::new(self.angle() * n)
+    pub fn powf(&self, n: N) -> Rotation2<N> {
+        Self::new(self.angle() * n)
     }
 
     /// The rotation angle returned as a 1-dimensional vector.
     #[inline]
-    pub fn scaled_axis(&self) -> OwnedColumnVector<N, U1, S::Alloc>
-        where S::Alloc: Allocator<N, U1, U1> {
-        ColumnVector::<_, U1, _>::new(self.angle())
+    pub fn scaled_axis(&self) -> VectorN<N, U1> {
+        Vector::<_, U1, _>::new(self.angle())
     }
 }
 
-impl<N, S> Rand for RotationBase<N, U2, S>
-where N: Real + Rand,
-      S: OwnedStorage<N, U2, U2>,
-      S::Alloc: OwnedAllocator<N, U2, U2, S> {
+impl<N: Real + Rand> Rand for Rotation2<N> {
     #[inline]
     fn rand<R: Rng>(rng: &mut R) -> Self {
         Self::new(rng.gen())
@@ -107,10 +98,8 @@ where N: Real + Rand,
 }
 
 #[cfg(feature="arbitrary")]
-impl<N, S> Arbitrary for RotationBase<N, U2, S>
-where N: Real + Arbitrary,
-      S: OwnedStorage<N, U2, U2> + Send,
-      S::Alloc: OwnedAllocator<N, U2, U2, S> {
+impl<N: Real + Arbitrary> Arbitrary for Rotation2<N>
+where Owned<N, U2, U2>: Send {
     #[inline]
     fn arbitrary<G: Gen>(g: &mut G) -> Self {
         Self::new(N::arbitrary(g))
@@ -120,32 +109,29 @@ where N: Real + Arbitrary,
 
 /*
  *
- * 3D RotationBase matrix.
+ * 3D Rotation matrix.
  *
  */
-impl<N, S> RotationBase<N, U3, S>
-where N: Real,
-      S: OwnedStorage<N, U3, U3>,
-      S::Alloc: OwnedAllocator<N, U3, U3, S> {
-
+impl<N: Real> Rotation3<N> {
     /// Builds a 3 dimensional rotation matrix from an axis and an angle.
     ///
     /// # Arguments
     ///   * `axisangle` - A vector representing the rotation. Its magnitude is the amount of rotation
     ///   in radian. Its direction is the axis of rotation.
-    pub fn new<SB: Storage<N, U3, U1>>(axisangle: ColumnVector<N, U3, SB>) -> Self {
-        let (axis, angle) = Unit::new_and_get(axisangle.into_owned());
+    pub fn new<SB: Storage<N, U3>>(axisangle: Vector<N, U3, SB>) -> Self {
+        let axisangle = axisangle.into_owned();
+        let (axis, angle) = Unit::new_and_get(axisangle);
         Self::from_axis_angle(&axis, angle)
     }
 
     /// Builds a 3D rotation matrix from an axis scaled by the rotation angle.
-    pub fn from_scaled_axis<SB: Storage<N, U3, U1>>(axisangle: ColumnVector<N, U3, SB>) -> Self {
+    pub fn from_scaled_axis<SB: Storage<N, U3>>(axisangle: Vector<N, U3, SB>) -> Self {
         Self::new(axisangle)
     }
 
     /// Builds a 3D rotation matrix from an axis and a rotation angle.
-    pub fn from_axis_angle<SB>(axis: &Unit<ColumnVector<N, U3, SB>>, angle: N) -> Self
-        where SB: Storage<N, U3, U1> {
+    pub fn from_axis_angle<SB>(axis: &Unit<Vector<N, U3, SB>>, angle: N) -> Self
+        where SB: Storage<N, U3> {
         if angle.is_zero() {
             Self::identity()
         }
@@ -160,7 +146,7 @@ where N: Real,
             let one_m_cos  = N::one() - cos;
 
             Self::from_matrix_unchecked(
-                SquareMatrix::<N, U3, S>::new(
+                MatrixN::<N, U3>::new(
                     (sqx + (N::one() - sqx) * cos),
                     (ux * uy * one_m_cos - uz * sin),
                     (ux * uz * one_m_cos + uy * sin),
@@ -184,7 +170,7 @@ where N: Real,
         let (sy, cy) = yaw.sin_cos();
 
         Self::from_matrix_unchecked(
-            SquareMatrix::<N, U3, S>::new(
+            MatrixN::<N, U3>::new(
                 cy * cp, cy * sp * sr - sy * cr, cy * sp * cr + sy * sr,
                 sy * cp, sy * sp * sr + cy * cr, sy * sp * cr - cy * sr,
                 -sp,     cp * sr,                cp * cr)
@@ -202,14 +188,14 @@ where N: Real,
     ///   collinear
     ///   to `dir`. Non-collinearity is not checked.
     #[inline]
-    pub fn new_observer_frame<SB, SC>(dir: &ColumnVector<N, U3, SB>, up: &ColumnVector<N, U3, SC>) -> Self
-    where SB: Storage<N, U3, U1>,
-          SC: Storage<N, U3, U1> {
+    pub fn new_observer_frame<SB, SC>(dir: &Vector<N, U3, SB>, up: &Vector<N, U3, SC>) -> Self
+    where SB: Storage<N, U3>,
+          SC: Storage<N, U3> {
         let zaxis = dir.normalize();
         let xaxis = up.cross(&zaxis).normalize();
         let yaxis = zaxis.cross(&xaxis).normalize();
 
-        Self::from_matrix_unchecked(SquareMatrix::<N, U3, S>::new(
+        Self::from_matrix_unchecked(MatrixN::<N, U3>::new(
                 xaxis.x, yaxis.x, zaxis.x,
                 xaxis.y, yaxis.y, zaxis.y,
                 xaxis.z, yaxis.z, zaxis.z))
@@ -227,9 +213,9 @@ where N: Real,
     ///   * up - A vector approximately aligned with required the vertical axis. The only
     ///   requirement of this parameter is to not be collinear to `target - eye`.
     #[inline]
-    pub fn look_at_rh<SB, SC>(dir: &ColumnVector<N, U3, SB>, up: &ColumnVector<N, U3, SC>) -> Self
-    where SB: Storage<N, U3, U1>,
-          SC: Storage<N, U3, U1> {
+    pub fn look_at_rh<SB, SC>(dir: &Vector<N, U3, SB>, up: &Vector<N, U3, SC>) -> Self
+    where SB: Storage<N, U3>,
+          SC: Storage<N, U3> {
         Self::new_observer_frame(&dir.neg(), up).inverse()
     }
 
@@ -244,9 +230,9 @@ where N: Real,
     ///   * up - A vector approximately aligned with required the vertical axis. The only
     ///   requirement of this parameter is to not be collinear to `target - eye`.
     #[inline]
-    pub fn look_at_lh<SB, SC>(dir: &ColumnVector<N, U3, SB>, up: &ColumnVector<N, U3, SC>) -> Self
-    where SB: Storage<N, U3, U1>,
-          SC: Storage<N, U3, U1> {
+    pub fn look_at_lh<SB, SC>(dir: &Vector<N, U3, SB>, up: &Vector<N, U3, SC>) -> Self
+    where SB: Storage<N, U3>,
+          SC: Storage<N, U3> {
             Self::new_observer_frame(dir, up).inverse()
     }
 
@@ -254,20 +240,20 @@ where N: Real,
     ///
     /// This is the rotation `R` such that `(R * a).angle(b) == 0 && (R * a).dot(b).is_positive()`.
     #[inline]
-    pub fn rotation_between<SB, SC>(a: &ColumnVector<N, U3, SB>, b: &ColumnVector<N, U3, SC>) -> Option<Self>
-        where SB: Storage<N, U3, U1>,
-              SC: Storage<N, U3, U1> {
+    pub fn rotation_between<SB, SC>(a: &Vector<N, U3, SB>, b: &Vector<N, U3, SC>) -> Option<Self>
+        where SB: Storage<N, U3>,
+              SC: Storage<N, U3> {
         Self::scaled_rotation_between(a, b, N::one())
     }
 
     /// The smallest rotation needed to make `a` and `b` collinear and point toward the same
     /// direction, raised to the power `s`.
     #[inline]
-    pub fn scaled_rotation_between<SB, SC>(a: &ColumnVector<N, U3, SB>, b: &ColumnVector<N, U3, SC>, n: N)
+    pub fn scaled_rotation_between<SB, SC>(a: &Vector<N, U3, SB>, b: &Vector<N, U3, SC>, n: N)
         -> Option<Self>
-        where SB: Storage<N, U3, U1>,
-              SC: Storage<N, U3, U1> {
-        // FIXME: code duplication with RotationBase.
+        where SB: Storage<N, U3>,
+              SC: Storage<N, U3> {
+        // FIXME: code duplication with Rotation.
         if let (Some(na), Some(nb)) = (a.try_normalize(N::zero()), b.try_normalize(N::zero())) {
             let c = na.cross(&nb);
 
@@ -287,26 +273,17 @@ where N: Real,
 
         Some(Self::identity())
     }
-}
 
-impl<N, S> RotationBase<N, U3, S>
-where N: Real,
-      S: Storage<N, U3, U3> {
     /// The rotation angle.
     #[inline]
     pub fn angle(&self) -> N {
         ((self.matrix()[(0, 0)] + self.matrix()[(1, 1)] + self.matrix()[(2, 2)] - N::one()) / ::convert(2.0)).acos()
     }
-}
 
-impl<N, S> RotationBase<N, U3, S>
-where N: Real,
-      S: Storage<N, U3, U3>,
-      S::Alloc: Allocator<N, U3, U1> {
     /// The rotation axis. Returns `None` if the rotation angle is zero or PI.
     #[inline]
-    pub fn axis(&self) -> Option<Unit<OwnedColumnVector<N, U3, S::Alloc>>> {
-        let axis = OwnedColumnVector::<N, U3, S::Alloc>::new(
+    pub fn axis(&self) -> Option<Unit<Vector3<N>>> {
+        let axis = VectorN::<N, U3>::new(
             self.matrix()[(2, 1)] - self.matrix()[(1, 2)],
             self.matrix()[(0, 2)] - self.matrix()[(2, 0)],
             self.matrix()[(1, 0)] - self.matrix()[(0, 1)]);
@@ -316,18 +293,18 @@ where N: Real,
 
     /// The rotation axis multiplied by the rotation angle.
     #[inline]
-    pub fn scaled_axis(&self) -> OwnedColumnVector<N, U3, S::Alloc> {
+    pub fn scaled_axis(&self) -> Vector3<N> {
         if let Some(axis) = self.axis() {
             axis.unwrap() * self.angle()
         }
         else {
-            ColumnVector::zero()
+            Vector::zero()
         }
     }
 
     /// The rotation angle needed to make `self` and `other` coincide.
     #[inline]
-    pub fn angle_to<SB: Storage<N, U3, U3>>(&self, other: &RotationBase<N, U3, SB>) -> N {
+    pub fn angle_to(&self, other: &Rotation3<N>) -> N {
         self.rotation_to(other).angle()
     }
 
@@ -335,47 +312,40 @@ where N: Real,
     ///
     /// The result is such that: `self.rotation_to(other) * self == other`.
     #[inline]
-    pub fn rotation_to<SB>(&self, other: &RotationBase<N, U3, SB>) -> OwnedRotation<N, U3, SB::Alloc>
-        where SB: Storage<N, U3, U3> {
+    pub fn rotation_to(&self, other: &Rotation3<N>) -> Rotation3<N> {
         other * self.inverse()
     }
 
     /// Raise the quaternion to a given floating power, i.e., returns the rotation with the same
     /// axis as `self` and an angle equal to `self.angle()` multiplied by `n`.
     #[inline]
-    pub fn powf(&self, n: N) -> OwnedRotation<N, U3, S::Alloc> {
+    pub fn powf(&self, n: N) -> Rotation3<N> {
         if let Some(axis) = self.axis() {
-            OwnedRotation::<_, _, S::Alloc>::from_axis_angle(&axis, self.angle() * n)
+            Self::from_axis_angle(&axis, self.angle() * n)
         }
         else if self.matrix()[(0, 0)] < N::zero() {
-            let minus_id = OwnedSquareMatrix::<N, U3, S::Alloc>::from_diagonal_element(-N::one());
-            OwnedRotation::<_, _, S::Alloc>::from_matrix_unchecked(minus_id)
+            let minus_id = MatrixN::<N, U3>::from_diagonal_element(-N::one());
+            Self::from_matrix_unchecked(minus_id)
         }
         else {
-            OwnedRotation::<_, _, S::Alloc>::identity()
+            Self::identity()
         }
     }
 }
 
-impl<N, S> Rand for RotationBase<N, U3, S>
-where N: Real + Rand,
-      S: OwnedStorage<N, U3, U3>,
-      S::Alloc: OwnedAllocator<N, U3, U3, S> +
-                Allocator<N, U3, U1> {
+impl<N: Real + Rand> Rand for Rotation3<N> {
     #[inline]
     fn rand<R: Rng>(rng: &mut R) -> Self {
-        Self::new(Vector3::rand(rng))
+        Self::new(VectorN::rand(rng))
     }
 }
 
 #[cfg(feature="arbitrary")]
-impl<N, S> Arbitrary for RotationBase<N, U3, S>
-where N: Real + Arbitrary,
-      S: OwnedStorage<N, U3, U3> + Send,
-      S::Alloc: OwnedAllocator<N, U3, U3, S> +
-                Allocator<N, U3, U1> {
+impl<N: Real + Arbitrary> Arbitrary for Rotation3<N>
+where Owned<N, U3, U3>: Send,
+      Owned<N, U3>: Send {
     #[inline]
     fn arbitrary<G: Gen>(g: &mut G) -> Self {
-        Self::new(Vector3::arbitrary(g))
+        Self::new(VectorN::arbitrary(g))
     }
 }

src/geometry/similarity.rs

@@ -1,47 +1,80 @@
 use std::fmt;
+use std::hash;
 use approx::ApproxEq;
 
-use alga::general::{ClosedMul, Real, SubsetOf};
+#[cfg(feature = "serde-serialize")]
+use serde;
+
+use alga::general::{Real, SubsetOf};
 use alga::linear::Rotation;
 
-use core::{Scalar, OwnedSquareMatrix};
+use core::{DefaultAllocator, MatrixN};
 use core::dimension::{DimName, DimNameSum, DimNameAdd, U1};
-use core::storage::{Storage, OwnedStorage};
-use core::allocator::{Allocator, OwnedAllocator};
-use geometry::{PointBase, TranslationBase, IsometryBase};
+use core::storage::Owned;
+use core::allocator::Allocator;
+use geometry::{Point, Translation, Isometry};
 
 
-/// A similarity that uses a data storage deduced from the allocator `A`.
-pub type OwnedSimilarityBase<N, D, A, R> =
-    SimilarityBase<N, D, <A as Allocator<N, D, U1>>::Buffer, R>;
-
 /// A similarity, i.e., an uniform scaling, followed by a rotation, followed by a translation.
 #[repr(C)]
-#[derive(Hash, Debug, Clone, Copy)]
+#[derive(Debug)]
 #[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
-pub struct SimilarityBase<N: Scalar, D: DimName, S, R> {
+#[cfg_attr(feature = "serde-serialize",
+    serde(bound(
+        serialize = "N: serde::Serialize,
+                     R: serde::Serialize,
+                     DefaultAllocator: Allocator<N, D>,
+                     Owned<N, D>: serde::Serialize")))]
+#[cfg_attr(feature = "serde-serialize",
+    serde(bound(
+        deserialize = "N: serde::Deserialize<'de>,
+                       R: serde::Deserialize<'de>,
+                       DefaultAllocator: Allocator<N, D>,
+                       Owned<N, D>: serde::Deserialize<'de>")))]
+pub struct Similarity<N: Real, D: DimName, R>
+    where DefaultAllocator: Allocator<N, D> {
     /// The part of this similarity that does not include the scaling factor.
-    pub isometry: IsometryBase<N, D, S, R>,
+    pub isometry: Isometry<N, D, R>,
     scaling:      N
 }
 
-impl<N, D: DimName, S, R> SimilarityBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real + hash::Hash, D: DimName + hash::Hash, R: hash::Hash> hash::Hash for Similarity<N, D, R>
+    where DefaultAllocator: Allocator<N, D>,
+          Owned<N, D>: hash::Hash {
+    fn hash<H: hash::Hasher>(&self, state: &mut H) {
+        self.isometry.hash(state);
+        self.scaling.hash(state);
+    }
+}
+
+impl<N: Real, D: DimName + Copy, R: Rotation<Point<N, D>> + Copy> Copy for Similarity<N, D, R>
+    where DefaultAllocator: Allocator<N, D>,
+          Owned<N, D>: Copy {
+}
+
+impl<N: Real, D: DimName, R: Rotation<Point<N, D>> + Clone> Clone for Similarity<N, D, R>
+    where DefaultAllocator: Allocator<N, D> {
+    #[inline]
+    fn clone(&self) -> Self {
+        Similarity::from_isometry(self.isometry.clone(), self.scaling)
+    }
+}
+
+impl<N: Real, D: DimName, R> Similarity<N, D, R>
+    where R: Rotation<Point<N, D>>,
+          DefaultAllocator: Allocator<N, D> {
     /// Creates a new similarity from its rotational and translational parts.
     #[inline]
-    pub fn from_parts(translation: TranslationBase<N, D, S>, rotation: R, scaling: N) -> SimilarityBase<N, D, S, R> {
-        SimilarityBase::from_isometry(IsometryBase::from_parts(translation, rotation), scaling)
+    pub fn from_parts(translation: Translation<N, D>, rotation: R, scaling: N) -> Similarity<N, D, R> {
+        Similarity::from_isometry(Isometry::from_parts(translation, rotation), scaling)
     }
 
     /// Creates a new similarity from its rotational and translational parts.
     #[inline]
-    pub fn from_isometry(isometry: IsometryBase<N, D, S, R>, scaling: N) -> SimilarityBase<N, D, S, R> {
+    pub fn from_isometry(isometry: Isometry<N, D, R>, scaling: N) -> Similarity<N, D, R> {
         assert!(!relative_eq!(scaling, N::zero()), "The scaling factor must not be zero.");
 
-        SimilarityBase {
+        Similarity {
             isometry: isometry,
             scaling:  scaling
         }
@@ -49,13 +82,13 @@ impl<N, D: DimName, S, R> SimilarityBase<N, D, S, R>
 
     /// Creates a new similarity that applies only a scaling factor.
     #[inline]
-    pub fn from_scaling(scaling: N) -> SimilarityBase<N, D, S, R> {
-        Self::from_isometry(IsometryBase::identity(), scaling)
+    pub fn from_scaling(scaling: N) -> Similarity<N, D, R> {
+        Self::from_isometry(Isometry::identity(), scaling)
     }
 
     /// Inverts `self`.
     #[inline]
-    pub fn inverse(&self) -> SimilarityBase<N, D, S, R> {
+    pub fn inverse(&self) -> Similarity<N, D, R> {
         let mut res = self.clone();
         res.inverse_mut();
         res
@@ -77,6 +110,12 @@ impl<N, D: DimName, S, R> SimilarityBase<N, D, S, R>
         self.scaling = scaling;
     }
 
+    /// The scaling factor of this similarity transformation.
+    #[inline]
+    pub fn scaling(&self) -> N {
+        self.scaling
+    }
+
     /// The similarity transformation that applies a scaling factor `scaling` before `self`.
     #[inline]
     pub fn prepend_scaling(&self, scaling: N) -> Self {
@@ -91,7 +130,7 @@ impl<N, D: DimName, S, R> SimilarityBase<N, D, S, R>
         assert!(!relative_eq!(scaling, N::zero()), "The similarity scaling factor must not be zero.");
 
         Self::from_parts(
-            TranslationBase::from_vector(&self.isometry.translation.vector * scaling),
+            Translation::from_vector(&self.isometry.translation.vector * scaling),
             self.isometry.rotation.clone(),
             self.scaling * scaling)
     }
@@ -115,7 +154,7 @@ impl<N, D: DimName, S, R> SimilarityBase<N, D, S, R>
 
     /// Appends to `self` the given translation in-place.
     #[inline]
-    pub fn append_translation_mut(&mut self, t: &TranslationBase<N, D, S>) {
+    pub fn append_translation_mut(&mut self, t: &Translation<N, D>) {
         self.isometry.append_translation_mut(t)
     }
 
@@ -128,7 +167,7 @@ impl<N, D: DimName, S, R> SimilarityBase<N, D, S, R>
     /// Appends in-place to `self` a rotation centered at the point `p`, i.e., the rotation that
     /// lets `p` invariant.
     #[inline]
-    pub fn append_rotation_wrt_point_mut(&mut self, r: &R, p: &PointBase<N, D, S>) {
+    pub fn append_rotation_wrt_point_mut(&mut self, r: &R, p: &Point<N, D>) {
         self.isometry.append_rotation_wrt_point_mut(r, p)
     }
 
@@ -145,16 +184,14 @@ impl<N, D: DimName, S, R> SimilarityBase<N, D, S, R>
 // and makes it harde to use it, e.g., for Transform × Isometry implementation.
 // This is OK since all constructors of the isometry enforce the Rotation bound already (and
 // explicit struct construction is prevented by the private scaling factor).
-impl<N, D: DimName, S, R> SimilarityBase<N, D, S, R>
-    where N: Scalar + ClosedMul,
-          S: Storage<N, D, U1> {
+impl<N: Real, D: DimName, R> Similarity<N, D, R>
+    where DefaultAllocator: Allocator<N, D> {
     /// Converts this similarity into its equivalent homogeneous transformation matrix.
     #[inline]
-    pub fn to_homogeneous(&self) -> OwnedSquareMatrix<N, DimNameSum<D, U1>, S::Alloc>
+    pub fn to_homogeneous(&self) -> MatrixN<N, DimNameSum<D, U1>>
         where D: DimNameAdd<U1>,
-              R: SubsetOf<OwnedSquareMatrix<N, DimNameSum<D, U1>, S::Alloc>>,
-              S::Alloc: Allocator<N, D, D> +
-                        Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
+              R: SubsetOf<MatrixN<N, DimNameSum<D, U1>>>,
+              DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
         let mut res = self.isometry.to_homogeneous();
 
         for e in res.fixed_slice_mut::<D, D>(0, 0).iter_mut() {
@@ -163,38 +200,26 @@ impl<N, D: DimName, S, R> SimilarityBase<N, D, S, R>
 
         res
     }
+}
 
-    /// The scaling factor of this similarity transformation.
+
+impl<N: Real, D: DimName, R> Eq for Similarity<N, D, R>
+    where R: Rotation<Point<N, D>> + Eq,
+          DefaultAllocator: Allocator<N, D> {
+}
+
+impl<N: Real, D: DimName, R> PartialEq for Similarity<N, D, R>
+    where R: Rotation<Point<N, D>> + PartialEq,
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
-    pub fn scaling(&self) -> N {
-        self.scaling
-    }
-}
-
-
-impl<N, D: DimName, S, R> Eq for SimilarityBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>> + Eq,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
-}
-
-impl<N, D: DimName, S, R> PartialEq for SimilarityBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>> + PartialEq,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
-    #[inline]
-    fn eq(&self, right: &SimilarityBase<N, D, S, R>) -> bool {
+    fn eq(&self, right: &Similarity<N, D, R>) -> bool {
         self.isometry == right.isometry && self.scaling == right.scaling
     }
 }
 
-impl<N, D: DimName, S, R> ApproxEq for SimilarityBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>> + ApproxEq<Epsilon = N::Epsilon>,
-          S::Alloc: OwnedAllocator<N, D, U1, S>,
+impl<N: Real, D: DimName, R> ApproxEq for Similarity<N, D, R>
+    where R: Rotation<Point<N, D>> + ApproxEq<Epsilon = N::Epsilon>,
+          DefaultAllocator: Allocator<N, D>,
           N::Epsilon: Copy {
     type Epsilon = N::Epsilon;
 
@@ -231,46 +256,16 @@ impl<N, D: DimName, S, R> ApproxEq for SimilarityBase<N, D, S, R>
  * Display
  *
  */
-impl<N, D: DimName, S, R> fmt::Display for SimilarityBase<N, D, S, R>
+impl<N, D: DimName, R> fmt::Display for Similarity<N, D, R>
     where N: Real + fmt::Display,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>> + fmt::Display,
-          S::Alloc: OwnedAllocator<N, D, U1, S> + Allocator<usize, D, U1> {
+          R: Rotation<Point<N, D>> + fmt::Display,
+          DefaultAllocator: Allocator<N, D> + Allocator<usize, D> {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         let precision = f.precision().unwrap_or(3);
 
-        try!(writeln!(f, "SimilarityBase {{"));
+        try!(writeln!(f, "Similarity {{"));
         try!(write!(f, "{:.*}", precision, self.isometry));
         try!(write!(f, "Scaling: {:.*}", precision, self.scaling));
         writeln!(f, "}}")
     }
 }
-
-/*
-//         /*
-//          *
-//          * ToHomogeneous
-//          *
-//          */
-//         impl<N: Real> ToHomogeneous<$homogeneous<N>> for $t<N> {
-//             #[inline]
-//             fn to_homogeneous(&self) -> $homogeneous<N> {
-//                 self.vector.to_homogeneous()
-//             }
-//         }
-
-
-//         /*
-//          *
-//          * Absolute
-//          *
-//          */
-//         impl<N: Absolute> Absolute for $t<N> {
-//             type AbsoluteValue = $submatrix<N::AbsoluteValue>;
-//
-//             #[inline]
-//             fn abs(m: &$t<N>) -> $submatrix<N::AbsoluteValue> {
-//                 Absolute::abs(&m.submatrix)
-//             }
-//         }
-*/

src/geometry/similarity_alga.rs

@@ -1,13 +1,13 @@
 use alga::general::{AbstractMagma, AbstractGroup, AbstractLoop, AbstractMonoid, AbstractQuasigroup,
                     AbstractSemigroup, Real, Inverse, Multiplicative, Identity};
-use alga::linear::{Transformation, AffineTransformation, Rotation, Similarity, ProjectiveTransformation};
+use alga::linear::{Transformation, AffineTransformation, Rotation, ProjectiveTransformation};
+use alga::linear::Similarity as AlgaSimilarity;
 
-use core::ColumnVector;
-use core::dimension::{DimName, U1};
-use core::storage::OwnedStorage;
-use core::allocator::OwnedAllocator;
+use core::{DefaultAllocator, VectorN};
+use core::dimension::DimName;
+use core::allocator::Allocator;
 
-use geometry::{SimilarityBase, TranslationBase, PointBase};
+use geometry::{Similarity, Translation, Point};
 
 
 /*
@@ -15,22 +15,18 @@ use geometry::{SimilarityBase, TranslationBase, PointBase};
  * Algebraic structures.
  *
  */
-impl<N, D: DimName, S, R> Identity<Multiplicative> for SimilarityBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R> Identity<Multiplicative> for Similarity<N, D, R>
+    where R: Rotation<Point<N, D>>,
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn identity() -> Self {
         Self::identity()
     }
 }
 
-impl<N, D: DimName, S, R> Inverse<Multiplicative> for SimilarityBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R> Inverse<Multiplicative> for Similarity<N, D, R>
+    where R: Rotation<Point<N, D>>,
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn inverse(&self) -> Self {
         self.inverse()
@@ -42,11 +38,9 @@ impl<N, D: DimName, S, R> Inverse<Multiplicative> for SimilarityBase<N, D, S, R>
     }
 }
 
-impl<N, D: DimName, S, R> AbstractMagma<Multiplicative> for SimilarityBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R> AbstractMagma<Multiplicative> for Similarity<N, D, R>
+    where R: Rotation<Point<N, D>>,
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn operate(&self, rhs: &Self) -> Self {
         self * rhs
@@ -55,11 +49,9 @@ impl<N, D: DimName, S, R> AbstractMagma<Multiplicative> for SimilarityBase<N, D,
 
 macro_rules! impl_multiplicative_structures(
     ($($marker: ident<$operator: ident>),* $(,)*) => {$(
-        impl<N, D: DimName, S, R> $marker<$operator> for SimilarityBase<N, D, S, R>
-            where N: Real,
-                  S: OwnedStorage<N, D, U1>,
-                  R: Rotation<PointBase<N, D, S>>,
-                  S::Alloc: OwnedAllocator<N, D, U1, S> { }
+        impl<N: Real, D: DimName, R> $marker<$operator> for Similarity<N, D, R>
+            where R: Rotation<Point<N, D>>,
+                  DefaultAllocator: Allocator<N, D> { }
     )*}
 );
 
@@ -76,49 +68,43 @@ impl_multiplicative_structures!(
  * Transformation groups.
  *
  */
-impl<N, D: DimName, S, R> Transformation<PointBase<N, D, S>> for SimilarityBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R> Transformation<Point<N, D>> for Similarity<N, D, R>
+    where R: Rotation<Point<N, D>>,
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
-    fn transform_point(&self, pt: &PointBase<N, D, S>) -> PointBase<N, D, S> {
+    fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
         self * pt
     }
 
     #[inline]
-    fn transform_vector(&self, v: &ColumnVector<N, D, S>) -> ColumnVector<N, D, S> {
+    fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
         self * v
     }
 }
 
-impl<N, D: DimName, S, R> ProjectiveTransformation<PointBase<N, D, S>> for SimilarityBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R> ProjectiveTransformation<Point<N, D>> for Similarity<N, D, R>
+    where R: Rotation<Point<N, D>>,
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
-    fn inverse_transform_point(&self, pt: &PointBase<N, D, S>) -> PointBase<N, D, S> {
+    fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
         self.isometry.inverse_transform_point(pt) / self.scaling()
     }
 
     #[inline]
-    fn inverse_transform_vector(&self, v: &ColumnVector<N, D, S>) -> ColumnVector<N, D, S> {
+    fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
         self.isometry.inverse_transform_vector(v) / self.scaling()
     }
 }
 
-impl<N, D: DimName, S, R> AffineTransformation<PointBase<N, D, S>> for SimilarityBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R> AffineTransformation<Point<N, D>> for Similarity<N, D, R>
+    where R: Rotation<Point<N, D>>,
+          DefaultAllocator: Allocator<N, D> {
     type NonUniformScaling = N;
     type Rotation          = R;
-    type Translation       = TranslationBase<N, D, S>;
+    type Translation       = Translation<N, D>;
 
     #[inline]
-    fn decompose(&self) -> (TranslationBase<N, D, S>, R, N, R) {
+    fn decompose(&self) -> (Translation<N, D>, R, N, R) {
         (self.isometry.translation.clone(), self.isometry.rotation.clone(), self.scaling(), R::identity())
     }
 
@@ -134,7 +120,7 @@ impl<N, D: DimName, S, R> AffineTransformation<PointBase<N, D, S>> for Similarit
 
     #[inline]
     fn append_rotation(&self, r: &Self::Rotation) -> Self {
-        SimilarityBase::from_isometry(self.isometry.append_rotation(r), self.scaling())
+        Similarity::from_isometry(self.isometry.append_rotation(r), self.scaling())
     }
 
     #[inline]
@@ -153,22 +139,20 @@ impl<N, D: DimName, S, R> AffineTransformation<PointBase<N, D, S>> for Similarit
     }
 
     #[inline]
-    fn append_rotation_wrt_point(&self, r: &Self::Rotation, p: &PointBase<N, D, S>) -> Option<Self> {
+    fn append_rotation_wrt_point(&self, r: &Self::Rotation, p: &Point<N, D>) -> Option<Self> {
         let mut res = self.clone();
         res.append_rotation_wrt_point_mut(r, p);
         Some(res)
     }
 }
 
-impl<N, D: DimName, S, R> Similarity<PointBase<N, D, S>> for SimilarityBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: Rotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R> AlgaSimilarity<Point<N, D>> for Similarity<N, D, R>
+    where R: Rotation<Point<N, D>>,
+          DefaultAllocator: Allocator<N, D> {
     type Scaling = N;
 
     #[inline]
-    fn translation(&self) -> TranslationBase<N, D, S> {
+    fn translation(&self) -> Translation<N, D> {
         self.isometry.translation()
     }
 

src/geometry/similarity_alias.rs

@@ -1,19 +1,15 @@
-use core::MatrixArray;
-use core::dimension::{U1, U2, U3};
+use core::dimension::{U2, U3};
 
-use geometry::{Rotation, SimilarityBase, UnitQuaternion, UnitComplex};
-
-/// A D-dimensional similarity.
-pub type Similarity<N, D> = SimilarityBase<N, D, MatrixArray<N, D, U1>, Rotation<N, D>>;
+use geometry::{Similarity, UnitQuaternion, UnitComplex, Rotation2, Rotation3};
 
 /// A 2-dimensional similarity.
-pub type Similarity2<N> = SimilarityBase<N, U2, MatrixArray<N, U2, U1>, UnitComplex<N>>;
+pub type Similarity2<N> = Similarity<N, U2, UnitComplex<N>>;
 
 /// A 3-dimensional similarity.
-pub type Similarity3<N> = SimilarityBase<N, U3, MatrixArray<N, U3, U1>, UnitQuaternion<N>>;
+pub type Similarity3<N> = Similarity<N, U3, UnitQuaternion<N>>;
 
 /// A 2-dimensional similarity using a rotation matrix for its rotation part.
-pub type SimilarityMatrix2<N> = Similarity<N, U2>;
+pub type SimilarityMatrix2<N> = Similarity<N, U2, Rotation2<N>>;
 
 /// A 3-dimensional similarity using a rotation matrix for its rotation part.
-pub type SimilarityMatrix3<N> = Similarity<N, U3>;
+pub type SimilarityMatrix3<N> = Similarity<N, U3, Rotation3<N>>;

src/geometry/similarity_construction.rs

@@ -1,5 +1,7 @@
 #[cfg(feature = "arbitrary")]
 use quickcheck::{Arbitrary, Gen};
+#[cfg(feature = "arbitrary")]
+use core::storage::Owned;
 
 use num::One;
 use rand::{Rng, Rand};
@@ -7,32 +9,27 @@ use rand::{Rng, Rand};
 use alga::general::Real;
 use alga::linear::Rotation as AlgaRotation;
 
-use core::ColumnVector;
-use core::dimension::{DimName, U1, U2, U3, U4};
-use core::allocator::{OwnedAllocator, Allocator};
-use core::storage::OwnedStorage;
+use core::{DefaultAllocator, Vector2, Vector3};
+use core::dimension::{DimName, U2, U3};
+use core::allocator::Allocator;
 
-use geometry::{PointBase, TranslationBase, RotationBase, SimilarityBase,
-               UnitComplex, UnitQuaternionBase, IsometryBase};
+use geometry::{Point, Translation, Similarity, UnitComplex, UnitQuaternion, Isometry,
+               Point3, Rotation2, Rotation3};
 
 
-impl<N, D: DimName, S, R> SimilarityBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: AlgaRotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R> Similarity<N, D, R>
+    where R: AlgaRotation<Point<N, D>>,
+          DefaultAllocator: Allocator<N, D> {
     /// Creates a new identity similarity.
     #[inline]
     pub fn identity() -> Self {
-        Self::from_isometry(IsometryBase::identity(), N::one())
+        Self::from_isometry(Isometry::identity(), N::one())
     }
 }
 
-impl<N, D: DimName, S, R> One for SimilarityBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: AlgaRotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R> One for Similarity<N, D, R>
+    where R: AlgaRotation<Point<N, D>>,
+          DefaultAllocator: Allocator<N, D> {
     /// Creates a new identity similarity.
     #[inline]
     fn one() -> Self {
@@ -40,11 +37,9 @@ impl<N, D: DimName, S, R> One for SimilarityBase<N, D, S, R>
     }
 }
 
-impl<N, D: DimName, S, R> Rand for SimilarityBase<N, D, S, R>
-    where N: Real + Rand,
-          S: OwnedStorage<N, D, U1>,
-          R: AlgaRotation<PointBase<N, D, S>> + Rand,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real + Rand, D: DimName, R> Rand for Similarity<N, D, R>
+    where R: AlgaRotation<Point<N, D>> + Rand,
+          DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn rand<G: Rng>(rng: &mut G) -> Self {
         let mut s = rng.gen();
@@ -56,26 +51,24 @@ impl<N, D: DimName, S, R> Rand for SimilarityBase<N, D, S, R>
     }
 }
 
-impl<N, D: DimName, S, R> SimilarityBase<N, D, S, R>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          R: AlgaRotation<PointBase<N, D, S>>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName, R> Similarity<N, D, R>
+    where R: AlgaRotation<Point<N, D>>,
+          DefaultAllocator: Allocator<N, D> {
     /// The similarity that applies tha scaling factor `scaling`, followed by the rotation `r` with
     /// its axis passing through the point `p`.
     #[inline]
-    pub fn rotation_wrt_point(r: R, p: PointBase<N, D, S>, scaling: N) -> Self {
+    pub fn rotation_wrt_point(r: R, p: Point<N, D>, scaling: N) -> Self {
         let shift = r.transform_vector(&-&p.coords);
-        Self::from_parts(TranslationBase::from_vector(shift + p.coords), r, scaling)
+        Self::from_parts(Translation::from_vector(shift + p.coords), r, scaling)
     }
 }
 
 #[cfg(feature = "arbitrary")]
-impl<N, D: DimName, S, R> Arbitrary for SimilarityBase<N, D, S, R>
+impl<N, D: DimName, R> Arbitrary for Similarity<N, D, R>
     where N: Real + Arbitrary + Send,
-          S: OwnedStorage<N, D, U1> + Send,
-          R: AlgaRotation<PointBase<N, D, S>> + Arbitrary + Send,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+          R: AlgaRotation<Point<N, D>> + Arbitrary + Send,
+          DefaultAllocator: Allocator<N, D>,
+          Owned<N, D>: Send {
     #[inline]
     fn arbitrary<G: Gen>(rng: &mut G) -> Self {
         let mut s = Arbitrary::arbitrary(rng);
@@ -94,45 +87,31 @@ impl<N, D: DimName, S, R> Arbitrary for SimilarityBase<N, D, S, R>
  */
 
 // 2D rotation.
-impl<N, S, SR> SimilarityBase<N, U2, S, RotationBase<N, U2, SR>>
-    where N: Real,
-          S:  OwnedStorage<N, U2, U1, Alloc = SR::Alloc>,
-          SR: OwnedStorage<N, U2, U2>,
-          S::Alloc:  OwnedAllocator<N, U2, U1, S>,
-          SR::Alloc: OwnedAllocator<N, U2, U2, SR> {
+impl<N: Real> Similarity<N, U2, Rotation2<N>> {
     /// Creates a new similarity from a translation and a rotation angle.
     #[inline]
-    pub fn new(translation: ColumnVector<N, U2, S>, angle: N, scaling: N) -> Self {
-        Self::from_parts(TranslationBase::from_vector(translation), RotationBase::<N, U2, SR>::new(angle), scaling)
+    pub fn new(translation: Vector2<N>, angle: N, scaling: N) -> Self {
+        Self::from_parts(Translation::from_vector(translation), Rotation2::new(angle), scaling)
     }
 }
 
-impl<N, S> SimilarityBase<N, U2, S, UnitComplex<N>>
-    where N: Real,
-          S: OwnedStorage<N, U2, U1>,
-          S::Alloc: OwnedAllocator<N, U2, U1, S> {
+impl<N: Real> Similarity<N, U2, UnitComplex<N>> {
     /// Creates a new similarity from a translation and a rotation angle.
     #[inline]
-    pub fn new(translation: ColumnVector<N, U2, S>, angle: N, scaling: N) -> Self {
-        Self::from_parts(TranslationBase::from_vector(translation), UnitComplex::new(angle), scaling)
+    pub fn new(translation: Vector2<N>, angle: N, scaling: N) -> Self {
+        Self::from_parts(Translation::from_vector(translation), UnitComplex::new(angle), scaling)
     }
 }
 
 // 3D rotation.
 macro_rules! similarity_construction_impl(
-    ($Rot: ty, $RotId: ident, $RRDim: ty, $RCDim: ty) => {
-        impl<N, S, SR> SimilarityBase<N, U3, S, $Rot>
-            where N: Real,
-                  S:  OwnedStorage<N, U3, U1, Alloc = SR::Alloc>,
-                  SR: OwnedStorage<N, $RRDim, $RCDim>,
-                  S::Alloc:  OwnedAllocator<N, U3, U1, S>,
-                  SR::Alloc: OwnedAllocator<N, $RRDim, $RCDim, SR> +
-                             Allocator<N, U3, U3> {
+    ($Rot: ty) => {
+        impl<N: Real> Similarity<N, U3, $Rot> {
             /// Creates a new similarity from a translation, rotation axis-angle, and scaling
             /// factor.
             #[inline]
-            pub fn new(translation: ColumnVector<N, U3, S>, axisangle: ColumnVector<N, U3, S>, scaling: N) -> Self {
-                Self::from_isometry(IsometryBase::<_, _, _, $Rot>::new(translation, axisangle), scaling)
+            pub fn new(translation: Vector3<N>, axisangle: Vector3<N>, scaling: N) -> Self {
+                Self::from_isometry(Isometry::<_, U3, $Rot>::new(translation, axisangle), scaling)
             }
 
             /// Creates an similarity that corresponds to the a scaling factor and a local frame of
@@ -147,12 +126,12 @@ macro_rules! similarity_construction_impl(
             ///   * up - Vertical direction. The only requirement of this parameter is to not be collinear
             ///   to `eye - at`. Non-collinearity is not checked.
             #[inline]
-            pub fn new_observer_frame(eye:    &PointBase<N, U3, S>,
-                                      target: &PointBase<N, U3, S>,
-                                      up:     &ColumnVector<N, U3, S>,
+            pub fn new_observer_frame(eye:    &Point3<N>,
+                                      target: &Point3<N>,
+                                      up:     &Vector3<N>,
                                       scaling: N)
                                       -> Self {
-                Self::from_isometry(IsometryBase::<_, _, _, $Rot>::new_observer_frame(eye, target, up), scaling)
+                Self::from_isometry(Isometry::<_, U3, $Rot>::new_observer_frame(eye, target, up), scaling)
             }
 
             /// Builds a right-handed look-at view matrix including scaling factor.
@@ -166,12 +145,12 @@ macro_rules! similarity_construction_impl(
             ///   * up - A vector approximately aligned with required the vertical axis. The only
             ///   requirement of this parameter is to not be collinear to `target - eye`.
             #[inline]
-            pub fn look_at_rh(eye:     &PointBase<N, U3, S>,
-                              target:  &PointBase<N, U3, S>,
-                              up:      &ColumnVector<N, U3, S>,
+            pub fn look_at_rh(eye:     &Point3<N>,
+                              target:  &Point3<N>,
+                              up:      &Vector3<N>,
                               scaling: N)
                               -> Self {
-                Self::from_isometry(IsometryBase::<_, _, _, $Rot>::look_at_rh(eye, target, up), scaling)
+                Self::from_isometry(Isometry::<_, U3, $Rot>::look_at_rh(eye, target, up), scaling)
             }
 
             /// Builds a left-handed look-at view matrix including a scaling factor.
@@ -185,16 +164,16 @@ macro_rules! similarity_construction_impl(
             ///   * up - A vector approximately aligned with required the vertical axis. The only
             ///   requirement of this parameter is to not be collinear to `target - eye`.
             #[inline]
-            pub fn look_at_lh(eye:     &PointBase<N, U3, S>,
-                              target:  &PointBase<N, U3, S>,
-                              up:      &ColumnVector<N, U3, S>,
+            pub fn look_at_lh(eye:     &Point3<N>,
+                              target:  &Point3<N>,
+                              up:      &Vector3<N>,
                               scaling: N)
                               -> Self {
-                Self::from_isometry(IsometryBase::<_, _, _, $Rot>::look_at_lh(eye, target, up), scaling)
+                Self::from_isometry(Isometry::<_, _, $Rot>::look_at_lh(eye, target, up), scaling)
             }
         }
     }
 );
 
-similarity_construction_impl!(RotationBase<N, U3, SR>, RotationBase, U3, U3);
-similarity_construction_impl!(UnitQuaternionBase<N, SR>, UnitQuaternionBase, U4, U1);
+similarity_construction_impl!(Rotation3<N>);
+similarity_construction_impl!(UnitQuaternion<N>);

src/geometry/similarity_conversion.rs

@@ -1,49 +1,46 @@
 use alga::general::{Real, SubsetOf, SupersetOf};
 use alga::linear::Rotation;
 
-use core::{SquareMatrix, OwnedSquareMatrix};
-use core::dimension::{DimName, DimNameAdd, DimNameSum, U1};
-use core::storage::OwnedStorage;
-use core::allocator::{Allocator, OwnedAllocator};
+use core::{DefaultAllocator, MatrixN};
+use core::dimension::{DimName, DimNameAdd, DimNameSum, DimMin, U1};
+use core::allocator::Allocator;
 
-use geometry::{PointBase, TranslationBase, IsometryBase, SimilarityBase, TransformBase, SuperTCategoryOf, TAffine};
+use geometry::{Point, Translation, Isometry, Similarity, Transform, SuperTCategoryOf, TAffine};
 
 /*
  * This file provides the following conversions:
  * =============================================
  *
- * SimilarityBase -> SimilarityBase
- * SimilarityBase -> TransformBase
- * SimilarityBase -> Matrix (homogeneous)
+ * Similarity -> Similarity
+ * Similarity -> Transform
+ * Similarity -> Matrix (homogeneous)
  */
 
 
-impl<N1, N2, D: DimName, SA, SB, R1, R2> SubsetOf<SimilarityBase<N2, D, SB, R2>> for SimilarityBase<N1, D, SA, R1>
+impl<N1, N2, D: DimName, R1, R2> SubsetOf<Similarity<N2, D, R2>> for Similarity<N1, D, R1>
     where N1: Real + SubsetOf<N2>,
           N2: Real + SupersetOf<N1>,
-          R1: Rotation<PointBase<N1, D, SA>> + SubsetOf<R2>,
-          R2: Rotation<PointBase<N2, D, SB>>,
-          SA: OwnedStorage<N1, D, U1>,
-          SB: OwnedStorage<N2, D, U1>,
-          SA::Alloc: OwnedAllocator<N1, D, U1, SA>,
-          SB::Alloc: OwnedAllocator<N2, D, U1, SB> {
+          R1: Rotation<Point<N1, D>> + SubsetOf<R2>,
+          R2: Rotation<Point<N2, D>>,
+          DefaultAllocator: Allocator<N1, D> +
+                            Allocator<N2, D> {
     #[inline]
-    fn to_superset(&self) -> SimilarityBase<N2, D, SB, R2> {
-        SimilarityBase::from_isometry(
+    fn to_superset(&self) -> Similarity<N2, D, R2> {
+        Similarity::from_isometry(
             self.isometry.to_superset(),
             self.scaling().to_superset()
         )
     }
 
     #[inline]
-    fn is_in_subset(sim: &SimilarityBase<N2, D, SB, R2>) -> bool {
-        ::is_convertible::<_, IsometryBase<N1, D, SA, R1>>(&sim.isometry) &&
+    fn is_in_subset(sim: &Similarity<N2, D, R2>) -> bool {
+        ::is_convertible::<_, Isometry<N1, D, R1>>(&sim.isometry) &&
         ::is_convertible::<_, N1>(&sim.scaling())
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(sim: &SimilarityBase<N2, D, SB, R2>) -> Self {
-        SimilarityBase::from_isometry(
+    unsafe fn from_superset_unchecked(sim: &Similarity<N2, D, R2>) -> Self {
+        Similarity::from_isometry(
             sim.isometry.to_subset_unchecked(),
             sim.scaling().to_subset_unchecked()
         )
@@ -51,65 +48,63 @@ impl<N1, N2, D: DimName, SA, SB, R1, R2> SubsetOf<SimilarityBase<N2, D, SB, R2>>
 }
 
 
-impl<N1, N2, D, SA, SB, R, C> SubsetOf<TransformBase<N2, D, SB, C>> for SimilarityBase<N1, D, SA, R>
+impl<N1, N2, D, R, C> SubsetOf<Transform<N2, D, C>> for Similarity<N1, D, R>
     where N1: Real,
           N2: Real + SupersetOf<N1>,
-          SA: OwnedStorage<N1, D, U1>,
-          SB: OwnedStorage<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>,
           C:  SuperTCategoryOf<TAffine>,
-          R: Rotation<PointBase<N1, D, SA>> +
-             SubsetOf<OwnedSquareMatrix<N1, DimNameSum<D, U1>, SA::Alloc>> + // needed by: .to_homogeneous()
-             SubsetOf<SquareMatrix<N2, DimNameSum<D, U1>, SB>>,              // needed by: ::convert_unchecked(mm)
-          D:  DimNameAdd<U1>,
-          SA::Alloc: OwnedAllocator<N1, D, U1, SA> +
+          R: Rotation<Point<N1, D>> +
+             SubsetOf<MatrixN<N1, DimNameSum<D, U1>>> +
+             SubsetOf<MatrixN<N2, DimNameSum<D, U1>>>,
+          D: DimNameAdd<U1> +
+             DimMin<D, Output = D>, // needed by .determinant()
+          DefaultAllocator: Allocator<N1, D>     +
                             Allocator<N1, D, D>  +                                // needed by R
                             Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>> + // needed by: .to_homogeneous()
-                     Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>,  // needed by R
-          SB::Alloc: OwnedAllocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>, SB> +
-                     Allocator<N2, D, D> +  // needed by: mm.fixed_slice_mut
-                     Allocator<N2, D, U1> + // needed by: m.fixed_slice
-                     Allocator<N2, U1, D> { // needed by: m.fixed_slice
+                            Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>> + // needed by R
+                            Allocator<(usize, usize), D> + // needed by .determinant()
+                            Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>> +
+                            Allocator<N2, D, D> +
+                            Allocator<N2, D>    {
     #[inline]
-    fn to_superset(&self) -> TransformBase<N2, D, SB, C> {
-        TransformBase::from_matrix_unchecked(self.to_homogeneous().to_superset())
+    fn to_superset(&self) -> Transform<N2, D, C> {
+        Transform::from_matrix_unchecked(self.to_homogeneous().to_superset())
     }
 
     #[inline]
-    fn is_in_subset(t: &TransformBase<N2, D, SB, C>) -> bool {
+    fn is_in_subset(t: &Transform<N2, D, C>) -> bool {
         <Self as SubsetOf<_>>::is_in_subset(t.matrix())
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(t: &TransformBase<N2, D, SB, C>) -> Self {
+    unsafe fn from_superset_unchecked(t: &Transform<N2, D, C>) -> Self {
         Self::from_superset_unchecked(t.matrix())
     }
 }
 
 
-impl<N1, N2, D, SA, SB, R> SubsetOf<SquareMatrix<N2, DimNameSum<D, U1>, SB>> for SimilarityBase<N1, D, SA, R>
+impl<N1, N2, D, R> SubsetOf<MatrixN<N2, DimNameSum<D, U1>>> for Similarity<N1, D, R>
     where N1: Real,
           N2: Real + SupersetOf<N1>,
-          SA: OwnedStorage<N1, D, U1>,
-          SB: OwnedStorage<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>,
-          R: Rotation<PointBase<N1, D, SA>> +
-             SubsetOf<OwnedSquareMatrix<N1, DimNameSum<D, U1>, SA::Alloc>> + // needed by: .to_homogeneous()
-             SubsetOf<SquareMatrix<N2, DimNameSum<D, U1>, SB>>,              // needed by: ::convert_unchecked(mm)
-          D:  DimNameAdd<U1>,
-          SA::Alloc: OwnedAllocator<N1, D, U1, SA> +
+          R: Rotation<Point<N1, D>> +
+             SubsetOf<MatrixN<N1, DimNameSum<D, U1>>> +
+             SubsetOf<MatrixN<N2, DimNameSum<D, U1>>>,
+          D: DimNameAdd<U1> +
+             DimMin<D, Output = D>, // needed by .determinant()
+          DefaultAllocator: Allocator<N1, D>     +
                             Allocator<N1, D, D>  +                                // needed by R
-                     Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>> + // needed by: .to_homogeneous()
-                     Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>,  // needed by R
-          SB::Alloc: OwnedAllocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>, SB> +
-                     Allocator<N2, D, D>  + // needed by: mm.fixed_slice_mut
-                     Allocator<N2, D, U1> + // needed by: m.fixed_slice
-                     Allocator<N2, U1, D> { // needed by: m.fixed_slice
+                            Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>> + // needed by .to_homogeneous()
+                            Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>> + // needed by R
+                            Allocator<(usize, usize), D> + // needed by .determinant()
+                            Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>> +
+                            Allocator<N2, D, D> +
+                            Allocator<N2, D>    {
     #[inline]
-    fn to_superset(&self) -> SquareMatrix<N2, DimNameSum<D, U1>, SB> {
+    fn to_superset(&self) -> MatrixN<N2, DimNameSum<D, U1>> {
         self.to_homogeneous().to_superset()
     }
 
     #[inline]
-    fn is_in_subset(m: &SquareMatrix<N2, DimNameSum<D, U1>, SB>) -> bool {
+    fn is_in_subset(m: &MatrixN<N2, DimNameSum<D, U1>>) -> bool {
         let mut rot = m.fixed_slice::<D, D>(0, 0).clone_owned();
         if rot.fixed_columns_mut::<U1>(0).try_normalize_mut(N2::zero()).is_some() &&
            rot.fixed_columns_mut::<U1>(1).try_normalize_mut(N2::zero()).is_some() &&
@@ -138,7 +133,7 @@ impl<N1, N2, D, SA, SB, R> SubsetOf<SquareMatrix<N2, DimNameSum<D, U1>, SB>> for
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(m: &SquareMatrix<N2, DimNameSum<D, U1>, SB>) -> Self {
+    unsafe fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self {
         let mut mm = m.clone_owned();
         let na = mm.fixed_slice_mut::<D, U1>(0, 0).normalize_mut();
         let nb = mm.fixed_slice_mut::<D, U1>(0, 1).normalize_mut();
@@ -156,7 +151,7 @@ impl<N1, N2, D, SA, SB, R> SubsetOf<SquareMatrix<N2, DimNameSum<D, U1>, SB>> for
         }
 
         let t = m.fixed_slice::<D, U1>(0, D::dim()).into_owned();
-        let t = TranslationBase::from_vector(::convert_unchecked(t));
+        let t = Translation::from_vector(::convert_unchecked(t));
 
         Self::from_parts(t, ::convert_unchecked(mm), ::convert_unchecked(scale))
     }

src/geometry/similarity_ops.rs

@@ -1,14 +1,13 @@
 use std::ops::{Mul, MulAssign, Div, DivAssign};
 
 use alga::general::Real;
-use alga::linear::Rotation;
+use alga::linear::Rotation as AlgaRotation;
 
-use core::ColumnVector;
+use core::{DefaultAllocator, VectorN};
 use core::dimension::{DimName, U1, U3, U4};
-use core::storage::OwnedStorage;
-use core::allocator::OwnedAllocator;
+use core::allocator::Allocator;
 
-use geometry::{PointBase, RotationBase, SimilarityBase, TranslationBase, UnitQuaternionBase, IsometryBase};
+use geometry::{Point, Rotation, Similarity, Translation, UnitQuaternion, Isometry};
 
 // FIXME: there are several cloning of rotations that we could probably get rid of (but we didn't
 // yet because that would require to add a bound like `where for<'a, 'b> &'a R: Mul<&'b R, Output = R>`
@@ -22,43 +21,43 @@ use geometry::{PointBase, RotationBase, SimilarityBase, TranslationBase, UnitQua
  *
  * (Operators)
  *
- * SimilarityBase × SimilarityBase
- * SimilarityBase × R
- * SimilarityBase × IsometryBase
+ * Similarity × Similarity
+ * Similarity × R
+ * Similarity × Isometry
  *
- * IsometryBase × SimilarityBase
- * IsometryBase ÷ SimilarityBase
+ * Isometry × Similarity
+ * Isometry ÷ Similarity
  *
  *
- * SimilarityBase ÷ SimilarityBase
- * SimilarityBase ÷ R
- * SimilarityBase ÷ IsometryBase
+ * Similarity ÷ Similarity
+ * Similarity ÷ R
+ * Similarity ÷ Isometry
  *
- * SimilarityBase × PointBase
- * SimilarityBase × ColumnVector
+ * Similarity × Point
+ * Similarity × Vector
  *
  *
- * SimilarityBase  × TranslationBase
- * TranslationBase × SimilarityBase
+ * Similarity  × Translation
+ * Translation × Similarity
  *
- * NOTE: The following are provided explicitly because we can't have R × SimilarityBase.
- * RotationBase   × SimilarityBase<RotationBase>
- * UnitQuaternion × SimilarityBase<UnitQuaternion>
+ * NOTE: The following are provided explicitly because we can't have R × Similarity.
+ * Rotation   × Similarity<Rotation>
+ * UnitQuaternion × Similarity<UnitQuaternion>
  *
- * RotationBase   ÷ SimilarityBase<RotationBase>
- * UnitQuaternion ÷ SimilarityBase<UnitQuaternion>
+ * Rotation   ÷ Similarity<Rotation>
+ * UnitQuaternion ÷ Similarity<UnitQuaternion>
  *
  * (Assignment Operators)
  *
- * SimilarityBase ×= TranslationBase
+ * Similarity ×= Translation
  *
- * SimilarityBase ×= SimilarityBase
- * SimilarityBase ×= IsometryBase
- * SimilarityBase ×= R
+ * Similarity ×= Similarity
+ * Similarity ×= Isometry
+ * Similarity ×= R
  *
- * SimilarityBase ÷= SimilarityBase
- * SimilarityBase ÷= IsometryBase
- * SimilarityBase ÷= R
+ * Similarity ÷= Similarity
+ * Similarity ÷= Isometry
+ * Similarity ÷= R
  *
  */
 
@@ -68,11 +67,9 @@ macro_rules! similarity_binop_impl(
     ($Op: ident, $op: ident;
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Output: ty;
      $action: expr; $($lives: tt),*) => {
-        impl<$($lives ,)* N, D: DimName, S, R> $Op<$Rhs> for $Lhs
-            where N: Real,
-                  S: OwnedStorage<N, D, U1>,
-                  R: Rotation<PointBase<N, D, S>>,
-                  S::Alloc: OwnedAllocator<N, D, U1, S> {
+        impl<$($lives ,)* N: Real, D: DimName, R> $Op<$Rhs> for $Lhs
+            where R: AlgaRotation<Point<N, D>>,
+                  DefaultAllocator: Allocator<N, D> {
             type Output = $Output;
 
             #[inline]
@@ -117,22 +114,18 @@ macro_rules! similarity_binop_assign_impl_all(
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty;
      [val] => $action_val: expr;
      [ref] => $action_ref: expr;) => {
-        impl<N, D: DimName, S, R> $OpAssign<$Rhs> for $Lhs
-            where N: Real,
-                  S: OwnedStorage<N, D, U1>,
-                  R: Rotation<PointBase<N, D, S>>,
-                  S::Alloc: OwnedAllocator<N, D, U1, S> {
+        impl<N: Real, D: DimName, R> $OpAssign<$Rhs> for $Lhs
+            where R: AlgaRotation<Point<N, D>>,
+                  DefaultAllocator: Allocator<N, D> {
             #[inline]
             fn $op_assign(&mut $lhs, $rhs: $Rhs) {
                 $action_val
             }
         }
 
-        impl<'b, N, D: DimName, S, R> $OpAssign<&'b $Rhs> for $Lhs
-            where N: Real,
-                  S: OwnedStorage<N, D, U1>,
-                  R: Rotation<PointBase<N, D, S>>,
-                  S::Alloc: OwnedAllocator<N, D, U1, S> {
+        impl<'b, N: Real, D: DimName, R> $OpAssign<&'b $Rhs> for $Lhs
+            where R: AlgaRotation<Point<N, D>>,
+                  DefaultAllocator: Allocator<N, D> {
             #[inline]
             fn $op_assign(&mut $lhs, $rhs: &'b $Rhs) {
                 $action_ref
@@ -141,11 +134,11 @@ macro_rules! similarity_binop_assign_impl_all(
     }
 );
 
-// SimilarityBase × SimilarityBase
-// SimilarityBase ÷ SimilarityBase
+// Similarity × Similarity
+// Similarity ÷ Similarity
 similarity_binop_impl_all!(
     Mul, mul;
-    self: SimilarityBase<N, D, S, R>, rhs: SimilarityBase<N, D, S, R>, Output = SimilarityBase<N, D, S, R>;
+    self: Similarity<N, D, R>, rhs: Similarity<N, D, R>, Output = Similarity<N, D, R>;
     [val val] => &self * &rhs;
     [ref val] =>  self * &rhs;
     [val ref] => &self *  rhs;
@@ -159,7 +152,7 @@ similarity_binop_impl_all!(
 
 similarity_binop_impl_all!(
     Div, div;
-    self: SimilarityBase<N, D, S, R>, rhs: SimilarityBase<N, D, S, R>, Output = SimilarityBase<N, D, S, R>;
+    self: Similarity<N, D, R>, rhs: Similarity<N, D, R>, Output = Similarity<N, D, R>;
     [val val] => self * rhs.inverse();
     [ref val] => self * rhs.inverse();
     [val ref] => self * rhs.inverse();
@@ -167,10 +160,10 @@ similarity_binop_impl_all!(
 );
 
 
-// SimilarityBase ×= TranslationBase
+// Similarity ×= Translation
 similarity_binop_assign_impl_all!(
     MulAssign, mul_assign;
-    self: SimilarityBase<N, D, S, R>, rhs: TranslationBase<N, D, S>;
+    self: Similarity<N, D, R>, rhs: Translation<N, D>;
     [val] => *self *= &rhs;
     [ref] => {
         let shift = self.isometry.rotation.transform_vector(&rhs.vector) * self.scaling();
@@ -179,11 +172,11 @@ similarity_binop_assign_impl_all!(
 );
 
 
-// SimilarityBase ×= SimilarityBase
-// SimilarityBase ÷= SimilarityBase
+// Similarity ×= Similarity
+// Similarity ÷= Similarity
 similarity_binop_assign_impl_all!(
     MulAssign, mul_assign;
-    self: SimilarityBase<N, D, S, R>, rhs: SimilarityBase<N, D, S, R>;
+    self: Similarity<N, D, R>, rhs: Similarity<N, D, R>;
     [val] => *self *= &rhs;
     [ref] => {
         *self *= &rhs.isometry;
@@ -194,18 +187,18 @@ similarity_binop_assign_impl_all!(
 
 similarity_binop_assign_impl_all!(
     DivAssign, div_assign;
-    self: SimilarityBase<N, D, S, R>, rhs: SimilarityBase<N, D, S, R>;
+    self: Similarity<N, D, R>, rhs: Similarity<N, D, R>;
     [val] => *self /= &rhs;
     // FIXME: don't invert explicitly.
     [ref] => *self *= rhs.inverse();
 );
 
 
-// SimilarityBase ×= IsometryBase
-// SimilarityBase ÷= IsometryBase
+// Similarity ×= Isometry
+// Similarity ÷= Isometry
 similarity_binop_assign_impl_all!(
     MulAssign, mul_assign;
-    self: SimilarityBase<N, D, S, R>, rhs: IsometryBase<N, D, S, R>;
+    self: Similarity<N, D, R>, rhs: Isometry<N, D, R>;
     [val] => *self *= &rhs;
     [ref] => {
         let shift = self.isometry.rotation.transform_vector(&rhs.translation.vector) * self.scaling();
@@ -217,18 +210,18 @@ similarity_binop_assign_impl_all!(
 
 similarity_binop_assign_impl_all!(
     DivAssign, div_assign;
-    self: SimilarityBase<N, D, S, R>, rhs: IsometryBase<N, D, S, R>;
+    self: Similarity<N, D, R>, rhs: Isometry<N, D, R>;
     [val] => *self /= &rhs;
     // FIXME: don't invert explicitly.
     [ref] => *self *= rhs.inverse();
 );
 
 
-// SimilarityBase ×= R
-// SimilarityBase ÷= R
+// Similarity ×= R
+// Similarity ÷= R
 similarity_binop_assign_impl_all!(
     MulAssign, mul_assign;
-    self: SimilarityBase<N, D, S, R>, rhs: R;
+    self: Similarity<N, D, R>, rhs: R;
     [val] => self.isometry.rotation *= rhs;
     [ref] => self.isometry.rotation *= rhs.clone();
 );
@@ -236,59 +229,59 @@ similarity_binop_assign_impl_all!(
 
 similarity_binop_assign_impl_all!(
     DivAssign, div_assign;
-    self: SimilarityBase<N, D, S, R>, rhs: R;
+    self: Similarity<N, D, R>, rhs: R;
     // FIXME: don't invert explicitly?
     [val] => *self *= rhs.inverse();
     [ref] => *self *= rhs.inverse();
 );
 
 
-// SimilarityBase × R
-// SimilarityBase ÷ R
+// Similarity × R
+// Similarity ÷ R
 similarity_binop_impl_all!(
     Mul, mul;
-    self: SimilarityBase<N, D, S, R>, rhs: R, Output = SimilarityBase<N, D, S, R>;
+    self: Similarity<N, D, R>, rhs: R, Output = Similarity<N, D, R>;
     [val val] => {
         let scaling = self.scaling();
-        SimilarityBase::from_isometry(self.isometry * rhs, scaling)
+        Similarity::from_isometry(self.isometry * rhs, scaling)
     };
-    [ref val] => SimilarityBase::from_isometry(&self.isometry * rhs, self.scaling());
+    [ref val] => Similarity::from_isometry(&self.isometry * rhs, self.scaling());
     [val ref] => {
         let scaling = self.scaling();
-        SimilarityBase::from_isometry(self.isometry * rhs, scaling)
+        Similarity::from_isometry(self.isometry * rhs, scaling)
     };
-    [ref ref] => SimilarityBase::from_isometry(&self.isometry * rhs, self.scaling());
+    [ref ref] => Similarity::from_isometry(&self.isometry * rhs, self.scaling());
 );
 
 
 
 similarity_binop_impl_all!(
     Div, div;
-    self: SimilarityBase<N, D, S, R>, rhs: R, Output = SimilarityBase<N, D, S, R>;
+    self: Similarity<N, D, R>, rhs: R, Output = Similarity<N, D, R>;
     [val val] => {
         let scaling = self.scaling();
-        SimilarityBase::from_isometry(self.isometry / rhs, scaling)
+        Similarity::from_isometry(self.isometry / rhs, scaling)
     };
-    [ref val] => SimilarityBase::from_isometry(&self.isometry / rhs, self.scaling());
+    [ref val] => Similarity::from_isometry(&self.isometry / rhs, self.scaling());
     [val ref] => {
         let scaling = self.scaling();
-        SimilarityBase::from_isometry(self.isometry / rhs, scaling)
+        Similarity::from_isometry(self.isometry / rhs, scaling)
     };
-    [ref ref] => SimilarityBase::from_isometry(&self.isometry / rhs, self.scaling());
+    [ref ref] => Similarity::from_isometry(&self.isometry / rhs, self.scaling());
 );
 
-// SimilarityBase × IsometryBase
-// SimilarityBase ÷ IsometryBase
+// Similarity × Isometry
+// Similarity ÷ Isometry
 similarity_binop_impl_all!(
     Mul, mul;
-    self: SimilarityBase<N, D, S, R>, rhs: IsometryBase<N, D, S, R>, Output = SimilarityBase<N, D, S, R>;
+    self: Similarity<N, D, R>, rhs: Isometry<N, D, R>, Output = Similarity<N, D, R>;
     [val val] => &self * &rhs;
     [ref val] => self * &rhs;
     [val ref] => &self * rhs;
     [ref ref] => {
         let shift = self.isometry.rotation.transform_vector(&rhs.translation.vector) * self.scaling();
-        SimilarityBase::from_parts(
-            TranslationBase::from_vector(&self.isometry.translation.vector + shift),
+        Similarity::from_parts(
+            Translation::from_vector(&self.isometry.translation.vector + shift),
             self.isometry.rotation.clone() * rhs.rotation.clone(),
             self.scaling())
     };
@@ -298,40 +291,40 @@ similarity_binop_impl_all!(
 
 similarity_binop_impl_all!(
     Div, div;
-    self: SimilarityBase<N, D, S, R>, rhs: IsometryBase<N, D, S, R>, Output = SimilarityBase<N, D, S, R>;
+    self: Similarity<N, D, R>, rhs: Isometry<N, D, R>, Output = Similarity<N, D, R>;
     [val val] => self * rhs.inverse();
     [ref val] => self * rhs.inverse();
     [val ref] => self * rhs.inverse();
     [ref ref] => self * rhs.inverse();
 );
 
-// IsometryBase × SimilarityBase
-// IsometryBase ÷ SimilarityBase
+// Isometry × Similarity
+// Isometry ÷ Similarity
 similarity_binop_impl_all!(
     Mul, mul;
-    self: IsometryBase<N, D, S, R>, rhs: SimilarityBase<N, D, S, R>, Output = SimilarityBase<N, D, S, R>;
+    self: Isometry<N, D, R>, rhs: Similarity<N, D, R>, Output = Similarity<N, D, R>;
     [val val] => {
         let scaling = rhs.scaling();
-        SimilarityBase::from_isometry(self * rhs.isometry, scaling)
+        Similarity::from_isometry(self * rhs.isometry, scaling)
     };
     [ref val] => {
         let scaling = rhs.scaling();
-        SimilarityBase::from_isometry(self * rhs.isometry, scaling)
+        Similarity::from_isometry(self * rhs.isometry, scaling)
     };
     [val ref] => {
         let scaling = rhs.scaling();
-        SimilarityBase::from_isometry(self * &rhs.isometry, scaling)
+        Similarity::from_isometry(self * &rhs.isometry, scaling)
     };
     [ref ref] => {
         let scaling = rhs.scaling();
-        SimilarityBase::from_isometry(self * &rhs.isometry, scaling)
+        Similarity::from_isometry(self * &rhs.isometry, scaling)
     };
 );
 
 
 similarity_binop_impl_all!(
     Div, div;
-    self: IsometryBase<N, D, S, R>, rhs: SimilarityBase<N, D, S, R>, Output = SimilarityBase<N, D, S, R>;
+    self: Isometry<N, D, R>, rhs: Similarity<N, D, R>, Output = Similarity<N, D, R>;
     [val val] => self * rhs.inverse();
     [ref val] => self * rhs.inverse();
     [val ref] => self * rhs.inverse();
@@ -339,10 +332,10 @@ similarity_binop_impl_all!(
 );
 
 
-// SimilarityBase × PointBase
+// Similarity × Point
 similarity_binop_impl_all!(
     Mul, mul;
-    self: SimilarityBase<N, D, S, R>, right: PointBase<N, D, S>, Output = PointBase<N, D, S>;
+    self: Similarity<N, D, R>, right: Point<N, D>, Output = Point<N, D>;
     [val val] => {
         let scaling = self.scaling();
         self.isometry.translation * (self.isometry.rotation.transform_point(&right) * scaling)
@@ -356,10 +349,10 @@ similarity_binop_impl_all!(
 );
 
 
-// SimilarityBase × Vector
+// Similarity × Vector
 similarity_binop_impl_all!(
     Mul, mul;
-    self: SimilarityBase<N, D, S, R>, right: ColumnVector<N, D, S>, Output = ColumnVector<N, D, S>;
+    self: Similarity<N, D, R>, right: VectorN<N, D>, Output = VectorN<N, D>;
     [val val] => self.isometry.rotation.transform_vector(&right) * self.scaling();
     [ref val] => self.isometry.rotation.transform_vector(&right) * self.scaling();
     [val ref] => self.isometry.rotation.transform_vector(right) * self.scaling();
@@ -367,37 +360,37 @@ similarity_binop_impl_all!(
 );
 
 
-// SimilarityBase × TranslationBase
+// Similarity × Translation
 similarity_binop_impl_all!(
     Mul, mul;
-    self: SimilarityBase<N, D, S, R>, right: TranslationBase<N, D, S>, Output = SimilarityBase<N, D, S, R>;
+    self: Similarity<N, D, R>, right: Translation<N, D>, Output = Similarity<N, D, R>;
     [val val] => &self * &right;
     [ref val] => self * &right;
     [val ref] => &self * right;
     [ref ref] => {
         let shift = self.isometry.rotation.transform_vector(&right.vector) * self.scaling();
-        SimilarityBase::from_parts(
-            TranslationBase::from_vector(&self.isometry.translation.vector + shift),
+        Similarity::from_parts(
+            Translation::from_vector(&self.isometry.translation.vector + shift),
             self.isometry.rotation.clone(),
             self.scaling())
     };
 );
 
 
-// TranslationBase × SimilarityBase
+// Translation × Similarity
 similarity_binop_impl_all!(
     Mul, mul;
-    self: TranslationBase<N, D, S>, right: SimilarityBase<N, D, S, R>, Output = SimilarityBase<N, D, S, R>;
+    self: Translation<N, D>, right: Similarity<N, D, R>, Output = Similarity<N, D, R>;
     [val val] => {
         let scaling = right.scaling();
-        SimilarityBase::from_isometry(self * right.isometry, scaling)
+        Similarity::from_isometry(self * right.isometry, scaling)
     };
     [ref val] => {
         let scaling = right.scaling();
-        SimilarityBase::from_isometry(self * right.isometry, scaling)
+        Similarity::from_isometry(self * right.isometry, scaling)
     };
-    [val ref] => SimilarityBase::from_isometry(self * &right.isometry, right.scaling());
-    [ref ref] => SimilarityBase::from_isometry(self * &right.isometry, right.scaling());
+    [val ref] => Similarity::from_isometry(self * &right.isometry, right.scaling());
+    [ref ref] => Similarity::from_isometry(self * &right.isometry, right.scaling());
 );
 
 
@@ -406,12 +399,9 @@ macro_rules! similarity_from_composition_impl(
      ($R1: ty, $C1: ty),($R2: ty, $C2: ty) $(for $Dims: ident: $DimsBound: ident),*;
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Output: ty;
      $action: expr; $($lives: tt),*) => {
-        impl<$($lives ,)* N $(, $Dims: $DimsBound)*, SA, SB> $Op<$Rhs> for $Lhs
-            where N: Real,
-                  SA: OwnedStorage<N, $R1, $C1>,
-                  SB: OwnedStorage<N, $R2, $C2, Alloc = SA::Alloc>,
-                  SA::Alloc: OwnedAllocator<N, $R1, $C1, SA>,
-                  SB::Alloc: OwnedAllocator<N, $R2, $C2, SB> {
+        impl<$($lives ,)* N: Real $(, $Dims: $DimsBound)*> $Op<$Rhs> for $Lhs
+            where DefaultAllocator: Allocator<N, $R1, $C1> +
+                                    Allocator<N, $R2, $C2> {
             type Output = $Output;
 
             #[inline]
@@ -458,25 +448,25 @@ macro_rules! similarity_from_composition_impl_all(
 );
 
 
-// RotationBase × SimilarityBase
+// Rotation × Similarity
 similarity_from_composition_impl_all!(
     Mul, mul;
     (D, D), (D, U1) for D: DimName;
-    self: RotationBase<N, D, SA>, right: SimilarityBase<N, D, SB, RotationBase<N, D, SA>>,
-    Output = SimilarityBase<N, D, SB, RotationBase<N, D, SA>>;
+    self: Rotation<N, D>, right: Similarity<N, D, Rotation<N, D>>,
+    Output = Similarity<N, D, Rotation<N, D>>;
     [val val] => &self * &right;
     [ref val] =>  self * &right;
     [val ref] => &self *  right;
-    [ref ref] => SimilarityBase::from_isometry(self * &right.isometry, right.scaling());
+    [ref ref] => Similarity::from_isometry(self * &right.isometry, right.scaling());
 );
 
 
-// RotationBase ÷ SimilarityBase
+// Rotation ÷ Similarity
 similarity_from_composition_impl_all!(
     Div, div;
     (D, D), (D, U1) for D: DimName;
-    self: RotationBase<N, D, SA>, right: SimilarityBase<N, D, SB, RotationBase<N, D, SA>>,
-    Output = SimilarityBase<N, D, SB, RotationBase<N, D, SA>>;
+    self: Rotation<N, D>, right: Similarity<N, D, Rotation<N, D>>,
+    Output = Similarity<N, D, Rotation<N, D>>;
     // FIXME: don't call iverse explicitly?
     [val val] => self * right.inverse();
     [ref val] => self * right.inverse();
@@ -485,25 +475,25 @@ similarity_from_composition_impl_all!(
 );
 
 
-// UnitQuaternion × SimilarityBase
+// UnitQuaternion × Similarity
 similarity_from_composition_impl_all!(
     Mul, mul;
     (U4, U1), (U3, U1);
-    self: UnitQuaternionBase<N, SA>, right: SimilarityBase<N, U3, SB, UnitQuaternionBase<N, SA>>,
-    Output = SimilarityBase<N, U3, SB, UnitQuaternionBase<N, SA>>;
+    self: UnitQuaternion<N>, right: Similarity<N, U3, UnitQuaternion<N>>,
+    Output = Similarity<N, U3, UnitQuaternion<N>>;
     [val val] => &self * &right;
     [ref val] =>  self * &right;
     [val ref] => &self *  right;
-    [ref ref] => SimilarityBase::from_isometry(self * &right.isometry, right.scaling());
+    [ref ref] => Similarity::from_isometry(self * &right.isometry, right.scaling());
 );
 
 
-// UnitQuaternion ÷ SimilarityBase
+// UnitQuaternion ÷ Similarity
 similarity_from_composition_impl_all!(
     Div, div;
     (U4, U1), (U3, U1);
-    self: UnitQuaternionBase<N, SA>, right: SimilarityBase<N, U3, SB, UnitQuaternionBase<N, SA>>,
-    Output = SimilarityBase<N, U3, SB, UnitQuaternionBase<N, SA>>;
+    self: UnitQuaternion<N>, right: Similarity<N, U3, UnitQuaternion<N>>,
+    Output = Similarity<N, U3, UnitQuaternion<N>>;
     // FIXME: don't call inverse explicitly?
     [val val] => self * right.inverse();
     [ref val] => self * right.inverse();

src/geometry/transform.rs

@@ -1,16 +1,15 @@
 use std::any::Any;
 use std::fmt::Debug;
 use std::marker::PhantomData;
-use approx::ApproxEq;
 
 #[cfg(feature = "serde-serialize")]
-use serde::{Serialize, Serializer, Deserialize, Deserializer};
+use serde;
 
-use alga::general::Field;
+use alga::general::Real;
 
-use core::{Scalar, SquareMatrix, OwnedSquareMatrix};
+use core::{DefaultAllocator, MatrixN};
 use core::dimension::{DimName, DimNameAdd, DimNameSum, U1};
-use core::storage::{Storage, StorageMut};
+use core::storage::Owned;
 use core::allocator::Allocator;
 
 /// Trait implemented by phantom types identifying the projective transformation type.
@@ -26,11 +25,9 @@ pub trait TCategory: Any + Debug + Copy + PartialEq + Send {
 
     /// Checks that the given matrix is a valid homogeneous representation of an element of the
     /// category `Self`.
-    fn check_homogeneous_invariants<N, D, S>(mat: &SquareMatrix<N, D, S>) -> bool
-        where N: Scalar + Field + ApproxEq,
-              D: DimName,
-              S: Storage<N, D, D>,
-              N::Epsilon: Copy;
+    fn check_homogeneous_invariants<N: Real, D: DimName>(mat: &MatrixN<N, D>) -> bool
+        where N::Epsilon: Copy,
+              DefaultAllocator: Allocator<N, D, D>;
 }
 
 /// Traits that gives the `Transform` category that is compatible with the result of the
@@ -68,22 +65,18 @@ pub enum TAffine { }
 
 impl TCategory for TGeneral {
     #[inline]
-    fn check_homogeneous_invariants<N, D, S>(_: &SquareMatrix<N, D, S>) -> bool
-        where N: Scalar + Field + ApproxEq,
-              D: DimName,
-              S: Storage<N, D, D>,
-              N::Epsilon: Copy {
+    fn check_homogeneous_invariants<N: Real, D: DimName>(_: &MatrixN<N, D>) -> bool
+        where N::Epsilon: Copy,
+              DefaultAllocator: Allocator<N, D, D> {
         true
     }
 }
 
 impl TCategory for TProjective {
     #[inline]
-    fn check_homogeneous_invariants<N, D, S>(mat: &SquareMatrix<N, D, S>) -> bool
-        where N: Scalar + Field + ApproxEq,
-              D: DimName,
-              S: Storage<N, D, D>,
-              N::Epsilon: Copy {
+    fn check_homogeneous_invariants<N: Real, D: DimName>(mat: &MatrixN<N, D>) -> bool
+        where N::Epsilon: Copy,
+              DefaultAllocator: Allocator<N, D, D> {
         mat.is_invertible()
     }
 }
@@ -95,11 +88,9 @@ impl TCategory for TAffine {
     }
 
     #[inline]
-    fn check_homogeneous_invariants<N, D, S>(mat: &SquareMatrix<N, D, S>) -> bool
-        where N: Scalar + Field + ApproxEq,
-              D: DimName,
-              S: Storage<N, D, D>,
-              N::Epsilon: Copy {
+    fn check_homogeneous_invariants<N: Real, D: DimName>(mat: &MatrixN<N, D>) -> bool
+        where N::Epsilon: Copy,
+              DefaultAllocator: Allocator<N, D, D> {
         let last = D::dim() - 1;
         mat.is_invertible()           &&
         mat[(last, last)] == N::one() &&
@@ -149,103 +140,98 @@ super_tcategory_impl!(
 );
 
 
-/// A transformation matrix that owns its data.
-pub type OwnedTransform<N, D, A, C>
-    = TransformBase<N, D, <A as Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>>::Buffer, C>;
-
-
 /// A transformation matrix in homogeneous coordinates.
 ///
 /// It is stored as a matrix with dimensions `(D + 1, D + 1)`, e.g., it stores a 4x4 matrix for a
 /// 3D transformation.
 #[repr(C)]
-#[derive(Debug, Clone, Copy)] // FIXME: Hash
-pub struct TransformBase<N: Scalar, D: DimNameAdd<U1>, S, C: TCategory> {
-    matrix:   SquareMatrix<N, DimNameSum<D, U1>, S>,
+#[derive(Debug)]
+pub struct Transform<N: Real, D: DimNameAdd<U1>, C: TCategory>
+    where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
 
+    matrix:   MatrixN<N, DimNameSum<D, U1>>,
     _phantom: PhantomData<C>
 }
 
+// FIXME
+// impl<N: Real + hash::Hash, D: DimNameAdd<U1> + hash::Hash, C: TCategory> hash::Hash for Transform<N, D, C>
+//     where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+//           Owned<N, DimNameSum<D, U1>, DimNameSum<D, U1>>: hash::Hash {
+//     fn hash<H: hash::Hasher>(&self, state: &mut H) {
+//         self.matrix.hash(state);
+//     }
+// }
+
+impl<N: Real, D: DimNameAdd<U1> + Copy, C: TCategory> Copy for Transform<N, D, C>
+    where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+          Owned<N, DimNameSum<D, U1>, DimNameSum<D, U1>>: Copy {
+}
+
+impl<N: Real, D: DimNameAdd<U1>, C: TCategory> Clone for Transform<N, D, C>
+    where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
+    #[inline]
+    fn clone(&self) -> Self {
+        Transform::from_matrix_unchecked(self.matrix.clone())
+    }
+}
+
 #[cfg(feature = "serde-serialize")]
-impl<N, D, S, C> Serialize for TransformBase<N, D, S, C>
-    where N: Scalar,
-          D: DimNameAdd<U1>,
-          C: TCategory,
-          SquareMatrix<N, DimNameSum<D, U1>, S>: Serialize,
-{
-    fn serialize<T>(&self, serializer: T) -> Result<T::Ok, T::Error>
-        where T: Serializer
-    {
+impl<N: Real, D: DimNameAdd<U1>, C: TCategory> serde::Serialize for Transform<N, D, C>
+where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+      Owned<N, DimNameSum<D, U1>, DimNameSum<D, U1>>: serde::Serialize {
+
+    fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
+        where S: serde::Serializer {
             self.matrix.serialize(serializer)
         }
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<'de, N, D, S, C> Deserialize<'de> for TransformBase<N, D, S, C>
-    where N: Scalar,
-          D: DimNameAdd<U1>,
-          C: TCategory,
-          SquareMatrix<N, DimNameSum<D, U1>, S>: Deserialize<'de>,
-{
-    fn deserialize<T>(deserializer: T) -> Result<Self, T::Error>
-        where T: Deserializer<'de>
-    {
-        SquareMatrix::deserialize(deserializer).map(|x| TransformBase { matrix: x, _phantom: PhantomData })
+impl<'a, N: Real, D: DimNameAdd<U1>, C: TCategory> serde::Deserialize<'a> for Transform<N, D, C>
+where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+      Owned<N, DimNameSum<D, U1>, DimNameSum<D, U1>>: serde::Deserialize<'a> {
+
+    fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
+        where Des: serde::Deserializer<'a> {
+            let matrix = MatrixN::<N, DimNameSum<D, U1>>::deserialize(deserializer)?;
+
+            Ok(Transform::from_matrix_unchecked(matrix))
         }
 }
 
-// XXX: for some reasons, implementing Clone and Copy manually causes an ICE…
 
-impl<N, D, S, C: TCategory> Eq for TransformBase<N, D, S, C>
-    where N: Scalar + Eq,
-          D: DimNameAdd<U1>,
-          S: Storage<N, DimNameSum<D, U1>, DimNameSum<D, U1>> { }
+impl<N: Real + Eq, D: DimNameAdd<U1>, C: TCategory> Eq for Transform<N, D, C>
+    where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> { }
 
-impl<N, D, S, C: TCategory> PartialEq for TransformBase<N, D, S, C>
-    where N: Scalar,
-          D: DimNameAdd<U1>,
-          S: Storage<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
+impl<N: Real, D: DimNameAdd<U1>, C: TCategory> PartialEq for Transform<N, D, C>
+    where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
     #[inline]
     fn eq(&self, right: &Self) -> bool {
         self.matrix == right.matrix
     }
 }
 
-impl<N, D, S, C: TCategory> TransformBase<N, D, S, C>
-    where N: Scalar,
-          D: DimNameAdd<U1>,
-          S: Storage<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
+impl<N: Real, D: DimNameAdd<U1>, C: TCategory> Transform<N, D, C>
+    where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
     /// Creates a new transformation from the given homogeneous matrix. The transformation category
     /// of `Self` is not checked to be verified by the given matrix.
     #[inline]
-    pub fn from_matrix_unchecked(matrix: SquareMatrix<N, DimNameSum<D, U1>, S>) -> Self {
-        TransformBase {
+    pub fn from_matrix_unchecked(matrix: MatrixN<N, DimNameSum<D, U1>>) -> Self {
+        Transform {
             matrix:   matrix,
             _phantom: PhantomData
         }
     }
 
-    /// Moves this transform into one that owns its data.
-    #[inline]
-    pub fn into_owned(self) -> OwnedTransform<N, D, S::Alloc, C> {
-        TransformBase::from_matrix_unchecked(self.matrix.into_owned())
-    }
-
-    /// Clones this transform into one that owns its data.
-    #[inline]
-    pub fn clone_owned(&self) -> OwnedTransform<N, D, S::Alloc, C> {
-        TransformBase::from_matrix_unchecked(self.matrix.clone_owned())
-    }
-
     /// The underlying matrix.
     #[inline]
-    pub fn unwrap(self) -> SquareMatrix<N, DimNameSum<D, U1>, S> {
+    pub fn unwrap(self) -> MatrixN<N, DimNameSum<D, U1>> {
         self.matrix
     }
 
     /// A reference to the underlynig matrix.
     #[inline]
-    pub fn matrix(&self) -> &SquareMatrix<N, DimNameSum<D, U1>, S> {
+    pub fn matrix(&self) -> &MatrixN<N, DimNameSum<D, U1>> {
         &self.matrix
     }
 
@@ -254,7 +240,7 @@ impl<N, D, S, C: TCategory> TransformBase<N, D, S, C>
     /// It is `_unchecked` because direct modifications of this matrix may break invariants
     /// identified by this transformation category.
     #[inline]
-    pub fn matrix_mut_unchecked(&mut self) -> &mut SquareMatrix<N, DimNameSum<D, U1>, S> {
+    pub fn matrix_mut_unchecked(&mut self) -> &mut MatrixN<N, DimNameSum<D, U1>> {
         &mut self.matrix
     }
 
@@ -265,28 +251,28 @@ impl<N, D, S, C: TCategory> TransformBase<N, D, S, C>
     /// `TAffine` because not all projective transformations are affine (the other way-round is
     /// valid though).
     #[inline]
-    pub fn set_category<CNew: SuperTCategoryOf<C>>(self) -> TransformBase<N, D, S, CNew> {
-        TransformBase::from_matrix_unchecked(self.matrix)
+    pub fn set_category<CNew: SuperTCategoryOf<C>>(self) -> Transform<N, D, CNew> {
+        Transform::from_matrix_unchecked(self.matrix)
+    }
+
+    /// Clones this transform into one that owns its data.
+    #[inline]
+    pub fn clone_owned(&self) -> Transform<N, D, C> {
+        Transform::from_matrix_unchecked(self.matrix.clone_owned())
     }
 
     /// Converts this transform into its equivalent homogeneous transformation matrix.
     #[inline]
-    pub fn to_homogeneous(&self) -> OwnedSquareMatrix<N, DimNameSum<D, U1>, S::Alloc> {
+    pub fn to_homogeneous(&self) -> MatrixN<N, DimNameSum<D, U1>> {
         self.matrix().clone_owned()
     }
-}
 
-impl<N, D, S, C> TransformBase<N, D, S, C>
-    where N: Scalar + Field + ApproxEq,
-          D: DimNameAdd<U1>,
-          C: TCategory,
-          S: Storage<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
     /// Attempts to invert this transformation. You may use `.inverse` instead of this
     /// transformation has a subcategory of `TProjective`.
     #[inline]
-    pub fn try_inverse(self) -> Option<OwnedTransform<N, D, S::Alloc, C>> {
+    pub fn try_inverse(self) -> Option<Transform<N, D, C>> {
         if let Some(m) = self.matrix.try_inverse() {
-            Some(TransformBase::from_matrix_unchecked(m))
+            Some(Transform::from_matrix_unchecked(m))
         }
         else {
             None
@@ -296,18 +282,12 @@ impl<N, D, S, C> TransformBase<N, D, S, C>
     /// Inverts this transformation. Use `.try_inverse` if this transform has the `TGeneral`
     /// category (it may not be invertible).
     #[inline]
-    pub fn inverse(self) -> OwnedTransform<N, D, S::Alloc, C>
+    pub fn inverse(self) -> Transform<N, D, C>
         where C: SubTCategoryOf<TProjective> {
         // FIXME: specialize for TAffine?
-        TransformBase::from_matrix_unchecked(self.matrix.try_inverse().unwrap())
-    }
+        Transform::from_matrix_unchecked(self.matrix.try_inverse().unwrap())
     }
 
-impl<N, D, S, C> TransformBase<N, D, S, C>
-    where N: Scalar + Field + ApproxEq,
-          D: DimNameAdd<U1>,
-          C: TCategory,
-          S: StorageMut<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
     /// Attempts to invert this transformation in-place. You may use `.inverse_mut` instead of this
     /// transformation has a subcategory of `TProjective`.
     #[inline]
@@ -324,14 +304,12 @@ impl<N, D, S, C> TransformBase<N, D, S, C>
     }
 }
 
-impl<N, D, S> TransformBase<N, D, S, TGeneral>
-    where N: Scalar,
-          D: DimNameAdd<U1>,
-          S: Storage<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
+impl<N: Real, D: DimNameAdd<U1>> Transform<N, D, TGeneral>
+    where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
     /// A mutable reference to underlying matrix. Use `.matrix_mut_unchecked` instead if this
     /// transformation category is not `TGeneral`.
     #[inline]
-    pub fn matrix_mut(&mut self) -> &mut SquareMatrix<N, DimNameSum<D, U1>, S> {
+    pub fn matrix_mut(&mut self) -> &mut MatrixN<N, DimNameSum<D, U1>> {
         self.matrix_mut_unchecked()
     }
 }
@@ -345,5 +323,4 @@ mod tests {
     fn checks_homogeneous_invariants_of_square_identity_matrix() {
         assert!(TAffine::check_homogeneous_invariants(&Matrix4::<f32>::identity()));
     }
-
 }

src/geometry/transform_alga.rs

@@ -1,15 +1,12 @@
-use approx::ApproxEq;
-
 use alga::general::{AbstractMagma, AbstractGroup, AbstractLoop, AbstractMonoid, AbstractQuasigroup,
-                    AbstractSemigroup, Field, Real, Inverse, Multiplicative, Identity};
+                    AbstractSemigroup, Real, Inverse, Multiplicative, Identity};
 use alga::linear::{Transformation, ProjectiveTransformation};
 
-use core::{Scalar, ColumnVector};
+use core::{DefaultAllocator, VectorN};
 use core::dimension::{DimNameSum, DimNameAdd, U1};
-use core::storage::OwnedStorage;
-use core::allocator::{Allocator, OwnedAllocator};
+use core::allocator::Allocator;
 
-use geometry::{PointBase, TransformBase, TCategory, SubTCategoryOf, TProjective};
+use geometry::{Point, Transform, TCategory, SubTCategoryOf, TProjective};
 
 
 /*
@@ -17,22 +14,18 @@ use geometry::{PointBase, TransformBase, TCategory, SubTCategoryOf, TProjective}
  * Algebraic structures.
  *
  */
-impl<N, D: DimNameAdd<U1>, S, C> Identity<Multiplicative> for TransformBase<N, D, S, C>
-    where N: Scalar + Field,
-          S: OwnedStorage<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
-          C: TCategory,
-          S::Alloc: OwnedAllocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>, S> {
+impl<N: Real, D: DimNameAdd<U1>, C> Identity<Multiplicative> for Transform<N, D, C>
+    where C: TCategory,
+          DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
     #[inline]
     fn identity() -> Self {
         Self::identity()
     }
 }
 
-impl<N, D: DimNameAdd<U1>, S, C> Inverse<Multiplicative> for TransformBase<N, D, S, C>
-    where N: Scalar + Field + ApproxEq,
-          S: OwnedStorage<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
-          C: SubTCategoryOf<TProjective>,
-          S::Alloc: OwnedAllocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>, S> {
+impl<N: Real, D: DimNameAdd<U1>, C> Inverse<Multiplicative> for Transform<N, D, C>
+    where C: SubTCategoryOf<TProjective>,
+          DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
     #[inline]
     fn inverse(&self) -> Self {
         self.clone().inverse()
@@ -44,11 +37,9 @@ impl<N, D: DimNameAdd<U1>, S, C> Inverse<Multiplicative> for TransformBase<N, D,
     }
 }
 
-impl<N, D: DimNameAdd<U1>, S, C> AbstractMagma<Multiplicative> for TransformBase<N, D, S, C>
-    where N: Scalar + Field,
-          S: OwnedStorage<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
-          C: TCategory,
-          S::Alloc: OwnedAllocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>, S> {
+impl<N: Real, D: DimNameAdd<U1>, C> AbstractMagma<Multiplicative> for Transform<N, D, C>
+    where C: TCategory,
+          DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
     #[inline]
     fn operate(&self, rhs: &Self) -> Self {
         self * rhs
@@ -57,21 +48,17 @@ impl<N, D: DimNameAdd<U1>, S, C> AbstractMagma<Multiplicative> for TransformBase
 
 macro_rules! impl_multiplicative_structures(
     ($($marker: ident<$operator: ident>),* $(,)*) => {$(
-        impl<N, D: DimNameAdd<U1>, S, C> $marker<$operator> for TransformBase<N, D, S, C>
-            where N: Scalar + Field,
-                  S: OwnedStorage<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
-                  C: TCategory,
-                  S::Alloc: OwnedAllocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>, S> { }
+        impl<N: Real, D: DimNameAdd<U1>, C> $marker<$operator> for Transform<N, D, C>
+            where C: TCategory,
+                  DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> { }
     )*}
 );
 
 macro_rules! impl_inversible_multiplicative_structures(
     ($($marker: ident<$operator: ident>),* $(,)*) => {$(
-        impl<N, D: DimNameAdd<U1>, S, C> $marker<$operator> for TransformBase<N, D, S, C>
-            where N: Scalar + Field + ApproxEq,
-                  S: OwnedStorage<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
-                  C: SubTCategoryOf<TProjective>,
-                  S::Alloc: OwnedAllocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>, S> { }
+        impl<N: Real, D: DimNameAdd<U1>, C> $marker<$operator> for Transform<N, D, C>
+            where C: SubTCategoryOf<TProjective>,
+                  DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> { }
     )*}
 );
 
@@ -91,64 +78,54 @@ impl_inversible_multiplicative_structures!(
  * Transformation groups.
  *
  */
-impl<N, D: DimNameAdd<U1>, SA, SB, C> Transformation<PointBase<N, D, SB>> for TransformBase<N, D, SA, C>
+impl<N, D: DimNameAdd<U1>, C> Transformation<Point<N, D>> for Transform<N, D, C>
     where N:  Real,
-          SA: OwnedStorage<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
-          SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
           C:  TCategory,
-          SA::Alloc: OwnedAllocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>, SA> +
+          DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> +
+                            Allocator<N, DimNameSum<D, U1>> +
                             Allocator<N, D, D> +
-                     Allocator<N, D, U1> +
-                     Allocator<N, U1, D>,
-          SB::Alloc: OwnedAllocator<N, D, U1, SB> {
+                            Allocator<N, D> {
     #[inline]
-    fn transform_point(&self, pt: &PointBase<N, D, SB>) -> PointBase<N, D, SB> {
+    fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
         self * pt
     }
 
     #[inline]
-    fn transform_vector(&self, v: &ColumnVector<N, D, SB>) -> ColumnVector<N, D, SB> {
+    fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
         self * v
     }
 }
 
-impl<N, D: DimNameAdd<U1>, SA, SB, C> ProjectiveTransformation<PointBase<N, D, SB>> for TransformBase<N, D, SA, C>
+impl<N, D: DimNameAdd<U1>, C> ProjectiveTransformation<Point<N, D>> for Transform<N, D, C>
     where N:  Real,
-          SA: OwnedStorage<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
-          SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
           C:  SubTCategoryOf<TProjective>,
-          SA::Alloc: OwnedAllocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>, SA> +
+          DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> +
+                            Allocator<N, DimNameSum<D, U1>> +
                             Allocator<N, D, D> +
-                     Allocator<N, D, U1> +
-                     Allocator<N, U1, D>,
-          SB::Alloc: OwnedAllocator<N, D, U1, SB> {
+                            Allocator<N, D> {
     #[inline]
-    fn inverse_transform_point(&self, pt: &PointBase<N, D, SB>) -> PointBase<N, D, SB> {
+    fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
         self.inverse() * pt
     }
 
     #[inline]
-    fn inverse_transform_vector(&self, v: &ColumnVector<N, D, SB>) -> ColumnVector<N, D, SB> {
+    fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
         self.inverse() * v
     }
 }
 
 // FIXME: we need to implement an SVD for this.
 //
-// impl<N, D: DimNameAdd<U1>, SA, SB, C> AffineTransformation<PointBase<N, D, SB>> for TransformBase<N, D, SA, C>
+// impl<N, D: DimNameAdd<U1>, C> AffineTransformation<Point<N, D>> for Transform<N, D, C>
 //     where N:  Real,
-//           SA: OwnedStorage<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
-//           SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
 //           C: SubTCategoryOf<TAffine>,
-//           SA::Alloc: OwnedAllocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>, SA> +
+//           DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> +
 //                             Allocator<N, D, D> +
-//                      Allocator<N, D, U1> +
-//                      Allocator<N, U1, D>,
-//           SB::Alloc: OwnedAllocator<N, D, U1, SB> {
-//     type PreRotation       = OwnedRotation<N, D, SA::Alloc>;
-//     type NonUniformScaling = OwnedColumnVector<N, D, SA::Alloc>;
-//     type PostRotation      = OwnedRotation<N, D, SA::Alloc>;
-//     type Translation       = OwnedTranslation<N, D, SA::Alloc>;
+//                             Allocator<N, D> {
+//     type PreRotation       = Rotation<N, D>;
+//     type NonUniformScaling = VectorN<N, D>;
+//     type PostRotation      = Rotation<N, D>;
+//     type Translation       = Translation<N, D>;
 // 
 //     #[inline]
 //     fn decompose(&self) -> (Self::Translation, Self::PostRotation, Self::NonUniformScaling, Self::PreRotation) {

src/geometry/transform_alias.rs

@@ -1,29 +1,17 @@
-use core::MatrixArray;
-use core::dimension::{U1, U2, U3, DimNameSum};
+use core::dimension::{U2, U3};
 
-use geometry::{TransformBase, TGeneral, TProjective, TAffine};
-
-/// A `D`-dimensional general transformation that may not be inversible. Stored as an homogeneous
-/// `(D + 1) × (D + 1)` matrix.
-pub type Transform<N, D> = TransformBase<N, D, MatrixArray<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, TGeneral>;
-
-/// An inversible `D`-dimensional general transformation. Stored as an homogeneous
-/// `(D + 1) × (D + 1)` matrix.
-pub type Projective<N, D> = TransformBase<N, D, MatrixArray<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, TProjective>;
-
-/// A `D`-dimensional affine transformation. Stored as an homogeneous `(D + 1) × (D + 1)` matrix.
-pub type Affine<N, D> = TransformBase<N, D, MatrixArray<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, TAffine>;
+use geometry::{Transform, TGeneral, TProjective, TAffine};
 
 /// A 2D general transformation that may not be inversible. Stored as an homogeneous 3x3 matrix.
-pub type Transform2<N> = Transform<N, U2>;
+pub type Transform2<N>  = Transform<N, U2, TGeneral>;
 /// An inversible 2D general transformation. Stored as an homogeneous 3x3 matrix.
-pub type Projective2<N> = Projective<N, U2>;
+pub type Projective2<N> = Transform<N, U2, TProjective>;
 /// A 2D affine transformation. Stored as an homogeneous 3x3 matrix.
-pub type Affine2<N> = Affine<N, U2>;
+pub type Affine2<N>     = Transform<N, U2, TAffine>;
 
 /// A 3D general transformation that may not be inversible. Stored as an homogeneous 4x4 matrix.
-pub type Transform3<N> = Transform<N, U3>;
+pub type Transform3<N>  = Transform<N, U3, TGeneral>;
 /// An inversible 3D general transformation. Stored as an homogeneous 4x4 matrix.
-pub type Projective3<N> = Projective<N, U3>;
+pub type Projective3<N> = Transform<N, U3, TProjective>;
 /// A 3D affine transformation. Stored as an homogeneous 4x4 matrix.
-pub type Affine3<N> = Affine<N, U3>;
+pub type Affine3<N>     = Transform<N, U3, TAffine>;

src/geometry/transform_construction.rs

@@ -1,32 +1,25 @@
-use num::{Zero, One};
+use num::One;
 
-use alga::general::Field;
+use alga::general::Real;
 
-use core::{Scalar, OwnedSquareMatrix};
+use core::{DefaultAllocator, MatrixN};
 use core::dimension::{DimNameAdd, DimNameSum, U1};
-use core::storage::OwnedStorage;
-use core::allocator::OwnedAllocator;
+use core::allocator::Allocator;
 
-use geometry::{TransformBase, TCategory};
+use geometry::{Transform, TCategory};
 
 
-impl<N, D, S, C: TCategory> TransformBase<N, D, S, C>
-    where N: Scalar + Zero + One,
-          D: DimNameAdd<U1>,
-          S: OwnedStorage<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
-          S::Alloc: OwnedAllocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>, S> {
+impl<N: Real, D: DimNameAdd<U1>, C: TCategory> Transform<N, D, C>
+    where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
     /// Creates a new identity transform.
     #[inline]
     pub fn identity() -> Self {
-        Self::from_matrix_unchecked(OwnedSquareMatrix::<N, _, S::Alloc>::identity())
+        Self::from_matrix_unchecked(MatrixN::<_, DimNameSum<D, U1>>::identity())
     }
 }
 
-impl<N, D, S, C: TCategory> One for TransformBase<N, D, S, C>
-    where N: Scalar + Field,
-          D: DimNameAdd<U1>,
-          S: OwnedStorage<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
-          S::Alloc: OwnedAllocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>, S> {
+impl<N: Real, D: DimNameAdd<U1>, C: TCategory> One for Transform<N, D, C>
+    where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
     /// Creates a new identity transform.
     #[inline]
     fn one() -> Self {

src/geometry/transform_conversion.rs

@@ -1,67 +1,60 @@
-use approx::ApproxEq;
+use alga::general::{SubsetOf, Real};
 
-use alga::general::{SubsetOf, Field};
-
-use core::{Scalar, SquareMatrix};
+use core::{DefaultAllocator, MatrixN};
 use core::dimension::{DimName, DimNameAdd, DimNameSum, U1};
-use core::storage::OwnedStorage;
-use core::allocator::OwnedAllocator;
+use core::allocator::Allocator;
 
-use geometry::{TransformBase, TCategory, SuperTCategoryOf};
+use geometry::{Transform, TCategory, SuperTCategoryOf};
 
 
-impl<N1, N2, D: DimName, SA, SB, C1, C2> SubsetOf<TransformBase<N2, D, SB, C2>> for TransformBase<N1, D, SA, C1>
-    where N1: Scalar + Field + ApproxEq + SubsetOf<N2>,
-          N2: Scalar + Field + ApproxEq,
+impl<N1, N2, D: DimName, C1, C2> SubsetOf<Transform<N2, D, C2>> for Transform<N1, D, C1>
+    where N1: Real + SubsetOf<N2>,
+          N2: Real,
           C1: TCategory,
           C2: SuperTCategoryOf<C1>,
           D: DimNameAdd<U1>,
-          SA: OwnedStorage<N1, DimNameSum<D, U1>, DimNameSum<D, U1>>,
-          SB: OwnedStorage<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>,
-          SA::Alloc: OwnedAllocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>, SA>,
-          SB::Alloc: OwnedAllocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>, SB>,
+          DefaultAllocator: Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>> +
+                            Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>,
           N1::Epsilon: Copy,
           N2::Epsilon: Copy {
     #[inline]
-    fn to_superset(&self) -> TransformBase<N2, D, SB, C2> {
-        TransformBase::from_matrix_unchecked(self.to_homogeneous().to_superset())
+    fn to_superset(&self) -> Transform<N2, D, C2> {
+        Transform::from_matrix_unchecked(self.to_homogeneous().to_superset())
     }
 
     #[inline]
-    fn is_in_subset(t: &TransformBase<N2, D, SB, C2>) -> bool {
+    fn is_in_subset(t: &Transform<N2, D, C2>) -> bool {
         <Self as SubsetOf<_>>::is_in_subset(t.matrix())
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(t: &TransformBase<N2, D, SB, C2>) -> Self {
+    unsafe fn from_superset_unchecked(t: &Transform<N2, D, C2>) -> Self {
         Self::from_superset_unchecked(t.matrix())
     }
 }
 
 
-impl<N1, N2, D: DimName, SA, SB, C> SubsetOf<SquareMatrix<N2, DimNameSum<D, U1>, SB>> for TransformBase<N1, D, SA, C>
-    where N1: Scalar + Field + ApproxEq + SubsetOf<N2>,
-          N2: Scalar + Field + ApproxEq,
+impl<N1, N2, D: DimName, C> SubsetOf<MatrixN<N2, DimNameSum<D, U1>>> for Transform<N1, D, C>
+    where N1: Real + SubsetOf<N2>,
+          N2: Real,
           C: TCategory,
           D: DimNameAdd<U1>,
-          SA: OwnedStorage<N1, DimNameSum<D, U1>, DimNameSum<D, U1>>,
-          SB: OwnedStorage<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>,
-          SA::Alloc: OwnedAllocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>, SA>,
-          SB::Alloc: OwnedAllocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>, SB>,
+          DefaultAllocator: Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>> +
+                            Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>,
           N1::Epsilon: Copy,
           N2::Epsilon: Copy {
     #[inline]
-    fn to_superset(&self) -> SquareMatrix<N2, DimNameSum<D, U1>, SB> {
+    fn to_superset(&self) -> MatrixN<N2, DimNameSum<D, U1>> {
         self.matrix().to_superset()
     }
 
     #[inline]
-    fn is_in_subset(m: &SquareMatrix<N2, DimNameSum<D, U1>, SB>) -> bool {
+    fn is_in_subset(m: &MatrixN<N2, DimNameSum<D, U1>>) -> bool {
         C::check_homogeneous_invariants(m)
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(m: &SquareMatrix<N2, DimNameSum<D, U1>, SB>) -> Self {
-        TransformBase::from_matrix_unchecked(::convert_ref_unchecked(m))
+    unsafe fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self {
+        Transform::from_matrix_unchecked(::convert_ref_unchecked(m))
     }
 }

src/geometry/transform_ops.rs

@@ -1,17 +1,15 @@
 use num::{Zero, One};
 use std::ops::{Index, IndexMut, Mul, MulAssign, Div, DivAssign};
-use approx::ApproxEq;
 
-use alga::general::{Field, Real, ClosedAdd, ClosedMul, ClosedNeg, SubsetOf};
+use alga::general::{Real, ClosedAdd, ClosedMul, SubsetOf};
 
-use core::{Scalar, ColumnVector, OwnedColumnVector, OwnedSquareMatrix};
-use core::storage::{Storage, StorageMut, OwnedStorage};
-use core::allocator::{Allocator, OwnedAllocator};
+use core::{DefaultAllocator, Scalar, VectorN, MatrixN};
+use core::allocator::Allocator;
 use core::dimension::{DimName, DimNameAdd, DimNameSum, U1, U3, U4};
 
-use geometry::{PointBase, OwnedPoint, TransformBase, OwnedTransform, TCategory, TCategoryMul,
-               SubTCategoryOf, SuperTCategoryOf, TGeneral, TProjective, TAffine, RotationBase,
-               UnitQuaternionBase, IsometryBase, SimilarityBase, TranslationBase};
+use geometry::{Point, Transform, TCategory, TCategoryMul,
+               SubTCategoryOf, SuperTCategoryOf, TGeneral, TProjective, TAffine, Rotation,
+               UnitQuaternion, Isometry, Similarity, Translation};
 
 /*
  *
@@ -23,55 +21,55 @@ use geometry::{PointBase, OwnedPoint, TransformBase, OwnedTransform, TCategory,
  *
  * (Operators)
  *
- * TransformBase × IsometryBase
- * TransformBase × RotationBase
- * TransformBase × SimilarityBase
- * TransformBase × TransformBase
- * TransformBase × UnitQuaternion
- * FIXME: TransformBase × UnitComplex
- * TransformBase × TranslationBase
- * TransformBase × ColumnVector
- * TransformBase × PointBase
+ * Transform × Isometry
+ * Transform × Rotation
+ * Transform × Similarity
+ * Transform × Transform
+ * Transform × UnitQuaternion
+ * FIXME: Transform × UnitComplex
+ * Transform × Translation
+ * Transform × Vector
+ * Transform × Point
  *
- * IsometryBase       × TransformBase
- * RotationBase       × TransformBase
- * SimilarityBase     × TransformBase
- * TranslationBase    × TransformBase
- * UnitQuaternionBase × TransformBase
- * FIXME: UnitComplex × TransformBase
+ * Isometry       × Transform
+ * Rotation       × Transform
+ * Similarity     × Transform
+ * Translation    × Transform
+ * UnitQuaternion × Transform
+ * FIXME: UnitComplex × Transform
  *
- * FIXME: TransformBase ÷ IsometryBase
- * TransformBase ÷ RotationBase
- * FIXME: TransformBase ÷ SimilarityBase
- * TransformBase ÷ TransformBase
- * TransformBase ÷ UnitQuaternion
- * TransformBase ÷ TranslationBase
+ * FIXME: Transform ÷ Isometry
+ * Transform ÷ Rotation
+ * FIXME: Transform ÷ Similarity
+ * Transform ÷ Transform
+ * Transform ÷ UnitQuaternion
+ * Transform ÷ Translation
  *
- * FIXME: IsometryBase       ÷ TransformBase
- * RotationBase       ÷ TransformBase
- * FIXME: SimilarityBase     ÷ TransformBase
- * TranslationBase    ÷ TransformBase
- * UnitQuaternionBase ÷ TransformBase
- * FIXME: UnitComplex ÷ TransformBase
+ * FIXME: Isometry       ÷ Transform
+ * Rotation       ÷ Transform
+ * FIXME: Similarity     ÷ Transform
+ * Translation    ÷ Transform
+ * UnitQuaternion ÷ Transform
+ * FIXME: UnitComplex ÷ Transform
  *
  *
  * (Assignment Operators)
  *
  *
- * TransformBase ×= TransformBase
- * TransformBase ×= SimilarityBase
- * TransformBase ×= IsometryBase
- * TransformBase ×= RotationBase
- * TransformBase ×= UnitQuaternionBase
- * FIXME: TransformBase ×= UnitComplex
- * TransformBase ×= TranslationBase
+ * Transform ×= Transform
+ * Transform ×= Similarity
+ * Transform ×= Isometry
+ * Transform ×= Rotation
+ * Transform ×= UnitQuaternion
+ * FIXME: Transform ×= UnitComplex
+ * Transform ×= Translation
  *
- * TransformBase ÷= TransformBase
- * FIXME: TransformBase ÷= SimilarityBase
- * FIXME: TransformBase ÷= IsometryBase
- * TransformBase ÷= RotationBase
- * TransformBase ÷= UnitQuaternionBase
- * FIXME: TransformBase ÷= UnitComplex
+ * Transform ÷= Transform
+ * FIXME: Transform ÷= Similarity
+ * FIXME: Transform ÷= Isometry
+ * Transform ÷= Rotation
+ * Transform ÷= UnitQuaternion
+ * FIXME: Transform ÷= UnitComplex
  *
  */
 
@@ -80,10 +78,9 @@ use geometry::{PointBase, OwnedPoint, TransformBase, OwnedTransform, TCategory,
  * Indexing.
  *
  */
-impl<N, D, S, C: TCategory> Index<(usize, usize)> for TransformBase<N, D, S, C>
-    where N: Scalar,
-          D: DimName + DimNameAdd<U1>,
-          S: Storage<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
+impl<N: Real, D, C: TCategory> Index<(usize, usize)> for Transform<N, D, C>
+    where D: DimName + DimNameAdd<U1>,
+          DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
     type Output = N;
 
     #[inline]
@@ -93,10 +90,9 @@ impl<N, D, S, C: TCategory> Index<(usize, usize)> for TransformBase<N, D, S, C>
 }
 
 // Only general transformations are mutably indexable.
-impl<N, D, S> IndexMut<(usize, usize)> for TransformBase<N, D, S, TGeneral>
-    where N: Scalar,
-          D: DimName + DimNameAdd<U1>,
-          S: StorageMut<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
+impl<N: Real, D> IndexMut<(usize, usize)> for Transform<N, D, TGeneral>
+    where D: DimName + DimNameAdd<U1>,
+          DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
     #[inline]
     fn index_mut(&mut self, ij: (usize, usize)) -> &mut N {
         self.matrix_mut().index_mut(ij)
@@ -104,14 +100,11 @@ impl<N, D, S> IndexMut<(usize, usize)> for TransformBase<N, D, S, TGeneral>
 }
 
 
-// TransformBase × ColumnVector
+// Transform × Vector
 md_impl_all!(
-    Mul, mul where N: Field;
-    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategory
-    where SA::Alloc: Allocator<N, D, D>
-    where SA::Alloc: Allocator<N, D, U1>
-    where SA::Alloc: Allocator<N, U1, D>;
-    self: TransformBase<N, D, SA, C>, rhs: ColumnVector<N, D, SB>, Output = OwnedColumnVector<N, D, SA::Alloc>;
+    Mul, mul where N: Real;
+    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategory;
+    self: Transform<N, D, C>, rhs: VectorN<N, D>, Output = VectorN<N, D>;
     [val val] => &self * &rhs;
     [ref val] =>  self * &rhs;
     [val ref] => &self *  rhs;
@@ -132,14 +125,12 @@ md_impl_all!(
 );
 
 
-// TransformBase × PointBase
+// Transform × Point
 md_impl_all!(
-    Mul, mul where N: Field;
+    Mul, mul where N: Real;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategory
-    where SA::Alloc: Allocator<N, D, D>
-    where SA::Alloc: Allocator<N, D, U1>
-    where SA::Alloc: Allocator<N, U1, D>;
-    self: TransformBase<N, D, SA, C>, rhs: PointBase<N, D, SB>, Output = OwnedPoint<N, D, SA::Alloc>;
+    where DefaultAllocator: Allocator<N, D, D>;
+    self: Transform<N, D, C>, rhs: Point<N, D>, Output = Point<N, D>;
     [val val] => &self * &rhs;
     [ref val] =>  self * &rhs;
     [val ref] => &self *  rhs;
@@ -161,11 +152,11 @@ md_impl_all!(
 );
 
 
-// TransformBase × TransformBase
+// Transform × Transform
 md_impl_all!(
-    Mul, mul;
+    Mul, mul where N: Real;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (DimNameSum<D, U1>, DimNameSum<D, U1>) for D: DimNameAdd<U1>, CA: TCategoryMul<CB>, CB: TCategory;
-    self: TransformBase<N, D, SA, CA>, rhs: TransformBase<N, D, SB, CB>, Output = OwnedTransform<N, D, SA::Alloc, CA::Representative>;
+    self: Transform<N, D, CA>, rhs: Transform<N, D, CB>, Output = Transform<N, D, CA::Representative>;
     [val val] => Self::Output::from_matrix_unchecked(self.unwrap() * rhs.unwrap());
     [ref val] => Self::Output::from_matrix_unchecked(self.matrix() * rhs.unwrap());
     [val ref] => Self::Output::from_matrix_unchecked(self.unwrap() * rhs.matrix());
@@ -173,12 +164,11 @@ md_impl_all!(
 );
 
 
-// TransformBase × RotationBase
+// Transform × Rotation
 md_impl_all!(
-    Mul, mul where N: One;
-    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, D) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>
-    where SB::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
-    self: TransformBase<N, D, SA, C>, rhs: RotationBase<N, D, SB>, Output = OwnedTransform<N, D, SA::Alloc, C::Representative>;
+    Mul, mul where N: Real;
+    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, D) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
+    self: Transform<N, D, C>, rhs: Rotation<N, D>, Output = Transform<N, D, C::Representative>;
     [val val] => Self::Output::from_matrix_unchecked(self.unwrap() * rhs.to_homogeneous());
     [ref val] => Self::Output::from_matrix_unchecked(self.matrix() * rhs.to_homogeneous());
     [val ref] => Self::Output::from_matrix_unchecked(self.unwrap() * rhs.to_homogeneous());
@@ -186,12 +176,11 @@ md_impl_all!(
 );
 
 
-// RotationBase × TransformBase
+// Rotation × Transform
 md_impl_all!(
-    Mul, mul where N: One;
-    (D, D), (DimNameSum<D, U1>, DimNameSum<D, U1>) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>
-    where SA::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
-    self: RotationBase<N, D, SA>, rhs: TransformBase<N, D, SB, C>, Output = OwnedTransform<N, D, SA::Alloc, C::Representative>;
+    Mul, mul where N: Real;
+    (D, D), (DimNameSum<D, U1>, DimNameSum<D, U1>) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
+    self: Rotation<N, D>, rhs: Transform<N, D, C>, Output = Transform<N, D, C::Representative>;
     [val val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.unwrap());
     [ref val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.unwrap());
     [val ref] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.matrix());
@@ -199,13 +188,11 @@ md_impl_all!(
 );
 
 
-// TransformBase × UnitQuaternionBase
+// Transform × UnitQuaternion
 md_impl_all!(
     Mul, mul where N: Real;
-    (U4, U4), (U4, U1) for C: TCategoryMul<TAffine>
-    where SB::Alloc: Allocator<N, U3, U3>
-    where SB::Alloc: Allocator<N, U4, U4>;
-    self: TransformBase<N, U3, SA, C>, rhs: UnitQuaternionBase<N, SB>, Output = OwnedTransform<N, U3, SA::Alloc, C::Representative>;
+    (U4, U4), (U4, U1) for C: TCategoryMul<TAffine>;
+    self: Transform<N, U3, C>, rhs: UnitQuaternion<N>, Output = Transform<N, U3, C::Representative>;
     [val val] => Self::Output::from_matrix_unchecked(self.unwrap() * rhs.to_homogeneous());
     [ref val] => Self::Output::from_matrix_unchecked(self.matrix() * rhs.to_homogeneous());
     [val ref] => Self::Output::from_matrix_unchecked(self.unwrap() * rhs.to_homogeneous());
@@ -213,13 +200,11 @@ md_impl_all!(
 );
 
 
-// UnitQuaternionBase × TransformBase
+// UnitQuaternion × Transform
 md_impl_all!(
     Mul, mul where N: Real;
-    (U4, U1), (U4, U4) for C: TCategoryMul<TAffine>
-    where SA::Alloc: Allocator<N, U3, U3>
-    where SA::Alloc: Allocator<N, U4, U4>;
-    self: UnitQuaternionBase<N, SA>, rhs: TransformBase<N, U3, SB, C>, Output = OwnedTransform<N, U3, SA::Alloc, C::Representative>;
+    (U4, U1), (U4, U4) for C: TCategoryMul<TAffine>;
+    self: UnitQuaternion<N>, rhs: Transform<N, U3, C>, Output = Transform<N, U3, C::Representative>;
     [val val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.unwrap());
     [ref val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.unwrap());
     [val ref] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.matrix());
@@ -228,26 +213,24 @@ md_impl_all!(
 
 
 
-// TransformBase × IsometryBase
+// Transform × Isometry
 md_impl_all!(
     Mul, mul where N: Real;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
-    for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<OwnedSquareMatrix<N, DimNameSum<D, U1>, SB::Alloc> >
-    where SB::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
-    self: TransformBase<N, D, SA, C>, rhs: IsometryBase<N, D, SB, R>, Output = OwnedTransform<N, D, SA::Alloc, C::Representative>;
+    for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
+    self: Transform<N, D, C>, rhs: Isometry<N, D, R>, Output = Transform<N, D, C::Representative>;
     [val val] => Self::Output::from_matrix_unchecked(self.unwrap() * rhs.to_homogeneous());
     [ref val] => Self::Output::from_matrix_unchecked(self.matrix() * rhs.to_homogeneous());
     [val ref] => Self::Output::from_matrix_unchecked(self.unwrap() * rhs.to_homogeneous());
     [ref ref] => Self::Output::from_matrix_unchecked(self.matrix() * rhs.to_homogeneous());
 );
 
-// IsometryBase × TransformBase
+// Isometry × Transform
 md_impl_all!(
     Mul, mul where N: Real;
     (D, U1), (DimNameSum<D, U1>, DimNameSum<D, U1>)
-    for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<OwnedSquareMatrix<N, DimNameSum<D, U1>, SA::Alloc> >
-    where SA::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
-    self: IsometryBase<N, D, SA, R>, rhs: TransformBase<N, D, SB, C>, Output = OwnedTransform<N, D, SA::Alloc, C::Representative>;
+    for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
+    self: Isometry<N, D, R>, rhs: Transform<N, D, C>, Output = Transform<N, D, C::Representative>;
     [val val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.unwrap());
     [ref val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.unwrap());
     [val ref] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.matrix());
@@ -255,28 +238,24 @@ md_impl_all!(
 );
 
 
-// TransformBase × SimilarityBase
+// Transform × Similarity
 md_impl_all!(
     Mul, mul where N: Real;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
-    for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<OwnedSquareMatrix<N, DimNameSum<D, U1>, SB::Alloc> >
-    where SB::Alloc: Allocator<N, D, D >
-    where SB::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
-    self: TransformBase<N, D, SA, C>, rhs: SimilarityBase<N, D, SB, R>, Output = OwnedTransform<N, D, SA::Alloc, C::Representative>;
+    for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
+    self: Transform<N, D, C>, rhs: Similarity<N, D, R>, Output = Transform<N, D, C::Representative>;
     [val val] => Self::Output::from_matrix_unchecked(self.unwrap() * rhs.to_homogeneous());
     [ref val] => Self::Output::from_matrix_unchecked(self.matrix() * rhs.to_homogeneous());
     [val ref] => Self::Output::from_matrix_unchecked(self.unwrap() * rhs.to_homogeneous());
     [ref ref] => Self::Output::from_matrix_unchecked(self.matrix() * rhs.to_homogeneous());
 );
 
-// SimilarityBase × TransformBase
+// Similarity × Transform
 md_impl_all!(
     Mul, mul where N: Real;
     (D, U1), (DimNameSum<D, U1>, DimNameSum<D, U1>)
-    for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<OwnedSquareMatrix<N, DimNameSum<D, U1>, SA::Alloc> >
-    where SA::Alloc: Allocator<N, D, D >
-    where SA::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
-    self: SimilarityBase<N, D, SA, R>, rhs: TransformBase<N, D, SB, C>, Output = OwnedTransform<N, D, SA::Alloc, C::Representative>;
+    for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
+    self: Similarity<N, D, R>, rhs: Transform<N, D, C>, Output = Transform<N, D, C::Representative>;
     [val val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.unwrap());
     [ref val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.unwrap());
     [val ref] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.matrix());
@@ -293,25 +272,23 @@ md_impl_all!(
  * `DimNameAdd` requirement).
  *
  */
-// TransformBase × TranslationBase
+// Transform × Translation
 md_impl_all!(
     Mul, mul where N: Real;
-    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>
-    where SB::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
-    self: TransformBase<N, D, SA, C>, rhs: TranslationBase<N, D, SB>, Output = OwnedTransform<N, D, SA::Alloc, C::Representative>;
+    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
+    self: Transform<N, D, C>, rhs: Translation<N, D>, Output = Transform<N, D, C::Representative>;
     [val val] => Self::Output::from_matrix_unchecked(self.unwrap() * rhs.to_homogeneous());
     [ref val] => Self::Output::from_matrix_unchecked(self.matrix() * rhs.to_homogeneous());
     [val ref] => Self::Output::from_matrix_unchecked(self.unwrap() * rhs.to_homogeneous());
     [ref ref] => Self::Output::from_matrix_unchecked(self.matrix() * rhs.to_homogeneous());
 );
 
-// TranslationBase × TransformBase
+// Translation × Transform
 md_impl_all!(
     Mul, mul where N: Real;
     (D, U1), (DimNameSum<D, U1>, DimNameSum<D, U1>)
-    for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>
-    where SA::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
-    self: TranslationBase<N, D, SA>, rhs: TransformBase<N, D, SB, C>, Output = OwnedTransform<N, D, SA::Alloc, C::Representative>;
+    for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
+    self: Translation<N, D>, rhs: Transform<N, D, C>, Output = Transform<N, D, C::Representative>;
     [val val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.unwrap());
     [ref val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.unwrap());
     [val ref] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.matrix());
@@ -320,23 +297,22 @@ md_impl_all!(
 
 
 
-// TransformBase ÷ TransformBase
+// Transform ÷ Transform
 md_impl_all!(
-    Div, div where N: ApproxEq, Field;
+    Div, div where N: Real;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (DimNameSum<D, U1>, DimNameSum<D, U1>) for D: DimNameAdd<U1>, CA: TCategoryMul<CB>, CB: SubTCategoryOf<TProjective>;
-    self: TransformBase<N, D, SA, CA>, rhs: TransformBase<N, D, SB, CB>, Output = OwnedTransform<N, D, SA::Alloc, CA::Representative>;
+    self: Transform<N, D, CA>, rhs: Transform<N, D, CB>, Output = Transform<N, D, CA::Representative>;
     [val val] => self * rhs.inverse();
     [ref val] => self * rhs.inverse();
     [val ref] => self * rhs.clone_owned().inverse();
     [ref ref] => self * rhs.clone_owned().inverse();
 );
 
-// TransformBase ÷ RotationBase
+// Transform ÷ Rotation
 md_impl_all!(
-    Div, div where N: One;
-    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, D) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>
-    where SB::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
-    self: TransformBase<N, D, SA, C>, rhs: RotationBase<N, D, SB>, Output = OwnedTransform<N, D, SA::Alloc, C::Representative>;
+    Div, div where N: Real;
+    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, D) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
+    self: Transform<N, D, C>, rhs: Rotation<N, D>, Output = Transform<N, D, C::Representative>;
     [val val] => self * rhs.inverse();
     [ref val] => self * rhs.inverse();
     [val ref] => self * rhs.inverse();
@@ -344,12 +320,11 @@ md_impl_all!(
 );
 
 
-// RotationBase ÷ TransformBase
+// Rotation ÷ Transform
 md_impl_all!(
-    Div, div where N: One;
-    (D, D), (DimNameSum<D, U1>, DimNameSum<D, U1>) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>
-    where SA::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
-    self: RotationBase<N, D, SA>, rhs: TransformBase<N, D, SB, C>, Output = OwnedTransform<N, D, SA::Alloc, C::Representative>;
+    Div, div where N: Real;
+    (D, D), (DimNameSum<D, U1>, DimNameSum<D, U1>) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
+    self: Rotation<N, D>, rhs: Transform<N, D, C>, Output = Transform<N, D, C::Representative>;
     [val val] => self.inverse() * rhs;
     [ref val] => self.inverse() * rhs;
     [val ref] => self.inverse() * rhs;
@@ -357,13 +332,11 @@ md_impl_all!(
 );
 
 
-// TransformBase ÷ UnitQuaternionBase
+// Transform ÷ UnitQuaternion
 md_impl_all!(
     Div, div where N: Real;
-    (U4, U4), (U4, U1) for C: TCategoryMul<TAffine>
-    where SB::Alloc: Allocator<N, U3, U3>
-    where SB::Alloc: Allocator<N, U4, U4>;
-    self: TransformBase<N, U3, SA, C>, rhs: UnitQuaternionBase<N, SB>, Output = OwnedTransform<N, U3, SA::Alloc, C::Representative>;
+    (U4, U4), (U4, U1) for C: TCategoryMul<TAffine>;
+    self: Transform<N, U3, C>, rhs: UnitQuaternion<N>, Output = Transform<N, U3, C::Representative>;
     [val val] => self * rhs.inverse();
     [ref val] => self * rhs.inverse();
     [val ref] => self * rhs.inverse();
@@ -371,13 +344,11 @@ md_impl_all!(
 );
 
 
-// UnitQuaternionBase ÷ TransformBase
+// UnitQuaternion ÷ Transform
 md_impl_all!(
     Div, div where N: Real;
-    (U4, U1), (U4, U4) for C: TCategoryMul<TAffine>
-    where SA::Alloc: Allocator<N, U3, U3>
-    where SA::Alloc: Allocator<N, U4, U4>;
-    self: UnitQuaternionBase<N, SA>, rhs: TransformBase<N, U3, SB, C>, Output = OwnedTransform<N, U3, SA::Alloc, C::Representative>;
+    (U4, U1), (U4, U4) for C: TCategoryMul<TAffine>;
+    self: UnitQuaternion<N>, rhs: Transform<N, U3, C>, Output = Transform<N, U3, C::Representative>;
     [val val] => self.inverse() * rhs;
     [ref val] => self.inverse() * rhs;
     [val ref] => self.inverse() * rhs;
@@ -386,26 +357,26 @@ md_impl_all!(
 
 
 
-//      // TransformBase ÷ IsometryBase
+//      // Transform ÷ Isometry
 //      md_impl_all!(
 //          Div, div where N: Real;
 //          (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
-//          for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<OwnedSquareMatrix<N, DimNameSum<D, U1>, SB::Alloc> >
+//          for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >
 //          where SB::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
-//          self: TransformBase<N, D, SA, C>, rhs: IsometryBase<N, D, SB, R>, Output = OwnedTransform<N, D, SA::Alloc, C::Representative>;
+//          self: Transform<N, D, C>, rhs: Isometry<N, D, R>, Output = Transform<N, D, C::Representative>;
 //          [val val] => Self::Output::from_matrix_unchecked(self.unwrap() * rhs.inverse().to_homogeneous());
 //          [ref val] => Self::Output::from_matrix_unchecked(self.matrix() * rhs.inverse().to_homogeneous());
 //          [val ref] => Self::Output::from_matrix_unchecked(self.unwrap() * rhs.inverse().to_homogeneous());
 //          [ref ref] => Self::Output::from_matrix_unchecked(self.matrix() * rhs.inverse().to_homogeneous());
 //      );
 
-//      // IsometryBase ÷ TransformBase
+//      // Isometry ÷ Transform
 //      md_impl_all!(
 //          Div, div where N: Real;
 //          (D, U1), (DimNameSum<D, U1>, DimNameSum<D, U1>)
-//          for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<OwnedSquareMatrix<N, DimNameSum<D, U1>, SA::Alloc> >
+//          for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >
 //          where SA::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
-//          self: IsometryBase<N, D, SA, R>, rhs: TransformBase<N, D, SB, C>, Output = OwnedTransform<N, D, SA::Alloc, C::Representative>;
+//          self: Isometry<N, D, R>, rhs: Transform<N, D, C>, Output = Transform<N, D, C::Representative>;
 //          [val val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.unwrap());
 //          [ref val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.unwrap());
 //          [val ref] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.matrix());
@@ -413,28 +384,28 @@ md_impl_all!(
 //      );
 
 
-//      // TransformBase ÷ SimilarityBase
+//      // Transform ÷ Similarity
 //      md_impl_all!(
 //          Div, div where N: Real;
 //          (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
-//          for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<OwnedSquareMatrix<N, DimNameSum<D, U1>, SB::Alloc> >
+//          for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >
 //          where SB::Alloc: Allocator<N, D, D >
 //          where SB::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
-//          self: TransformBase<N, D, SA, C>, rhs: SimilarityBase<N, D, SB, R>, Output = OwnedTransform<N, D, SA::Alloc, C::Representative>;
+//          self: Transform<N, D, C>, rhs: Similarity<N, D, R>, Output = Transform<N, D, C::Representative>;
 //          [val val] => Self::Output::from_matrix_unchecked(self.unwrap() * rhs.to_homogeneous());
 //          [ref val] => Self::Output::from_matrix_unchecked(self.matrix() * rhs.to_homogeneous());
 //          [val ref] => Self::Output::from_matrix_unchecked(self.unwrap() * rhs.to_homogeneous());
 //          [ref ref] => Self::Output::from_matrix_unchecked(self.matrix() * rhs.to_homogeneous());
 //      );
 
-//      // SimilarityBase ÷ TransformBase
+//      // Similarity ÷ Transform
 //      md_impl_all!(
 //          Div, div where N: Real;
 //          (D, U1), (DimNameSum<D, U1>, DimNameSum<D, U1>)
-//          for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<OwnedSquareMatrix<N, DimNameSum<D, U1>, SA::Alloc> >
+//          for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >
 //          where SA::Alloc: Allocator<N, D, D >
 //          where SA::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
-//          self: SimilarityBase<N, D, SA, R>, rhs: TransformBase<N, D, SB, C>, Output = OwnedTransform<N, D, SA::Alloc, C::Representative>;
+//          self: Similarity<N, D, R>, rhs: Transform<N, D, C>, Output = Transform<N, D, C::Representative>;
 //          [val val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.unwrap());
 //          [ref val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.unwrap());
 //          [val ref] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.matrix());
@@ -443,25 +414,23 @@ md_impl_all!(
 
 
 
-// TransformBase ÷ TranslationBase
+// Transform ÷ Translation
 md_impl_all!(
     Div, div where N: Real;
-    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>
-    where SB::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
-    self: TransformBase<N, D, SA, C>, rhs: TranslationBase<N, D, SB>, Output = OwnedTransform<N, D, SA::Alloc, C::Representative>;
+    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
+    self: Transform<N, D, C>, rhs: Translation<N, D>, Output = Transform<N, D, C::Representative>;
     [val val] => self * rhs.inverse();
     [ref val] => self * rhs.inverse();
     [val ref] => self * rhs.inverse();
     [ref ref] => self * rhs.inverse();
 );
 
-// TranslationBase ÷ TransformBase
+// Translation ÷ Transform
 md_impl_all!(
     Div, div where N: Real;
     (D, U1), (DimNameSum<D, U1>, DimNameSum<D, U1>)
-    for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>
-    where SA::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
-    self: TranslationBase<N, D, SA>, rhs: TransformBase<N, D, SB, C>, Output = OwnedTransform<N, D, SA::Alloc, C::Representative>;
+    for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
+    self: Translation<N, D>, rhs: Transform<N, D, C>, Output = Transform<N, D, C::Representative>;
     [val val] => self.inverse() * rhs;
     [ref val] => self.inverse() * rhs;
     [val ref] => self.inverse() * rhs;
@@ -469,36 +438,33 @@ md_impl_all!(
 );
 
 
-// TransformBase ×= TransformBase
+// Transform ×= Transform
 md_assign_impl_all!(
-    MulAssign, mul_assign;
+    MulAssign, mul_assign where N: Real;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (DimNameSum<D, U1>, DimNameSum<D, U1>) for D: DimNameAdd<U1>, CA: TCategory, CB: SubTCategoryOf<CA>;
-    self: TransformBase<N, D, SA, CA>, rhs: TransformBase<N, D, SB, CB>;
+    self: Transform<N, D, CA>, rhs: Transform<N, D, CB>;
     [val] => *self.matrix_mut_unchecked() *= rhs.unwrap();
     [ref] => *self.matrix_mut_unchecked() *= rhs.matrix();
 );
 
 
-// TransformBase ×= SimilarityBase
+// Transform ×= Similarity
 md_assign_impl_all!(
-    MulAssign, mul_assign;
+    MulAssign, mul_assign where N: Real;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
-    for D: DimNameAdd<U1>, C: TCategory, R: SubsetOf<OwnedSquareMatrix<N, DimNameSum<D, U1>, SB::Alloc> >
-    where SB::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >
-    where SB::Alloc: Allocator<N, D, D>;
-    self: TransformBase<N, D, SA, C>, rhs: SimilarityBase<N, D, SB, R>;
+    for D: DimNameAdd<U1>, C: TCategory, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
+    self: Transform<N, D, C>, rhs: Similarity<N, D, R>;
     [val] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
     [ref] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
 );
 
 
-// TransformBase ×= IsometryBase
+// Transform ×= Isometry
 md_assign_impl_all!(
-    MulAssign, mul_assign;
+    MulAssign, mul_assign where N: Real;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
-    for D: DimNameAdd<U1>, C: TCategory, R: SubsetOf<OwnedSquareMatrix<N, DimNameSum<D, U1>, SB::Alloc> >
-    where SB::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
-    self: TransformBase<N, D, SA, C>, rhs: IsometryBase<N, D, SB, R>;
+    for D: DimNameAdd<U1>, C: TCategory, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
+    self: Transform<N, D, C>, rhs: Isometry<N, D, R>;
     [val] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
     [ref] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
 );
@@ -511,105 +477,94 @@ md_assign_impl_all!(
  * `DimNameAdd` requirement).
  *
  */
-// TransformBase ×= TranslationBase
-md_assign_impl_all!(
-    MulAssign, mul_assign where N: One;
-    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategory
-    where SB::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
-    self: TransformBase<N, D, SA, C>, rhs: TranslationBase<N, D, SB>;
-    [val] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
-    [ref] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
-);
-
-
-// TransformBase ×= RotationBase
-md_assign_impl_all!(
-    MulAssign, mul_assign where N: One;
-    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, D) for D: DimNameAdd<U1>, C: TCategory
-    where SB::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
-    self: TransformBase<N, D, SA, C>, rhs: RotationBase<N, D, SB>;
-    [val] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
-    [ref] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
-);
-
-
-// TransformBase ×= UnitQuaternionBase
+// Transform ×= Translation
 md_assign_impl_all!(
     MulAssign, mul_assign where N: Real;
-    (U4, U4), (U4, U1) for C: TCategory
-    where SB::Alloc: Allocator<N, U3, U3>
-    where SB::Alloc: Allocator<N, U4, U4>;
-    self: TransformBase<N, U3, SA, C>, rhs: UnitQuaternionBase<N, SB>;
+    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategory;
+    self: Transform<N, D, C>, rhs: Translation<N, D>;
     [val] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
     [ref] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
 );
 
 
-// TransformBase ÷= TransformBase
+// Transform ×= Rotation
 md_assign_impl_all!(
-    DivAssign, div_assign where N: Field, ApproxEq;
+    MulAssign, mul_assign where N: Real;
+    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, D) for D: DimNameAdd<U1>, C: TCategory;
+    self: Transform<N, D, C>, rhs: Rotation<N, D>;
+    [val] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
+    [ref] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
+);
+
+
+// Transform ×= UnitQuaternion
+md_assign_impl_all!(
+    MulAssign, mul_assign where N: Real;
+    (U4, U4), (U4, U1) for C: TCategory;
+    self: Transform<N, U3, C>, rhs: UnitQuaternion<N>;
+    [val] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
+    [ref] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
+);
+
+
+// Transform ÷= Transform
+md_assign_impl_all!(
+    DivAssign, div_assign where N: Real;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (DimNameSum<D, U1>, DimNameSum<D, U1>)
     for D: DimNameAdd<U1>, CA: SuperTCategoryOf<CB>, CB: SubTCategoryOf<TProjective>;
-    self: TransformBase<N, D, SA, CA>, rhs: TransformBase<N, D, SB, CB>;
+    self: Transform<N, D, CA>, rhs: Transform<N, D, CB>;
     [val] => *self *= rhs.clone_owned().inverse();
     [ref] => *self *= rhs.clone_owned().inverse();
 );
 
 
-//      // TransformBase ÷= SimilarityBase
+//      // Transform ÷= Similarity
 //      md_assign_impl_all!(
 //          DivAssign, div_assign;
 //          (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
-//          for D: DimNameAdd<U1>, C: TCategory, R: SubsetOf<OwnedSquareMatrix<N, DimNameSum<D, U1>, SB::Alloc> >
-//          where SB::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >
-//          where SB::Alloc: Allocator<N, D, D>;
-//          self: TransformBase<N, D, SA, C>, rhs: SimilarityBase<N, D, SB, R>;
+//          for D: DimNameAdd<U1>, C: TCategory, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
+//          self: Transform<N, D, C>, rhs: Similarity<N, D, R>;
 //          [val] => *self *= rhs.inverse();
 //          [ref] => *self *= rhs.inverse();
 //      );
 //      
 //      
-//      // TransformBase ÷= IsometryBase
+//      // Transform ÷= Isometry
 //      md_assign_impl_all!(
 //          DivAssign, div_assign;
 //          (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
-//          for D: DimNameAdd<U1>, C: TCategory, R: SubsetOf<OwnedSquareMatrix<N, DimNameSum<D, U1>, SB::Alloc> >
-//          where SB::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
-//          self: TransformBase<N, D, SA, C>, rhs: IsometryBase<N, D, SB, R>;
+//          for D: DimNameAdd<U1>, C: TCategory, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
+//          self: Transform<N, D, C>, rhs: Isometry<N, D, R>;
 //          [val] => *self *= rhs.inverse();
 //          [ref] => *self *= rhs.inverse();
 //      );
 
 
-// TransformBase ÷= TranslationBase
-md_assign_impl_all!(
-    DivAssign, div_assign where N: One, ClosedNeg;
-    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategory
-    where SB::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
-    self: TransformBase<N, D, SA, C>, rhs: TranslationBase<N, D, SB>;
-    [val] => *self *= rhs.inverse();
-    [ref] => *self *= rhs.inverse();
-);
-
-
-// TransformBase ÷= RotationBase
-md_assign_impl_all!(
-    DivAssign, div_assign where N: One;
-    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, D) for D: DimNameAdd<U1>, C: TCategory
-    where SB::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
-    self: TransformBase<N, D, SA, C>, rhs: RotationBase<N, D, SB>;
-    [val] => *self *= rhs.inverse();
-    [ref] => *self *= rhs.inverse();
-);
-
-
-// TransformBase ÷= UnitQuaternionBase
+// Transform ÷= Translation
 md_assign_impl_all!(
     DivAssign, div_assign where N: Real;
-    (U4, U4), (U4, U1) for C: TCategory
-    where SB::Alloc: Allocator<N, U3, U3>
-    where SB::Alloc: Allocator<N, U4, U4>;
-    self: TransformBase<N, U3, SA, C>, rhs: UnitQuaternionBase<N, SB>;
+    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategory;
+    self: Transform<N, D, C>, rhs: Translation<N, D>;
+    [val] => *self *= rhs.inverse();
+    [ref] => *self *= rhs.inverse();
+);
+
+
+// Transform ÷= Rotation
+md_assign_impl_all!(
+    DivAssign, div_assign where N: Real;
+    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, D) for D: DimNameAdd<U1>, C: TCategory;
+    self: Transform<N, D, C>, rhs: Rotation<N, D>;
+    [val] => *self *= rhs.inverse();
+    [ref] => *self *= rhs.inverse();
+);
+
+
+// Transform ÷= UnitQuaternion
+md_assign_impl_all!(
+    DivAssign, div_assign where N: Real;
+    (U4, U4), (U4, U1) for C: TCategory;
+    self: Transform<N, U3, C>, rhs: UnitQuaternion<N>;
     [val] => *self *= rhs.inverse();
     [ref] => *self *= rhs.inverse();
 );

src/geometry/translation.rs

@@ -1,114 +1,124 @@
 use num::{Zero, One};
+use std::hash;
 use std::fmt;
 use approx::ApproxEq;
 
 #[cfg(feature = "serde-serialize")]
-use serde::{Serialize, Serializer, Deserialize, Deserializer};
+use serde;
 
 use alga::general::{Real, ClosedNeg};
 
-use core::{Scalar, ColumnVector, OwnedSquareMatrix};
+use core::{DefaultAllocator, Scalar, MatrixN, VectorN};
 use core::dimension::{DimName, DimNameSum, DimNameAdd, U1};
-use core::storage::{Storage, StorageMut, Owned};
+use core::storage::Owned;
 use core::allocator::Allocator;
 
-/// A translation with an owned vector storage.
-pub type OwnedTranslation<N, D, S> = TranslationBase<N, D, Owned<N, D, U1, <S as Storage<N, D, U1>>::Alloc>>;
-
 /// A translation.
 #[repr(C)]
-#[derive(Hash, Debug, Clone, Copy)]
-pub struct TranslationBase<N: Scalar, D: DimName, S/*: Storage<N, D, U1>*/> {
+#[derive(Debug)]
+pub struct Translation<N: Scalar, D: DimName>
+    where DefaultAllocator: Allocator<N, D> {
     /// The translation coordinates, i.e., how much is added to a point's coordinates when it is
     /// translated.
-    pub vector: ColumnVector<N, D, S>
+    pub vector: VectorN<N, D>
+}
+
+impl<N: Scalar + hash::Hash, D: DimName + hash::Hash> hash::Hash for Translation<N, D>
+    where DefaultAllocator: Allocator<N, D>,
+          Owned<N, D>: hash::Hash {
+    fn hash<H: hash::Hasher>(&self, state: &mut H) {
+        self.vector.hash(state)
+    }
+}
+
+impl<N: Scalar, D: DimName> Copy for Translation<N, D>
+    where DefaultAllocator: Allocator<N, D>,
+          Owned<N, D>: Copy { }
+
+impl<N: Scalar, D: DimName> Clone for Translation<N, D>
+    where DefaultAllocator: Allocator<N, D>,
+          Owned<N, D>: Clone {
+    #[inline]
+    fn clone(&self) -> Self {
+        Translation::from_vector(self.vector.clone())
+    }
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<N, D, S> Serialize for TranslationBase<N, D, S>
-    where N: Scalar,
-          D: DimName,
-          ColumnVector<N, D, S>: Serialize,
-{
-    fn serialize<T>(&self, serializer: T) -> Result<T::Ok, T::Error>
-        where T: Serializer
-    {
+impl<N: Scalar, D: DimName> serde::Serialize for Translation<N, D>
+where DefaultAllocator: Allocator<N, D>,
+      Owned<N, D>: serde::Serialize {
+
+    fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
+        where S: serde::Serializer {
             self.vector.serialize(serializer)
         }
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<'de, N, D, S> Deserialize<'de> for TranslationBase<N, D, S>
-    where N: Scalar,
-          D: DimName,
-          ColumnVector<N, D, S>: Deserialize<'de>,
-{
-    fn deserialize<T>(deserializer: T) -> Result<Self, T::Error>
-        where T: Deserializer<'de>
-    {
-        ColumnVector::deserialize(deserializer).map(|x| TranslationBase { vector: x })
+impl<'a, N: Scalar, D: DimName> serde::Deserialize<'a> for Translation<N, D>
+where DefaultAllocator: Allocator<N, D>,
+      Owned<N, D>: serde::Deserialize<'a> {
+
+    fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
+        where Des: serde::Deserializer<'a> {
+            let matrix = VectorN::<N, D>::deserialize(deserializer)?;
+
+            Ok(Translation::from_vector(matrix))
         }
 }
 
-impl<N, D: DimName, S> TranslationBase<N, D, S>
-    where N: Scalar,
-          S: Storage<N, D, U1> {
+impl<N: Scalar, D: DimName> Translation<N, D>
+    where DefaultAllocator: Allocator<N, D> {
     /// Creates a new translation from the given vector.
     #[inline]
-    pub fn from_vector(vector: ColumnVector<N, D, S>) -> TranslationBase<N, D, S> {
-        TranslationBase {
+    pub fn from_vector(vector: VectorN<N, D>) -> Translation<N, D> {
+        Translation {
             vector: vector
         }
     }
 
     /// Inverts `self`.
     #[inline]
-    pub fn inverse(&self) -> OwnedTranslation<N, D, S>
+    pub fn inverse(&self) -> Translation<N, D>
         where N: ClosedNeg {
-        TranslationBase::from_vector(-&self.vector)
+        Translation::from_vector(-&self.vector)
     }
 
     /// Converts this translation into its equivalent homogeneous transformation matrix.
     #[inline]
-    pub fn to_homogeneous(&self) -> OwnedSquareMatrix<N, DimNameSum<D, U1>, S::Alloc>
+    pub fn to_homogeneous(&self) -> MatrixN<N, DimNameSum<D, U1>>
         where N: Zero + One,
               D: DimNameAdd<U1>,
-              S::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
-        let mut res = OwnedSquareMatrix::<N, _, S::Alloc>::identity();
+              DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> {
+        let mut res = MatrixN::<N, DimNameSum<D, U1>>::identity();
         res.fixed_slice_mut::<D, U1>(0, D::dim()).copy_from(&self.vector);
 
         res
     }
-}
 
-
-impl<N, D: DimName, S> TranslationBase<N, D, S>
-    where N: Scalar + ClosedNeg,
-          S: StorageMut<N, D, U1> {
     /// Inverts `self` in-place.
     #[inline]
-    pub fn inverse_mut(&mut self) {
+    pub fn inverse_mut(&mut self)
+        where N: ClosedNeg {
         self.vector.neg_mut()
     }
 }
 
-impl<N, D: DimName, S> Eq for TranslationBase<N, D, S>
-    where N: Scalar + Eq,
-          S: Storage<N, D, U1> {
+impl<N: Scalar + Eq, D: DimName> Eq for Translation<N, D>
+    where DefaultAllocator: Allocator<N, D> {
 }
 
-impl<N, D: DimName, S> PartialEq for TranslationBase<N, D, S>
-    where N: Scalar + PartialEq,
-          S: Storage<N, D, U1> {
+impl<N: Scalar + PartialEq, D: DimName> PartialEq for Translation<N, D>
+    where DefaultAllocator: Allocator<N, D> {
     #[inline]
-    fn eq(&self, right: &TranslationBase<N, D, S>) -> bool {
+    fn eq(&self, right: &Translation<N, D>) -> bool {
         self.vector == right.vector
     }
 }
 
-impl<N, D: DimName, S> ApproxEq for TranslationBase<N, D, S>
-    where N: Scalar + ApproxEq,
-          S: Storage<N, D, U1>,
+impl<N: Scalar + ApproxEq, D: DimName> ApproxEq for Translation<N, D>
+    where DefaultAllocator: Allocator<N, D>,
           N::Epsilon: Copy {
     type Epsilon = N::Epsilon;
 
@@ -143,31 +153,14 @@ impl<N, D: DimName, S> ApproxEq for TranslationBase<N, D, S>
  * Display
  *
  */
-impl<N, D: DimName, S> fmt::Display for TranslationBase<N, D, S>
-    where N: Real + fmt::Display,
-          S: Storage<N, D, U1>,
-          S::Alloc: Allocator<usize, D, U1> {
+impl<N: Real + fmt::Display, D: DimName> fmt::Display for Translation<N, D>
+    where DefaultAllocator: Allocator<N, D> +
+                            Allocator<usize, D> {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         let precision = f.precision().unwrap_or(3);
 
-        try!(writeln!(f, "TranslationBase {{"));
+        try!(writeln!(f, "Translation {{"));
         try!(write!(f, "{:.*}", precision, self.vector));
         writeln!(f, "}}")
     }
 }
-
-
-//          //         /*
-//          //          *
-//          //          * Absolute
-//          //          *
-//          //          */
-//          //         impl<N: Absolute> Absolute for $t<N> {
-//          //             type AbsoluteValue = $submatrix<N::AbsoluteValue>;
-//          //
-//          //             #[inline]
-//          //             fn abs(m: &$t<N>) -> $submatrix<N::AbsoluteValue> {
-//          //                 Absolute::abs(&m.submatrix)
-//          //             }
-//          //         }
-//          */

src/geometry/translation_alga.rs

@@ -1,14 +1,14 @@
 use alga::general::{AbstractMagma, AbstractGroup, AbstractLoop, AbstractMonoid, AbstractQuasigroup,
                     AbstractSemigroup, Real, Inverse, Multiplicative, Identity, Id};
 use alga::linear::{Transformation, ProjectiveTransformation, Similarity, AffineTransformation,
-                   Isometry, DirectIsometry, Translation};
+                   Isometry, DirectIsometry};
+use alga::linear::Translation as AlgaTranslation;
 
-use core::ColumnVector;
-use core::dimension::{DimName, U1};
-use core::storage::OwnedStorage;
-use core::allocator::OwnedAllocator;
+use core::{DefaultAllocator, VectorN};
+use core::dimension::DimName;
+use core::allocator::Allocator;
 
-use geometry::{TranslationBase, PointBase};
+use geometry::{Translation, Point};
 
 
 /*
@@ -16,20 +16,16 @@ use geometry::{TranslationBase, PointBase};
  * Algebraic structures.
  *
  */
-impl<N, D: DimName, S> Identity<Multiplicative> for TranslationBase<N, D, S>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName> Identity<Multiplicative> for Translation<N, D>
+    where DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn identity() -> Self {
         Self::identity()
     }
 }
 
-impl<N, D: DimName, S> Inverse<Multiplicative> for TranslationBase<N, D, S>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName> Inverse<Multiplicative> for Translation<N, D>
+    where DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn inverse(&self) -> Self {
         self.inverse()
@@ -41,10 +37,8 @@ impl<N, D: DimName, S> Inverse<Multiplicative> for TranslationBase<N, D, S>
     }
 }
 
-impl<N, D: DimName, S> AbstractMagma<Multiplicative> for TranslationBase<N, D, S>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName> AbstractMagma<Multiplicative> for Translation<N, D>
+    where DefaultAllocator: Allocator<N, D> {
     #[inline]
     fn operate(&self, rhs: &Self) -> Self {
         self * rhs
@@ -53,10 +47,8 @@ impl<N, D: DimName, S> AbstractMagma<Multiplicative> for TranslationBase<N, D, S
 
 macro_rules! impl_multiplicative_structures(
     ($($marker: ident<$operator: ident>),* $(,)*) => {$(
-        impl<N, D: DimName, S> $marker<$operator> for TranslationBase<N, D, S>
-            where N: Real,
-                  S: OwnedStorage<N, D, U1>,
-                  S::Alloc: OwnedAllocator<N, D, U1, S> { }
+        impl<N: Real, D: DimName> $marker<$operator> for Translation<N, D>
+            where DefaultAllocator: Allocator<N, D> { }
     )*}
 );
 
@@ -73,40 +65,34 @@ impl_multiplicative_structures!(
  * Transformation groups.
  *
  */
-impl<N, D: DimName, S> Transformation<PointBase<N, D, S>> for TranslationBase<N, D, S>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName> Transformation<Point<N, D>> for Translation<N, D>
+    where DefaultAllocator: Allocator<N, D> {
     #[inline]
-    fn transform_point(&self, pt: &PointBase<N, D, S>) -> PointBase<N, D, S> {
+    fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
         pt + &self.vector
     }
 
     #[inline]
-    fn transform_vector(&self, v: &ColumnVector<N, D, S>) -> ColumnVector<N, D, S> {
+    fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
         v.clone()
     }
 }
 
-impl<N, D: DimName, S> ProjectiveTransformation<PointBase<N, D, S>> for TranslationBase<N, D, S>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName> ProjectiveTransformation<Point<N, D>> for Translation<N, D>
+    where DefaultAllocator: Allocator<N, D> {
     #[inline]
-    fn inverse_transform_point(&self, pt: &PointBase<N, D, S>) -> PointBase<N, D, S> {
+    fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
         pt - &self.vector
     }
 
     #[inline]
-    fn inverse_transform_vector(&self, v: &ColumnVector<N, D, S>) -> ColumnVector<N, D, S> {
+    fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
         v.clone()
     }
 }
 
-impl<N, D: DimName, S> AffineTransformation<PointBase<N, D, S>> for TranslationBase<N, D, S>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName> AffineTransformation<Point<N, D>> for Translation<N, D>
+    where DefaultAllocator: Allocator<N, D> {
     type Rotation          = Id;
     type NonUniformScaling = Id;
     type Translation       = Self;
@@ -148,10 +134,9 @@ impl<N, D: DimName, S> AffineTransformation<PointBase<N, D, S>> for TranslationB
 }
 
 
-impl<N, D: DimName, S> Similarity<PointBase<N, D, S>> for TranslationBase<N, D, S>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName> Similarity<Point<N, D>> for Translation<N, D>
+    where DefaultAllocator: Allocator<N, D> {
+
     type Scaling = Id;
 
     #[inline]
@@ -172,10 +157,8 @@ impl<N, D: DimName, S> Similarity<PointBase<N, D, S>> for TranslationBase<N, D,
 
 macro_rules! marker_impl(
     ($($Trait: ident),*) => {$(
-        impl<N, D: DimName, S> $Trait<PointBase<N, D, S>> for TranslationBase<N, D, S>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> { }
+        impl<N: Real, D: DimName> $Trait<Point<N, D>> for Translation<N, D>
+            where DefaultAllocator: Allocator<N, D> { }
     )*}
 );
 
@@ -183,17 +166,15 @@ marker_impl!(Isometry, DirectIsometry);
 
 
 /// Subgroups of the n-dimensional translation group `T(n)`.
-impl<N, D: DimName, S> Translation<PointBase<N, D, S>> for TranslationBase<N, D, S>
-    where N: Real,
-          S: OwnedStorage<N, D, U1>,
-          S::Alloc: OwnedAllocator<N, D, U1, S> {
+impl<N: Real, D: DimName> AlgaTranslation<Point<N, D>> for Translation<N, D>
+    where DefaultAllocator: Allocator<N, D> {
     #[inline]
-    fn to_vector(&self) -> ColumnVector<N, D, S> {
+    fn to_vector(&self) -> VectorN<N, D> {
         self.vector.clone()
     }
 
     #[inline]
-    fn from_vector(v: ColumnVector<N, D, S>) -> Option<Self> {
+    fn from_vector(v: VectorN<N, D>) -> Option<Self> {
         Some(Self::from_vector(v))
     }
 
@@ -203,7 +184,7 @@ impl<N, D: DimName, S> Translation<PointBase<N, D, S>> for TranslationBase<N, D,
     }
 
     #[inline]
-    fn translation_between(a: &PointBase<N, D, S>, b: &PointBase<N, D, S>) -> Option<Self> {
+    fn translation_between(a: &Point<N, D>, b: &Point<N, D>) -> Option<Self> {
         Some(Self::from_vector(b - a))
     }
 }