Merge pull request #187 from sebcrozet/full_names

Use full names for everything.

.travis.yml

@@ -3,5 +3,5 @@ language: rust
 script:
     - rustc --version
     - cargo --version
-    - cargo build --verbose
+    - cargo build --verbose --features "arbitrary generic_sizes"
     - cargo test --verbose --features arbitrary

CHANGELOG.md

@@ -4,13 +4,27 @@ documented here.
 
 This project adheres to [Semantic Versioning](http://semver.org/).
 
+## [0.8.0]
+## Modified
+  * Almost everything (types, methods, and traits) now use full names instead
+    of abbreviations (e.g. `Vec3` becomes `Vector3`). Most changes are abvious.
+    Note however that:
+    - `::sqnorm` becomes `::norm_squared`.
+    - `::sqdist` becomes `::distance_squared`.
+    - `::abs`, `::min`, etc. did not change as this is a common name for
+      absolute values on, e.g., the libc.
+    - Dynamically sized structures keep the `D` prefix, e.g., `DMat` becomes
+      `DMatrix`.
+  * All files with abbreviated names have been renamed to their full version,
+    e.g., `vec.rs` becomes `vector.rs`.
+
 ## [0.7.0]
 ### Added
   * Added implementation of assignement operators (+=, -=, etc.) for
     everything.
 ### Modified
   * Points and vectors are now linked to each other with associated types
-    (on the PntAsVec trait).
+    (on the PointAsVector trait).
 
 
 ## [0.6.0]
@@ -20,22 +34,22 @@ you [there](http://users.nphysics.org)!
 ### Added
   * Added a dependency to [generic-array](https://crates.io/crates/generic-array). Feature-gated:
     requires `features="generic_sizes"`.
-  * Added statically sized vectors with user-defined sizes: `VecN`. Feature-gated: requires
+  * Added statically sized vectors with user-defined sizes: `VectorN`. Feature-gated: requires
     `features="generic_sizes"`.
   * Added similarity transformations (an uniform scale followed by a rotation followed by a
-    translation): `Sim2`, `Sim3`.
+    translation): `Similarity2`, `Similarity3`.
 
 ### Removed
-  * Removed zero-sized elements `Vec0`, `Pnt0`.
+  * Removed zero-sized elements `Vector0`, `Point0`.
-  * Removed 4-dimensional transformations `Rot4` and `Iso4` (which had an implementation to incomplete to be useful).
+  * Removed 4-dimensional transformations `Rotation4` and `Isometry4` (which had an implementation to incomplete to be useful).
 
 ### Modified
   * Vectors are now multipliable with isometries. This will result into a pure rotation (this is how
   vectors differ from point semantically: they design directions so they are not translatable).
-  * `{Iso3, Rot3}::look_at` reimplemented and renamed to `::look_at_rh` and `::look_at_lh` to agree
+  * `{Isometry3, Rotation3}::look_at` reimplemented and renamed to `::look_at_rh` and `::look_at_lh` to agree
   with the computer graphics community (in particular, the GLM library). Use the `::look_at_rh`
   variant to build a view matrix that
   may be successfully used with `Persp` and `Ortho`.
-  * The old `{Iso3, Rot3}::look_at` implementations are now called `::new_observer_frame`.
+  * The old `{Isometry3, Rotation3}::look_at` implementations are now called `::new_observer_frame`.
   * Rename every `fov` on `Persp` to `fovy`.
   * Fixed the perspective and orthographic projection matrices.

Makefile

@@ -1,16 +1,19 @@
 tmp=_git_distcheck
 
 all:
-	cargo build --release --features arbitrary
+	cargo build --release --features "arbitrary generic_sizes"
 
 test:
-	cargo test
+	cargo test --features "arbitrary generic_sizes"
+
 
 bench:
-	cargo bench
+	cargo bench --features "arbitrary generic_sizes"
+
 
 doc:
-	cargo doc --no-deps
+	cargo doc --no-deps --features "arbitrary generic_sizes"
+
 
 clean:
 	cargo clean

README.md

@@ -16,22 +16,22 @@ All the functionality of **nalgebra** is grouped in one place: the root module `
 module re-exports everything and includes free functions for all traits methods performing
 out-of-place operations.
 
-* You can import the whole prelude using:
+Thus, you can import the whole prelude using:
 
 ```.ignore
 use nalgebra::*;
 ```
 
-The preferred way to use **nalgebra** is to import types and traits explicitly, and call
+However, the recommended way to use **nalgebra** is to import types and traits
-free-functions using the `na::` prefix:
+explicitly, and call free-functions using the `na::` prefix:
 
 ```.rust
 extern crate nalgebra as na;
-use na::{Vec3, Rot3, Rotation};
+use na::{Vector3, Rotation3, Rotation};
 
 fn main() {
-    let     a = Vec3::new(1.0f64, 1.0, 1.0);
+    let     a = Vector3::new(1.0f64, 1.0, 1.0);
-    let mut b = Rot3::new(na::zero());
+    let mut b = Rotation3::new(na::zero());
 
     b.append_rotation_mut(&a);
 
@@ -44,17 +44,17 @@ fn main() {
 **nalgebra** is meant to be a general-purpose, low-dimensional, linear algebra library, with
 an optimized set of tools for computer graphics and physics. Those features include:
 
-* Vectors with predefined static sizes: `Vec1`, `Vec2`, `Vec3`, `Vec4`, `Vec5`, `Vec6`.
+* Vectors with predefined static sizes: `Vector1`, `Vector2`, `Vector3`, `Vector4`, `Vector5`, `Vector6`.
-* Vector with a user-defined static size: `VecN` (available only with the `generic_sizes` feature).
+* Vector with a user-defined static size: `VectorN` (available only with the `generic_sizes` feature).
-* Points with static sizes: `Pnt1`, `Pnt2`, `Pnt3`, `Pnt4`, `Pnt5`, `Pnt6`.
+* Points with static sizes: `Point1`, `Point2`, `Point3`, `Point4`, `Point5`, `Point6`.
-* Square matrices with static sizes: `Mat1`, `Mat2`, `Mat3`, `Mat4`, `Mat5`, `Mat6 `.
+* Square matrices with static sizes: `Matrix1`, `Matrix2`, `Matrix3`, `Matrix4`, `Matrix5`, `Matrix6 `.
-* Rotation matrices: `Rot2`, `Rot3`
+* Rotation matrices: `Rotation2`, `Rotation3`
-* Quaternions: `Quat`, `UnitQuat`.
+* Quaternions: `Quaternion`, `UnitQuaternion`.
-* Isometries (translation ⨯ rotation): `Iso2`, `Iso3`
+* Isometrymetries (translation ⨯ rotation): `Isometry2`, `Isometry3`
-* Similarity transformations (translation ⨯ rotation ⨯ uniform scale): `Sim2`, `Sim3`.
+* Similarity transformations (translation ⨯ rotation ⨯ uniform scale): `Similarity2`, `Similarity3`.
-* 3D projections for computer graphics: `Persp3`, `PerspMat3`, `Ortho3`, `OrthoMat3`.
+* 3D projections for computer graphics: `Persp3`, `PerspMatrix3`, `Ortho3`, `OrthoMatrix3`.
-* Dynamically sized heap-allocated vector: `DVec`.
+* Dynamically sized heap-allocated vector: `DVector`.
-* Dynamically sized stack-allocated vectors with a maximum size: `DVec1` to `DVec6`.
+* Dynamically sized stack-allocated vectors with a maximum size: `DVector1` to `DVector6`.
-* Dynamically sized heap-allocated (square or rectangular) matrix: `DMat`.
+* Dynamically sized heap-allocated (square or rectangular) matrix: `DMatrix`.
-* Linear algebra and data analysis operators: `Cov`, `Mean`, `qr`, `cholesky`.
+* Linear algebra and data analysis operators: `Covariance`, `Mean`, `qr`, `cholesky`.
 * Almost one trait per functionality: useful for generic programming.

benches/construction.rs

@@ -6,14 +6,14 @@ extern crate nalgebra as na;
 
 use rand::{IsaacRng, Rng};
 use test::Bencher;
-use na::{UnitQuat, Rot2, Rot3, Vec1, Vec3};
+use na::{UnitQuaternion, Rotation2, Rotation3, Vector1, Vector3};
 
 #[path="common/macros.rs"]
 mod macros;
 
-bench_construction!(_bench_quat_from_axisangle, UnitQuat::new, axisangle: Vec3<f32>);
+bench_construction!(_bench_quaternion_from_axisangle, UnitQuaternion::new, axisangle: Vector3<f32>);
-bench_construction!(_bench_rot2_from_axisangle, Rot2::new, axisangle: Vec1<f32>);
+bench_construction!(_bench_rot2_from_axisangle, Rotation2::new, axisangle: Vector1<f32>);
-bench_construction!(_bench_rot3_from_axisangle, Rot3::new, axisangle: Vec3<f32>);
+bench_construction!(_bench_rot3_from_axisangle, Rotation3::new, axisangle: Vector3<f32>);
 
-bench_construction!(_bench_quat_from_euler_angles, UnitQuat::new_with_euler_angles, roll: f32, pitch: f32, yaw: f32);
+bench_construction!(_bench_quaternion_from_euler_angles, UnitQuaternion::new_with_euler_angles, roll: f32, pitch: f32, yaw: f32);
-bench_construction!(_bench_rot3_from_euler_angles, Rot3::new_with_euler_angles, roll: f32, pitch: f32, yaw: f32);
+bench_construction!(_bench_rot3_from_euler_angles, Rotation3::new_with_euler_angles, roll: f32, pitch: f32, yaw: f32);

benches/dmat.rs

@@ -4,14 +4,14 @@ extern crate test;
 extern crate nalgebra as na;
 
 use test::Bencher;
-use na::{DVec, DMat};
+use na::{DVector, DMatrix};
 
-macro_rules! bench_mul_dmat(
+macro_rules! bench_mul_dmatrix(
     ($bh: expr, $nrows: expr, $ncols: expr) => {
         {
             $bh.iter(|| {
-                let a:     DMat<f64> = DMat::new_random($nrows, $ncols);
+                let a:     DMatrix<f64> = DMatrix::new_random($nrows, $ncols);
-                let mut b: DMat<f64> = DMat::new_random($nrows, $ncols);
+                let mut b: DMatrix<f64> = DMatrix::new_random($nrows, $ncols);
 
                 for _ in 0usize .. 1000 {
                     // XXX: the clone here is highly undesirable!
@@ -24,36 +24,36 @@ macro_rules! bench_mul_dmat(
 
 #[bench]
 fn bench_mul_dmat2(bh: &mut Bencher) {
-    bench_mul_dmat!(bh, 2, 2);
+    bench_mul_dmatrix!(bh, 2, 2);
 }
 
 #[bench]
 fn bench_mul_dmat3(bh: &mut Bencher) {
-    bench_mul_dmat!(bh, 3, 3);
+    bench_mul_dmatrix!(bh, 3, 3);
 }
 
 #[bench]
 fn bench_mul_dmat4(bh: &mut Bencher) {
-    bench_mul_dmat!(bh, 4, 4);
+    bench_mul_dmatrix!(bh, 4, 4);
 }
 
 #[bench]
 fn bench_mul_dmat5(bh: &mut Bencher) {
-    bench_mul_dmat!(bh, 5, 5);
+    bench_mul_dmatrix!(bh, 5, 5);
 }
 
 #[bench]
 fn bench_mul_dmat6(bh: &mut Bencher) {
-    bench_mul_dmat!(bh, 6, 6);
+    bench_mul_dmatrix!(bh, 6, 6);
 }
 
-macro_rules! bench_mul_dmat_dvec(
+macro_rules! bench_mul_dmat_dvector(
     ($bh: expr, $nrows: expr, $ncols: expr) => {
         {
 
             $bh.iter(|| {
-                let m : DMat<f64>     = DMat::new_random($nrows, $ncols);
+                let m : DMatrix<f64>     = DMatrix::new_random($nrows, $ncols);
-                let mut v : DVec<f64> = DVec::new_random($ncols);
+                let mut v : DVector<f64> = DVector::new_random($ncols);
 
                 for _ in 0usize .. 1000 {
                     // XXX: the clone here is highly undesirable!
@@ -66,25 +66,25 @@ macro_rules! bench_mul_dmat_dvec(
 
 #[bench]
 fn bench_mul_dmat_dvec2(bh: &mut Bencher) {
-    bench_mul_dmat_dvec!(bh, 2, 2);
+    bench_mul_dmat_dvector!(bh, 2, 2);
 }
 
 #[bench]
 fn bench_mul_dmat_dvec3(bh: &mut Bencher) {
-    bench_mul_dmat_dvec!(bh, 3, 3);
+    bench_mul_dmat_dvector!(bh, 3, 3);
 }
 
 #[bench]
 fn bench_mul_dmat_dvec4(bh: &mut Bencher) {
-    bench_mul_dmat_dvec!(bh, 4, 4);
+    bench_mul_dmat_dvector!(bh, 4, 4);
 }
 
 #[bench]
 fn bench_mul_dmat_dvec5(bh: &mut Bencher) {
-    bench_mul_dmat_dvec!(bh, 5, 5);
+    bench_mul_dmat_dvector!(bh, 5, 5);
 }
 
 #[bench]
 fn bench_mul_dmat_dvec6(bh: &mut Bencher) {
-    bench_mul_dmat_dvec!(bh, 6, 6);
+    bench_mul_dmat_dvector!(bh, 6, 6);
 }

benches/mat.rs

@@ -6,40 +6,40 @@ extern crate nalgebra as na;
 
 use rand::{IsaacRng, Rng};
 use test::Bencher;
-use na::{Vec2, Vec3, Vec4, Mat2, Mat3, Mat4};
+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, Mat2<f32>, Mat2<f32>, mul);
+bench_binop!(_bench_mat2_mul_m, Matrix2<f32>, Matrix2<f32>, mul);
-bench_binop!(_bench_mat3_mul_m, Mat3<f32>, Mat3<f32>, mul);
+bench_binop!(_bench_mat3_mul_m, Matrix3<f32>, Matrix3<f32>, mul);
-bench_binop!(_bench_mat4_mul_m, Mat4<f32>, Mat4<f32>, mul);
+bench_binop!(_bench_mat4_mul_m, Matrix4<f32>, Matrix4<f32>, mul);
 
-bench_binop!(_bench_mat2_add_m, Mat2<f32>, Mat2<f32>, add);
+bench_binop!(_bench_mat2_add_m, Matrix2<f32>, Matrix2<f32>, add);
-bench_binop!(_bench_mat3_add_m, Mat3<f32>, Mat3<f32>, add);
+bench_binop!(_bench_mat3_add_m, Matrix3<f32>, Matrix3<f32>, add);
-bench_binop!(_bench_mat4_add_m, Mat4<f32>, Mat4<f32>, add);
+bench_binop!(_bench_mat4_add_m, Matrix4<f32>, Matrix4<f32>, add);
 
-bench_binop!(_bench_mat2_sub_m, Mat2<f32>, Mat2<f32>, sub);
+bench_binop!(_bench_mat2_sub_m, Matrix2<f32>, Matrix2<f32>, sub);
-bench_binop!(_bench_mat3_sub_m, Mat3<f32>, Mat3<f32>, sub);
+bench_binop!(_bench_mat3_sub_m, Matrix3<f32>, Matrix3<f32>, sub);
-bench_binop!(_bench_mat4_sub_m, Mat4<f32>, Mat4<f32>, sub);
+bench_binop!(_bench_mat4_sub_m, Matrix4<f32>, Matrix4<f32>, sub);
 
-bench_binop!(_bench_mat2_mul_v, Mat2<f32>, Vec2<f32>, mul);
+bench_binop!(_bench_mat2_mul_v, Matrix2<f32>, Vector2<f32>, mul);
-bench_binop!(_bench_mat3_mul_v, Mat3<f32>, Vec3<f32>, mul);
+bench_binop!(_bench_mat3_mul_v, Matrix3<f32>, Vector3<f32>, mul);
-bench_binop!(_bench_mat4_mul_v, Mat4<f32>, Vec4<f32>, mul);
+bench_binop!(_bench_mat4_mul_v, Matrix4<f32>, Vector4<f32>, mul);
 
-bench_binop!(_bench_mat2_mul_s, Mat2<f32>, f32, mul);
+bench_binop!(_bench_mat2_mul_s, Matrix2<f32>, f32, mul);
-bench_binop!(_bench_mat3_mul_s, Mat3<f32>, f32, mul);
+bench_binop!(_bench_mat3_mul_s, Matrix3<f32>, f32, mul);
-bench_binop!(_bench_mat4_mul_s, Mat4<f32>, f32, mul);
+bench_binop!(_bench_mat4_mul_s, Matrix4<f32>, f32, mul);
 
-bench_binop!(_bench_mat2_div_s, Mat2<f32>, f32, div);
+bench_binop!(_bench_mat2_div_s, Matrix2<f32>, f32, div);
-bench_binop!(_bench_mat3_div_s, Mat3<f32>, f32, div);
+bench_binop!(_bench_mat3_div_s, Matrix3<f32>, f32, div);
-bench_binop!(_bench_mat4_div_s, Mat4<f32>, f32, div);
+bench_binop!(_bench_mat4_div_s, Matrix4<f32>, f32, div);
 
-bench_unop!(_bench_mat2_inv, Mat2<f32>, inv);
+bench_unop!(_bench_mat2_inv, Matrix2<f32>, inverse);
-bench_unop!(_bench_mat3_inv, Mat3<f32>, inv);
+bench_unop!(_bench_mat3_inv, Matrix3<f32>, inverse);
-bench_unop!(_bench_mat4_inv, Mat4<f32>, inv);
+bench_unop!(_bench_mat4_inv, Matrix4<f32>, inverse);
 
-bench_unop!(_bench_mat2_transpose, Mat2<f32>, transpose);
+bench_unop!(_bench_mat2_transpose, Matrix2<f32>, transpose);
-bench_unop!(_bench_mat3_transpose, Mat3<f32>, transpose);
+bench_unop!(_bench_mat3_transpose, Matrix3<f32>, transpose);
-bench_unop!(_bench_mat4_transpose, Mat4<f32>, transpose);
+bench_unop!(_bench_mat4_transpose, Matrix4<f32>, transpose);

benches/quat.rs

@@ -6,19 +6,19 @@ extern crate nalgebra as na;
 
 use rand::{IsaacRng, Rng};
 use test::Bencher;
-use na::{Quat, UnitQuat, Vec3};
+use na::{Quaternion, UnitQuaternion, Vector3};
 use std::ops::{Add, Sub, Mul, Div};
 
 #[path="common/macros.rs"]
 mod macros;
 
-bench_binop!(_bench_quat_add_q, Quat<f32>, Quat<f32>, add);
+bench_binop!(_bench_quaternion_add_q, Quaternion<f32>, Quaternion<f32>, add);
-bench_binop!(_bench_quat_sub_q, Quat<f32>, Quat<f32>, sub);
+bench_binop!(_bench_quaternion_sub_q, Quaternion<f32>, Quaternion<f32>, sub);
-bench_binop!(_bench_quat_mul_q, Quat<f32>, Quat<f32>, mul);
+bench_binop!(_bench_quaternion_mul_q, Quaternion<f32>, Quaternion<f32>, mul);
-// bench_binop!(_bench_quat_div_q, Quat<f32>, Quat<f32>, div)
+// bench_binop!(_bench_quaternion_div_q, Quaternion<f32>, Quaternion<f32>, div)
-bench_binop!(_bench_quat_mul_v, UnitQuat<f32>, Vec3<f32>, mul);
+bench_binop!(_bench_quaternion_mul_v, UnitQuaternion<f32>, Vector3<f32>, mul);
-bench_binop!(_bench_quat_mul_s, Quat<f32>, f32, mul);
+bench_binop!(_bench_quaternion_mul_s, Quaternion<f32>, f32, mul);
-bench_binop!(_bench_quat_div_s, Quat<f32>, f32, div);
+bench_binop!(_bench_quaternion_div_s, Quaternion<f32>, f32, div);
-bench_unop!(_bench_quat_inv, Quat<f32>, inv);
+bench_unop!(_bench_quaternion_inv, Quaternion<f32>, inverse);
-bench_unop_self!(_bench_quat_conjugate, Quat<f32>, conjugate);
+bench_unop_self!(_bench_quaternion_conjugate, Quaternion<f32>, conjugate);
-bench_unop!(_bench_quat_normalize, Quat<f32>, normalize);
+bench_unop!(_bench_quaternion_normalize, Quaternion<f32>, normalize);

benches/vec.rs

@@ -9,104 +9,104 @@ extern crate nalgebra as na;
 
 use rand::{IsaacRng, Rng};
 use test::Bencher;
-use na::{Vec2, Vec3, Vec4};
+use na::{Vector2, Vector3, Vector4};
 use std::ops::{Add, Sub, Mul, Div};
 
 #[path="common/macros.rs"]
 mod macros;
 
-bench_binop!(_bench_vec2_add_v, Vec2<f32>, Vec2<f32>, add);
+bench_binop!(_bench_vec2_add_v, Vector2<f32>, Vector2<f32>, add);
-bench_binop!(_bench_vec3_add_v, Vec3<f32>, Vec3<f32>, add);
+bench_binop!(_bench_vec3_add_v, Vector3<f32>, Vector3<f32>, add);
-bench_binop!(_bench_vec4_add_v, Vec4<f32>, Vec4<f32>, add);
+bench_binop!(_bench_vec4_add_v, Vector4<f32>, Vector4<f32>, add);
 
-bench_binop!(_bench_vec2_sub_v, Vec2<f32>, Vec2<f32>, sub);
+bench_binop!(_bench_vec2_sub_v, Vector2<f32>, Vector2<f32>, sub);
-bench_binop!(_bench_vec3_sub_v, Vec3<f32>, Vec3<f32>, sub);
+bench_binop!(_bench_vec3_sub_v, Vector3<f32>, Vector3<f32>, sub);
-bench_binop!(_bench_vec4_sub_v, Vec4<f32>, Vec4<f32>, sub);
+bench_binop!(_bench_vec4_sub_v, Vector4<f32>, Vector4<f32>, sub);
 
-bench_binop!(_bench_vec2_mul_v, Vec2<f32>, Vec2<f32>, mul);
+bench_binop!(_bench_vec2_mul_v, Vector2<f32>, Vector2<f32>, mul);
-bench_binop!(_bench_vec3_mul_v, Vec3<f32>, Vec3<f32>, mul);
+bench_binop!(_bench_vec3_mul_v, Vector3<f32>, Vector3<f32>, mul);
-bench_binop!(_bench_vec4_mul_v, Vec4<f32>, Vec4<f32>, mul);
+bench_binop!(_bench_vec4_mul_v, Vector4<f32>, Vector4<f32>, mul);
 
-bench_binop!(_bench_vec2_div_v, Vec2<f32>, Vec2<f32>, div);
+bench_binop!(_bench_vec2_div_v, Vector2<f32>, Vector2<f32>, div);
-bench_binop!(_bench_vec3_div_v, Vec3<f32>, Vec3<f32>, div);
+bench_binop!(_bench_vec3_div_v, Vector3<f32>, Vector3<f32>, div);
-bench_binop!(_bench_vec4_div_v, Vec4<f32>, Vec4<f32>, div);
+bench_binop!(_bench_vec4_div_v, Vector4<f32>, Vector4<f32>, div);
 
-bench_binop!(_bench_vec2_add_s, Vec2<f32>, f32, add);
+bench_binop!(_bench_vec2_add_s, Vector2<f32>, f32, add);
-bench_binop!(_bench_vec3_add_s, Vec3<f32>, f32, add);
+bench_binop!(_bench_vec3_add_s, Vector3<f32>, f32, add);
-bench_binop!(_bench_vec4_add_s, Vec4<f32>, f32, add);
+bench_binop!(_bench_vec4_add_s, Vector4<f32>, f32, add);
 
-bench_binop!(_bench_vec2_sub_s, Vec2<f32>, f32, sub);
+bench_binop!(_bench_vec2_sub_s, Vector2<f32>, f32, sub);
-bench_binop!(_bench_vec3_sub_s, Vec3<f32>, f32, sub);
+bench_binop!(_bench_vec3_sub_s, Vector3<f32>, f32, sub);
-bench_binop!(_bench_vec4_sub_s, Vec4<f32>, f32, sub);
+bench_binop!(_bench_vec4_sub_s, Vector4<f32>, f32, sub);
 
-bench_binop!(_bench_vec2_mul_s, Vec2<f32>, f32, mul);
+bench_binop!(_bench_vec2_mul_s, Vector2<f32>, f32, mul);
-bench_binop!(_bench_vec3_mul_s, Vec3<f32>, f32, mul);
+bench_binop!(_bench_vec3_mul_s, Vector3<f32>, f32, mul);
-bench_binop!(_bench_vec4_mul_s, Vec4<f32>, f32, mul);
+bench_binop!(_bench_vec4_mul_s, Vector4<f32>, f32, mul);
 
-bench_binop!(_bench_vec2_div_s, Vec2<f32>, f32, div);
+bench_binop!(_bench_vec2_div_s, Vector2<f32>, f32, div);
-bench_binop!(_bench_vec3_div_s, Vec3<f32>, f32, div);
+bench_binop!(_bench_vec3_div_s, Vector3<f32>, f32, div);
-bench_binop!(_bench_vec4_div_s, Vec4<f32>, f32, div);
+bench_binop!(_bench_vec4_div_s, Vector4<f32>, f32, div);
 
-bench_binop_na!(_bench_vec2_dot, Vec2<f32>, Vec2<f32>, dot);
+bench_binop_na!(_bench_vec2_dot, Vector2<f32>, Vector2<f32>, dot);
-bench_binop_na!(_bench_vec3_dot, Vec3<f32>, Vec3<f32>, dot);
+bench_binop_na!(_bench_vec3_dot, Vector3<f32>, Vector3<f32>, dot);
-bench_binop_na!(_bench_vec4_dot, Vec4<f32>, Vec4<f32>, dot);
+bench_binop_na!(_bench_vec4_dot, Vector4<f32>, Vector4<f32>, dot);
 
-bench_binop_na!(_bench_vec3_cross, Vec3<f32>, Vec3<f32>, cross);
+bench_binop_na!(_bench_vec3_cross, Vector3<f32>, Vector3<f32>, cross);
 
-bench_unop!(_bench_vec2_norm, Vec2<f32>, norm);
+bench_unop!(_bench_vec2_norm, Vector2<f32>, norm);
-bench_unop!(_bench_vec3_norm, Vec3<f32>, norm);
+bench_unop!(_bench_vec3_norm, Vector3<f32>, norm);
-bench_unop!(_bench_vec4_norm, Vec4<f32>, norm);
+bench_unop!(_bench_vec4_norm, Vector4<f32>, norm);
 
-bench_unop!(_bench_vec2_normalize, Vec2<f32>, normalize);
+bench_unop!(_bench_vec2_normalize, Vector2<f32>, normalize);
-bench_unop!(_bench_vec3_normalize, Vec3<f32>, normalize);
+bench_unop!(_bench_vec3_normalize, Vector3<f32>, normalize);
-bench_unop!(_bench_vec4_normalize, Vec4<f32>, normalize);
+bench_unop!(_bench_vec4_normalize, Vector4<f32>, normalize);
 
 #[cfg(feature = "generic_sizes")]
 mod bench_vecn {
     use typenum::{U2, U3, U4};
-    use na::VecN;
+    use na::VectorN;
 
-    bench_binop!(_bench_vecn2_add_v, VecN<f32, U2>, VecN<f32, U2>, add);
+    bench_binop!(_bench_vecn2_add_v, VectorN<f32, U2>, VectorN<f32, U2>, add);
-    bench_binop!(_bench_vecn3_add_v, VecN<f32, U3>, VecN<f32, U3>, add);
+    bench_binop!(_bench_vecn3_add_v, VectorN<f32, U3>, VectorN<f32, U3>, add);
-    bench_binop!(_bench_vecn4_add_v, VecN<f32, U4>, VecN<f32, U4>, add);
+    bench_binop!(_bench_vecn4_add_v, VectorN<f32, U4>, VectorN<f32, U4>, add);
 
-    bench_binop!(_bench_vecn2_sub_v, VecN<f32, U2>, VecN<f32, U2>, sub);
+    bench_binop!(_bench_vecn2_sub_v, VectorN<f32, U2>, VectorN<f32, U2>, sub);
-    bench_binop!(_bench_vecn3_sub_v, VecN<f32, U3>, VecN<f32, U3>, sub);
+    bench_binop!(_bench_vecn3_sub_v, VectorN<f32, U3>, VectorN<f32, U3>, sub);
-    bench_binop!(_bench_vecn4_sub_v, VecN<f32, U4>, VecN<f32, U4>, sub);
+    bench_binop!(_bench_vecn4_sub_v, VectorN<f32, U4>, VectorN<f32, U4>, sub);
 
-    bench_binop!(_bench_vecn2_mul_v, VecN<f32, U2>, VecN<f32, U2>, mul);
+    bench_binop!(_bench_vecn2_mul_v, VectorN<f32, U2>, VectorN<f32, U2>, mul);
-    bench_binop!(_bench_vecn3_mul_v, VecN<f32, U3>, VecN<f32, U3>, mul);
+    bench_binop!(_bench_vecn3_mul_v, VectorN<f32, U3>, VectorN<f32, U3>, mul);
-    bench_binop!(_bench_vecn4_mul_v, VecN<f32, U4>, VecN<f32, U4>, mul);
+    bench_binop!(_bench_vecn4_mul_v, VectorN<f32, U4>, VectorN<f32, U4>, mul);
 
-    bench_binop!(_bench_vecn2_div_v, VecN<f32, U2>, VecN<f32, U2>, div);
+    bench_binop!(_bench_vecn2_div_v, VectorN<f32, U2>, VectorN<f32, U2>, div);
-    bench_binop!(_bench_vecn3_div_v, VecN<f32, U3>, VecN<f32, U3>, div);
+    bench_binop!(_bench_vecn3_div_v, VectorN<f32, U3>, VectorN<f32, U3>, div);
-    bench_binop!(_bench_vecn4_div_v, VecN<f32, U4>, VecN<f32, U4>, div);
+    bench_binop!(_bench_vecn4_div_v, VectorN<f32, U4>, VectorN<f32, U4>, div);
 
-    bench_binop!(_bench_vecn2_add_s, VecN<f32, U2>, f32, add);
+    bench_binop!(_bench_vecn2_add_s, VectorN<f32, U2>, f32, add);
-    bench_binop!(_bench_vecn3_add_s, VecN<f32, U3>, f32, add);
+    bench_binop!(_bench_vecn3_add_s, VectorN<f32, U3>, f32, add);
-    bench_binop!(_bench_vecn4_add_s, VecN<f32, U4>, f32, add);
+    bench_binop!(_bench_vecn4_add_s, VectorN<f32, U4>, f32, add);
 
-    bench_binop!(_bench_vecn2_sub_s, VecN<f32, U2>, f32, sub);
+    bench_binop!(_bench_vecn2_sub_s, VectorN<f32, U2>, f32, sub);
-    bench_binop!(_bench_vecn3_sub_s, VecN<f32, U3>, f32, sub);
+    bench_binop!(_bench_vecn3_sub_s, VectorN<f32, U3>, f32, sub);
-    bench_binop!(_bench_vecn4_sub_s, VecN<f32, U4>, f32, sub);
+    bench_binop!(_bench_vecn4_sub_s, VectorN<f32, U4>, f32, sub);
 
-    bench_binop!(_bench_vecn2_mul_s, VecN<f32, U2>, f32, mul);
+    bench_binop!(_bench_vecn2_mul_s, VectorN<f32, U2>, f32, mul);
-    bench_binop!(_bench_vecn3_mul_s, VecN<f32, U3>, f32, mul);
+    bench_binop!(_bench_vecn3_mul_s, VectorN<f32, U3>, f32, mul);
-    bench_binop!(_bench_vecn4_mul_s, VecN<f32, U4>, f32, mul);
+    bench_binop!(_bench_vecn4_mul_s, VectorN<f32, U4>, f32, mul);
 
-    bench_binop!(_bench_vecn2_div_s, VecN<f32, U2>, f32, div);
+    bench_binop!(_bench_vecn2_div_s, VectorN<f32, U2>, f32, div);
-    bench_binop!(_bench_vecn3_div_s, VecN<f32, U3>, f32, div);
+    bench_binop!(_bench_vecn3_div_s, VectorN<f32, U3>, f32, div);
-    bench_binop!(_bench_vecn4_div_s, VecN<f32, U4>, f32, div);
+    bench_binop!(_bench_vecn4_div_s, VectorN<f32, U4>, f32, div);
 
-    bench_binop_na!(_bench_vecn2_dot, VecN<f32, U2>, VecN<f32, U2>, dot);
+    bench_binop_na!(_bench_vecn2_dot, VectorN<f32, U2>, VectorN<f32, U2>, dot);
-    bench_binop_na!(_bench_vecn3_dot, VecN<f32, U3>, VecN<f32, U3>, dot);
+    bench_binop_na!(_bench_vecn3_dot, VectorN<f32, U3>, VectorN<f32, U3>, dot);
-    bench_binop_na!(_bench_vecn4_dot, VecN<f32, U4>, VecN<f32, U4>, dot);
+    bench_binop_na!(_bench_vecn4_dot, VectorN<f32, U4>, VectorN<f32, U4>, dot);
 
-    bench_unop!(_bench_vecn2_norm, VecN<f32, U2>, norm);
+    bench_unop!(_bench_vecn2_norm, VectorN<f32, U2>, norm);
-    bench_unop!(_bench_vecn3_norm, VecN<f32, U3>, norm);
+    bench_unop!(_bench_vecn3_norm, VectorN<f32, U3>, norm);
-    bench_unop!(_bench_vecn4_norm, VecN<f32, U4>, norm);
+    bench_unop!(_bench_vecn4_norm, VectorN<f32, U4>, norm);
 
-    bench_unop!(_bench_vecn2_normalize, VecN<f32, U2>, normalize);
+    bench_unop!(_bench_vecn2_normalize, VectorN<f32, U2>, normalize);
-    bench_unop!(_bench_vecn3_normalize, VecN<f32, U3>, normalize);
+    bench_unop!(_bench_vecn3_normalize, VectorN<f32, U3>, normalize);
-    bench_unop!(_bench_vecn4_normalize, VecN<f32, U4>, normalize);
+    bench_unop!(_bench_vecn4_normalize, VectorN<f32, U4>, normalize);
 }

src/lib.rs

@@ -14,22 +14,22 @@ All the functionality of **nalgebra** is grouped in one place: the root module `
 module re-exports everything and includes free functions for all traits methods performing
 out-of-place operations.
 
-* You can import the whole prelude using:
+Thus, you can import the whole prelude using:
 
 ```.ignore
 use nalgebra::*;
 ```
 
-The preferred way to use **nalgebra** is to import types and traits explicitly, and call
+However, the recommended way to use **nalgebra** is to import types and traits explicitly, and call
 free-functions using the `na::` prefix:
 
 ```.rust
 extern crate nalgebra as na;
-use na::{Vec3, Rot3, Rotation};
+use na::{Vector3, Rotation3, Rotation};
 
 fn main() {
-    let     a = Vec3::new(1.0f64, 1.0, 1.0);
+    let     a = Vector3::new(1.0f64, 1.0, 1.0);
-    let mut b = Rot3::new(na::zero());
+    let mut b = Rotation3::new(na::zero());
 
     b.append_rotation_mut(&a);
 
@@ -41,19 +41,19 @@ fn main() {
 **nalgebra** is meant to be a general-purpose, low-dimensional, linear algebra library, with
 an optimized set of tools for computer graphics and physics. Those features include:
 
-* Vectors with predefined static sizes: `Vec1`, `Vec2`, `Vec3`, `Vec4`, `Vec5`, `Vec6`.
+* Vectors with predefined static sizes: `Vector1`, `Vector2`, `Vector3`, `Vector4`, `Vector5`, `Vector6`.
-* Vector with a user-defined static size: `VecN` (available only with the `generic_sizes` feature).
+* Vector with a user-defined static size: `VectorN` (available only with the `generic_sizes` feature).
-* Points with static sizes: `Pnt1`, `Pnt2`, `Pnt3`, `Pnt4`, `Pnt5`, `Pnt6`.
+* Points with static sizes: `Point1`, `Point2`, `Point3`, `Point4`, `Point5`, `Point6`.
-* Square matrices with static sizes: `Mat1`, `Mat2`, `Mat3`, `Mat4`, `Mat5`, `Mat6 `.
+* Square matrices with static sizes: `Matrix1`, `Matrix2`, `Matrix3`, `Matrix4`, `Matrix5`, `Matrix6 `.
-* Rotation matrices: `Rot2`, `Rot3`
+* Rotation matrices: `Rotation2`, `Rotation3`
-* Quaternions: `Quat`, `UnitQuat`.
+* Quaternions: `Quaternion`, `UnitQuaternion`.
-* Isometries (translation ⨯ rotation): `Iso2`, `Iso3`
+* Isometrymetries (translation ⨯ rotation): `Isometry2`, `Isometry3`
-* Similarity transformations (translation ⨯ rotation ⨯ uniform scale): `Sim2`, `Sim3`.
+* Similarity transformations (translation ⨯ rotation ⨯ uniform scale): `Similarity2`, `Similarity3`.
-* 3D projections for computer graphics: `Persp3`, `PerspMat3`, `Ortho3`, `OrthoMat3`.
+* 3D projections for computer graphics: `Perspective3`, `PerspectiveMatrix3`, `Orthographic3`, `OrthographicMatrix3`.
-* Dynamically sized heap-allocated vector: `DVec`.
+* Dynamically sized heap-allocated vector: `DVector`.
-* Dynamically sized stack-allocated vectors with a maximum size: `DVec1` to `DVec6`.
+* Dynamically sized stack-allocated vectors with a maximum size: `DVector1` to `DVector6`.
-* Dynamically sized heap-allocated (square or rectangular) matrix: `DMat`.
+* Dynamically sized heap-allocated (square or rectangular) matrix: `DMatrix`.
-* Linear algebra and data analysis operators: `Cov`, `Mean`, `qr`, `cholesky`.
+* Linear algebra and data analysis operators: `Covariance`, `Mean`, `qr`, `cholesky`.
 * Almost one trait per functionality: useful for generic programming.
 
 
@@ -98,39 +98,39 @@ pub use traits::{
     BaseNum,
     Bounded,
     Cast,
-    Col,
+    Column,
-    ColSlice, RowSlice,
+    ColumnSlice, RowSlice,
-    Cov,
+    Covariance,
     Cross,
     CrossMatrix,
-    Det,
+    Determinant,
-    Diag,
+    Diagonal,
-    Dim,
+    Dimension,
     Dot,
     EigenQR,
     Eye,
-    FloatPnt,
+    FloatPoint,
-    FloatVec,
+    FloatVector,
     FromHomogeneous,
     Indexable,
-    Inv,
+    Inverse,
     Iterable,
     IterableMut,
-    Mat,
+    Matrix,
     Mean,
     Norm,
-    NumPnt,
+    NumPoint,
-    NumVec,
+    NumVector,
-    Orig,
+    Origin,
     Outer,
-    POrd,
+    PartialOrder,
-    POrdering,
+    PartialOrdering,
-    PntAsVec,
+    PointAsVector,
     Repeat,
     Rotate, Rotation, RotationMatrix, RotationWithTranslation, RotationTo,
     Row,
     Shape,
-    SquareMat,
+    SquareMatrix,
     ToHomogeneous,
     Transform, Transformation,
     Translate, Translation,
@@ -139,22 +139,22 @@ pub use traits::{
 };
 
 #[cfg(feature="generic_sizes")]
-pub use structs::VecN;
+pub use structs::VectorN;
 
 pub use structs::{
     Identity,
-    DMat, DMat1, DMat2,  DMat3,  DMat4,  DMat5,  DMat6,
+    DMatrix, DMatrix1, DMatrix2,  DMatrix3,  DMatrix4,  DMatrix5,  DMatrix6,
-    DVec, DVec1, DVec2,  DVec3,  DVec4,  DVec5,  DVec6,
+    DVector, DVector1, DVector2,  DVector3,  DVector4,  DVector5,  DVector6,
-    Iso2, Iso3,
+    Isometry2, Isometry3,
-    Sim2, Sim3,
+    Similarity2, Similarity3,
-    Mat1, Mat2, Mat3, Mat4,
+    Matrix1, Matrix2, Matrix3, Matrix4,
-    Mat5, Mat6,
+    Matrix5, Matrix6,
-    Rot2, Rot3,
+    Rotation2, Rotation3,
-    Vec1, Vec2, Vec3, Vec4, Vec5, Vec6,
+    Vector1, Vector2, Vector3, Vector4, Vector5, Vector6,
-    Pnt1, Pnt2, Pnt3, Pnt4, Pnt5, Pnt6,
+    Point1, Point2, Point3, Point4, Point5, Point6,
-    Persp3, PerspMat3,
+    Perspective3, PerspectiveMatrix3,
-    Ortho3, OrthoMat3,
+    Orthographic3, OrthographicMatrix3,
-    Quat, UnitQuat
+    Quaternion, UnitQuaternion
 };
 
 pub use linalg::{
@@ -202,63 +202,63 @@ pub fn min<T: Ord>(a: T, b: T) -> T {
 
 /// Returns the infimum of `a` and `b`.
 #[inline(always)]
-pub fn inf<T: POrd>(a: &T, b: &T) -> T {
+pub fn inf<T: PartialOrder>(a: &T, b: &T) -> T {
-    POrd::inf(a, b)
+    PartialOrder::inf(a, b)
 }
 
 /// Returns the supremum of `a` and `b`.
 #[inline(always)]
-pub fn sup<T: POrd>(a: &T, b: &T) -> T {
+pub fn sup<T: PartialOrder>(a: &T, b: &T) -> T {
-    POrd::sup(a, b)
+    PartialOrder::sup(a, b)
 }
 
 /// Compare `a` and `b` using a partial ordering relation.
 #[inline(always)]
-pub fn partial_cmp<T: POrd>(a: &T, b: &T) -> POrdering {
+pub fn partial_cmp<T: PartialOrder>(a: &T, b: &T) -> PartialOrdering {
-    POrd::partial_cmp(a, b)
+    PartialOrder::partial_cmp(a, b)
 }
 
 /// Returns `true` iff `a` and `b` are comparable and `a < b`.
 #[inline(always)]
-pub fn partial_lt<T: POrd>(a: &T, b: &T) -> bool {
+pub fn partial_lt<T: PartialOrder>(a: &T, b: &T) -> bool {
-    POrd::partial_lt(a, b)
+    PartialOrder::partial_lt(a, b)
 }
 
 /// Returns `true` iff `a` and `b` are comparable and `a <= b`.
 #[inline(always)]
-pub fn partial_le<T: POrd>(a: &T, b: &T) -> bool {
+pub fn partial_le<T: PartialOrder>(a: &T, b: &T) -> bool {
-    POrd::partial_le(a, b)
+    PartialOrder::partial_le(a, b)
 }
 
 /// Returns `true` iff `a` and `b` are comparable and `a > b`.
 #[inline(always)]
-pub fn partial_gt<T: POrd>(a: &T, b: &T) -> bool {
+pub fn partial_gt<T: PartialOrder>(a: &T, b: &T) -> bool {
-    POrd::partial_gt(a, b)
+    PartialOrder::partial_gt(a, b)
 }
 
 /// Returns `true` iff `a` and `b` are comparable and `a >= b`.
 #[inline(always)]
-pub fn partial_ge<T: POrd>(a: &T, b: &T) -> bool {
+pub fn partial_ge<T: PartialOrder>(a: &T, b: &T) -> bool {
-    POrd::partial_ge(a, b)
+    PartialOrder::partial_ge(a, b)
 }
 
 /// Return the minimum of `a` and `b` if they are comparable.
 #[inline(always)]
-pub fn partial_min<'a, T: POrd>(a: &'a T, b: &'a T) -> Option<&'a T> {
+pub fn partial_min<'a, T: PartialOrder>(a: &'a T, b: &'a T) -> Option<&'a T> {
-    POrd::partial_min(a, b)
+    PartialOrder::partial_min(a, b)
 }
 
 /// Return the maximum of `a` and `b` if they are comparable.
 #[inline(always)]
-pub fn partial_max<'a, T: POrd>(a: &'a T, b: &'a T) -> Option<&'a T> {
+pub fn partial_max<'a, T: PartialOrder>(a: &'a T, b: &'a T) -> Option<&'a T> {
-    POrd::partial_max(a, b)
+    PartialOrder::partial_max(a, b)
 }
 
 /// Clamp `value` between `min` and `max`. Returns `None` if `value` is not comparable to
 /// `min` or `max`.
 #[inline(always)]
-pub fn partial_clamp<'a, T: POrd>(value: &'a T, min: &'a T, max: &'a T) -> Option<&'a T> {
+pub fn partial_clamp<'a, T: PartialOrder>(value: &'a T, min: &'a T, max: &'a T) -> Option<&'a T> {
-    POrd::partial_clamp(value, min, max)
+    PartialOrder::partial_clamp(value, min, max)
 }
 
 //
@@ -305,34 +305,34 @@ pub fn one<T: One>() -> T {
 
 /// Returns the trivial origin of an affine space.
 #[inline(always)]
-pub fn orig<P: Orig>() -> P {
+pub fn origin<P: Origin>() -> P {
-    Orig::orig()
+    Origin::origin()
 }
 
 /// Returns the center of two points.
 #[inline]
-pub fn center<N: BaseFloat, P: FloatPnt<N>>(a: &P, b: &P) -> P
+pub fn center<N: BaseFloat, P: FloatPoint<N>>(a: &P, b: &P) -> P
-        where <P as PntAsVec>::Vec: Norm<N>
+        where <P as PointAsVector>::Vector: Norm<N>
 {
     let _2 = one::<N>() + one();
-    (*a + b.to_vec()) / _2
+    (*a + b.to_vector()) / _2
 }
 
 /*
- * FloatPnt
+ * FloatPoint
  */
 /// Returns the distance between two points.
 #[inline(always)]
-pub fn dist<N: BaseFloat, P: FloatPnt<N>>(a: &P, b: &P) -> N where <P as PntAsVec>::Vec: Norm<N> {
+pub fn distance<N: BaseFloat, P: FloatPoint<N>>(a: &P, b: &P) -> N where <P as PointAsVector>::Vector: Norm<N> {
-    a.dist(b)
+    a.distance(b)
 }
 
 /// Returns the squared distance between two points.
 #[inline(always)]
-pub fn sqdist<N: BaseFloat, P: FloatPnt<N>>(a: &P, b: &P) -> N 
+pub fn distance_squared<N: BaseFloat, P: FloatPoint<N>>(a: &P, b: &P) -> N 
-        where <P as PntAsVec>::Vec: Norm<N>
+        where <P as PointAsVector>::Vector: Norm<N>
 {
-    a.sqdist(b)
+    a.distance_squared(b)
 }
 
 /*
@@ -343,13 +343,13 @@ pub fn sqdist<N: BaseFloat, P: FloatPnt<N>>(a: &P, b: &P) -> N
 ///
 /// ```rust
 /// extern crate nalgebra as na;
-/// use na::{Vec3, Iso3};
+/// use na::{Vector3, Isometry3};
 ///
 /// fn main() {
-///     let t     = Iso3::new(Vec3::new(1.0f64, 1.0, 1.0), na::zero());
+///     let t     = Isometry3::new(Vector3::new(1.0f64, 1.0, 1.0), na::zero());
 ///     let trans = na::translation(&t);
 ///
-///     assert!(trans == Vec3::new(1.0, 1.0, 1.0));
+///     assert!(trans == Vector3::new(1.0, 1.0, 1.0));
 /// }
 /// ```
 #[inline(always)]
@@ -361,18 +361,18 @@ pub fn translation<V, M: Translation<V>>(m: &M) -> V {
 ///
 /// ```rust
 /// extern crate nalgebra as na;
-/// use na::{Vec3, Iso3};
+/// use na::{Vector3, Isometry3};
 ///
 /// fn main() {
-///     let t      = Iso3::new(Vec3::new(1.0f64, 1.0, 1.0), na::zero());
+///     let t      = Isometry3::new(Vector3::new(1.0f64, 1.0, 1.0), na::zero());
-///     let itrans = na::inv_translation(&t);
+///     let itrans = na::inverse_translation(&t);
 ///
-///     assert!(itrans == Vec3::new(-1.0, -1.0, -1.0));
+///     assert!(itrans == Vector3::new(-1.0, -1.0, -1.0));
 /// }
 /// ```
 #[inline(always)]
-pub fn inv_translation<V, M: Translation<V>>(m: &M) -> V {
+pub fn inverse_translation<V, M: Translation<V>>(m: &M) -> V {
-    m.inv_translation()
+    m.inverse_translation()
 }
 
 /// Applies the translation `v` to a copy of `m`.
@@ -389,15 +389,15 @@ pub fn append_translation<V, M: Translation<V>>(m: &M, v: &V) -> M {
 ///
 /// ```rust
 /// extern crate nalgebra as na;
-/// use na::{Pnt3, Vec3, Iso3};
+/// use na::{Point3, Vector3, Isometry3};
 ///
 /// fn main() {
-///     let t  = Iso3::new(Vec3::new(1.0f64, 1.0, 1.0), na::zero());
+///     let t  = Isometry3::new(Vector3::new(1.0f64, 1.0, 1.0), na::zero());
-///     let p  = Pnt3::new(2.0, 2.0, 2.0);
+///     let p  = Point3::new(2.0, 2.0, 2.0);
 ///
 ///     let tp = na::translate(&t, &p);
 ///
-///     assert!(tp == Pnt3::new(3.0, 3.0, 3.0))
+///     assert!(tp == Point3::new(3.0, 3.0, 3.0))
 /// }
 /// ```
 #[inline(always)]
@@ -409,19 +409,19 @@ pub fn translate<P, M: Translate<P>>(m: &M, p: &P) -> P {
 ///
 /// ```rust
 /// extern crate nalgebra as na;
-/// use na::{Pnt3, Vec3, Iso3};
+/// use na::{Point3, Vector3, Isometry3};
 ///
 /// fn main() {
-///     let t  = Iso3::new(Vec3::new(1.0f64, 1.0, 1.0), na::zero());
+///     let t  = Isometry3::new(Vector3::new(1.0f64, 1.0, 1.0), na::zero());
-///     let p  = Pnt3::new(2.0, 2.0, 2.0);
+///     let p  = Point3::new(2.0, 2.0, 2.0);
 ///
-///     let tp = na::inv_translate(&t, &p);
+///     let tp = na::inverse_translate(&t, &p);
 ///
-///     assert!(na::approx_eq(&tp, &Pnt3::new(1.0, 1.0, 1.0)))
+///     assert!(na::approx_eq(&tp, &Point3::new(1.0, 1.0, 1.0)))
 /// }
 #[inline(always)]
-pub fn inv_translate<P, M: Translate<P>>(m: &M, p: &P) -> P {
+pub fn inverse_translate<P, M: Translate<P>>(m: &M, p: &P) -> P {
-    m.inv_translate(p)
+    m.inverse_translate(p)
 }
 
 /*
@@ -432,12 +432,12 @@ pub fn inv_translate<P, M: Translate<P>>(m: &M, p: &P) -> P {
 ///
 /// ```rust
 /// extern crate nalgebra as na;
-/// use na::{Vec3, Rot3};
+/// use na::{Vector3, Rotation3};
 ///
 /// fn main() {
-///     let t = Rot3::new(Vec3::new(1.0f64, 1.0, 1.0));
+///     let t = Rotation3::new(Vector3::new(1.0f64, 1.0, 1.0));
 ///
-///     assert!(na::approx_eq(&na::rotation(&t), &Vec3::new(1.0, 1.0, 1.0)));
+///     assert!(na::approx_eq(&na::rotation(&t), &Vector3::new(1.0, 1.0, 1.0)));
 /// }
 /// ```
 #[inline(always)]
@@ -450,17 +450,17 @@ pub fn rotation<V, M: Rotation<V>>(m: &M) -> V {
 ///
 /// ```rust
 /// extern crate nalgebra as na;
-/// use na::{Vec3, Rot3};
+/// use na::{Vector3, Rotation3};
 ///
 /// fn main() {
-///     let t = Rot3::new(Vec3::new(1.0f64, 1.0, 1.0));
+///     let t = Rotation3::new(Vector3::new(1.0f64, 1.0, 1.0));
 ///
-///     assert!(na::approx_eq(&na::inv_rotation(&t), &Vec3::new(-1.0, -1.0, -1.0)));
+///     assert!(na::approx_eq(&na::inverse_rotation(&t), &Vector3::new(-1.0, -1.0, -1.0)));
 /// }
 /// ```
 #[inline(always)]
-pub fn inv_rotation<V, M: Rotation<V>>(m: &M) -> V {
+pub fn inverse_rotation<V, M: Rotation<V>>(m: &M) -> V {
-    m.inv_rotation()
+    m.inverse_rotation()
 }
 
 // FIXME: this example is a bit shity
@@ -468,14 +468,14 @@ pub fn inv_rotation<V, M: Rotation<V>>(m: &M) -> V {
 ///
 /// ```rust
 /// extern crate nalgebra as na;
-/// use na::{Vec3, Rot3};
+/// use na::{Vector3, Rotation3};
 ///
 /// fn main() {
-///     let t  = Rot3::new(Vec3::new(0.0f64, 0.0, 0.0));
+///     let t  = Rotation3::new(Vector3::new(0.0f64, 0.0, 0.0));
-///     let v  = Vec3::new(1.0, 1.0, 1.0);
+///     let v  = Vector3::new(1.0, 1.0, 1.0);
 ///     let rt = na::append_rotation(&t, &v);
 ///
-///     assert!(na::approx_eq(&na::rotation(&rt), &Vec3::new(1.0, 1.0, 1.0)))
+///     assert!(na::approx_eq(&na::rotation(&rt), &Vector3::new(1.0, 1.0, 1.0)))
 /// }
 /// ```
 #[inline(always)]
@@ -488,14 +488,14 @@ pub fn append_rotation<V, M: Rotation<V>>(m: &M, v: &V) -> M {
 ///
 /// ```rust
 /// extern crate nalgebra as na;
-/// use na::{Vec3, Rot3};
+/// use na::{Vector3, Rotation3};
 ///
 /// fn main() {
-///     let t  = Rot3::new(Vec3::new(0.0f64, 0.0, 0.0));
+///     let t  = Rotation3::new(Vector3::new(0.0f64, 0.0, 0.0));
-///     let v  = Vec3::new(1.0, 1.0, 1.0);
+///     let v  = Vector3::new(1.0, 1.0, 1.0);
 ///     let rt = na::prepend_rotation(&t, &v);
 ///
-///     assert!(na::approx_eq(&na::rotation(&rt), &Vec3::new(1.0, 1.0, 1.0)))
+///     assert!(na::approx_eq(&na::rotation(&rt), &Vector3::new(1.0, 1.0, 1.0)))
 /// }
 /// ```
 #[inline(always)]
@@ -511,15 +511,15 @@ pub fn prepend_rotation<V, M: Rotation<V>>(m: &M, v: &V) -> M {
 ///
 /// ```rust
 /// extern crate nalgebra as na;
-/// use na::{BaseFloat, Rot3, Vec3};
+/// use na::{BaseFloat, Rotation3, Vector3};
 ///
 /// fn main() {
-///     let t  = Rot3::new(Vec3::new(0.0f64, 0.0, 0.5 * <f64 as BaseFloat>::pi()));
+///     let t  = Rotation3::new(Vector3::new(0.0f64, 0.0, 0.5 * <f64 as BaseFloat>::pi()));
-///     let v  = Vec3::new(1.0, 0.0, 0.0);
+///     let v  = Vector3::new(1.0, 0.0, 0.0);
 ///
 ///     let tv = na::rotate(&t, &v);
 ///
-///     assert!(na::approx_eq(&tv, &Vec3::new(0.0, 1.0, 0.0)))
+///     assert!(na::approx_eq(&tv, &Vector3::new(0.0, 1.0, 0.0)))
 /// }
 /// ```
 #[inline(always)]
@@ -532,20 +532,20 @@ pub fn rotate<V, M: Rotate<V>>(m: &M, v: &V) -> V {
 ///
 /// ```rust
 /// extern crate nalgebra as na;
-/// use na::{BaseFloat, Rot3, Vec3};
+/// use na::{BaseFloat, Rotation3, Vector3};
 ///
 /// fn main() {
-///     let t  = Rot3::new(Vec3::new(0.0f64, 0.0, 0.5 * <f64 as BaseFloat>::pi()));
+///     let t  = Rotation3::new(Vector3::new(0.0f64, 0.0, 0.5 * <f64 as BaseFloat>::pi()));
-///     let v  = Vec3::new(1.0, 0.0, 0.0);
+///     let v  = Vector3::new(1.0, 0.0, 0.0);
 ///
-///     let tv = na::inv_rotate(&t, &v);
+///     let tv = na::inverse_rotate(&t, &v);
 ///
-///     assert!(na::approx_eq(&tv, &Vec3::new(0.0, -1.0, 0.0)))
+///     assert!(na::approx_eq(&tv, &Vector3::new(0.0, -1.0, 0.0)))
 /// }
 /// ```
 #[inline(always)]
-pub fn inv_rotate<V, M: Rotate<V>>(m: &M, v: &V) -> V {
+pub fn inverse_rotate<V, M: Rotate<V>>(m: &M, v: &V) -> V {
-    m.inv_rotate(v)
+    m.inverse_rotate(v)
 }
 
 /*
@@ -594,13 +594,13 @@ pub fn rotation_between<V: RotationTo>(a: &V, b: &V) -> V::DeltaRotationType {
 
 /// Builds a rotation matrix from `r`.
 #[inline(always)]
-pub fn to_rot_mat<N, LV, AV, R, M>(r: &R) -> M
+pub fn to_rotation_matrix<N, LV, AV, R, M>(r: &R) -> M
     where R: RotationMatrix<N, LV, AV, Output = M>,
-          M: SquareMat<N, LV> + Rotation<AV> + Copy,
+          M: SquareMatrix<N, LV> + Rotation<AV> + Copy,
           LV: Mul<M, Output = LV>
 {
     // FIXME: rust-lang/rust#20413
-    r.to_rot_mat()
+    r.to_rotation_matrix()
 }
 
 /*
@@ -625,8 +625,8 @@ pub fn transformation<T, M: Transformation<T>>(m: &M) -> T {
 
 /// Gets the inverse transformation applicable by `m`.
 #[inline(always)]
-pub fn inv_transformation<T, M: Transformation<T>>(m: &M) -> T {
+pub fn inverse_transformation<T, M: Transformation<T>>(m: &M) -> T {
-    m.inv_transformation()
+    m.inverse_transformation()
 }
 
 /// Gets a transformed copy of `m`.
@@ -647,8 +647,8 @@ pub fn transform<V, M: Transform<V>>(m: &M, v: &V) -> V {
 
 /// Applies an inverse transformation to a vector.
 #[inline(always)]
-pub fn inv_transform<V, M: Transform<V>>(m: &M, v: &V) -> V {
+pub fn inverse_transform<V, M: Transform<V>>(m: &M, v: &V) -> V {
-    m.inv_transform(v)
+    m.inverse_transform(v)
 }
 
 /*
@@ -673,8 +673,8 @@ pub fn norm<V: Norm<N>, N: BaseFloat>(v: &V) -> N {
 
 /// Computes the squared L2 norm of a vector.
 #[inline(always)]
-pub fn sqnorm<V: Norm<N>, N: BaseFloat>(v: &V) -> N {
+pub fn norm_squared<V: Norm<N>, N: BaseFloat>(v: &V) -> N {
-    Norm::sqnorm(v)
+    Norm::norm_squared(v)
 }
 
 /// Gets the normalized version of a vector.
@@ -684,12 +684,12 @@ pub fn normalize<V: Norm<N>, N: BaseFloat>(v: &V) -> V {
 }
 
 /*
- * Det<N>
+ * Determinant<N>
  */
 /// Computes the determinant of a square matrix.
 #[inline(always)]
-pub fn det<M: Det<N>, N>(m: &M) -> N {
+pub fn determinant<M: Determinant<N>, N>(m: &M) -> N {
-    Det::det(m)
+    Determinant::determinant(m)
 }
 
 /*
@@ -780,13 +780,13 @@ pub fn abs<M: Absolute<Res>, Res>(m: &M) -> Res {
 }
 
 /*
- * Inv
+ * Inverse
  */
 
 /// Gets an inverted copy of a matrix.
 #[inline(always)]
-pub fn inv<M: Inv>(m: &M) -> Option<M> {
+pub fn inverse<M: Inverse>(m: &M) -> Option<M> {
-    Inv::inv(m)
+    Inverse::inverse(m)
 }
 
 /*
@@ -810,13 +810,13 @@ pub fn outer<V: Outer>(a: &V, b: &V) -> V::OuterProductType {
 }
 
 /*
- * Cov<M>
+ * Covariance<M>
  */
 
 /// Computes the covariance of a set of observations.
 #[inline(always)]
-pub fn cov<M: Cov<Res>, Res>(observations: &M) -> Res {
+pub fn covariance<M: Covariance<Res>, Res>(observations: &M) -> Res {
-    Cov::cov(observations)
+    Covariance::covariance(observations)
 }
 
 /*
@@ -851,8 +851,8 @@ pub fn eigen_qr<N, V, M>(m: &M, eps: &N, niter: usize) -> (M, V)
  */
 /// Construct the identity matrix for a given dimension
 #[inline(always)]
-pub fn new_identity<M: Eye>(dim: usize) -> M {
+pub fn new_identity<M: Eye>(dimension: usize) -> M {
-    Eye::new_identity(dim)
+    Eye::new_identity(dimension)
 }
 
 
@@ -894,27 +894,27 @@ pub fn canonical_basis_element<V: Basis>(i: usize) -> Option<V> {
  */
 
 /*
- * Col<C>
+ * Column<C>
  */
 
 /*
- * Diag<V>
+ * Diagonal<V>
  */
 /// Gets the diagonal of a square matrix.
 #[inline(always)]
-pub fn diag<M: Diag<V>, V>(m: &M) -> V {
+pub fn diagonal<M: Diagonal<V>, V>(m: &M) -> V {
-    m.diag()
+    m.diagonal()
 }
 
 /*
- * Dim
+ * Dimension
  */
 /// Gets the dimension an object lives in.
 ///
-/// Same as `Dim::dim::(None::<V>)`.
+/// Same as `Dimension::dimension::(None::<V>)`.
 #[inline(always)]
-pub fn dim<V: Dim>() -> usize {
+pub fn dimension<V: Dimension>() -> usize {
-    Dim::dim(None::<V>)
+    Dimension::dimension(None::<V>)
 }
 
 /// Gets the indexable range of an object.
@@ -931,10 +931,10 @@ pub fn shape<V: Shape<I>, I>(v: &V) -> I {
 /// For primitive types, this is the same as the `as` keywords.
 /// The following properties are preserved by a cast:
 ///
-/// * Type-level geometric invariants cannot be broken (eg. a cast from Rot3<f64> to Rot3<i64> is
+/// * Type-level geometric invariants cannot be broken (eg. a cast from Rotation3<f64> to Rotation3<i64> is
 /// not possible)
-/// * A cast to a type with more type-level invariants cannot be done (eg. a cast from Mat<f64> to
+/// * A cast to a type with more type-level invariants cannot be done (eg. a cast from Matrix<f64> to
-/// Rot3<f64> is not possible)
+/// Rotation3<f64> is not possible)
 /// * For primitive types an unbounded cast is done using the `as` keyword (this is different from
 /// the standard library which makes bound-checking to ensure eg. that a i64 is not out of the
 /// range of an i32 when a cast from i64 to i32 is done).

src/linalg/decompositions.rs

@@ -1,31 +1,31 @@
 use traits::operations::{Transpose, ApproxEq};
-use traits::structure::{ColSlice, Eye, Indexable, Diag, SquareMat, BaseFloat, Cast};
+use traits::structure::{ColumnSlice, Eye, Indexable, Diagonal, SquareMatrix, BaseFloat, Cast};
 use traits::geometry::Norm;
 use std::cmp;
 use std::ops::{Mul, Add, Sub};
 
 /// Get the householder matrix corresponding to a reflexion to the hyperplane
-/// defined by `vec`. It can be a reflexion contained in a subspace.
+/// defined by `vector`. It can be a reflexion contained in a subspace.
 ///
 /// # Arguments
-/// * `dim` - the dimension of the space the resulting matrix operates in
+/// * `dimension` - the dimension of the space the resulting matrix operates in
 /// * `start` - the starting dimension of the subspace of the reflexion
-/// * `vec` - the vector defining the reflection.
+/// * `vector` - the vector defining the reflection.
-pub fn householder_matrix<N, V, M>(dim: usize, start: usize, vec: V) -> M
+pub fn householder_matrix<N, V, M>(dimension: usize, start: usize, vector: V) -> M
     where N: BaseFloat,
           M: Eye + Indexable<(usize, usize), N>,
           V: Indexable<usize, N> {
-    let mut qk : M = Eye::new_identity(dim);
+    let mut qk : M = Eye::new_identity(dimension);
-    let subdim = vec.shape();
+    let subdim = vector.shape();
 
     let stop = subdim + start;
 
-    assert!(dim >= stop);
+    assert!(dimension >= stop);
 
     for j in start .. stop {
         for i in start .. stop {
             unsafe {
-                let vv = vec.unsafe_at(i - start) * vec.unsafe_at(j - start);
+                let vv = vector.unsafe_at(i - start) * vector.unsafe_at(j - start);
                 let qkij = qk.unsafe_at((i, j));
                 qk.unsafe_set((i, j), qkij - vv - vv);
             }
@@ -41,7 +41,7 @@ pub fn householder_matrix<N, V, M>(dim: usize, start: usize, vec: V) -> M
 pub fn qr<N, V, M>(m: &M) -> (M, M)
     where N: BaseFloat,
           V: Indexable<usize, N> + Norm<N>,
-          M: Copy + Eye + ColSlice<V> + Transpose + Indexable<(usize, usize), N> +
+          M: Copy + Eye + ColumnSlice<V> + Transpose + Indexable<(usize, usize), N> +
              Mul<M, Output = M> {
     let (rows, cols) = m.shape();
     assert!(rows >= cols);
@@ -76,29 +76,29 @@ pub fn eigen_qr<N, V, VS, M>(m: &M, eps: &N, niter: usize) -> (M, V)
     where N:  BaseFloat,
           V:  Mul<M, Output = V>,
           VS: Indexable<usize, N> + Norm<N>,
-          M:  Indexable<(usize, usize), N> + SquareMat<N, V> + Add<M, Output = M> +
+          M:  Indexable<(usize, usize), N> + SquareMatrix<N, V> + Add<M, Output = M> +
-              Sub<M, Output = M> + ColSlice<VS> +
+              Sub<M, Output = M> + ColumnSlice<VS> +
               ApproxEq<N> + Copy {
 
     let (mut eigenvectors, mut eigenvalues) = hessenberg(m);
 
     // Allocate arrays for Givens rotation components
-    let mut c = Vec::<N>::with_capacity(::dim::<M>() - 1);
+    let mut c = Vec::<N>::with_capacity(::dimension::<M>() - 1);
-    let mut s = Vec::<N>::with_capacity(::dim::<M>() - 1);
+    let mut s = Vec::<N>::with_capacity(::dimension::<M>() - 1);
 
-    if ::dim::<M>() == 1 {
+    if ::dimension::<M>() == 1 {
-        return (eigenvectors, eigenvalues.diag());
+        return (eigenvectors, eigenvalues.diagonal());
     }
 
     unsafe { 
-        c.set_len(::dim::<M>() - 1);
+        c.set_len(::dimension::<M>() - 1);
-        s.set_len(::dim::<M>() - 1);
+        s.set_len(::dimension::<M>() - 1);
     }
 
     let mut iter = 0;
-    let mut curdim = ::dim::<M>() - 1;
+    let mut curdim = ::dimension::<M>() - 1;
 
-    for _ in 0 .. ::dim::<M>() {
+    for _ in 0 .. ::dimension::<M>() {
 
         let mut stop = false;
 
@@ -113,12 +113,12 @@ pub fn eigen_qr<N, V, VS, M>(m: &M, eps: &N, niter: usize) -> (M, V)
                 let d = eigenvalues.unsafe_at((curdim, curdim));
 
                 let trace = a + d;
-                let det = a * d - b * c;
+                let determinant = a * d - b * c;
 
                 let constquarter: N = Cast::from(0.25f64);
                 let consthalf: N = Cast::from(0.5f64);
 
-                let e = (constquarter * trace * trace - det).sqrt();
+                let e = (constquarter * trace * trace - determinant).sqrt();
 
                 let lambda1 = consthalf * trace + e;
                 let lambda2 = consthalf * trace - e;
@@ -207,7 +207,7 @@ pub fn eigen_qr<N, V, VS, M>(m: &M, eps: &N, niter: usize) -> (M, V)
 
             // Givens rotation from right applied to eigenvectors
             for k in 0 .. curdim {
-                for i in 0 .. ::dim::<M>() {
+                for i in 0 .. ::dimension::<M>() {
 
                     unsafe {
                         let a = eigenvectors.unsafe_at((i, k));
@@ -254,7 +254,7 @@ pub fn eigen_qr<N, V, VS, M>(m: &M, eps: &N, niter: usize) -> (M, V)
 
     }
 
-    (eigenvectors, eigenvalues.diag())
+    (eigenvectors, eigenvalues.diagonal())
 }
 
 /// Cholesky decomposition G of a square symmetric positive definite matrix A, such that A = G * G^T
@@ -265,8 +265,8 @@ pub fn cholesky<N, V, VS, M>(m: &M) -> Result<M, &'static str>
     where N:  BaseFloat,
           V:  Mul<M, Output = V>,
           VS: Indexable<usize, N> + Norm<N>,
-          M:  Indexable<(usize, usize), N> + SquareMat<N, V> + Add<M, Output = M> +
+          M:  Indexable<(usize, usize), N> + SquareMatrix<N, V> + Add<M, Output = M> +
-              Sub<M, Output = M> + ColSlice<VS> +
+              Sub<M, Output = M> + ColumnSlice<VS> +
               ApproxEq<N> + Copy {
 
     let mut out = m.clone().transpose();
@@ -317,7 +317,7 @@ pub fn cholesky<N, V, VS, M>(m: &M) -> Result<M, &'static str>
 pub fn hessenberg<N, V, M>(m: &M) -> (M, M)
     where N: BaseFloat,
           V: Indexable<usize, N> + Norm<N>,
-          M: Copy + Eye + ColSlice<V> + Transpose + Indexable<(usize, usize), N> +
+          M: Copy + Eye + ColumnSlice<V> + Transpose + Indexable<(usize, usize), N> +
              Mul<M, Output = M> {
     
     let mut h = m.clone();

src/structs/dmatrix.rs

@@ -7,41 +7,41 @@ use std::ops::{Add, Sub, Mul, Div, AddAssign, SubAssign, MulAssign, Index, Index
 use std::fmt::{Debug, Formatter, Result};
 use rand::{self, Rand};
 use num::{Zero, One};
-use structs::dvec::{DVec, DVec1, DVec2, DVec3, DVec4, DVec5, DVec6};
+use structs::dvector::{DVector, DVector1, DVector2, DVector3, DVector4, DVector5, DVector6};
-use traits::operations::{ApproxEq, Inv, Transpose, Mean, Cov};
+use traits::operations::{ApproxEq, Inverse, Transpose, Mean, Covariance};
-use traits::structure::{Cast, Col, ColSlice, Row, RowSlice, Diag, DiagMut, Eye, Indexable, Shape, BaseNum};
+use traits::structure::{Cast, Column, ColumnSlice, Row, RowSlice, Diagonal, DiagMut, Eye, Indexable, Shape, BaseNum};
 #[cfg(feature="arbitrary")]
 use quickcheck::{Arbitrary, Gen};
 
 
 /// Matrix with dimensions unknown at compile-time.
 #[derive(Eq, PartialEq, Clone)]
-pub struct DMat<N> {
+pub struct DMatrix<N> {
     nrows: usize,
     ncols: usize,
     mij:   Vec<N>
 }
 
-impl<N> DMat<N> {
+impl<N> DMatrix<N> {
     /// Creates an uninitialized matrix.
     #[inline]
-    pub unsafe fn new_uninitialized(nrows: usize, ncols: usize) -> DMat<N> {
+    pub unsafe fn new_uninitialized(nrows: usize, ncols: usize) -> DMatrix<N> {
-        let mut vec = Vec::with_capacity(nrows * ncols);
+        let mut vector = Vec::with_capacity(nrows * ncols);
-        vec.set_len(nrows * ncols);
+        vector.set_len(nrows * ncols);
 
-        DMat {
+        DMatrix {
             nrows: nrows,
             ncols: ncols,
-            mij:   vec
+            mij:   vector
         }
     }
 }
 
-impl<N: Clone + Copy> DMat<N> {
+impl<N: Clone + Copy> DMatrix<N> {
     /// Builds a matrix filled with a given constant.
     #[inline]
-    pub fn from_elem(nrows: usize, ncols: usize, val: N) -> DMat<N> {
+    pub fn from_elem(nrows: usize, ncols: usize, val: N) -> DMatrix<N> {
-        DMat {
+        DMatrix {
             nrows: nrows,
             ncols: ncols,
             mij:   repeat(val).take(nrows * ncols).collect()
@@ -50,35 +50,35 @@ impl<N: Clone + Copy> DMat<N> {
 
     /// Builds a matrix filled with the components provided by a vector.
     /// The vector contains the matrix data in row-major order.
-    /// Note that `from_col_vec` is much faster than `from_row_vec` since a `DMat` stores its data
+    /// Note that `from_col_vector` is much faster than `from_row_vector` since a `DMatrix` stores its data
     /// in column-major order.
     ///
     /// The vector must have exactly `nrows * ncols` elements.
     #[inline]
-    pub fn from_row_vec(nrows: usize, ncols: usize, vec: &[N]) -> DMat<N> {
+    pub fn from_row_vector(nrows: usize, ncols: usize, vector: &[N]) -> DMatrix<N> {
-        DMat::from_row_iter(nrows, ncols, vec.to_vec())
+        DMatrix::from_row_iter(nrows, ncols, vector.to_vec())
     }
 
     /// Builds a matrix filled with the components provided by a vector.
     /// The vector contains the matrix data in column-major order.
-    /// Note that `from_col_vec` is much faster than `from_row_vec` since a `DMat` stores its data
+    /// Note that `from_col_vector` is much faster than `from_row_vector` since a `DMatrix` stores its data
     /// in column-major order.
     ///
     /// The vector must have exactly `nrows * ncols` elements.
     #[inline]
-    pub fn from_col_vec(nrows: usize, ncols: usize, vec: &[N]) -> DMat<N> {
+    pub fn from_col_vector(nrows: usize, ncols: usize, vector: &[N]) -> DMatrix<N> {
-        DMat::from_col_iter(nrows, ncols, vec.to_vec())
+        DMatrix::from_col_iter(nrows, ncols, vector.to_vec())
     }
 
     /// Builds a matrix filled with the components provided by a source that may be moved into an iterator.
     /// The source contains the matrix data in row-major order.
-    /// Note that `from_col_iter` is much faster than `from_row_iter` since a `DMat` stores its data
+    /// Note that `from_col_iter` is much faster than `from_row_iter` since a `DMatrix` stores its data
     /// in column-major order.
     ///
     /// The source must have exactly `nrows * ncols` elements.
     #[inline]
-    pub fn from_row_iter<I: IntoIterator<Item = N>>(nrows: usize, ncols: usize, param: I) -> DMat<N> {
+    pub fn from_row_iter<I: IntoIterator<Item = N>>(nrows: usize, ncols: usize, param: I) -> DMatrix<N> {
-        let mut res = DMat::from_col_iter(ncols, nrows, param);
+        let mut res = DMatrix::from_col_iter(ncols, nrows, param);
 
         // we transpose because the buffer is row_major
         res.transpose_mut();
@@ -89,17 +89,17 @@ impl<N: Clone + Copy> DMat<N> {
 
     /// Builds a matrix filled with the components provided by a source that may be moved into an iterator.
     /// The source contains the matrix data in column-major order.
-    /// Note that `from_col_iter` is much faster than `from_row_iter` since a `DMat` stores its data
+    /// Note that `from_col_iter` is much faster than `from_row_iter` since a `DMatrix` stores its data
     /// in column-major order.
     ///
     /// The source must have exactly `nrows * ncols` elements.
     #[inline]
-    pub fn from_col_iter<I: IntoIterator<Item = N>>(nrows: usize, ncols: usize, param: I) -> DMat<N> {
+    pub fn from_col_iter<I: IntoIterator<Item = N>>(nrows: usize, ncols: usize, param: I) -> DMatrix<N> {
         let mij: Vec<N> = param.into_iter().collect();
 
         assert!(nrows * ncols == mij.len(), "The ammount of data provided does not matches the matrix size.");
 
-        DMat {
+        DMatrix {
             nrows: nrows,
             ncols: ncols,
             mij:   mij
@@ -107,11 +107,11 @@ impl<N: Clone + Copy> DMat<N> {
     }
 }
 
-impl<N> DMat<N> {
+impl<N> DMatrix<N> {
     /// Builds a matrix filled with the results of a function applied to each of its component coordinates.
     #[inline(always)]
-    pub fn from_fn<F: FnMut(usize, usize) -> N>(nrows: usize, ncols: usize, mut f: F) -> DMat<N> {
+    pub fn from_fn<F: FnMut(usize, usize) -> N>(nrows: usize, ncols: usize, mut f: F) -> DMatrix<N> {
-        DMat {
+        DMatrix {
             nrows: nrows,
             ncols: ncols,
             mij:   (0 .. nrows * ncols).map(|i| { let m = i / nrows; f(i - m * nrows, m) }).collect()
@@ -121,83 +121,83 @@ impl<N> DMat<N> {
     /// Transforms this matrix into an array. This consumes the matrix and is O(1).
     /// The returned vector contains the matrix data in column-major order.
     #[inline]
-    pub fn into_vec(self) -> Vec<N> {
+    pub fn into_vector(self) -> Vec<N> {
         self.mij
     }
 }
 
-dmat_impl!(DMat, DVec);
+dmat_impl!(DMatrix, DVector);
 
 
 /// A stack-allocated dynamically sized matrix with at most one row and column.
-pub struct DMat1<N> {
+pub struct DMatrix1<N> {
     nrows: usize,
     ncols: usize,
     mij:   [N; 1 * 1],
 }
 
-small_dmat_impl!(DMat1, DVec1, 1, 0);
+small_dmat_impl!(DMatrix1, DVector1, 1, 0);
-small_dmat_from_impl!(DMat1, 1, ::zero());
+small_dmat_from_impl!(DMatrix1, 1, ::zero());
 
 
 /// A stack-allocated dynamically sized square or rectangular matrix with at most 2 rows and columns.
-pub struct DMat2<N> {
+pub struct DMatrix2<N> {
     nrows: usize,
     ncols: usize,
     mij:   [N; 2 * 2],
 }
 
-small_dmat_impl!(DMat2, DVec2, 2, 0, 1,
+small_dmat_impl!(DMatrix2, DVector2, 2, 0, 1,
                                   2, 3);
-small_dmat_from_impl!(DMat2, 2, ::zero(), ::zero(),
+small_dmat_from_impl!(DMatrix2, 2, ::zero(), ::zero(),
                                 ::zero(), ::zero());
 
 
 /// A stack-allocated dynamically sized square or rectangular matrix with at most 3 rows and columns.
-pub struct DMat3<N> {
+pub struct DMatrix3<N> {
     nrows: usize,
     ncols: usize,
     mij:   [N; 3 * 3],
 }
 
-small_dmat_impl!(DMat3, DVec3, 3, 0, 1, 2,
+small_dmat_impl!(DMatrix3, DVector3, 3, 0, 1, 2,
                                   3, 4, 5,
                                   6, 7, 8);
-small_dmat_from_impl!(DMat3, 3, ::zero(), ::zero(), ::zero(),
+small_dmat_from_impl!(DMatrix3, 3, ::zero(), ::zero(), ::zero(),
                                 ::zero(), ::zero(), ::zero(),
                                 ::zero(), ::zero(), ::zero());
 
 
 /// A stack-allocated dynamically sized square or rectangular matrix with at most 4 rows and columns.
-pub struct DMat4<N> {
+pub struct DMatrix4<N> {
     nrows: usize,
     ncols: usize,
     mij:   [N; 4 * 4],
 }
 
-small_dmat_impl!(DMat4, DVec4, 4,  0,  1,  2,  3,
+small_dmat_impl!(DMatrix4, DVector4, 4,  0,  1,  2,  3,
                                    4,  5,  6,  7,
                                    8,  9,  10, 11,
                                    12, 13, 14, 15);
-small_dmat_from_impl!(DMat4, 4, ::zero(), ::zero(), ::zero(), ::zero(),
+small_dmat_from_impl!(DMatrix4, 4, ::zero(), ::zero(), ::zero(), ::zero(),
                                 ::zero(), ::zero(), ::zero(), ::zero(),
                                 ::zero(), ::zero(), ::zero(), ::zero(),
                                 ::zero(), ::zero(), ::zero(), ::zero());
 
 
 /// A stack-allocated dynamically sized square or rectangular matrix with at most 5 rows and columns.
-pub struct DMat5<N> {
+pub struct DMatrix5<N> {
     nrows: usize,
     ncols: usize,
     mij:   [N; 5 * 5],
 }
 
-small_dmat_impl!(DMat5, DVec5, 5, 0,  1,  2,  3,  4,
+small_dmat_impl!(DMatrix5, DVector5, 5, 0,  1,  2,  3,  4,
                                   5,  6,  7,  8,  9,
                                   10, 11, 12, 13, 14,
                                   15, 16, 17, 18, 19,
                                   20, 21, 22, 23, 24);
-small_dmat_from_impl!(DMat5, 5, ::zero(), ::zero(), ::zero(), ::zero(), ::zero(),
+small_dmat_from_impl!(DMatrix5, 5, ::zero(), ::zero(), ::zero(), ::zero(), ::zero(),
                                 ::zero(), ::zero(), ::zero(), ::zero(), ::zero(),
                                 ::zero(), ::zero(), ::zero(), ::zero(), ::zero(),
                                 ::zero(), ::zero(), ::zero(), ::zero(), ::zero(),
@@ -205,19 +205,19 @@ small_dmat_from_impl!(DMat5, 5, ::zero(), ::zero(), ::zero(), ::zero(), ::zero()
 
 
 /// A stack-allocated dynamically sized square or rectangular matrix with at most 6 rows and columns.
-pub struct DMat6<N> {
+pub struct DMatrix6<N> {
     nrows: usize,
     ncols: usize,
     mij:   [N; 6 * 6],
 }
 
-small_dmat_impl!(DMat6, DVec6, 6, 0,  1,  2,  3,  4,  5,
+small_dmat_impl!(DMatrix6, DVector6, 6, 0,  1,  2,  3,  4,  5,
                                   6,  7,  8,  9,  10, 11,
                                   12, 13, 14, 15, 16, 17,
                                   18, 19, 20, 21, 22, 23,
                                   24, 25, 26, 27, 28, 29,
                                   30, 31, 32, 33, 34, 35);
-small_dmat_from_impl!(DMat6, 6, ::zero(), ::zero(), ::zero(), ::zero(), ::zero(), ::zero(),
+small_dmat_from_impl!(DMatrix6, 6, ::zero(), ::zero(), ::zero(), ::zero(), ::zero(), ::zero(),
                                 ::zero(), ::zero(), ::zero(), ::zero(), ::zero(), ::zero(),
                                 ::zero(), ::zero(), ::zero(), ::zero(), ::zero(), ::zero(),
                                 ::zero(), ::zero(), ::zero(), ::zero(), ::zero(), ::zero(),

src/structs/dvec.rs

@@ -1,164 +0,0 @@
-//! Vector with dimensions unknown at compile-time.
-
-use std::slice::{Iter, IterMut};
-use std::iter::{FromIterator, IntoIterator};
-use std::iter::repeat;
-use std::ops::{Add, Sub, Mul, Div, Neg, AddAssign, SubAssign, MulAssign, DivAssign, Index, IndexMut};
-use std::mem;
-use rand::{self, Rand};
-use num::{Zero, One};
-use structs::DMat;
-use traits::operations::{ApproxEq, Axpy, Mean, Outer};
-use traits::geometry::{Dot, Norm};
-use traits::structure::{Iterable, IterableMut, Indexable, Shape, BaseFloat, BaseNum, Cast};
-#[cfg(feature="arbitrary")]
-use quickcheck::{Arbitrary, Gen};
-
-/// Heap allocated, dynamically sized vector.
-#[derive(Eq, PartialEq, Debug, Clone)]
-pub struct DVec<N> {
-    /// Components of the vector. Contains as much elements as the vector dimension.
-    pub at: Vec<N>
-}
-
-impl<N> DVec<N> {
-    /// Creates an uninitialized vec.
-    #[inline]
-    pub unsafe fn new_uninitialized(dim: usize) -> DVec<N> {
-        let mut vec = Vec::with_capacity(dim);
-        vec.set_len(dim);
-
-        DVec {
-            at: vec
-        }
-    }
-}
-
-impl<N: Clone> DVec<N> {
-    /// Builds a vector filled with a constant.
-    #[inline]
-    pub fn from_elem(dim: usize, elem: N) -> DVec<N> {
-        DVec { at: repeat(elem).take(dim).collect() }
-    }
-
-    /// Builds a vector filled with the components provided by a vector.
-    ///
-    /// The vector must have at least `dim` elements.
-    #[inline]
-    pub fn from_slice(dim: usize, vec: &[N]) -> DVec<N> {
-        assert!(dim <= vec.len());
-
-        DVec {
-            at: vec[.. dim].to_vec()
-        }
-    }
-}
-
-impl<N> DVec<N> {
-    /// Builds a vector filled with the results of a function applied to each of its component coordinates.
-    #[inline(always)]
-    pub fn from_fn<F: FnMut(usize) -> N>(dim: usize, mut f: F) -> DVec<N> {
-        DVec { at: (0 .. dim).map(|i| f(i)).collect() }
-    }
-
-    /// The vector length.
-    #[inline]
-    pub fn len(&self) -> usize {
-        self.at.len()
-    }
-}
-
-impl<N> FromIterator<N> for DVec<N> {
-    #[inline]
-    fn from_iter<I: IntoIterator<Item = N>>(param: I) -> DVec<N> {
-        DVec { at: param.into_iter().collect() }
-    }
-}
-
-impl<N: Copy + BaseNum> Outer for DVec<N> {
-    type OuterProductType = DMat<N>;
-
-    #[inline]
-    fn outer(&self, other: &DVec<N>) -> DMat<N> {
-        let mut res = unsafe { DMat::new_uninitialized(self.at.len(), other.at.len()) };
-
-        for i in 0 .. self.at.len() {
-            for j in 0 .. other.at.len() {
-                unsafe {
-                    res.unsafe_set((i, j), self.unsafe_at(i) * other.unsafe_at(j));
-                }
-            }
-        }
-
-        res
-    }
-}
-
-#[cfg(feature="arbitrary")]
-impl<N: Arbitrary> Arbitrary for DVec<N> {
-    fn arbitrary<G: Gen>(g: &mut G) -> DVec<N> {
-        DVec { at: Arbitrary::arbitrary(g) }
-    }
-}
-
-
-dvec_impl!(DVec);
-
-/// Stack-allocated, dynamically sized vector with a maximum size of 1.
-pub struct DVec1<N> {
-    at:  [N; 1],
-    dim: usize
-}
-
-small_dvec_impl!(DVec1, 1, 0);
-small_dvec_from_impl!(DVec1, 1, ::zero());
-
-
-/// Stack-allocated, dynamically sized vector with a maximum size of 2.
-pub struct DVec2<N> {
-    at:  [N; 2],
-    dim: usize
-}
-
-small_dvec_impl!(DVec2, 2, 0, 1);
-small_dvec_from_impl!(DVec2, 2, ::zero(), ::zero());
-
-
-/// Stack-allocated, dynamically sized vector with a maximum size of 3.
-pub struct DVec3<N> {
-    at:  [N; 3],
-    dim: usize
-}
-
-small_dvec_impl!(DVec3, 3, 0, 1, 2);
-small_dvec_from_impl!(DVec3, 3, ::zero(), ::zero(), ::zero());
-
-
-/// Stack-allocated, dynamically sized vector with a maximum size of 4.
-pub struct DVec4<N> {
-    at:  [N; 4],
-    dim: usize
-}
-
-small_dvec_impl!(DVec4, 4, 0, 1, 2, 3);
-small_dvec_from_impl!(DVec4, 4, ::zero(), ::zero(), ::zero(), ::zero());
-
-
-/// Stack-allocated, dynamically sized vector with a maximum size of 5.
-pub struct DVec5<N> {
-    at:  [N; 5],
-    dim: usize
-}
-
-small_dvec_impl!(DVec5, 5, 0, 1, 2, 3, 4);
-small_dvec_from_impl!(DVec5, 5, ::zero(), ::zero(), ::zero(), ::zero(), ::zero());
-
-
-/// Stack-allocated, dynamically sized vector with a maximum size of 6.
-pub struct DVec6<N> {
-    at:  [N; 6],
-    dim: usize
-}
-
-small_dvec_impl!(DVec6, 6, 0, 1, 2, 3, 4, 5);
-small_dvec_from_impl!(DVec6, 6, ::zero(), ::zero(), ::zero(), ::zero(), ::zero(), ::zero());

src/structs/dvec_macros.rs

@@ -1,243 +0,0 @@
-#![macro_use]
-
-macro_rules! dvec_impl(
-    ($dvec: ident) => (
-        vecn_dvec_common_impl!($dvec);
-
-        impl<N: Zero + Copy + Clone> $dvec<N> {
-            /// Builds a vector filled with zeros.
-            ///
-            /// # Arguments
-            /// * `dim` - The dimension of the vector.
-            #[inline]
-            pub fn new_zeros(dim: usize) -> $dvec<N> {
-                $dvec::from_elem(dim, ::zero())
-            }
-        }
-
-        impl<N: One + Zero + Copy + Clone> $dvec<N> {
-            /// Builds a vector filled with ones.
-            ///
-            /// # Arguments
-            /// * `dim` - The dimension of the vector.
-            #[inline]
-            pub fn new_ones(dim: usize) -> $dvec<N> {
-                $dvec::from_elem(dim, ::one())
-            }
-        }
-
-        impl<N: Rand + Zero> $dvec<N> {
-            /// Builds a vector filled with random values.
-            #[inline]
-            pub fn new_random(dim: usize) -> $dvec<N> {
-                $dvec::from_fn(dim, |_| rand::random())
-            }
-        }
-
-        impl<N: BaseFloat + ApproxEq<N>> $dvec<N> {
-            /// Computes the canonical basis for the given dimension. A canonical basis is a set of
-            /// vectors, mutually orthogonal, with all its component equal to 0.0 except one which is equal
-            /// to 1.0.
-            pub fn canonical_basis_with_dim(dim: usize) -> Vec<$dvec<N>> {
-                let mut res : Vec<$dvec<N>> = Vec::new();
-
-                for i in 0 .. dim {
-                    let mut basis_element : $dvec<N> = $dvec::new_zeros(dim);
-
-                    basis_element[i] = ::one();
-
-                    res.push(basis_element);
-                }
-
-                res
-            }
-
-            /// Computes a basis of the space orthogonal to the vector. If the input vector is of dimension
-            /// `n`, this will return `n - 1` vectors.
-            pub fn orthogonal_subspace_basis(&self) -> Vec<$dvec<N>> {
-                // compute the basis of the orthogonal subspace using Gram-Schmidt
-                // orthogonalization algorithm
-                let     dim                 = self.len();
-                let mut res : Vec<$dvec<N>> = Vec::new();
-
-                for i in 0 .. dim {
-                    let mut basis_element : $dvec<N> = $dvec::new_zeros(self.len());
-
-                    basis_element[i] = ::one();
-
-                    if res.len() == dim - 1 {
-                        break;
-                    }
-
-                    let mut elt = basis_element.clone();
-
-                    elt.axpy(&-::dot(&basis_element, self), self);
-
-                    for v in res.iter() {
-                        let proj = ::dot(&elt, v);
-                        elt.axpy(&-proj, v)
-                    };
-
-                    if !ApproxEq::approx_eq(&Norm::sqnorm(&elt), &::zero()) {
-                        res.push(Norm::normalize(&elt));
-                    }
-                }
-
-                assert!(res.len() == dim - 1);
-
-                res
-            }
-        }
-    )
-);
-
-macro_rules! small_dvec_impl (
-    ($dvec: ident, $dim: expr, $($idx: expr),*) => (
-        dvec_impl!($dvec);
-
-        impl<N> $dvec<N> {
-            /// The number of elements of this vector.
-            #[inline]
-            pub fn len(&self) -> usize {
-                self.dim
-            }
-
-            /// Creates an uninitialized vec of dimension `dim`.
-            #[inline]
-            pub unsafe fn new_uninitialized(dim: usize) -> $dvec<N> {
-                assert!(dim <= $dim, "The chosen dimension is too high for that type of \
-                                      stack-allocated dynamic vector. Consider using the \
-                                      heap-allocated vector: DVec.");
-
-                $dvec {
-                    at:  mem::uninitialized(),
-                    dim: dim
-                }
-            }
-        }
-
-        impl<N: PartialEq> PartialEq for $dvec<N> {
-            #[inline]
-            fn eq(&self, other: &$dvec<N>) -> bool {
-                if self.len() != other.len() {
-                    return false; // FIXME: fail instead?
-                }
-
-                for (a, b) in self.as_ref().iter().zip(other.as_ref().iter()) {
-                    if *a != *b {
-                        return false;
-                    }
-                }
-
-                true
-            }
-        }
-
-        impl<N: Clone> Clone for $dvec<N> {
-            fn clone(&self) -> $dvec<N> {
-                let at: [N; $dim] = [ $( self.at[$idx].clone(), )* ];
-
-                $dvec {
-                    at:  at,
-                    dim: self.dim
-                }
-            }
-        }
-    )
-);
-
-macro_rules! small_dvec_from_impl (
-    ($dvec: ident, $dim: expr, $($zeros: expr),*) => (
-        impl<N: Copy + Zero> $dvec<N> {
-            /// Builds a vector filled with a constant.
-            #[inline]
-            pub fn from_elem(dim: usize, elem: N) -> $dvec<N> {
-                assert!(dim <= $dim);
-
-                let mut at: [N; $dim] = [ $( $zeros, )* ];
-
-                for n in &mut at[.. dim] {
-                    *n = elem;
-                }
-
-                $dvec {
-                    at:  at,
-                    dim: dim
-                }
-            }
-        }
-
-        impl<N: Copy + Zero> $dvec<N> {
-            /// Builds a vector filled with the components provided by a vector.
-            ///
-            /// The vector must have at least `dim` elements.
-            #[inline]
-            pub fn from_slice(dim: usize, vec: &[N]) -> $dvec<N> {
-                assert!(dim <= vec.len() && dim <= $dim);
-
-                // FIXME: not safe.
-                let mut at: [N; $dim] = [ $( $zeros, )* ];
-
-                for (curr, other) in vec.iter().zip(at.iter_mut()) {
-                    *other = *curr;
-                }
-
-                $dvec {
-                    at:  at,
-                    dim: dim
-                }
-            }
-        }
-
-        impl<N: Zero> $dvec<N> {
-            /// Builds a vector filled with the result of a function.
-            #[inline(always)]
-            pub fn from_fn<F: FnMut(usize) -> N>(dim: usize, mut f: F) -> $dvec<N> {
-                assert!(dim <= $dim);
-
-                let mut at: [N; $dim] = [ $( $zeros, )* ];
-
-                for i in 0 .. dim {
-                    at[i] = f(i);
-                }
-
-                $dvec {
-                    at:  at,
-                    dim: dim
-                }
-            }
-        }
-
-        impl<N: Zero> FromIterator<N> for $dvec<N> {
-            #[inline]
-            fn from_iter<I: IntoIterator<Item = N>>(param: I) -> $dvec<N> {
-                let mut at: [N; $dim] = [ $( $zeros, )* ];
-
-                let mut dim = 0;
-
-                for n in param.into_iter() {
-                    if dim == $dim {
-                        break;
-                    }
-
-                    at[dim] = n;
-
-                    dim = dim + 1;
-                }
-
-                $dvec {
-                    at:  at,
-                    dim: dim
-                }
-            }
-        }
-
-        #[cfg(feature="arbitrary")]
-        impl<N: Arbitrary + Zero> Arbitrary for $dvec<N> {
-            #[inline]
-            fn arbitrary<G: Gen>(g: &mut G) -> $dvec<N> {
-                $dvec::from_fn(g.gen_range(0, $dim), |_| Arbitrary::arbitrary(g))
-            }
-        }
-    )
-);

src/structs/dvector.rs

@@ -0,0 +1,164 @@
+//! Vector with dimensions unknown at compile-time.
+
+use std::slice::{Iter, IterMut};
+use std::iter::{FromIterator, IntoIterator};
+use std::iter::repeat;
+use std::ops::{Add, Sub, Mul, Div, Neg, AddAssign, SubAssign, MulAssign, DivAssign, Index, IndexMut};
+use std::mem;
+use rand::{self, Rand};
+use num::{Zero, One};
+use structs::DMatrix;
+use traits::operations::{ApproxEq, Axpy, Mean, Outer};
+use traits::geometry::{Dot, Norm};
+use traits::structure::{Iterable, IterableMut, Indexable, Shape, BaseFloat, BaseNum, Cast};
+#[cfg(feature="arbitrary")]
+use quickcheck::{Arbitrary, Gen};
+
+/// Heap allocated, dynamically sized vector.
+#[derive(Eq, PartialEq, Debug, Clone)]
+pub struct DVector<N> {
+    /// Components of the vector. Contains as much elements as the vector dimension.
+    pub at: Vec<N>
+}
+
+impl<N> DVector<N> {
+    /// Creates an uninitialized vector.
+    #[inline]
+    pub unsafe fn new_uninitialized(dimension: usize) -> DVector<N> {
+        let mut vector = Vec::with_capacity(dimension);
+        vector.set_len(dimension);
+
+        DVector {
+            at: vector
+        }
+    }
+}
+
+impl<N: Clone> DVector<N> {
+    /// Builds a vector filled with a constant.
+    #[inline]
+    pub fn from_elem(dimension: usize, elem: N) -> DVector<N> {
+        DVector { at: repeat(elem).take(dimension).collect() }
+    }
+
+    /// Builds a vector filled with the components provided by a vector.
+    ///
+    /// The vector must have at least `dimension` elements.
+    #[inline]
+    pub fn from_slice(dimension: usize, vector: &[N]) -> DVector<N> {
+        assert!(dimension <= vector.len());
+
+        DVector {
+            at: vector[.. dimension].to_vec()
+        }
+    }
+}
+
+impl<N> DVector<N> {
+    /// Builds a vector filled with the results of a function applied to each of its component coordinates.
+    #[inline(always)]
+    pub fn from_fn<F: FnMut(usize) -> N>(dimension: usize, mut f: F) -> DVector<N> {
+        DVector { at: (0 .. dimension).map(|i| f(i)).collect() }
+    }
+
+    /// The vector length.
+    #[inline]
+    pub fn len(&self) -> usize {
+        self.at.len()
+    }
+}
+
+impl<N> FromIterator<N> for DVector<N> {
+    #[inline]
+    fn from_iter<I: IntoIterator<Item = N>>(param: I) -> DVector<N> {
+        DVector { at: param.into_iter().collect() }
+    }
+}
+
+impl<N: Copy + BaseNum> Outer for DVector<N> {
+    type OuterProductType = DMatrix<N>;
+
+    #[inline]
+    fn outer(&self, other: &DVector<N>) -> DMatrix<N> {
+        let mut res = unsafe { DMatrix::new_uninitialized(self.at.len(), other.at.len()) };
+
+        for i in 0 .. self.at.len() {
+            for j in 0 .. other.at.len() {
+                unsafe {
+                    res.unsafe_set((i, j), self.unsafe_at(i) * other.unsafe_at(j));
+                }
+            }
+        }
+
+        res
+    }
+}
+
+#[cfg(feature="arbitrary")]
+impl<N: Arbitrary> Arbitrary for DVector<N> {
+    fn arbitrary<G: Gen>(g: &mut G) -> DVector<N> {
+        DVector { at: Arbitrary::arbitrary(g) }
+    }
+}
+
+
+dvec_impl!(DVector);
+
+/// Stack-allocated, dynamically sized vector with a maximum size of 1.
+pub struct DVector1<N> {
+    at:  [N; 1],
+    dimension: usize
+}
+
+small_dvec_impl!(DVector1, 1, 0);
+small_dvec_from_impl!(DVector1, 1, ::zero());
+
+
+/// Stack-allocated, dynamically sized vector with a maximum size of 2.
+pub struct DVector2<N> {
+    at:  [N; 2],
+    dimension: usize
+}
+
+small_dvec_impl!(DVector2, 2, 0, 1);
+small_dvec_from_impl!(DVector2, 2, ::zero(), ::zero());
+
+
+/// Stack-allocated, dynamically sized vector with a maximum size of 3.
+pub struct DVector3<N> {
+    at:  [N; 3],
+    dimension: usize
+}
+
+small_dvec_impl!(DVector3, 3, 0, 1, 2);
+small_dvec_from_impl!(DVector3, 3, ::zero(), ::zero(), ::zero());
+
+
+/// Stack-allocated, dynamically sized vector with a maximum size of 4.
+pub struct DVector4<N> {
+    at:  [N; 4],
+    dimension: usize
+}
+
+small_dvec_impl!(DVector4, 4, 0, 1, 2, 3);
+small_dvec_from_impl!(DVector4, 4, ::zero(), ::zero(), ::zero(), ::zero());
+
+
+/// Stack-allocated, dynamically sized vector with a maximum size of 5.
+pub struct DVector5<N> {
+    at:  [N; 5],
+    dimension: usize
+}
+
+small_dvec_impl!(DVector5, 5, 0, 1, 2, 3, 4);
+small_dvec_from_impl!(DVector5, 5, ::zero(), ::zero(), ::zero(), ::zero(), ::zero());
+
+
+/// Stack-allocated, dynamically sized vector with a maximum size of 6.
+pub struct DVector6<N> {
+    at:  [N; 6],
+    dimension: usize
+}
+
+small_dvec_impl!(DVector6, 6, 0, 1, 2, 3, 4, 5);
+small_dvec_from_impl!(DVector6, 6, ::zero(), ::zero(), ::zero(), ::zero(), ::zero(), ::zero());

src/structs/dvector_macros.rs

@@ -0,0 +1,243 @@
+#![macro_use]
+
+macro_rules! dvec_impl(
+    ($dvector: ident) => (
+        vecn_dvec_common_impl!($dvector);
+
+        impl<N: Zero + Copy + Clone> $dvector<N> {
+            /// Builds a vector filled with zeros.
+            ///
+            /// # Arguments
+            /// * `dimension` - The dimension of the vector.
+            #[inline]
+            pub fn new_zeros(dimension: usize) -> $dvector<N> {
+                $dvector::from_elem(dimension, ::zero())
+            }
+        }
+
+        impl<N: One + Zero + Copy + Clone> $dvector<N> {
+            /// Builds a vector filled with ones.
+            ///
+            /// # Arguments
+            /// * `dimension` - The dimension of the vector.
+            #[inline]
+            pub fn new_ones(dimension: usize) -> $dvector<N> {
+                $dvector::from_elem(dimension, ::one())
+            }
+        }
+
+        impl<N: Rand + Zero> $dvector<N> {
+            /// Builds a vector filled with random values.
+            #[inline]
+            pub fn new_random(dimension: usize) -> $dvector<N> {
+                $dvector::from_fn(dimension, |_| rand::random())
+            }
+        }
+
+        impl<N: BaseFloat + ApproxEq<N>> $dvector<N> {
+            /// Computes the canonical basis for the given dimension. A canonical basis is a set of
+            /// vectors, mutually orthogonal, with all its component equal to 0.0 except one which is equal
+            /// to 1.0.
+            pub fn canonical_basis_with_dim(dimension: usize) -> Vec<$dvector<N>> {
+                let mut res : Vec<$dvector<N>> = Vec::new();
+
+                for i in 0 .. dimension {
+                    let mut basis_element : $dvector<N> = $dvector::new_zeros(dimension);
+
+                    basis_element[i] = ::one();
+
+                    res.push(basis_element);
+                }
+
+                res
+            }
+
+            /// Computes a basis of the space orthogonal to the vector. If the input vector is of dimension
+            /// `n`, this will return `n - 1` vectors.
+            pub fn orthogonal_subspace_basis(&self) -> Vec<$dvector<N>> {
+                // compute the basis of the orthogonal subspace using Gram-Schmidt
+                // orthogonalization algorithm
+                let     dimension                 = self.len();
+                let mut res : Vec<$dvector<N>> = Vec::new();
+
+                for i in 0 .. dimension {
+                    let mut basis_element : $dvector<N> = $dvector::new_zeros(self.len());
+
+                    basis_element[i] = ::one();
+
+                    if res.len() == dimension - 1 {
+                        break;
+                    }
+
+                    let mut elt = basis_element.clone();
+
+                    elt.axpy(&-::dot(&basis_element, self), self);
+
+                    for v in res.iter() {
+                        let proj = ::dot(&elt, v);
+                        elt.axpy(&-proj, v)
+                    };
+
+                    if !ApproxEq::approx_eq(&Norm::norm_squared(&elt), &::zero()) {
+                        res.push(Norm::normalize(&elt));
+                    }
+                }
+
+                assert!(res.len() == dimension - 1);
+
+                res
+            }
+        }
+    )
+);
+
+macro_rules! small_dvec_impl (
+    ($dvector: ident, $dimension: expr, $($idx: expr),*) => (
+        dvec_impl!($dvector);
+
+        impl<N> $dvector<N> {
+            /// The number of elements of this vector.
+            #[inline]
+            pub fn len(&self) -> usize {
+                self.dimension
+            }
+
+            /// Creates an uninitialized vector of dimension `dimension`.
+            #[inline]
+            pub unsafe fn new_uninitialized(dimension: usize) -> $dvector<N> {
+                assert!(dimension <= $dimension, "The chosen dimension is too high for that type of \
+                                      stack-allocated dynamic vector. Consider using the \
+                                      heap-allocated vector: DVector.");
+
+                $dvector {
+                    at:  mem::uninitialized(),
+                    dimension: dimension
+                }
+            }
+        }
+
+        impl<N: PartialEq> PartialEq for $dvector<N> {
+            #[inline]
+            fn eq(&self, other: &$dvector<N>) -> bool {
+                if self.len() != other.len() {
+                    return false; // FIXME: fail instead?
+                }
+
+                for (a, b) in self.as_ref().iter().zip(other.as_ref().iter()) {
+                    if *a != *b {
+                        return false;
+                    }
+                }
+
+                true
+            }
+        }
+
+        impl<N: Clone> Clone for $dvector<N> {
+            fn clone(&self) -> $dvector<N> {
+                let at: [N; $dimension] = [ $( self.at[$idx].clone(), )* ];
+
+                $dvector {
+                    at:  at,
+                    dimension: self.dimension
+                }
+            }
+        }
+    )
+);
+
+macro_rules! small_dvec_from_impl (
+    ($dvector: ident, $dimension: expr, $($zeros: expr),*) => (
+        impl<N: Copy + Zero> $dvector<N> {
+            /// Builds a vector filled with a constant.
+            #[inline]
+            pub fn from_elem(dimension: usize, elem: N) -> $dvector<N> {
+                assert!(dimension <= $dimension);
+
+                let mut at: [N; $dimension] = [ $( $zeros, )* ];
+
+                for n in &mut at[.. dimension] {
+                    *n = elem;
+                }
+
+                $dvector {
+                    at:  at,
+                    dimension: dimension
+                }
+            }
+        }
+
+        impl<N: Copy + Zero> $dvector<N> {
+            /// Builds a vector filled with the components provided by a vector.
+            ///
+            /// The vector must have at least `dimension` elements.
+            #[inline]
+            pub fn from_slice(dimension: usize, vector: &[N]) -> $dvector<N> {
+                assert!(dimension <= vector.len() && dimension <= $dimension);
+
+                // FIXME: not safe.
+                let mut at: [N; $dimension] = [ $( $zeros, )* ];
+
+                for (curr, other) in vector.iter().zip(at.iter_mut()) {
+                    *other = *curr;
+                }
+
+                $dvector {
+                    at:  at,
+                    dimension: dimension
+                }
+            }
+        }
+
+        impl<N: Zero> $dvector<N> {
+            /// Builds a vector filled with the result of a function.
+            #[inline(always)]
+            pub fn from_fn<F: FnMut(usize) -> N>(dimension: usize, mut f: F) -> $dvector<N> {
+                assert!(dimension <= $dimension);
+
+                let mut at: [N; $dimension] = [ $( $zeros, )* ];
+
+                for i in 0 .. dimension {
+                    at[i] = f(i);
+                }
+
+                $dvector {
+                    at:  at,
+                    dimension: dimension
+                }
+            }
+        }
+
+        impl<N: Zero> FromIterator<N> for $dvector<N> {
+            #[inline]
+            fn from_iter<I: IntoIterator<Item = N>>(param: I) -> $dvector<N> {
+                let mut at: [N; $dimension] = [ $( $zeros, )* ];
+
+                let mut dimension = 0;
+
+                for n in param.into_iter() {
+                    if dimension == $dimension {
+                        break;
+                    }
+
+                    at[dimension] = n;
+
+                    dimension = dimension + 1;
+                }
+
+                $dvector {
+                    at:  at,
+                    dimension: dimension
+                }
+            }
+        }
+
+        #[cfg(feature="arbitrary")]
+        impl<N: Arbitrary + Zero> Arbitrary for $dvector<N> {
+            #[inline]
+            fn arbitrary<G: Gen>(g: &mut G) -> $dvector<N> {
+                $dvector::from_fn(g.gen_range(0, $dimension), |_| Arbitrary::arbitrary(g))
+            }
+        }
+    )
+);

src/structs/iso.rs

@@ -1,144 +0,0 @@
-use std::fmt;
-use std::ops::{Add, Sub, Mul, Neg, MulAssign};
-
-use rand::{Rand, Rng};
-use num::One;
-use structs::mat::{Mat3, Mat4};
-use traits::structure::{Cast, Dim, Col, BaseFloat, BaseNum};
-use traits::operations::{Inv, ApproxEq};
-use traits::geometry::{RotationMatrix, Rotation, Rotate, AbsoluteRotate, Transform, Transformation,
-                       Translate, Translation, ToHomogeneous};
-use structs::vec::{Vec1, Vec2, Vec3};
-use structs::pnt::{Pnt2, Pnt3};
-use structs::rot::{Rot2, Rot3};
-
-#[cfg(feature="arbitrary")]
-use quickcheck::{Arbitrary, Gen};
-
-
-/// Two dimensional **direct** isometry.
-///
-/// This is the composition of a rotation followed by a translation. Vectors `Vec2` are not
-/// affected by the translational component of this transformation while points `Pnt2` are.
-/// Isometries conserve angles and distances, hence do not allow shearing nor scaling.
-#[repr(C)]
-#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Debug, Copy)]
-pub struct Iso2<N> {
-    /// The rotation applicable by this isometry.
-    pub rotation:    Rot2<N>,
-    /// The translation applicable by this isometry.
-    pub translation: Vec2<N>
-}
-
-/// Three dimensional **direct** isometry.
-///
-/// This is the composition of a rotation followed by a translation. Vectors `Vec3` are not
-/// affected by the translational component of this transformation while points `Pnt3` are.
-/// Isometries conserve angles and distances, hence do not allow shearing nor scaling.
-#[repr(C)]
-#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Debug, Copy)]
-pub struct Iso3<N> {
-    /// The rotation applicable by this isometry.
-    pub rotation:    Rot3<N>,
-    /// The translation applicable by this isometry.
-    pub translation: Vec3<N>
-}
-
-impl<N: Clone + BaseFloat> Iso3<N> {
-    /// Creates an isometry that corresponds to the local frame of an observer standing at the
-    /// point `eye` and looking toward `target`.
-    ///
-    /// It maps the view direction `target - eye` to the positive `z` axis and the origin to the
-    /// `eye`.
-    ///
-    /// # Arguments
-    ///   * eye - The observer position.
-    ///   * target - The target position.
-    ///   * 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: &Pnt3<N>, target: &Pnt3<N>, up: &Vec3<N>) -> Iso3<N> {
-        let new_rotmat = Rot3::new_observer_frame(&(*target - *eye), up);
-        Iso3::new_with_rotmat(eye.as_vec().clone(), new_rotmat)
-    }
-
-    /// Builds a right-handed look-at view matrix.
-    ///
-    /// This conforms to the common notion of right handed look-at matrix from the computer
-    /// graphics community.
-    ///
-    /// # Arguments
-    ///   * eye - The eye position.
-    ///   * target - The target position.
-    ///   * 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: &Pnt3<N>, target: &Pnt3<N>, up: &Vec3<N>) -> Iso3<N> {
-        let rot   = Rot3::look_at_rh(&(*target - *eye), up);
-        let trans = rot * (-*eye);
-
-        Iso3::new_with_rotmat(trans.to_vec(), rot)
-    }
-
-    /// Builds a left-handed look-at view matrix.
-    ///
-    /// This conforms to the common notion of left handed look-at matrix from the computer
-    /// graphics community.
-    ///
-    /// # Arguments
-    ///   * eye - The eye position.
-    ///   * target - The target position.
-    ///   * 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: &Pnt3<N>, target: &Pnt3<N>, up: &Vec3<N>) -> Iso3<N> {
-        let rot   = Rot3::look_at_lh(&(*target - *eye), up);
-        let trans = rot * (-*eye);
-
-        Iso3::new_with_rotmat(trans.to_vec(), rot)
-    }
-}
-
-iso_impl!(Iso2, Rot2, Vec2, Vec1);
-rotation_matrix_impl!(Iso2, Rot2, Vec2, Vec1);
-rotation_impl!(Iso2, Rot2, Vec1);
-dim_impl!(Iso2, 2);
-one_impl!(Iso2);
-absolute_rotate_impl!(Iso2, Vec2);
-rand_impl!(Iso2);
-approx_eq_impl!(Iso2);
-to_homogeneous_impl!(Iso2, Mat3);
-inv_impl!(Iso2);
-transform_impl!(Iso2, Pnt2);
-transformation_impl!(Iso2);
-rotate_impl!(Iso2, Vec2);
-translation_impl!(Iso2, Vec2);
-translate_impl!(Iso2, Pnt2);
-iso_mul_iso_impl!(Iso2);
-iso_mul_rot_impl!(Iso2, Rot2);
-iso_mul_pnt_impl!(Iso2, Pnt2);
-iso_mul_vec_impl!(Iso2, Vec2);
-arbitrary_iso_impl!(Iso2);
-iso_display_impl!(Iso2);
-
-iso_impl!(Iso3, Rot3, Vec3, Vec3);
-rotation_matrix_impl!(Iso3, Rot3, Vec3, Vec3);
-rotation_impl!(Iso3, Rot3, Vec3);
-dim_impl!(Iso3, 3);
-one_impl!(Iso3);
-absolute_rotate_impl!(Iso3, Vec3);
-rand_impl!(Iso3);
-approx_eq_impl!(Iso3);
-to_homogeneous_impl!(Iso3, Mat4);
-inv_impl!(Iso3);
-transform_impl!(Iso3, Pnt3);
-transformation_impl!(Iso3);
-rotate_impl!(Iso3, Vec3);
-translation_impl!(Iso3, Vec3);
-translate_impl!(Iso3, Pnt3);
-iso_mul_iso_impl!(Iso3);
-iso_mul_rot_impl!(Iso3, Rot3);
-iso_mul_pnt_impl!(Iso3, Pnt3);
-iso_mul_vec_impl!(Iso3, Vec3);
-arbitrary_iso_impl!(Iso3);
-iso_display_impl!(Iso3);

src/structs/isometry.rs

@@ -0,0 +1,144 @@
+use std::fmt;
+use std::ops::{Add, Sub, Mul, Neg, MulAssign};
+
+use rand::{Rand, Rng};
+use num::One;
+use structs::matrix::{Matrix3, Matrix4};
+use traits::structure::{Cast, Dimension, Column, BaseFloat, BaseNum};
+use traits::operations::{Inverse, ApproxEq};
+use traits::geometry::{RotationMatrix, Rotation, Rotate, AbsoluteRotate, Transform, Transformation,
+                       Translate, Translation, ToHomogeneous};
+use structs::vector::{Vector1, Vector2, Vector3};
+use structs::point::{Point2, Point3};
+use structs::rotation::{Rotation2, Rotation3};
+
+#[cfg(feature="arbitrary")]
+use quickcheck::{Arbitrary, Gen};
+
+
+/// Two dimensional **direct** isometry.
+///
+/// This is the composition of a rotation followed by a translation. Vectors `Vector2` are not
+/// affected by the translational component of this transformation while points `Point2` are.
+/// Isometrymetries conserve angles and distances, hence do not allow shearing nor scaling.
+#[repr(C)]
+#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Debug, Copy)]
+pub struct Isometry2<N> {
+    /// The rotation applicable by this isometry.
+    pub rotation:    Rotation2<N>,
+    /// The translation applicable by this isometry.
+    pub translation: Vector2<N>
+}
+
+/// Three dimensional **direct** isometry.
+///
+/// This is the composition of a rotation followed by a translation. Vectors `Vector3` are not
+/// affected by the translational component of this transformation while points `Point3` are.
+/// Isometrymetries conserve angles and distances, hence do not allow shearing nor scaling.
+#[repr(C)]
+#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Debug, Copy)]
+pub struct Isometry3<N> {
+    /// The rotation applicable by this isometry.
+    pub rotation:    Rotation3<N>,
+    /// The translation applicable by this isometry.
+    pub translation: Vector3<N>
+}
+
+impl<N: Clone + BaseFloat> Isometry3<N> {
+    /// Creates an isometry that corresponds to the local frame of an observer standing at the
+    /// point `eye` and looking toward `target`.
+    ///
+    /// It maps the view direction `target - eye` to the positive `z` axis and the origin to the
+    /// `eye`.
+    ///
+    /// # Arguments
+    ///   * eye - The observer position.
+    ///   * target - The target position.
+    ///   * 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: &Point3<N>, target: &Point3<N>, up: &Vector3<N>) -> Isometry3<N> {
+        let new_rotation_matrix = Rotation3::new_observer_frame(&(*target - *eye), up);
+        Isometry3::new_with_rotation_matrix(eye.as_vector().clone(), new_rotation_matrix)
+    }
+
+    /// Builds a right-handed look-at view matrix.
+    ///
+    /// This conforms to the common notion of right handed look-at matrix from the computer
+    /// graphics community.
+    ///
+    /// # Arguments
+    ///   * eye - The eye position.
+    ///   * target - The target position.
+    ///   * 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: &Point3<N>, target: &Point3<N>, up: &Vector3<N>) -> Isometry3<N> {
+        let rotation   = Rotation3::look_at_rh(&(*target - *eye), up);
+        let trans = rotation * (-*eye);
+
+        Isometry3::new_with_rotation_matrix(trans.to_vector(), rotation)
+    }
+
+    /// Builds a left-handed look-at view matrix.
+    ///
+    /// This conforms to the common notion of left handed look-at matrix from the computer
+    /// graphics community.
+    ///
+    /// # Arguments
+    ///   * eye - The eye position.
+    ///   * target - The target position.
+    ///   * 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: &Point3<N>, target: &Point3<N>, up: &Vector3<N>) -> Isometry3<N> {
+        let rotation   = Rotation3::look_at_lh(&(*target - *eye), up);
+        let trans = rotation * (-*eye);
+
+        Isometry3::new_with_rotation_matrix(trans.to_vector(), rotation)
+    }
+}
+
+isometry_impl!(Isometry2, Rotation2, Vector2, Vector1);
+rotation_matrix_impl!(Isometry2, Rotation2, Vector2, Vector1);
+rotation_impl!(Isometry2, Rotation2, Vector1);
+dim_impl!(Isometry2, 2);
+one_impl!(Isometry2);
+absolute_rotate_impl!(Isometry2, Vector2);
+rand_impl!(Isometry2);
+approx_eq_impl!(Isometry2);
+to_homogeneous_impl!(Isometry2, Matrix3);
+inverse_impl!(Isometry2);
+transform_impl!(Isometry2, Point2);
+transformation_impl!(Isometry2);
+rotate_impl!(Isometry2, Vector2);
+translation_impl!(Isometry2, Vector2);
+translate_impl!(Isometry2, Point2);
+isometry_mul_isometry_impl!(Isometry2);
+isometry_mul_rotation_impl!(Isometry2, Rotation2);
+isometry_mul_point_impl!(Isometry2, Point2);
+isometry_mul_vec_impl!(Isometry2, Vector2);
+arbitrary_isometry_impl!(Isometry2);
+isometry_display_impl!(Isometry2);
+
+isometry_impl!(Isometry3, Rotation3, Vector3, Vector3);
+rotation_matrix_impl!(Isometry3, Rotation3, Vector3, Vector3);
+rotation_impl!(Isometry3, Rotation3, Vector3);
+dim_impl!(Isometry3, 3);
+one_impl!(Isometry3);
+absolute_rotate_impl!(Isometry3, Vector3);
+rand_impl!(Isometry3);
+approx_eq_impl!(Isometry3);
+to_homogeneous_impl!(Isometry3, Matrix4);
+inverse_impl!(Isometry3);
+transform_impl!(Isometry3, Point3);
+transformation_impl!(Isometry3);
+rotate_impl!(Isometry3, Vector3);
+translation_impl!(Isometry3, Vector3);
+translate_impl!(Isometry3, Point3);
+isometry_mul_isometry_impl!(Isometry3);
+isometry_mul_rotation_impl!(Isometry3, Rotation3);
+isometry_mul_point_impl!(Isometry3, Point3);
+isometry_mul_vec_impl!(Isometry3, Vector3);
+arbitrary_isometry_impl!(Isometry3);
+isometry_display_impl!(Isometry3);

src/structs/isometry_macros.rs

@@ -1,20 +1,20 @@
 #![macro_use]
 
-macro_rules! iso_impl(
+macro_rules! isometry_impl(
-    ($t: ident, $submat: ident, $subvec: ident, $subrotvec: ident) => (
+    ($t: ident, $submatrix: ident, $subvector: ident, $subrotvector: ident) => (
         impl<N: BaseFloat> $t<N> {
             /// Creates a new isometry from an axis-angle rotation, and a vector.
             #[inline]
-            pub fn new(translation: $subvec<N>, rotation: $subrotvec<N>) -> $t<N> {
+            pub fn new(translation: $subvector<N>, rotation: $subrotvector<N>) -> $t<N> {
                 $t {
-                    rotation:    $submat::new(rotation),
+                    rotation:    $submatrix::new(rotation),
                     translation: translation
                 }
             }
 
             /// Creates a new isometry from a rotation matrix and a vector.
             #[inline]
-            pub fn new_with_rotmat(translation: $subvec<N>, rotation: $submat<N>) -> $t<N> {
+            pub fn new_with_rotation_matrix(translation: $subvector<N>, rotation: $submatrix<N>) -> $t<N> {
                 $t {
                     rotation:    rotation,
                     translation: translation
@@ -25,13 +25,13 @@ macro_rules! iso_impl(
 );
 
 macro_rules! rotation_matrix_impl(
-    ($t: ident, $trot: ident, $tlv: ident, $tav: ident) => (
+    ($t: ident, $trotation: ident, $tlv: ident, $tav: ident) => (
         impl<N: Cast<f64> + BaseFloat>
         RotationMatrix<N, $tlv<N>, $tav<N>> for $t<N> {
-            type Output = $trot<N>;
+            type Output = $trotation<N>;
 
             #[inline]
-            fn to_rot_mat(&self) -> $trot<N> {
+            fn to_rotation_matrix(&self) -> $trotation<N> {
                 self.rotation
             }
         }
@@ -40,11 +40,11 @@ macro_rules! rotation_matrix_impl(
 
 
 macro_rules! dim_impl(
-    ($t: ident, $dim: expr) => (
+    ($t: ident, $dimension: expr) => (
-        impl<N> Dim for $t<N> {
+        impl<N> Dimension for $t<N> {
             #[inline]
-            fn dim(_: Option<$t<N>>) -> usize {
+            fn dimension(_: Option<$t<N>>) -> usize {
-                $dim
+                $dimension
             }
         }
     )
@@ -55,20 +55,20 @@ macro_rules! one_impl(
         impl<N: BaseFloat> One for $t<N> {
             #[inline]
             fn one() -> $t<N> {
-                $t::new_with_rotmat(::zero(), ::one())
+                $t::new_with_rotation_matrix(::zero(), ::one())
             }
         }
     )
 );
 
-macro_rules! iso_mul_iso_impl(
+macro_rules! isometry_mul_isometry_impl(
     ($t: ident) => (
         impl<N: BaseFloat> Mul<$t<N>> for $t<N> {
             type Output = $t<N>;
 
             #[inline]
             fn mul(self, right: $t<N>) -> $t<N> {
-                $t::new_with_rotmat(
+                $t::new_with_rotation_matrix(
                     self.translation + self.rotation * right.translation,
                     self.rotation * right.rotation)
             }
@@ -84,38 +84,38 @@ macro_rules! iso_mul_iso_impl(
     )
 );
 
-macro_rules! iso_mul_rot_impl(
+macro_rules! isometry_mul_rotation_impl(
-    ($t: ident, $rot: ident) => (
+    ($t: ident, $rotation: ident) => (
-        impl<N: BaseFloat> Mul<$rot<N>> for $t<N> {
+        impl<N: BaseFloat> Mul<$rotation<N>> for $t<N> {
             type Output = $t<N>;
 
             #[inline]
-            fn mul(self, right: $rot<N>) -> $t<N> {
+            fn mul(self, right: $rotation<N>) -> $t<N> {
-                $t::new_with_rotmat(self.translation, self.rotation * right)
+                $t::new_with_rotation_matrix(self.translation, self.rotation * right)
             }
         }
 
-        impl<N: BaseFloat> Mul<$t<N>> for $rot<N> {
+        impl<N: BaseFloat> Mul<$t<N>> for $rotation<N> {
             type Output = $t<N>;
 
             #[inline]
             fn mul(self, right: $t<N>) -> $t<N> {
-                $t::new_with_rotmat(
+                $t::new_with_rotation_matrix(
                     self * right.translation,
                     self * right.rotation)
             }
         }
 
-        impl<N: BaseFloat> MulAssign<$rot<N>> for $t<N> {
+        impl<N: BaseFloat> MulAssign<$rotation<N>> for $t<N> {
             #[inline]
-            fn mul_assign(&mut self, right: $rot<N>) {
+            fn mul_assign(&mut self, right: $rotation<N>) {
                 self.rotation *= right
             }
         }
     )
 );
 
-macro_rules! iso_mul_pnt_impl(
+macro_rules! isometry_mul_point_impl(
     ($t: ident, $tv: ident) => (
         impl<N: BaseNum> Mul<$tv<N>> for $t<N> {
             type Output = $tv<N>;
@@ -128,7 +128,7 @@ macro_rules! iso_mul_pnt_impl(
     )
 );
 
-macro_rules! iso_mul_vec_impl(
+macro_rules! isometry_mul_vec_impl(
     ($t: ident, $tv: ident) => (
         impl<N: BaseNum> Mul<$tv<N>> for $t<N> {
             type Output = $tv<N>;
@@ -150,7 +150,7 @@ macro_rules! translation_impl(
             }
 
             #[inline]
-            fn inv_translation(&self) -> $tv<N> {
+            fn inverse_translation(&self) -> $tv<N> {
                 -self.translation
             }
 
@@ -161,7 +161,7 @@ macro_rules! translation_impl(
 
             #[inline]
             fn append_translation(&self, t: &$tv<N>) -> $t<N> {
-                $t::new_with_rotmat(*t + self.translation, self.rotation)
+                $t::new_with_rotation_matrix(*t + self.translation, self.rotation)
             }
 
             #[inline]
@@ -171,7 +171,7 @@ macro_rules! translation_impl(
 
             #[inline]
             fn prepend_translation(&self, t: &$tv<N>) -> $t<N> {
-                $t::new_with_rotmat(self.translation + self.rotation * *t, self.rotation)
+                $t::new_with_rotation_matrix(self.translation + self.rotation * *t, self.rotation)
             }
 
             #[inline]
@@ -191,7 +191,7 @@ macro_rules! translate_impl(
             }
 
             #[inline]
-            fn inv_translate(&self, v: &$tv<N>) -> $tv<N> {
+            fn inverse_translate(&self, v: &$tv<N>) -> $tv<N> {
                 *v - self.translation
             }
         }
@@ -199,7 +199,7 @@ macro_rules! translate_impl(
 );
 
 macro_rules! rotation_impl(
-    ($t: ident, $trot: ident, $tav: ident) => (
+    ($t: ident, $trotation: ident, $tav: ident) => (
         impl<N: Cast<f64> + BaseFloat> Rotation<$tav<N>> for $t<N> {
             #[inline]
             fn rotation(&self) -> $tav<N> {
@@ -207,43 +207,43 @@ macro_rules! rotation_impl(
             }
 
             #[inline]
-            fn inv_rotation(&self) -> $tav<N> {
+            fn inverse_rotation(&self) -> $tav<N> {
-                self.rotation.inv_rotation()
+                self.rotation.inverse_rotation()
             }
 
             #[inline]
-            fn append_rotation_mut(&mut self, rot: &$tav<N>) {
+            fn append_rotation_mut(&mut self, rotation: &$tav<N>) {
-                let delta = $trot::new(*rot);
+                let delta = $trotation::new(*rotation);
 
                 self.rotation    = delta * self.rotation;
                 self.translation = delta * self.translation;
             }
 
             #[inline]
-            fn append_rotation(&self, rot: &$tav<N>) -> $t<N> {
+            fn append_rotation(&self, rotation: &$tav<N>) -> $t<N> {
-                let delta = $trot::new(*rot);
+                let delta = $trotation::new(*rotation);
 
-                $t::new_with_rotmat(delta * self.translation, delta * self.rotation)
+                $t::new_with_rotation_matrix(delta * self.translation, delta * self.rotation)
             }
 
             #[inline]
-            fn prepend_rotation_mut(&mut self, rot: &$tav<N>) {
+            fn prepend_rotation_mut(&mut self, rotation: &$tav<N>) {
-                let delta = $trot::new(*rot);
+                let delta = $trotation::new(*rotation);
 
                 self.rotation = self.rotation * delta;
             }
 
             #[inline]
-            fn prepend_rotation(&self, rot: &$tav<N>) -> $t<N> {
+            fn prepend_rotation(&self, rotation: &$tav<N>) -> $t<N> {
-                let delta = $trot::new(*rot);
+                let delta = $trotation::new(*rotation);
 
-                $t::new_with_rotmat(self.translation, self.rotation * delta)
+                $t::new_with_rotation_matrix(self.translation, self.rotation * delta)
             }
 
             #[inline]
-            fn set_rotation(&mut self, rot: $tav<N>) {
+            fn set_rotation(&mut self, rotation: $tav<N>) {
                 // FIXME: should the translation be changed too?
-                self.rotation.set_rotation(rot)
+                self.rotation.set_rotation(rotation)
             }
         }
     )
@@ -258,8 +258,8 @@ macro_rules! rotate_impl(
             }
 
             #[inline]
-            fn inv_rotate(&self, v: &$tv<N>) -> $tv<N> {
+            fn inverse_rotate(&self, v: &$tv<N>) -> $tv<N> {
-                self.rotation.inv_rotate(v)
+                self.rotation.inverse_rotate(v)
             }
         }
     )
@@ -272,9 +272,9 @@ macro_rules! transformation_impl(
                 *self
             }
 
-            fn inv_transformation(&self) -> $t<N> {
+            fn inverse_transformation(&self) -> $t<N> {
                 // inversion will never fails
-                Inv::inv(self).unwrap()
+                Inverse::inverse(self).unwrap()
             }
 
             fn append_transformation_mut(&mut self, t: &$t<N>) {
@@ -309,28 +309,28 @@ macro_rules! transform_impl(
             }
 
             #[inline]
-            fn inv_transform(&self, p: &$tp<N>) -> $tp<N> {
+            fn inverse_transform(&self, p: &$tp<N>) -> $tp<N> {
-                self.rotation.inv_transform(&(*p - self.translation))
+                self.rotation.inverse_transform(&(*p - self.translation))
             }
         }
     )
 );
 
-macro_rules! inv_impl(
+macro_rules! inverse_impl(
     ($t: ident) => (
-        impl<N: BaseNum + Neg<Output = N>> Inv for $t<N> {
+        impl<N: BaseNum + Neg<Output = N>> Inverse for $t<N> {
             #[inline]
-            fn inv_mut(&mut self) -> bool {
+            fn inverse_mut(&mut self) -> bool {
-                self.rotation.inv_mut();
+                self.rotation.inverse_mut();
                 self.translation = self.rotation * -self.translation;
                 // always succeed
                 true
             }
 
             #[inline]
-            fn inv(&self) -> Option<$t<N>> {
+            fn inverse(&self) -> Option<$t<N>> {
                 let mut res = *self;
-                res.inv_mut();
+                res.inverse_mut();
                 // always succeed
                 Some(res)
             }
@@ -345,9 +345,9 @@ macro_rules! to_homogeneous_impl(
                 let mut res = self.rotation.to_homogeneous();
 
                 // copy the translation
-                let dim = Dim::dim(None::<$th<N>>);
+                let dimension = Dimension::dimension(None::<$th<N>>);
 
-                res.set_col(dim - 1, self.translation.as_pnt().to_homogeneous().to_vec());
+                res.set_col(dimension - 1, self.translation.as_point().to_homogeneous().to_vector());
 
                 res
             }
@@ -405,12 +405,12 @@ macro_rules! absolute_rotate_impl(
     )
 );
 
-macro_rules! arbitrary_iso_impl(
+macro_rules! arbitrary_isometry_impl(
     ($t: ident) => (
         #[cfg(feature="arbitrary")]
         impl<N: Arbitrary + BaseFloat> Arbitrary for $t<N> {
             fn arbitrary<G: Gen>(g: &mut G) -> $t<N> {
-                $t::new_with_rotmat(
+                $t::new_with_rotation_matrix(
                     Arbitrary::arbitrary(g),
                     Arbitrary::arbitrary(g)
                 )
@@ -419,7 +419,7 @@ macro_rules! arbitrary_iso_impl(
     )
 );
 
-macro_rules! iso_display_impl(
+macro_rules! isometry_display_impl(
     ($t: ident) => (
         impl<N: fmt::Display + BaseFloat> fmt::Display for $t<N> {
             fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
@@ -428,12 +428,12 @@ macro_rules! iso_display_impl(
                 if let Some(precision) = f.precision() {
                     try!(writeln!(f, "... translation: {:.*}", precision, self.translation));
                     try!(writeln!(f, "... rotation matrix:"));
-                    try!(write!(f, "{:.*}", precision, *self.rotation.submat()));
+                    try!(write!(f, "{:.*}", precision, *self.rotation.submatrix()));
                 }
                 else {
                     try!(writeln!(f, "... translation: {}", self.translation));
                     try!(writeln!(f, "... rotation matrix:"));
-                    try!(write!(f, "{}", *self.rotation.submat()));
+                    try!(write!(f, "{}", *self.rotation.submatrix()));
                 }
 
                 writeln!(f, "}}")

src/structs/matrix.rs

@@ -1,4 +1,4 @@
-//! Matrices with dimensions known at compile-time.
+//! Matrixrices with dimensions known at compile-time.
 
 #![allow(missing_docs)] // we allow missing to avoid having to document the mij components.
 
@@ -9,14 +9,14 @@ use std::slice::{Iter, IterMut};
 use rand::{Rand, Rng};
 use num::{Zero, One};
 use traits::operations::ApproxEq;
-use structs::vec::{Vec1, Vec2, Vec3, Vec4, Vec5, Vec6};
+use structs::vector::{Vector1, Vector2, Vector3, Vector4, Vector5, Vector6};
-use structs::pnt::{Pnt1, Pnt4, Pnt5, Pnt6};
+use structs::point::{Point1, Point4, Point5, Point6};
-use structs::dvec::{DVec1, DVec2, DVec3, DVec4, DVec5, DVec6};
+use structs::dvector::{DVector1, DVector2, DVector3, DVector4, DVector5, DVector6};
 
-use traits::structure::{Cast, Row, Col, Iterable, IterableMut, Dim, Indexable, Eye, ColSlice,
+use traits::structure::{Cast, Row, Column, Iterable, IterableMut, Dimension, Indexable, Eye, ColumnSlice,
-                        RowSlice, Diag, DiagMut, Shape, BaseFloat, BaseNum, Repeat};
+                        RowSlice, Diagonal, DiagMut, Shape, BaseFloat, BaseNum, Repeat};
-use traits::operations::{Absolute, Transpose, Inv, Outer, EigenQR, Mean};
+use traits::operations::{Absolute, Transpose, Inverse, Outer, EigenQR, Mean};
-use traits::geometry::{ToHomogeneous, FromHomogeneous, Orig};
+use traits::geometry::{ToHomogeneous, FromHomogeneous, Origin};
 use linalg;
 #[cfg(feature="arbitrary")]
 use quickcheck::{Arbitrary, Gen};
@@ -38,331 +38,331 @@ impl Identity {
 /// Square matrix of dimension 1.
 #[repr(C)]
 #[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
-pub struct Mat1<N> {
+pub struct Matrix1<N> {
     pub m11: N
 }
 
-eye_impl!(Mat1, 1, m11);
+eye_impl!(Matrix1, 1, m11);
 
-mat_impl!(Mat1, m11);
+mat_impl!(Matrix1, m11);
-repeat_impl!(Mat1, m11);
+repeat_impl!(Matrix1, m11);
-conversion_impl!(Mat1, 1);
+conversion_impl!(Matrix1, 1);
-mat_cast_impl!(Mat1, m11);
+mat_cast_impl!(Matrix1, m11);
-add_impl!(Mat1, m11);
+add_impl!(Matrix1, m11);
-sub_impl!(Mat1, m11);
+sub_impl!(Matrix1, m11);
-scalar_add_impl!(Mat1, m11);
+scalar_add_impl!(Matrix1, m11);
-scalar_sub_impl!(Mat1, m11);
+scalar_sub_impl!(Matrix1, m11);
-scalar_mul_impl!(Mat1, m11);
+scalar_mul_impl!(Matrix1, m11);
-scalar_div_impl!(Mat1, m11);
+scalar_div_impl!(Matrix1, m11);
-absolute_impl!(Mat1, m11);
+absolute_impl!(Matrix1, m11);
-zero_impl!(Mat1, m11);
+zero_impl!(Matrix1, m11);
-one_impl!(Mat1, ::one);
+one_impl!(Matrix1, ::one);
-iterable_impl!(Mat1, 1);
+iterable_impl!(Matrix1, 1);
-iterable_mut_impl!(Mat1, 1);
+iterable_mut_impl!(Matrix1, 1);
-at_fast_impl!(Mat1, 1);
+at_fast_impl!(Matrix1, 1);
-dim_impl!(Mat1, 1);
+dim_impl!(Matrix1, 1);
-indexable_impl!(Mat1, 1);
+indexable_impl!(Matrix1, 1);
-index_impl!(Mat1, 1);
+index_impl!(Matrix1, 1);
-mat_mul_mat_impl!(Mat1, 1);
+mat_mul_mat_impl!(Matrix1, 1);
-mat_mul_vec_impl!(Mat1, Vec1, 1, ::zero);
+mat_mul_vec_impl!(Matrix1, Vector1, 1, ::zero);
-vec_mul_mat_impl!(Mat1, Vec1, 1, ::zero);
+vec_mul_mat_impl!(Matrix1, Vector1, 1, ::zero);
-mat_mul_pnt_impl!(Mat1, Pnt1, 1, Orig::orig);
+mat_mul_point_impl!(Matrix1, Point1, 1, Origin::origin);
-pnt_mul_mat_impl!(Mat1, Pnt1, 1, Orig::orig);
+point_mul_mat_impl!(Matrix1, Point1, 1, Origin::origin);
-// (specialized); inv_impl!(Mat1, 1);
+// (specialized); inverse_impl!(Matrix1, 1);
-transpose_impl!(Mat1, 1);
+transpose_impl!(Matrix1, 1);
-approx_eq_impl!(Mat1);
+approx_eq_impl!(Matrix1);
-row_impl!(Mat1, Vec1, 1);
+row_impl!(Matrix1, Vector1, 1);
-col_impl!(Mat1, Vec1, 1);
+col_impl!(Matrix1, Vector1, 1);
-col_slice_impl!(Mat1, Vec1, DVec1, 1);
+col_slice_impl!(Matrix1, Vector1, DVector1, 1);
-row_slice_impl!(Mat1, Vec1, DVec1, 1);
+row_slice_impl!(Matrix1, Vector1, DVector1, 1);
-diag_impl!(Mat1, Vec1, 1);
+diag_impl!(Matrix1, Vector1, 1);
-to_homogeneous_impl!(Mat1, Mat2, 1, 2);
+to_homogeneous_impl!(Matrix1, Matrix2, 1, 2);
-from_homogeneous_impl!(Mat1, Mat2, 1, 2);
+from_homogeneous_impl!(Matrix1, Matrix2, 1, 2);
-outer_impl!(Vec1, Mat1);
+outer_impl!(Vector1, Matrix1);
-eigen_qr_impl!(Mat1, Vec1);
+eigen_qr_impl!(Matrix1, Vector1);
-arbitrary_impl!(Mat1, m11);
+arbitrary_impl!(Matrix1, m11);
-rand_impl!(Mat1, m11);
+rand_impl!(Matrix1, m11);
-mean_impl!(Mat1, Vec1, 1);
+mean_impl!(Matrix1, Vector1, 1);
-mat_display_impl!(Mat1, 1);
+mat_display_impl!(Matrix1, 1);
 
 /// Square matrix of dimension 2.
 #[repr(C)]
 #[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
-pub struct Mat2<N> {
+pub struct Matrix2<N> {
     pub m11: N, pub m21: N,
     pub m12: N, pub m22: N
 }
 
-eye_impl!(Mat2, 2, m11, m22);
+eye_impl!(Matrix2, 2, m11, m22);
 
-mat_impl!(Mat2, m11, m12,
+mat_impl!(Matrix2, m11, m12,
                 m21, m22);
-repeat_impl!(Mat2, m11, m12,
+repeat_impl!(Matrix2, m11, m12,
                    m21, m22);
-conversion_impl!(Mat2, 2);
+conversion_impl!(Matrix2, 2);
-mat_cast_impl!(Mat2, m11, m12,
+mat_cast_impl!(Matrix2, m11, m12,
                      m21, m22);
-add_impl!(Mat2, m11, m12, m21, m22);
+add_impl!(Matrix2, m11, m12, m21, m22);
-sub_impl!(Mat2, m11, m12, m21, m22);
+sub_impl!(Matrix2, m11, m12, m21, m22);
-scalar_add_impl!(Mat2, m11, m12, m21, m22);
+scalar_add_impl!(Matrix2, m11, m12, m21, m22);
-scalar_sub_impl!(Mat2, m11, m12, m21, m22);
+scalar_sub_impl!(Matrix2, m11, m12, m21, m22);
-scalar_mul_impl!(Mat2, m11, m12, m21, m22);
+scalar_mul_impl!(Matrix2, m11, m12, m21, m22);
-scalar_div_impl!(Mat2, m11, m12, m21, m22);
+scalar_div_impl!(Matrix2, m11, m12, m21, m22);
-absolute_impl!(Mat2, m11, m12,
+absolute_impl!(Matrix2, m11, m12,
                      m21, m22);
-zero_impl!(Mat2, m11, m12,
+zero_impl!(Matrix2, m11, m12,
                  m21, m22);
-one_impl!(Mat2, ::one,  ::zero,
+one_impl!(Matrix2, ::one,  ::zero,
                 ::zero, ::one);
-iterable_impl!(Mat2, 2);
+iterable_impl!(Matrix2, 2);
-iterable_mut_impl!(Mat2, 2);
+iterable_mut_impl!(Matrix2, 2);
-dim_impl!(Mat2, 2);
+dim_impl!(Matrix2, 2);
-indexable_impl!(Mat2, 2);
+indexable_impl!(Matrix2, 2);
-index_impl!(Mat2, 2);
+index_impl!(Matrix2, 2);
-at_fast_impl!(Mat2, 2);
+at_fast_impl!(Matrix2, 2);
-// (specialized); mul_impl!(Mat2, 2);
+// (specialized); mul_impl!(Matrix2, 2);
-// (specialized); rmul_impl!(Mat2, Vec2, 2);
+// (specialized); rmul_impl!(Matrix2, Vector2, 2);
-// (specialized); lmul_impl!(Mat2, Vec2, 2);
+// (specialized); lmul_impl!(Matrix2, Vector2, 2);
-// (specialized); inv_impl!(Mat2, 2);
+// (specialized); inverse_impl!(Matrix2, 2);
-transpose_impl!(Mat2, 2);
+transpose_impl!(Matrix2, 2);
-approx_eq_impl!(Mat2);
+approx_eq_impl!(Matrix2);
-row_impl!(Mat2, Vec2, 2);
+row_impl!(Matrix2, Vector2, 2);
-col_impl!(Mat2, Vec2, 2);
+col_impl!(Matrix2, Vector2, 2);
-col_slice_impl!(Mat2, Vec2, DVec2, 2);
+col_slice_impl!(Matrix2, Vector2, DVector2, 2);
-row_slice_impl!(Mat2, Vec2, DVec2, 2);
+row_slice_impl!(Matrix2, Vector2, DVector2, 2);
-diag_impl!(Mat2, Vec2, 2);
+diag_impl!(Matrix2, Vector2, 2);
-to_homogeneous_impl!(Mat2, Mat3, 2, 3);
+to_homogeneous_impl!(Matrix2, Matrix3, 2, 3);
-from_homogeneous_impl!(Mat2, Mat3, 2, 3);
+from_homogeneous_impl!(Matrix2, Matrix3, 2, 3);
-outer_impl!(Vec2, Mat2);
+outer_impl!(Vector2, Matrix2);
-eigen_qr_impl!(Mat2, Vec2);
+eigen_qr_impl!(Matrix2, Vector2);
-arbitrary_impl!(Mat2, m11, m12, m21, m22);
+arbitrary_impl!(Matrix2, m11, m12, m21, m22);
-rand_impl!(Mat2, m11, m12, m21, m22);
+rand_impl!(Matrix2, m11, m12, m21, m22);
-mean_impl!(Mat2, Vec2, 2);
+mean_impl!(Matrix2, Vector2, 2);
-mat_display_impl!(Mat2, 2);
+mat_display_impl!(Matrix2, 2);
 
 /// Square matrix of dimension 3.
 #[repr(C)]
 #[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
-pub struct Mat3<N> {
+pub struct Matrix3<N> {
     pub m11: N, pub m21: N, pub m31: N,
     pub m12: N, pub m22: N, pub m32: N,
     pub m13: N, pub m23: N, pub m33: N
 }
 
-eye_impl!(Mat3, 3, m11, m22, m33);
+eye_impl!(Matrix3, 3, m11, m22, m33);
 
-mat_impl!(Mat3, m11, m12, m13,
+mat_impl!(Matrix3, m11, m12, m13,
                 m21, m22, m23,
                 m31, m32, m33);
-repeat_impl!(Mat3, m11, m12, m13,
+repeat_impl!(Matrix3, m11, m12, m13,
                    m21, m22, m23,
                    m31, m32, m33);
-conversion_impl!(Mat3, 3);
+conversion_impl!(Matrix3, 3);
-mat_cast_impl!(Mat3, m11, m12, m13,
+mat_cast_impl!(Matrix3, m11, m12, m13,
                      m21, m22, m23,
                      m31, m32, m33);
-add_impl!(Mat3,
+add_impl!(Matrix3,
     m11, m12, m13,
     m21, m22, m23,
     m31, m32, m33
 );
-sub_impl!(Mat3,
+sub_impl!(Matrix3,
     m11, m12, m13,
     m21, m22, m23,
     m31, m32, m33
 );
-scalar_add_impl!(Mat3,
+scalar_add_impl!(Matrix3,
     m11, m12, m13,
     m21, m22, m23,
     m31, m32, m33
 );
-scalar_sub_impl!(Mat3,
+scalar_sub_impl!(Matrix3,
     m11, m12, m13,
     m21, m22, m23,
     m31, m32, m33
 );
-scalar_mul_impl!(Mat3,
+scalar_mul_impl!(Matrix3,
     m11, m12, m13,
     m21, m22, m23,
     m31, m32, m33
 );
-scalar_div_impl!(Mat3,
+scalar_div_impl!(Matrix3,
     m11, m12, m13,
     m21, m22, m23,
     m31, m32, m33
 );
-absolute_impl!(Mat3,
+absolute_impl!(Matrix3,
     m11, m12, m13,
     m21, m22, m23,
     m31, m32, m33
 );
-zero_impl!(Mat3,
+zero_impl!(Matrix3,
     m11, m12, m13,
     m21, m22, m23,
     m31, m32, m33
 );
-one_impl!(Mat3, ::one , ::zero, ::zero,
+one_impl!(Matrix3, ::one , ::zero, ::zero,
                 ::zero, ::one , ::zero,
                 ::zero, ::zero, ::one);
-iterable_impl!(Mat3, 3);
+iterable_impl!(Matrix3, 3);
-iterable_mut_impl!(Mat3, 3);
+iterable_mut_impl!(Matrix3, 3);
-dim_impl!(Mat3, 3);
+dim_impl!(Matrix3, 3);
-indexable_impl!(Mat3, 3);
+indexable_impl!(Matrix3, 3);
-index_impl!(Mat3, 3);
+index_impl!(Matrix3, 3);
-at_fast_impl!(Mat3, 3);
+at_fast_impl!(Matrix3, 3);
-// (specialized); mul_impl!(Mat3, 3);
+// (specialized); mul_impl!(Matrix3, 3);
-// (specialized); rmul_impl!(Mat3, Vec3, 3);
+// (specialized); rmul_impl!(Matrix3, Vector3, 3);
-// (specialized); lmul_impl!(Mat3, Vec3, 3);
+// (specialized); lmul_impl!(Matrix3, Vector3, 3);
-// (specialized); inv_impl!(Mat3, 3);
+// (specialized); inverse_impl!(Matrix3, 3);
-transpose_impl!(Mat3, 3);
+transpose_impl!(Matrix3, 3);
-approx_eq_impl!(Mat3);
+approx_eq_impl!(Matrix3);
-// (specialized); row_impl!(Mat3, Vec3, 3);
+// (specialized); row_impl!(Matrix3, Vector3, 3);
-// (specialized); col_impl!(Mat3, Vec3, 3);
+// (specialized); col_impl!(Matrix3, Vector3, 3);
-col_slice_impl!(Mat3, Vec3, DVec3, 3);
+col_slice_impl!(Matrix3, Vector3, DVector3, 3);
-row_slice_impl!(Mat3, Vec3, DVec3, 3);
+row_slice_impl!(Matrix3, Vector3, DVector3, 3);
-diag_impl!(Mat3, Vec3, 3);
+diag_impl!(Matrix3, Vector3, 3);
-to_homogeneous_impl!(Mat3, Mat4, 3, 4);
+to_homogeneous_impl!(Matrix3, Matrix4, 3, 4);
-from_homogeneous_impl!(Mat3, Mat4, 3, 4);
+from_homogeneous_impl!(Matrix3, Matrix4, 3, 4);
-outer_impl!(Vec3, Mat3);
+outer_impl!(Vector3, Matrix3);
-eigen_qr_impl!(Mat3, Vec3);
+eigen_qr_impl!(Matrix3, Vector3);
-arbitrary_impl!(Mat3,
+arbitrary_impl!(Matrix3,
     m11, m12, m13,
     m21, m22, m23,
     m31, m32, m33
 );
-rand_impl!(Mat3,
+rand_impl!(Matrix3,
     m11, m12, m13,
     m21, m22, m23,
     m31, m32, m33
 );
-mean_impl!(Mat3, Vec3, 3);
+mean_impl!(Matrix3, Vector3, 3);
-mat_display_impl!(Mat3, 3);
+mat_display_impl!(Matrix3, 3);
 
 /// Square matrix of dimension 4.
 #[repr(C)]
 #[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
-pub struct Mat4<N> {
+pub struct Matrix4<N> {
     pub m11: N, pub m21: N, pub m31: N, pub m41: N,
     pub m12: N, pub m22: N, pub m32: N, pub m42: N,
     pub m13: N, pub m23: N, pub m33: N, pub m43: N,
     pub m14: N, pub m24: N, pub m34: N, pub m44: N
 }
 
-eye_impl!(Mat4, 4, m11, m22, m33, m44);
+eye_impl!(Matrix4, 4, m11, m22, m33, m44);
 
-mat_impl!(Mat4,
+mat_impl!(Matrix4,
   m11, m12, m13, m14,
   m21, m22, m23, m24,
   m31, m32, m33, m34,
   m41, m42, m43, m44
 );
-repeat_impl!(Mat4,
+repeat_impl!(Matrix4,
   m11, m12, m13, m14,
   m21, m22, m23, m24,
   m31, m32, m33, m34,
   m41, m42, m43, m44
 );
-conversion_impl!(Mat4, 4);
+conversion_impl!(Matrix4, 4);
-mat_cast_impl!(Mat4,
+mat_cast_impl!(Matrix4,
   m11, m12, m13, m14,
   m21, m22, m23, m24,
   m31, m32, m33, m34,
   m41, m42, m43, m44
 );
-add_impl!(Mat4,
+add_impl!(Matrix4,
   m11, m12, m13, m14,
   m21, m22, m23, m24,
   m31, m32, m33, m34,
   m41, m42, m43, m44
 );
-sub_impl!(Mat4,
+sub_impl!(Matrix4,
   m11, m12, m13, m14,
   m21, m22, m23, m24,
   m31, m32, m33, m34,
   m41, m42, m43, m44
 );
-scalar_add_impl!(Mat4,
+scalar_add_impl!(Matrix4,
   m11, m12, m13, m14,
   m21, m22, m23, m24,
   m31, m32, m33, m34,
   m41, m42, m43, m44
 );
-scalar_sub_impl!(Mat4,
+scalar_sub_impl!(Matrix4,
   m11, m12, m13, m14,
   m21, m22, m23, m24,
   m31, m32, m33, m34,
   m41, m42, m43, m44
 );
-scalar_mul_impl!(Mat4,
+scalar_mul_impl!(Matrix4,
   m11, m12, m13, m14,
   m21, m22, m23, m24,
   m31, m32, m33, m34,
   m41, m42, m43, m44
 );
-scalar_div_impl!(Mat4,
+scalar_div_impl!(Matrix4,
   m11, m12, m13, m14,
   m21, m22, m23, m24,
   m31, m32, m33, m34,
   m41, m42, m43, m44
 );
-absolute_impl!(Mat4,
+absolute_impl!(Matrix4,
   m11, m12, m13, m14,
   m21, m22, m23, m24,
   m31, m32, m33, m34,
   m41, m42, m43, m44
 );
-zero_impl!(Mat4,
+zero_impl!(Matrix4,
   m11, m12, m13, m14,
   m21, m22, m23, m24,
   m31, m32, m33, m34,
   m41, m42, m43, m44
 );
-one_impl!(Mat4, ::one  , ::zero, ::zero, ::zero,
+one_impl!(Matrix4, ::one  , ::zero, ::zero, ::zero,
                 ::zero, ::one  , ::zero, ::zero,
                 ::zero, ::zero, ::one  , ::zero,
                 ::zero, ::zero, ::zero, ::one);
-iterable_impl!(Mat4, 4);
+iterable_impl!(Matrix4, 4);
-iterable_mut_impl!(Mat4, 4);
+iterable_mut_impl!(Matrix4, 4);
-dim_impl!(Mat4, 4);
+dim_impl!(Matrix4, 4);
-indexable_impl!(Mat4, 4);
+indexable_impl!(Matrix4, 4);
-index_impl!(Mat4, 4);
+index_impl!(Matrix4, 4);
-at_fast_impl!(Mat4, 4);
+at_fast_impl!(Matrix4, 4);
-mat_mul_mat_impl!(Mat4, 4);
+mat_mul_mat_impl!(Matrix4, 4);
-mat_mul_vec_impl!(Mat4, Vec4, 4, ::zero);
+mat_mul_vec_impl!(Matrix4, Vector4, 4, ::zero);
-vec_mul_mat_impl!(Mat4, Vec4, 4, ::zero);
+vec_mul_mat_impl!(Matrix4, Vector4, 4, ::zero);
-mat_mul_pnt_impl!(Mat4, Pnt4, 4, Orig::orig);
+mat_mul_point_impl!(Matrix4, Point4, 4, Origin::origin);
-pnt_mul_mat_impl!(Mat4, Pnt4, 4, Orig::orig);
+point_mul_mat_impl!(Matrix4, Point4, 4, Origin::origin);
-inv_impl!(Mat4, 4);
+inverse_impl!(Matrix4, 4);
-transpose_impl!(Mat4, 4);
+transpose_impl!(Matrix4, 4);
-approx_eq_impl!(Mat4);
+approx_eq_impl!(Matrix4);
-row_impl!(Mat4, Vec4, 4);
+row_impl!(Matrix4, Vector4, 4);
-col_impl!(Mat4, Vec4, 4);
+col_impl!(Matrix4, Vector4, 4);
-col_slice_impl!(Mat4, Vec4, DVec4, 4);
+col_slice_impl!(Matrix4, Vector4, DVector4, 4);
-row_slice_impl!(Mat4, Vec4, DVec4, 4);
+row_slice_impl!(Matrix4, Vector4, DVector4, 4);
-diag_impl!(Mat4, Vec4, 4);
+diag_impl!(Matrix4, Vector4, 4);
-to_homogeneous_impl!(Mat4, Mat5, 4, 5);
+to_homogeneous_impl!(Matrix4, Matrix5, 4, 5);
-from_homogeneous_impl!(Mat4, Mat5, 4, 5);
+from_homogeneous_impl!(Matrix4, Matrix5, 4, 5);
-outer_impl!(Vec4, Mat4);
+outer_impl!(Vector4, Matrix4);
-eigen_qr_impl!(Mat4, Vec4);
+eigen_qr_impl!(Matrix4, Vector4);
-arbitrary_impl!(Mat4,
+arbitrary_impl!(Matrix4,
   m11, m12, m13, m14,
   m21, m22, m23, m24,
   m31, m32, m33, m34,
   m41, m42, m43, m44
 );
-rand_impl!(Mat4,
+rand_impl!(Matrix4,
   m11, m12, m13, m14,
   m21, m22, m23, m24,
   m31, m32, m33, m34,
   m41, m42, m43, m44
 );
-mean_impl!(Mat4, Vec4, 4);
+mean_impl!(Matrix4, Vector4, 4);
-mat_display_impl!(Mat4, 4);
+mat_display_impl!(Matrix4, 4);
 
 /// Square matrix of dimension 5.
 #[repr(C)]
 #[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
-pub struct Mat5<N> {
+pub struct Matrix5<N> {
     pub m11: N, pub m21: N, pub m31: N, pub m41: N, pub m51: N,
     pub m12: N, pub m22: N, pub m32: N, pub m42: N, pub m52: N,
     pub m13: N, pub m23: N, pub m33: N, pub m43: N, pub m53: N,
@@ -370,137 +370,137 @@ pub struct Mat5<N> {
     pub m15: N, pub m25: N, pub m35: N, pub m45: N, pub m55: N
 }
 
-eye_impl!(Mat5, 5, m11, m22, m33, m44, m55);
+eye_impl!(Matrix5, 5, m11, m22, m33, m44, m55);
 
-mat_impl!(Mat5,
+mat_impl!(Matrix5,
   m11, m12, m13, m14, m15,
   m21, m22, m23, m24, m25,
   m31, m32, m33, m34, m35,
   m41, m42, m43, m44, m45,
   m51, m52, m53, m54, m55
 );
-repeat_impl!(Mat5,
+repeat_impl!(Matrix5,
   m11, m12, m13, m14, m15,
   m21, m22, m23, m24, m25,
   m31, m32, m33, m34, m35,
   m41, m42, m43, m44, m45,
   m51, m52, m53, m54, m55
 );
-conversion_impl!(Mat5, 5);
+conversion_impl!(Matrix5, 5);
-mat_cast_impl!(Mat5,
+mat_cast_impl!(Matrix5,
   m11, m12, m13, m14, m15,
   m21, m22, m23, m24, m25,
   m31, m32, m33, m34, m35,
   m41, m42, m43, m44, m45,
   m51, m52, m53, m54, m55
 );
-absolute_impl!(Mat5,
+absolute_impl!(Matrix5,
   m11, m12, m13, m14, m15,
   m21, m22, m23, m24, m25,
   m31, m32, m33, m34, m35,
   m41, m42, m43, m44, m45,
   m51, m52, m53, m54, m55
 );
-zero_impl!(Mat5,
+zero_impl!(Matrix5,
   m11, m12, m13, m14, m15,
   m21, m22, m23, m24, m25,
   m31, m32, m33, m34, m35,
   m41, m42, m43, m44, m45,
   m51, m52, m53, m54, m55
 );
-one_impl!(Mat5,
+one_impl!(Matrix5,
   ::one  , ::zero, ::zero, ::zero, ::zero,
   ::zero, ::one  , ::zero, ::zero, ::zero,
   ::zero, ::zero, ::one  , ::zero, ::zero,
   ::zero, ::zero, ::zero, ::one  , ::zero,
   ::zero, ::zero, ::zero, ::zero, ::one
 );
-add_impl!(Mat5,
+add_impl!(Matrix5,
   m11, m12, m13, m14, m15,
   m21, m22, m23, m24, m25,
   m31, m32, m33, m34, m35,
   m41, m42, m43, m44, m45,
   m51, m52, m53, m54, m55
 );
-sub_impl!(Mat5,
+sub_impl!(Matrix5,
   m11, m12, m13, m14, m15,
   m21, m22, m23, m24, m25,
   m31, m32, m33, m34, m35,
   m41, m42, m43, m44, m45,
   m51, m52, m53, m54, m55
 );
-scalar_add_impl!(Mat5,
+scalar_add_impl!(Matrix5,
   m11, m12, m13, m14, m15,
   m21, m22, m23, m24, m25,
   m31, m32, m33, m34, m35,
   m41, m42, m43, m44, m45,
   m51, m52, m53, m54, m55
 );
-scalar_sub_impl!(Mat5,
+scalar_sub_impl!(Matrix5,
   m11, m12, m13, m14, m15,
   m21, m22, m23, m24, m25,
   m31, m32, m33, m34, m35,
   m41, m42, m43, m44, m45,
   m51, m52, m53, m54, m55
 );
-scalar_mul_impl!(Mat5,
+scalar_mul_impl!(Matrix5,
   m11, m12, m13, m14, m15,
   m21, m22, m23, m24, m25,
   m31, m32, m33, m34, m35,
   m41, m42, m43, m44, m45,
   m51, m52, m53, m54, m55
 );
-scalar_div_impl!(Mat5,
+scalar_div_impl!(Matrix5,
   m11, m12, m13, m14, m15,
   m21, m22, m23, m24, m25,
   m31, m32, m33, m34, m35,
   m41, m42, m43, m44, m45,
   m51, m52, m53, m54, m55
 );
-iterable_impl!(Mat5, 5);
+iterable_impl!(Matrix5, 5);
-iterable_mut_impl!(Mat5, 5);
+iterable_mut_impl!(Matrix5, 5);
-dim_impl!(Mat5, 5);
+dim_impl!(Matrix5, 5);
-indexable_impl!(Mat5, 5);
+indexable_impl!(Matrix5, 5);
-index_impl!(Mat5, 5);
+index_impl!(Matrix5, 5);
-at_fast_impl!(Mat5, 5);
+at_fast_impl!(Matrix5, 5);
-mat_mul_mat_impl!(Mat5, 5);
+mat_mul_mat_impl!(Matrix5, 5);
-mat_mul_vec_impl!(Mat5, Vec5, 5, ::zero);
+mat_mul_vec_impl!(Matrix5, Vector5, 5, ::zero);
-vec_mul_mat_impl!(Mat5, Vec5, 5, ::zero);
+vec_mul_mat_impl!(Matrix5, Vector5, 5, ::zero);
-mat_mul_pnt_impl!(Mat5, Pnt5, 5, Orig::orig);
+mat_mul_point_impl!(Matrix5, Point5, 5, Origin::origin);
-pnt_mul_mat_impl!(Mat5, Pnt5, 5, Orig::orig);
+point_mul_mat_impl!(Matrix5, Point5, 5, Origin::origin);
-inv_impl!(Mat5, 5);
+inverse_impl!(Matrix5, 5);
-transpose_impl!(Mat5, 5);
+transpose_impl!(Matrix5, 5);
-approx_eq_impl!(Mat5);
+approx_eq_impl!(Matrix5);
-row_impl!(Mat5, Vec5, 5);
+row_impl!(Matrix5, Vector5, 5);
-col_impl!(Mat5, Vec5, 5);
+col_impl!(Matrix5, Vector5, 5);
-col_slice_impl!(Mat5, Vec5, DVec5, 5);
+col_slice_impl!(Matrix5, Vector5, DVector5, 5);
-row_slice_impl!(Mat5, Vec5, DVec5, 5);
+row_slice_impl!(Matrix5, Vector5, DVector5, 5);
-diag_impl!(Mat5, Vec5, 5);
+diag_impl!(Matrix5, Vector5, 5);
-to_homogeneous_impl!(Mat5, Mat6, 5, 6);
+to_homogeneous_impl!(Matrix5, Matrix6, 5, 6);
-from_homogeneous_impl!(Mat5, Mat6, 5, 6);
+from_homogeneous_impl!(Matrix5, Matrix6, 5, 6);
-outer_impl!(Vec5, Mat5);
+outer_impl!(Vector5, Matrix5);
-eigen_qr_impl!(Mat5, Vec5);
+eigen_qr_impl!(Matrix5, Vector5);
-arbitrary_impl!(Mat5,
+arbitrary_impl!(Matrix5,
   m11, m12, m13, m14, m15,
   m21, m22, m23, m24, m25,
   m31, m32, m33, m34, m35,
   m41, m42, m43, m44, m45,
   m51, m52, m53, m54, m55
 );
-rand_impl!(Mat5,
+rand_impl!(Matrix5,
   m11, m12, m13, m14, m15,
   m21, m22, m23, m24, m25,
   m31, m32, m33, m34, m35,
   m41, m42, m43, m44, m45,
   m51, m52, m53, m54, m55
 );
-mean_impl!(Mat5, Vec5, 5);
+mean_impl!(Matrix5, Vector5, 5);
-mat_display_impl!(Mat5, 5);
+mat_display_impl!(Matrix5, 5);
 
 /// Square matrix of dimension 6.
 #[repr(C)]
 #[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
-pub struct Mat6<N> {
+pub struct Matrix6<N> {
     pub m11: N, pub m21: N, pub m31: N, pub m41: N, pub m51: N, pub m61: N,
     pub m12: N, pub m22: N, pub m32: N, pub m42: N, pub m52: N, pub m62: N,
     pub m13: N, pub m23: N, pub m33: N, pub m43: N, pub m53: N, pub m63: N,
@@ -509,9 +509,9 @@ pub struct Mat6<N> {
     pub m16: N, pub m26: N, pub m36: N, pub m46: N, pub m56: N, pub m66: N
 }
 
-eye_impl!(Mat6, 6, m11, m22, m33, m44, m55, m66);
+eye_impl!(Matrix6, 6, m11, m22, m33, m44, m55, m66);
 
-mat_impl!(Mat6,
+mat_impl!(Matrix6,
   m11, m12, m13, m14, m15, m16,
   m21, m22, m23, m24, m25, m26,
   m31, m32, m33, m34, m35, m36,
@@ -519,7 +519,7 @@ mat_impl!(Mat6,
   m51, m52, m53, m54, m55, m56,
   m61, m62, m63, m64, m65, m66
 );
-repeat_impl!(Mat6,
+repeat_impl!(Matrix6,
   m11, m12, m13, m14, m15, m16,
   m21, m22, m23, m24, m25, m26,
   m31, m32, m33, m34, m35, m36,
@@ -527,8 +527,8 @@ repeat_impl!(Mat6,
   m51, m52, m53, m54, m55, m56,
   m61, m62, m63, m64, m65, m66
 );
-conversion_impl!(Mat6, 6);
+conversion_impl!(Matrix6, 6);
-mat_cast_impl!(Mat6,
+mat_cast_impl!(Matrix6,
   m11, m12, m13, m14, m15, m16,
   m21, m22, m23, m24, m25, m26,
   m31, m32, m33, m34, m35, m36,
@@ -536,7 +536,7 @@ mat_cast_impl!(Mat6,
   m51, m52, m53, m54, m55, m56,
   m61, m62, m63, m64, m65, m66
 );
-add_impl!(Mat6,
+add_impl!(Matrix6,
   m11, m12, m13, m14, m15, m16,
   m21, m22, m23, m24, m25, m26,
   m31, m32, m33, m34, m35, m36,
@@ -544,7 +544,7 @@ add_impl!(Mat6,
   m51, m52, m53, m54, m55, m56,
   m61, m62, m63, m64, m65, m66
 );
-sub_impl!(Mat6,
+sub_impl!(Matrix6,
   m11, m12, m13, m14, m15, m16,
   m21, m22, m23, m24, m25, m26,
   m31, m32, m33, m34, m35, m36,
@@ -552,7 +552,7 @@ sub_impl!(Mat6,
   m51, m52, m53, m54, m55, m56,
   m61, m62, m63, m64, m65, m66
 );
-scalar_add_impl!(Mat6,
+scalar_add_impl!(Matrix6,
   m11, m12, m13, m14, m15, m16,
   m21, m22, m23, m24, m25, m26,
   m31, m32, m33, m34, m35, m36,
@@ -560,7 +560,7 @@ scalar_add_impl!(Mat6,
   m51, m52, m53, m54, m55, m56,
   m61, m62, m63, m64, m65, m66
 );
-scalar_sub_impl!(Mat6,
+scalar_sub_impl!(Matrix6,
   m11, m12, m13, m14, m15, m16,
   m21, m22, m23, m24, m25, m26,
   m31, m32, m33, m34, m35, m36,
@@ -568,7 +568,7 @@ scalar_sub_impl!(Mat6,
   m51, m52, m53, m54, m55, m56,
   m61, m62, m63, m64, m65, m66
 );
-scalar_mul_impl!(Mat6,
+scalar_mul_impl!(Matrix6,
   m11, m12, m13, m14, m15, m16,
   m21, m22, m23, m24, m25, m26,
   m31, m32, m33, m34, m35, m36,
@@ -576,7 +576,7 @@ scalar_mul_impl!(Mat6,
   m51, m52, m53, m54, m55, m56,
   m61, m62, m63, m64, m65, m66
 );
-scalar_div_impl!(Mat6,
+scalar_div_impl!(Matrix6,
   m11, m12, m13, m14, m15, m16,
   m21, m22, m23, m24, m25, m26,
   m31, m32, m33, m34, m35, m36,
@@ -584,15 +584,15 @@ scalar_div_impl!(Mat6,
   m51, m52, m53, m54, m55, m56,
   m61, m62, m63, m64, m65, m66
 );
-absolute_impl!(Mat6, m11, m12, m13, m14, m15, m16, m21, m22, m23, m24, m25, m26,
+absolute_impl!(Matrix6, m11, m12, m13, m14, m15, m16, m21, m22, m23, m24, m25, m26,
   m31, m32, m33, m34, m35, m36, m41, m42, m43, m44, m45, m46, m51, m52, m53, m54, m55, m56,
   m61, m62, m63, m64, m65, m66);
 
-zero_impl!(Mat6, m11, m12, m13, m14, m15, m16, m21, m22, m23, m24, m25, m26,
+zero_impl!(Matrix6, m11, m12, m13, m14, m15, m16, m21, m22, m23, m24, m25, m26,
   m31, m32, m33, m34, m35, m36, m41, m42, m43, m44, m45, m46, m51, m52, m53, m54, m55, m56,
   m61, m62, m63, m64, m65, m66);
 
-one_impl!(Mat6,
+one_impl!(Matrix6,
   ::one  , ::zero, ::zero, ::zero, ::zero, ::zero,
   ::zero, ::one  , ::zero, ::zero, ::zero, ::zero,
   ::zero, ::zero, ::one  , ::zero, ::zero, ::zero,
@@ -600,28 +600,28 @@ one_impl!(Mat6,
   ::zero, ::zero, ::zero, ::zero, ::one  , ::zero,
   ::zero, ::zero, ::zero, ::zero, ::zero, ::one
 );
-iterable_impl!(Mat6, 6);
+iterable_impl!(Matrix6, 6);
-iterable_mut_impl!(Mat6, 6);
+iterable_mut_impl!(Matrix6, 6);
-dim_impl!(Mat6, 6);
+dim_impl!(Matrix6, 6);
-indexable_impl!(Mat6, 6);
+indexable_impl!(Matrix6, 6);
-index_impl!(Mat6, 6);
+index_impl!(Matrix6, 6);
-at_fast_impl!(Mat6, 6);
+at_fast_impl!(Matrix6, 6);
-mat_mul_mat_impl!(Mat6, 6);
+mat_mul_mat_impl!(Matrix6, 6);
-mat_mul_vec_impl!(Mat6, Vec6, 6, ::zero);
+mat_mul_vec_impl!(Matrix6, Vector6, 6, ::zero);
-vec_mul_mat_impl!(Mat6, Vec6, 6, ::zero);
+vec_mul_mat_impl!(Matrix6, Vector6, 6, ::zero);
-mat_mul_pnt_impl!(Mat6, Pnt6, 6, Orig::orig);
+mat_mul_point_impl!(Matrix6, Point6, 6, Origin::origin);
-pnt_mul_mat_impl!(Mat6, Pnt6, 6, Orig::orig);
+point_mul_mat_impl!(Matrix6, Point6, 6, Origin::origin);
-inv_impl!(Mat6, 6);
+inverse_impl!(Matrix6, 6);
-transpose_impl!(Mat6, 6);
+transpose_impl!(Matrix6, 6);
-approx_eq_impl!(Mat6);
+approx_eq_impl!(Matrix6);
-row_impl!(Mat6, Vec6, 6);
+row_impl!(Matrix6, Vector6, 6);
-col_impl!(Mat6, Vec6, 6);
+col_impl!(Matrix6, Vector6, 6);
-col_slice_impl!(Mat6, Vec6, DVec6, 6);
+col_slice_impl!(Matrix6, Vector6, DVector6, 6);
-row_slice_impl!(Mat6, Vec6, DVec6, 6);
+row_slice_impl!(Matrix6, Vector6, DVector6, 6);
-diag_impl!(Mat6, Vec6, 6);
+diag_impl!(Matrix6, Vector6, 6);
-outer_impl!(Vec6, Mat6);
+outer_impl!(Vector6, Matrix6);
-eigen_qr_impl!(Mat6, Vec6);
+eigen_qr_impl!(Matrix6, Vector6);
-arbitrary_impl!(Mat6,
+arbitrary_impl!(Matrix6,
   m11, m12, m13, m14, m15, m16,
   m21, m22, m23, m24, m25, m26,
   m31, m32, m33, m34, m35, m36,
@@ -629,7 +629,7 @@ arbitrary_impl!(Mat6,
   m51, m52, m53, m54, m55, m56,
   m61, m62, m63, m64, m65, m66
 );
-rand_impl!(Mat6,
+rand_impl!(Matrix6,
   m11, m12, m13, m14, m15, m16,
   m21, m22, m23, m24, m25, m26,
   m31, m32, m33, m34, m35, m36,
@@ -637,5 +637,5 @@ rand_impl!(Mat6,
   m51, m52, m53, m54, m55, m56,
   m61, m62, m63, m64, m65, m66
 );
-mean_impl!(Mat6, Vec6, 6);
+mean_impl!(Matrix6, Vector6, 6);
-mat_display_impl!(Mat6, 6);
+mat_display_impl!(Matrix6, 6);

src/structs/matrix_macros.rs

@@ -14,37 +14,37 @@ macro_rules! mat_impl(
 );
 
 macro_rules! conversion_impl(
-    ($t: ident, $dim: expr) => (
+    ($t: ident, $dimension: expr) => (
-        impl<N> AsRef<[[N; $dim]; $dim]> for $t<N> {
+        impl<N> AsRef<[[N; $dimension]; $dimension]> for $t<N> {
             #[inline]
-            fn as_ref(&self) -> &[[N; $dim]; $dim] {
+            fn as_ref(&self) -> &[[N; $dimension]; $dimension] {
                 unsafe {
                     mem::transmute(self)
                 }
             }
         }
 
-        impl<N> AsMut<[[N; $dim]; $dim]> for $t<N> {
+        impl<N> AsMut<[[N; $dimension]; $dimension]> for $t<N> {
             #[inline]
-            fn as_mut(&mut self) -> &mut [[N; $dim]; $dim] {
+            fn as_mut(&mut self) -> &mut [[N; $dimension]; $dimension] {
                 unsafe {
                     mem::transmute(self)
                 }
             }
         }
 
-        impl<'a, N> From<&'a [[N; $dim]; $dim]> for &'a $t<N> {
+        impl<'a, N> From<&'a [[N; $dimension]; $dimension]> for &'a $t<N> {
             #[inline]
-            fn from(arr: &'a [[N; $dim]; $dim]) -> &'a $t<N> {
+            fn from(arr: &'a [[N; $dimension]; $dimension]) -> &'a $t<N> {
                 unsafe {
                     mem::transmute(arr)
                 }
             }
         }
 
-        impl<'a, N> From<&'a mut [[N; $dim]; $dim]> for &'a mut $t<N> {
+        impl<'a, N> From<&'a mut [[N; $dimension]; $dimension]> for &'a mut $t<N> {
             #[inline]
-            fn from(arr: &'a mut [[N; $dim]; $dim]) -> &'a mut $t<N> {
+            fn from(arr: &'a mut [[N; $dimension]; $dimension]) -> &'a mut $t<N> {
                 unsafe {
                     mem::transmute(arr)
                 }
@@ -54,18 +54,18 @@ macro_rules! conversion_impl(
 );
 
 macro_rules! at_fast_impl(
-    ($t: ident, $dim: expr) => (
+    ($t: ident, $dimension: expr) => (
         impl<N: Copy> $t<N> {
             #[inline]
             pub unsafe fn at_fast(&self, (i, j): (usize, usize)) -> N {
-                (*mem::transmute::<&$t<N>, &[N; $dim * $dim]>(self)
+                (*mem::transmute::<&$t<N>, &[N; $dimension * $dimension]>(self)
-                 .get_unchecked(i + j * $dim))
+                 .get_unchecked(i + j * $dimension))
             }
 
             #[inline]
             pub unsafe fn set_fast(&mut self, (i, j): (usize, usize), val: N) {
-                (*mem::transmute::<&mut $t<N>, &mut [N; $dim * $dim]>(self)
+                (*mem::transmute::<&mut $t<N>, &mut [N; $dimension * $dimension]>(self)
-                 .get_unchecked_mut(i + j * $dim)) = val
+                 .get_unchecked_mut(i + j * $dimension)) = val
             }
         }
     )
@@ -259,10 +259,10 @@ macro_rules! mat_sub_scalar_impl(
 
 
 macro_rules! eye_impl(
-    ($t: ident, $dim: expr, $($comp_diagN: ident),+) => (
+    ($t: ident, $dimension: expr, $($comp_diagN: ident),+) => (
         impl<N: Zero + One> Eye for $t<N> {
-            fn new_identity(dim: usize) -> $t<N> {
+            fn new_identity(dimension: usize) -> $t<N> {
-                assert!(dim == $dim);
+                assert!(dimension == $dimension);
                 let mut eye: $t<N> = ::zero();
                 $(eye.$comp_diagN = ::one();)+
                 eye
@@ -295,12 +295,12 @@ macro_rules! absolute_impl(
 );
 
 macro_rules! iterable_impl(
-  ($t: ident, $dim: expr) => (
+  ($t: ident, $dimension: expr) => (
     impl<N> Iterable<N> for $t<N> {
         #[inline]
         fn iter<'l>(&'l self) -> Iter<'l, N> {
             unsafe {
-                mem::transmute::<&'l $t<N>, &'l [N; $dim * $dim]>(self).iter()
+                mem::transmute::<&'l $t<N>, &'l [N; $dimension * $dimension]>(self).iter()
             }
         }
     }
@@ -308,12 +308,12 @@ macro_rules! iterable_impl(
 );
 
 macro_rules! iterable_mut_impl(
-  ($t: ident, $dim: expr) => (
+  ($t: ident, $dimension: expr) => (
     impl<N> IterableMut<N> for $t<N> {
         #[inline]
         fn iter_mut<'l>(&'l mut self) -> IterMut<'l, N> {
             unsafe {
-                mem::transmute::<&'l mut $t<N>, &'l mut [N; $dim * $dim]>(self).iter_mut()
+                mem::transmute::<&'l mut $t<N>, &'l mut [N; $dimension * $dimension]>(self).iter_mut()
             }
         }
     }
@@ -350,22 +350,22 @@ macro_rules! zero_impl(
 );
 
 macro_rules! dim_impl(
-  ($t: ident, $dim: expr) => (
+  ($t: ident, $dimension: expr) => (
-    impl<N> Dim for $t<N> {
+    impl<N> Dimension for $t<N> {
         #[inline]
-        fn dim(_: Option<$t<N>>) -> usize {
+        fn dimension(_: Option<$t<N>>) -> usize {
-            $dim
+            $dimension
         }
     }
   )
 );
 
 macro_rules! indexable_impl(
-  ($t: ident, $dim: expr) => (
+  ($t: ident, $dimension: expr) => (
     impl<N> Shape<(usize, usize)> for $t<N> {
         #[inline]
         fn shape(&self) -> (usize, usize) {
-            ($dim, $dim)
+            ($dimension, $dimension)
         }
     }
 
@@ -373,32 +373,32 @@ macro_rules! indexable_impl(
         #[inline]
         fn swap(&mut self, (i1, j1): (usize, usize), (i2, j2): (usize, usize)) {
             unsafe {
-              mem::transmute::<&mut $t<N>, &mut [N; $dim * $dim]>(self)
+              mem::transmute::<&mut $t<N>, &mut [N; $dimension * $dimension]>(self)
-                .swap(i1 + j1 * $dim, i2 + j2 * $dim)
+                .swap(i1 + j1 * $dimension, i2 + j2 * $dimension)
             }
         }
 
         #[inline]
         unsafe fn unsafe_at(&self, (i, j): (usize, usize)) -> N {
-            (*mem::transmute::<&$t<N>, &[N; $dim * $dim]>(self).get_unchecked(i + j * $dim))
+            (*mem::transmute::<&$t<N>, &[N; $dimension * $dimension]>(self).get_unchecked(i + j * $dimension))
         }
 
         #[inline]
         unsafe fn unsafe_set(&mut self, (i, j): (usize, usize), val: N) {
-            (*mem::transmute::<&mut $t<N>, &mut [N; $dim * $dim]>(self).get_unchecked_mut(i + j * $dim)) = val
+            (*mem::transmute::<&mut $t<N>, &mut [N; $dimension * $dimension]>(self).get_unchecked_mut(i + j * $dimension)) = val
         }
     }
   )
 );
 
 macro_rules! index_impl(
-    ($t: ident, $dim: expr) => (
+    ($t: ident, $dimension: expr) => (
         impl<N> Index<(usize, usize)> for $t<N> {
             type Output = N;
 
             fn index(&self, (i, j): (usize, usize)) -> &N {
                 unsafe {
-                    &mem::transmute::<&$t<N>, & [N; $dim * $dim]>(self)[i + j * $dim]
+                    &mem::transmute::<&$t<N>, & [N; $dimension * $dimension]>(self)[i + j * $dimension]
                 }
             }
         }
@@ -406,7 +406,7 @@ macro_rules! index_impl(
         impl<N> IndexMut<(usize, usize)> for $t<N> {
             fn index_mut(&mut self, (i, j): (usize, usize)) -> &mut N {
                 unsafe {
-                    &mut mem::transmute::<&mut $t<N>, &mut [N; $dim * $dim]>(self)[i + j * $dim]
+                    &mut mem::transmute::<&mut $t<N>, &mut [N; $dimension * $dimension]>(self)[i + j * $dimension]
                 }
             }
         }
@@ -414,23 +414,23 @@ macro_rules! index_impl(
 );
 
 macro_rules! col_slice_impl(
-    ($t: ident, $tv: ident, $slice: ident, $dim: expr) => (
+    ($t: ident, $tv: ident, $slice: ident, $dimension: expr) => (
-        impl<N: Clone + Copy + Zero> ColSlice<$slice<N>> for $t<N> {
+        impl<N: Clone + Copy + Zero> ColumnSlice<$slice<N>> for $t<N> {
             fn col_slice(&self, cid: usize, rstart: usize, rend: usize) -> $slice<N> {
-                let col = self.col(cid);
+                let column = self.column(cid);
 
-                $slice::from_slice(rend - rstart, &col.as_ref()[rstart .. rend])
+                $slice::from_slice(rend - rstart, &column.as_ref()[rstart .. rend])
             }
         }
     )
 );
 
 macro_rules! row_impl(
-  ($t: ident, $tv: ident, $dim: expr) => (
+  ($t: ident, $tv: ident, $dimension: expr) => (
     impl<N: Copy + Zero> Row<$tv<N>> for $t<N> {
         #[inline]
         fn nrows(&self) -> usize {
-            Dim::dim(None::<$t<N>>)
+            Dimension::dimension(None::<$t<N>>)
         }
 
         #[inline]
@@ -455,7 +455,7 @@ macro_rules! row_impl(
 );
 
 macro_rules! row_slice_impl(
-    ($t: ident, $tv: ident, $slice: ident, $dim: expr) => (
+    ($t: ident, $tv: ident, $slice: ident, $dimension: expr) => (
         impl<N: Clone + Copy + Zero> RowSlice<$slice<N>> for $t<N> {
             fn row_slice(&self, rid: usize, cstart: usize, cend: usize) -> $slice<N> {
                 let row = self.row(rid);
@@ -467,26 +467,26 @@ macro_rules! row_slice_impl(
 );
 
 macro_rules! col_impl(
-  ($t: ident, $tv: ident, $dim: expr) => (
+  ($t: ident, $tv: ident, $dimension: expr) => (
-    impl<N: Copy + Zero> Col<$tv<N>> for $t<N> {
+    impl<N: Copy + Zero> Column<$tv<N>> for $t<N> {
         #[inline]
         fn ncols(&self) -> usize {
-            Dim::dim(None::<$t<N>>)
+            Dimension::dimension(None::<$t<N>>)
         }
 
         #[inline]
-        fn set_col(&mut self, col: usize, v: $tv<N>) {
+        fn set_col(&mut self, column: usize, v: $tv<N>) {
             for (i, e) in v.iter().enumerate() {
-                self[(i, col)] = *e;
+                self[(i, column)] = *e;
             }
         }
 
         #[inline]
-        fn col(&self, col: usize) -> $tv<N> {
+        fn column(&self, column: usize) -> $tv<N> {
             let mut res: $tv<N> = ::zero();
 
             for (i, e) in res.iter_mut().enumerate() {
-                *e = self[(i, col)];
+                *e = self[(i, column)];
             }
 
             res
@@ -496,34 +496,34 @@ macro_rules! col_impl(
 );
 
 macro_rules! diag_impl(
-    ($t: ident, $tv: ident, $dim: expr) => (
+    ($t: ident, $tv: ident, $dimension: expr) => (
-        impl<N: Copy + Zero> Diag<$tv<N>> for $t<N> {
+        impl<N: Copy + Zero> Diagonal<$tv<N>> for $t<N> {
             #[inline]
-            fn from_diag(diag: &$tv<N>) -> $t<N> {
+            fn from_diagonal(diagonal: &$tv<N>) -> $t<N> {
                 let mut res: $t<N> = ::zero();
 
-                res.set_diag(diag);
+                res.set_diagonal(diagonal);
 
                 res
             }
 
             #[inline]
-            fn diag(&self) -> $tv<N> {
+            fn diagonal(&self) -> $tv<N> {
-                let mut diag: $tv<N> = ::zero();
+                let mut diagonal: $tv<N> = ::zero();
 
-                for i in 0 .. $dim {
+                for i in 0 .. $dimension {
-                    unsafe { diag.unsafe_set(i, self.unsafe_at((i, i))) }
+                    unsafe { diagonal.unsafe_set(i, self.unsafe_at((i, i))) }
                 }
 
-                diag
+                diagonal
             }
         }
 
         impl<N: Copy + Zero> DiagMut<$tv<N>> for $t<N> {
             #[inline]
-            fn set_diag(&mut self, diag: &$tv<N>) {
+            fn set_diagonal(&mut self, diagonal: &$tv<N>) {
-                for i in 0 .. $dim {
+                for i in 0 .. $dimension {
-                    unsafe { self.unsafe_set((i, i), diag.unsafe_at(i)) }
+                    unsafe { self.unsafe_set((i, i), diagonal.unsafe_at(i)) }
                 }
             }
         }
@@ -531,19 +531,19 @@ macro_rules! diag_impl(
 );
 
 macro_rules! mat_mul_mat_impl(
-  ($t: ident, $dim: expr) => (
+  ($t: ident, $dimension: expr) => (
     impl<N: Copy + BaseNum> Mul<$t<N>> for $t<N> {
         type Output = $t<N>;
         #[inline]
         fn mul(self, right: $t<N>) -> $t<N> {
             let mut res: $t<N> = ::zero();
 
-            for i in 0 .. $dim {
+            for i in 0 .. $dimension {
-                for j in 0 .. $dim {
+                for j in 0 .. $dimension {
                     let mut acc: N = ::zero();
 
                     unsafe {
-                        for k in 0 .. $dim {
+                        for k in 0 .. $dimension {
                             acc = acc + self.at_fast((i, k)) * right.at_fast((k, j));
                         }
 
@@ -568,7 +568,7 @@ macro_rules! mat_mul_mat_impl(
 );
 
 macro_rules! vec_mul_mat_impl(
-  ($t: ident, $v: ident, $dim: expr, $zero: expr) => (
+  ($t: ident, $v: ident, $dimension: expr, $zero: expr) => (
     impl<N: Copy + BaseNum> Mul<$t<N>> for $v<N> {
         type Output = $v<N>;
 
@@ -576,8 +576,8 @@ macro_rules! vec_mul_mat_impl(
         fn mul(self, right: $t<N>) -> $v<N> {
             let mut res : $v<N> = $zero();
 
-            for i in 0..$dim {
+            for i in 0..$dimension {
-                for j in 0..$dim {
+                for j in 0..$dimension {
                     unsafe {
                         let val = res.at_fast(i) + self.at_fast(j) * right.at_fast((j, i));
                         res.set_fast(i, val)
@@ -601,7 +601,7 @@ macro_rules! vec_mul_mat_impl(
 );
 
 macro_rules! mat_mul_vec_impl(
-  ($t: ident, $v: ident, $dim: expr, $zero: expr) => (
+  ($t: ident, $v: ident, $dimension: expr, $zero: expr) => (
     impl<N: Copy + BaseNum> Mul<$v<N>> for $t<N> {
         type Output = $v<N>;
 
@@ -609,8 +609,8 @@ macro_rules! mat_mul_vec_impl(
         fn mul(self, right: $v<N>) -> $v<N> {
             let mut res : $v<N> = $zero();
 
-            for i in 0 .. $dim {
+            for i in 0 .. $dimension {
-                for j in 0 .. $dim {
+                for j in 0 .. $dimension {
                     unsafe {
                         let val = res.at_fast(i) + self.at_fast((i, j)) * right.at_fast(j);
                         res.set_fast(i, val)
@@ -624,26 +624,26 @@ macro_rules! mat_mul_vec_impl(
   )
 );
 
-macro_rules! pnt_mul_mat_impl(
+macro_rules! point_mul_mat_impl(
-  ($t: ident, $v: ident, $dim: expr, $zero: expr) => (
+  ($t: ident, $v: ident, $dimension: expr, $zero: expr) => (
-      vec_mul_mat_impl!($t, $v, $dim, $zero);
+      vec_mul_mat_impl!($t, $v, $dimension, $zero);
   )
 );
 
-macro_rules! mat_mul_pnt_impl(
+macro_rules! mat_mul_point_impl(
-  ($t: ident, $v: ident, $dim: expr, $zero: expr) => (
+  ($t: ident, $v: ident, $dimension: expr, $zero: expr) => (
-      mat_mul_vec_impl!($t, $v, $dim, $zero);
+      mat_mul_vec_impl!($t, $v, $dimension, $zero);
   )
 );
 
-macro_rules! inv_impl(
+macro_rules! inverse_impl(
-  ($t: ident, $dim: expr) => (
+  ($t: ident, $dimension: expr) => (
     impl<N: Copy + BaseNum>
-    Inv for $t<N> {
+    Inverse for $t<N> {
         #[inline]
-        fn inv(&self) -> Option<$t<N>> {
+        fn inverse(&self) -> Option<$t<N>> {
             let mut res : $t<N> = *self;
-            if res.inv_mut() {
+            if res.inverse_mut() {
                 Some(res)
             }
             else {
@@ -651,18 +651,18 @@ macro_rules! inv_impl(
             }
         }
 
-        fn inv_mut(&mut self) -> bool {
+        fn inverse_mut(&mut self) -> bool {
             let mut res: $t<N> = ::one();
 
             // inversion using Gauss-Jordan elimination
-            for k in 0..$dim {
+            for k in 0..$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 != $dim {
+                while n0 != $dimension {
                     if self[(n0, k)] != ::zero() {
                         break;
                     }
@@ -670,13 +670,13 @@ macro_rules! inv_impl(
                     n0 = n0 + 1;
                 }
 
-                if n0 == $dim {
+                if n0 == $dimension {
                     return false
                 }
 
                 // swap pivot line
                 if n0 != k {
-                    for j in 0..$dim {
+                    for j in 0..$dimension {
                         self.swap((n0, j), (k, j));
                         res.swap((n0, j), (k, j));
                     }
@@ -684,26 +684,26 @@ macro_rules! inv_impl(
 
                 let pivot = self[(k, k)];
 
-                for j in k..$dim {
+                for j in k..$dimension {
                     let selfval = self[(k, j)] / pivot;
                     self[(k, j)] = selfval;
                 }
 
-                for j in 0..$dim {
+                for j in 0..$dimension {
                     let resval = res[(k, j)] / pivot;
                     res[(k, j)] = resval;
                 }
 
-                for l in 0..$dim {
+                for l in 0..$dimension {
                     if l != k {
                         let normalizer = self[(l, k)];
 
-                        for j in k..$dim {
+                        for j in k..$dimension {
                             let selfval = self[(l, j)] - self[(k, j)] * normalizer;
                             self[(l, j)] = selfval;
                         }
 
-                        for j in 0..$dim {
+                        for j in 0..$dimension {
                             let resval  = res[(l, j)] - res[(k, j)] * normalizer;
                             res[(l, j)] = resval;
                         }
@@ -720,7 +720,7 @@ macro_rules! inv_impl(
 );
 
 macro_rules! transpose_impl(
-  ($t: ident, $dim: expr) => (
+  ($t: ident, $dimension: expr) => (
     impl<N: Copy> Transpose for $t<N> {
         #[inline]
         fn transpose(&self) -> $t<N> {
@@ -732,7 +732,7 @@ macro_rules! transpose_impl(
 
         #[inline]
         fn transpose_mut(&mut self) {
-            for i in 1..$dim {
+            for i in 1..$dimension {
                 for j in 0..i {
                     self.swap((i, j), (j, i))
                 }
@@ -771,14 +771,14 @@ macro_rules! approx_eq_impl(
 );
 
 macro_rules! to_homogeneous_impl(
-  ($t: ident, $t2: ident, $dim: expr, $dim2: expr) => (
+  ($t: ident, $t2: ident, $dimension: expr, $dim2: expr) => (
     impl<N: BaseNum + Copy> ToHomogeneous<$t2<N>> for $t<N> {
         #[inline]
         fn to_homogeneous(&self) -> $t2<N> {
             let mut res: $t2<N> = ::one();
 
-            for i in 0..$dim {
+            for i in 0..$dimension {
-                for j in 0..$dim {
+                for j in 0..$dimension {
                     res[(i, j)] = self[(i, j)]
                 }
             }
@@ -790,14 +790,14 @@ macro_rules! to_homogeneous_impl(
 );
 
 macro_rules! from_homogeneous_impl(
-  ($t: ident, $t2: ident, $dim: expr, $dim2: expr) => (
+  ($t: ident, $t2: ident, $dimension: expr, $dim2: expr) => (
     impl<N: BaseNum + Copy> FromHomogeneous<$t2<N>> for $t<N> {
         #[inline]
         fn from(m: &$t2<N>) -> $t<N> {
             let mut res: $t<N> = ::one();
 
-            for i in 0..$dim {
+            for i in 0..$dimension {
-                for j in 0..$dim {
+                for j in 0..$dimension {
                     res[(i, j)] = m[(i, j)]
                 }
             }
@@ -819,8 +819,8 @@ macro_rules! outer_impl(
             #[inline]
             fn outer(&self, other: &$t<N>) -> $m<N> {
                 let mut res: $m<N> = ::zero();
-                for i in 0..Dim::dim(None::<$t<N>>) {
+                for i in 0..Dimension::dimension(None::<$t<N>>) {
-                    for j in 0..Dim::dim(None::<$t<N>>) {
+                    for j in 0..Dimension::dimension(None::<$t<N>>) {
                         res[(i, j)] = self[i] * other[j]
                     }
                 }
@@ -843,14 +843,14 @@ macro_rules! eigen_qr_impl(
 
 
 macro_rules! mean_impl(
-    ($t: ident, $v: ident, $dim: expr) => (
+    ($t: ident, $v: ident, $dimension: expr) => (
         impl<N: BaseNum + Cast<f64> + Clone> Mean<$v<N>> for $t<N> {
             fn mean(&self) -> $v<N> {
                 let mut res: $v<N> = ::zero();
-                let normalizer: N  = Cast::from(1.0f64 / $dim as f64);
+                let normalizer: N  = Cast::from(1.0f64 / $dimension as f64);
         
-                for i in 0 .. $dim {
+                for i in 0 .. $dimension {
-                    for j in 0 .. $dim {
+                    for j in 0 .. $dimension {
                         unsafe {
                             let acc = res.unsafe_at(j) + self.unsafe_at((i, j)) * normalizer;
                             res.unsafe_set(j, acc);
@@ -865,7 +865,7 @@ macro_rules! mean_impl(
 );
 
 macro_rules! mat_display_impl(
-    ($t: ident, $dim: expr) => (
+    ($t: ident, $dimension: expr) => (
         impl<N: fmt::Display + BaseFloat> fmt::Display for $t<N> {
             // XXX: will will not always work correctly due to rounding errors.
             fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
@@ -888,8 +888,8 @@ macro_rules! mat_display_impl(
 
                 let mut max_decimal_length = 0;
                 let mut decimal_lengths: $t<usize> = ::zero();
-                for i in 0 .. $dim {
+                for i in 0 .. $dimension {
-                    for j in 0 .. $dim {
+                    for j in 0 .. $dimension {
                         decimal_lengths[(i, j)] = integral_length(&self[(i, j)].clone());
                         max_decimal_length = ::max(max_decimal_length, decimal_lengths[(i, j)]);
                     }
@@ -898,11 +898,11 @@ macro_rules! mat_display_impl(
                 let precision = f.precision().unwrap_or(3);
                 let max_number_length = max_decimal_length + precision + 1;
 
-                try!(writeln!(f, "  ┌ {:>width$} ┐", "", width = max_number_length * $dim + $dim - 1));
+                try!(writeln!(f, "  ┌ {:>width$} ┐", "", width = max_number_length * $dimension + $dimension - 1));
 
-                for i in 0 .. $dim {
+                for i in 0 .. $dimension {
                     try!(write!(f, "  │"));
-                    for j in 0 .. $dim {
+                    for j in 0 .. $dimension {
                         let number_length = decimal_lengths[(i, j)] + precision + 1;
                         let pad = max_number_length - number_length;
                         try!(write!(f, " {:>thepad$}", "", thepad = pad));
@@ -911,7 +911,7 @@ macro_rules! mat_display_impl(
                     try!(writeln!(f, " │"));
                 }
 
-                writeln!(f, "  └ {:>width$} ┘", "", width = max_number_length * $dim + $dim - 1)
+                writeln!(f, "  └ {:>width$} ┘", "", width = max_number_length * $dimension + $dimension - 1)
             }
         }
     )

src/structs/mod.rs

@@ -1,49 +1,49 @@
 //! Data structures and implementations.
 
-pub use self::dmat::{DMat, DMat1, DMat2, DMat3, DMat4, DMat5, DMat6};
+pub use self::dmatrix::{DMatrix, DMatrix1, DMatrix2, DMatrix3, DMatrix4, DMatrix5, DMatrix6};
-pub use self::dvec::{DVec, DVec1, DVec2, DVec3, DVec4, DVec5, DVec6};
+pub use self::dvector::{DVector, DVector1, DVector2, DVector3, DVector4, DVector5, DVector6};
-pub use self::vec::{Vec1, Vec2, Vec3, Vec4, Vec5, Vec6};
+pub use self::vector::{Vector1, Vector2, Vector3, Vector4, Vector5, Vector6};
-pub use self::pnt::{Pnt1, Pnt2, Pnt3, Pnt4, Pnt5, Pnt6};
+pub use self::point::{Point1, Point2, Point3, Point4, Point5, Point6};
-pub use self::mat::{Identity, Mat1, Mat2, Mat3, Mat4, Mat5, Mat6};
+pub use self::matrix::{Identity, Matrix1, Matrix2, Matrix3, Matrix4, Matrix5, Matrix6};
-pub use self::rot::{Rot2, Rot3};
+pub use self::rotation::{Rotation2, Rotation3};
-pub use self::iso::{Iso2, Iso3};
+pub use self::isometry::{Isometry2, Isometry3};
-pub use self::sim::{Sim2, Sim3};
+pub use self::similarity::{Similarity2, Similarity3};
-pub use self::persp::{Persp3, PerspMat3};
+pub use self::perspective::{Perspective3, PerspectiveMatrix3};
-pub use self::ortho::{Ortho3, OrthoMat3};
+pub use self::orthographic::{Orthographic3, OrthographicMatrix3};
-pub use self::quat::{Quat, UnitQuat};
+pub use self::quaternion::{Quaternion, UnitQuaternion};
 
 #[cfg(feature="generic_sizes")]
-pub use self::vecn::VecN;
+pub use self::vectorn::VectorN;
 
-mod dmat_macros;
+mod dmatrix_macros;
-mod dmat;
+mod dmatrix;
-mod vecn_macros;
+mod vectorn_macros;
 #[cfg(feature="generic_sizes")]
-mod vecn;
+mod vectorn;
-mod dvec_macros;
+mod dvector_macros;
-mod dvec;
+mod dvector;
-mod vec_macros;
+mod vector_macros;
-mod vec;
+mod vector;
-mod pnt_macros;
+mod point_macros;
-mod pnt;
+mod point;
-mod quat;
+mod quaternion;
-mod mat_macros;
+mod matrix_macros;
-mod mat;
+mod matrix;
-mod rot_macros;
+mod rotation_macros;
-mod rot;
+mod rotation;
-mod iso_macros;
+mod isometry_macros;
-mod iso;
+mod isometry;
-mod sim_macros;
+mod similarity_macros;
-mod sim;
+mod similarity;
-mod persp;
+mod perspective;
-mod ortho;
+mod orthographic;
 
 // Specialization for some 1d, 2d and 3d operations.
 #[doc(hidden)]
-mod spec {
+mod specializations {
     mod identity;
-    mod mat;
+    mod matrix;
-    mod vec;
+    mod vector;
     mod primitives;
     // mod complex;
 }

src/structs/orthographic.rs

@@ -1,5 +1,5 @@
 use traits::structure::{BaseFloat, Cast};
-use structs::{Pnt3, Vec3, Mat4};
+use structs::{Point3, Vector3, Matrix4};
 
 #[cfg(feature="arbitrary")]
 use quickcheck::{Arbitrary, Gen};
@@ -11,7 +11,7 @@ use quickcheck::{Arbitrary, Gen};
 /// `(-1, -1, -1)` to `(1, 1, 1)`. Reading or modifying its individual properties is cheap but
 /// applying the transformation is costly.
 #[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Debug, Copy)]
-pub struct Ortho3<N> {
+pub struct Orthographic3<N> {
     left:   N,
     right:  N,
     bottom: N,
@@ -26,18 +26,18 @@ pub struct Ortho3<N> {
 /// `(-1, -1, -1)` to `(1, 1, 1)`. Reading or modifying its individual properties is costly but
 /// applying the transformation is cheap.
 #[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Debug, Copy)]
-pub struct OrthoMat3<N> {
+pub struct OrthographicMatrix3<N> {
-    mat: Mat4<N>
+    matrix: Matrix4<N>
 }
 
-impl<N: BaseFloat> Ortho3<N> {
+impl<N: BaseFloat> Orthographic3<N> {
     /// Creates a new 3D orthographic projection.
-    pub fn new(left: N, right: N, bottom: N, top: N, znear: N, zfar: N) -> Ortho3<N> {
+    pub fn new(left: N, right: N, bottom: N, top: N, znear: N, zfar: N) -> Orthographic3<N> {
         assert!(!::is_zero(&(zfar - znear)));
         assert!(!::is_zero(&(left - right)));
         assert!(!::is_zero(&(top - bottom)));
 
-        Ortho3 {
+        Orthographic3 {
             left:   left,
             right:  right,
             bottom: bottom,
@@ -48,30 +48,30 @@ impl<N: BaseFloat> Ortho3<N> {
     }
 
     /// Builds a 4D projection matrix (using homogeneous coordinates) for this projection.
-    pub fn to_mat(&self) -> Mat4<N> {
+    pub fn to_matrix(&self) -> Matrix4<N> {
-        self.to_persp_mat().mat
+        self.to_orthographic_matrix().matrix
     }
 
-    /// Build a `OrthoMat3` representing this projection.
+    /// Build a `OrthographicMatrix3` representing this projection.
-    pub fn to_persp_mat(&self) -> OrthoMat3<N> {
+    pub fn to_orthographic_matrix(&self) -> OrthographicMatrix3<N> {
-        OrthoMat3::new(self.left, self.right, self.bottom, self.top, self.znear, self.zfar)
+        OrthographicMatrix3::new(self.left, self.right, self.bottom, self.top, self.znear, self.zfar)
     }
 }
 
 #[cfg(feature="arbitrary")]
-impl<N: Arbitrary + BaseFloat> Arbitrary for Ortho3<N> {
+impl<N: Arbitrary + BaseFloat> Arbitrary for Orthographic3<N> {
-    fn arbitrary<G: Gen>(g: &mut G) -> Ortho3<N> {
+    fn arbitrary<G: Gen>(g: &mut G) -> Orthographic3<N> {
         let left   = Arbitrary::arbitrary(g);
         let right  = reject(g, |x: &N| *x > left);
         let bottom = Arbitrary::arbitrary(g);
         let top    = reject(g, |x: &N| *x > bottom);
         let znear  = Arbitrary::arbitrary(g);
         let zfar   = reject(g, |x: &N| *x > znear);
-        Ortho3::new(left, right, bottom, top, znear, zfar)
+        Orthographic3::new(left, right, bottom, top, znear, zfar)
     }
 }
 
-impl<N: BaseFloat + Clone> Ortho3<N> {
+impl<N: BaseFloat + Clone> Orthographic3<N> {
     /// The smallest x-coordinate of the view cuboid.
     #[inline]
     pub fn left(&self) -> N {
@@ -152,29 +152,29 @@ impl<N: BaseFloat + Clone> Ortho3<N> {
 
     /// Projects a point.
     #[inline]
-    pub fn project_pnt(&self, p: &Pnt3<N>) -> Pnt3<N> {
+    pub fn project_point(&self, p: &Point3<N>) -> Point3<N> {
         // FIXME: optimize that
-        self.to_persp_mat().project_pnt(p)
+        self.to_orthographic_matrix().project_point(p)
     }
 
     /// Projects a vector.
     #[inline]
-    pub fn project_vec(&self, p: &Vec3<N>) -> Vec3<N> {
+    pub fn project_vector(&self, p: &Vector3<N>) -> Vector3<N> {
         // FIXME: optimize that
-        self.to_persp_mat().project_vec(p)
+        self.to_orthographic_matrix().project_vector(p)
     }
 }
 
-impl<N: BaseFloat> OrthoMat3<N> {
+impl<N: BaseFloat> OrthographicMatrix3<N> {
     /// Creates a new orthographic projection matrix.
-    pub fn new(left: N, right: N, bottom: N, top: N, znear: N, zfar: N) -> OrthoMat3<N> {
+    pub fn new(left: N, right: N, bottom: N, top: N, znear: N, zfar: N) -> OrthographicMatrix3<N> {
         assert!(left < right, "The left corner must be farther than the right corner.");
         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 mat: Mat4<N> = ::one();
+        let matrix: Matrix4<N> = ::one();
 
-        let mut res = OrthoMat3 { mat: mat };
+        let mut res = OrthographicMatrix3 { matrix: matrix };
         res.set_left_and_right(left, right);
         res.set_bottom_and_top(bottom, top);
         res.set_znear_and_zfar(znear, zfar);
@@ -183,7 +183,7 @@ impl<N: BaseFloat> OrthoMat3<N> {
     }
 
     /// Creates a new orthographic projection matrix from an aspect ratio and the vertical field of view.
-    pub fn new_with_fov(aspect: N, vfov: N, znear: N, zfar: N) -> OrthoMat3<N> {
+    pub fn new_with_fov(aspect: N, vfov: N, znear: N, zfar: N) -> OrthographicMatrix3<N> {
         assert!(znear < zfar, "The far plane must be farther than the near plane.");
         assert!(!::is_zero(&aspect));
 
@@ -192,59 +192,59 @@ impl<N: BaseFloat> OrthoMat3<N> {
         let width  = zfar * (vfov / _2).tan();
         let height = width / aspect;
 
-        OrthoMat3::new(-width / _2, width / _2, -height / _2, height / _2, znear, zfar)
+        OrthographicMatrix3::new(-width / _2, width / _2, -height / _2, height / _2, znear, zfar)
     }
 
     /// Creates a new orthographic matrix from a 4D matrix.
     ///
     /// This is unsafe because the input matrix is not checked to be a orthographic projection.
     #[inline]
-    pub unsafe fn new_with_mat(mat: Mat4<N>) -> OrthoMat3<N> {
+    pub unsafe fn new_with_matrix(matrix: Matrix4<N>) -> OrthographicMatrix3<N> {
-        OrthoMat3 {
+        OrthographicMatrix3 {
-            mat: mat
+            matrix: matrix
         }
     }
 
     /// Returns a reference to the 4D matrix (using homogeneous coordinates) of this projection.
     #[inline]
-    pub fn as_mat<'a>(&'a self) -> &'a Mat4<N> {
+    pub fn as_matrix<'a>(&'a self) -> &'a Matrix4<N> {
-        &self.mat
+        &self.matrix
     }
 
     /// The smallest x-coordinate of the view cuboid.
     #[inline]
     pub fn left(&self) -> N {
-        (-::one::<N>() - self.mat.m14) / self.mat.m11
+        (-::one::<N>() - self.matrix.m14) / self.matrix.m11
     }
 
     /// The largest x-coordinate of the view cuboid.
     #[inline]
     pub fn right(&self) -> N {
-        (::one::<N>() - self.mat.m14) / self.mat.m11
+        (::one::<N>() - self.matrix.m14) / self.matrix.m11
     }
 
     /// The smallest y-coordinate of the view cuboid.
     #[inline]
     pub fn bottom(&self) -> N {
-        (-::one::<N>() - self.mat.m24) / self.mat.m22
+        (-::one::<N>() - self.matrix.m24) / self.matrix.m22
     }
 
     /// The largest y-coordinate of the view cuboid.
     #[inline]
     pub fn top(&self) -> N {
-        (::one::<N>() - self.mat.m24) / self.mat.m22
+        (::one::<N>() - self.matrix.m24) / self.matrix.m22
     }
 
     /// The near plane offset of the view cuboid.
     #[inline]
     pub fn znear(&self) -> N {
-        (::one::<N>() + self.mat.m34) / self.mat.m33
+        (::one::<N>() + self.matrix.m34) / self.matrix.m33
     }
 
     /// The far plane offset of the view cuboid.
     #[inline]
     pub fn zfar(&self) -> N {
-        (-::one::<N>() + self.mat.m34) / self.mat.m33
+        (-::one::<N>() + self.matrix.m34) / self.matrix.m33
     }
 
     /// Sets the smallest x-coordinate of the view cuboid.
@@ -293,65 +293,65 @@ impl<N: BaseFloat> OrthoMat3<N> {
     #[inline]
     pub fn set_left_and_right(&mut self, left: N, right: N) {
         assert!(left < right, "The left corner must be farther than the right corner.");
-        self.mat.m11 = <N as Cast<f64>>::from(2.0) / (right - left);
+        self.matrix.m11 = <N as Cast<f64>>::from(2.0) / (right - left);
-        self.mat.m14 = -(right + left) / (right - left);
+        self.matrix.m14 = -(right + left) / (right - left);
     }
 
     /// Sets the view cuboid coordinates along the `y` axis.
     #[inline]
     pub fn set_bottom_and_top(&mut self, bottom: N, top: N) {
         assert!(bottom < top, "The top corner must be higher than the bottom corner.");
-        self.mat.m22 = <N as Cast<f64>>::from(2.0) / (top - bottom);
+        self.matrix.m22 = <N as Cast<f64>>::from(2.0) / (top - bottom);
-        self.mat.m24 = -(top + bottom) / (top - bottom);
+        self.matrix.m24 = -(top + bottom) / (top - bottom);
     }
 
     /// Sets the near and far plane offsets of the view cuboid.
     #[inline]
     pub fn set_znear_and_zfar(&mut self, znear: N, zfar: N) {
         assert!(!::is_zero(&(zfar - znear)));
-        self.mat.m33 = -<N as Cast<f64>>::from(2.0) / (zfar - znear);
+        self.matrix.m33 = -<N as Cast<f64>>::from(2.0) / (zfar - znear);
-        self.mat.m34 = -(zfar + znear) / (zfar - znear);
+        self.matrix.m34 = -(zfar + znear) / (zfar - znear);
     }
 
     /// Projects a point.
     #[inline]
-    pub fn project_pnt(&self, p: &Pnt3<N>) -> Pnt3<N> {
+    pub fn project_point(&self, p: &Point3<N>) -> Point3<N> {
-        Pnt3::new(
+        Point3::new(
-            self.mat.m11 * p.x + self.mat.m14,
+            self.matrix.m11 * p.x + self.matrix.m14,
-            self.mat.m22 * p.y + self.mat.m24,
+            self.matrix.m22 * p.y + self.matrix.m24,
-            self.mat.m33 * p.z + self.mat.m34
+            self.matrix.m33 * p.z + self.matrix.m34
         )
     }
 
     /// Projects a vector.
     #[inline]
-    pub fn project_vec(&self, p: &Vec3<N>) -> Vec3<N> {
+    pub fn project_vector(&self, p: &Vector3<N>) -> Vector3<N> {
-        Vec3::new(
+        Vector3::new(
-            self.mat.m11 * p.x,
+            self.matrix.m11 * p.x,
-            self.mat.m22 * p.y,
+            self.matrix.m22 * p.y,
-            self.mat.m33 * p.z
+            self.matrix.m33 * p.z
         )
     }
 }
 
-impl<N: BaseFloat + Clone> OrthoMat3<N> {
+impl<N: BaseFloat + Clone> OrthographicMatrix3<N> {
     /// Returns the 4D matrix (using homogeneous coordinates) of this projection.
     #[inline]
-    pub fn to_mat<'a>(&'a self) -> Mat4<N> {
+    pub fn to_matrix<'a>(&'a self) -> Matrix4<N> {
-        self.mat.clone()
+        self.matrix.clone()
     }
 }
 
 #[cfg(feature="arbitrary")]
-impl<N: Arbitrary + BaseFloat> Arbitrary for OrthoMat3<N> {
+impl<N: Arbitrary + BaseFloat> Arbitrary for OrthographicMatrix3<N> {
-    fn arbitrary<G: Gen>(g: &mut G) -> OrthoMat3<N> {
+    fn arbitrary<G: Gen>(g: &mut G) -> OrthographicMatrix3<N> {
-        let x: Ortho3<N> = Arbitrary::arbitrary(g);
+        let x: Orthographic3<N> = Arbitrary::arbitrary(g);
-        x.to_persp_mat()
+        x.to_orthographic_matrix()
     }
 }
 
 
-/// Simple helper function for rejection sampling
+/// Similarityple helper function for rejection sampling
 #[cfg(feature="arbitrary")]
 #[inline]
 pub fn reject<G: Gen, F: FnMut(&T) -> bool, T: Arbitrary>(g: &mut G, f: F) -> T {

src/structs/perspective.rs

@@ -1,5 +1,5 @@
 use traits::structure::BaseFloat;
-use structs::{Pnt3, Vec3, Mat4};
+use structs::{Point3, Vector3, Matrix4};
 
 #[cfg(feature="arbitrary")]
 use quickcheck::{Arbitrary, Gen};
@@ -11,9 +11,9 @@ use quickcheck::{Arbitrary, Gen};
 /// `(1, 1, 1)`. Reading or modifying its individual properties is cheap but applying the
 /// transformation is costly.
 #[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Debug, Copy)]
-pub struct Persp3<N> {
+pub struct Perspective3<N> {
     aspect: N,
-    fovy:    N,
+    fovy:   N,
     znear:  N,
     zfar:   N
 }
@@ -24,46 +24,46 @@ pub struct Persp3<N> {
 /// `(1, 1, 1)`. Reading or modifying its individual properties is costly but applying the
 /// transformation is cheap.
 #[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Debug, Copy)]
-pub struct PerspMat3<N> {
+pub struct PerspectiveMatrix3<N> {
-    mat: Mat4<N>
+    matrix: Matrix4<N>
 }
 
-impl<N: BaseFloat> Persp3<N> {
+impl<N: BaseFloat> Perspective3<N> {
     /// Creates a new 3D perspective projection.
-    pub fn new(aspect: N, fovy: N, znear: N, zfar: N) -> Persp3<N> {
+    pub fn new(aspect: N, fovy: N, znear: N, zfar: N) -> Perspective3<N> {
         assert!(!::is_zero(&(zfar - znear)));
         assert!(!::is_zero(&aspect));
 
-        Persp3 {
+        Perspective3 {
             aspect: aspect,
-            fovy:    fovy,
+            fovy:   fovy,
             znear:  znear,
             zfar:   zfar
         }
     }
 
     /// Builds a 4D projection matrix (using homogeneous coordinates) for this projection.
-    pub fn to_mat(&self) -> Mat4<N> {
+    pub fn to_matrix(&self) -> Matrix4<N> {
-        self.to_persp_mat().mat
+        self.to_perspective_matrix().matrix
     }
 
-    /// Build a `PerspMat3` representing this projection.
+    /// Build a `PerspectiveMatrix3` representing this projection.
-    pub fn to_persp_mat(&self) -> PerspMat3<N> {
+    pub fn to_perspective_matrix(&self) -> PerspectiveMatrix3<N> {
-        PerspMat3::new(self.aspect, self.fovy, self.znear, self.zfar)
+        PerspectiveMatrix3::new(self.aspect, self.fovy, self.znear, self.zfar)
     }
 }
 
 #[cfg(feature="arbitrary")]
-impl<N: Arbitrary + BaseFloat> Arbitrary for Persp3<N> {
+impl<N: Arbitrary + BaseFloat> Arbitrary for Perspective3<N> {
-    fn arbitrary<G: Gen>(g: &mut G) -> Persp3<N> {
+    fn arbitrary<G: Gen>(g: &mut G) -> Perspective3<N> {
-        use structs::ortho::reject;
+        use structs::orthographic::reject;
         let znear = Arbitrary::arbitrary(g);
         let zfar = reject(g, |&x: &N| !::is_zero(&(x - znear)));
-        Persp3::new(Arbitrary::arbitrary(g), Arbitrary::arbitrary(g), znear, zfar)
+        Perspective3::new(Arbitrary::arbitrary(g), Arbitrary::arbitrary(g), znear, zfar)
     }
 }
 
-impl<N: BaseFloat + Clone> Persp3<N> {
+impl<N: BaseFloat + Clone> Perspective3<N> {
     /// Gets the `width / height` aspect ratio.
     #[inline]
     pub fn aspect(&self) -> N {
@@ -122,33 +122,33 @@ impl<N: BaseFloat + Clone> Persp3<N> {
 
     /// Projects a point.
     #[inline]
-    pub fn project_pnt(&self, p: &Pnt3<N>) -> Pnt3<N> {
+    pub fn project_point(&self, p: &Point3<N>) -> Point3<N> {
         // FIXME: optimize that
-        self.to_persp_mat().project_pnt(p)
+        self.to_perspective_matrix().project_point(p)
     }
 
     /// Projects a vector.
     #[inline]
-    pub fn project_vec(&self, p: &Vec3<N>) -> Vec3<N> {
+    pub fn project_vector(&self, p: &Vector3<N>) -> Vector3<N> {
         // FIXME: optimize that
-        self.to_persp_mat().project_vec(p)
+        self.to_perspective_matrix().project_vector(p)
     }
 }
 
-impl<N: BaseFloat> PerspMat3<N> {
+impl<N: BaseFloat> PerspectiveMatrix3<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) -> PerspMat3<N> {
+    pub fn new(aspect: N, fovy: N, znear: N, zfar: N) -> PerspectiveMatrix3<N> {
         assert!(!::is_zero(&(znear - zfar)));
         assert!(!::is_zero(&aspect));
 
-        let mat: Mat4<N> = ::one();
+        let matrix: Matrix4<N> = ::one();
 
-        let mut res = PerspMat3 { mat: mat };
+        let mut res = PerspectiveMatrix3 { matrix: matrix };
         res.set_fovy(fovy);
         res.set_aspect(aspect);
         res.set_znear_and_zfar(znear, zfar);
-        res.mat.m44 = ::zero();
+        res.matrix.m44 = ::zero();
-        res.mat.m43 = -::one::<N>();
+        res.matrix.m43 = -::one::<N>();
 
         res
     }
@@ -157,22 +157,22 @@ impl<N: BaseFloat> PerspMat3<N> {
     ///
     /// This is unsafe because the input matrix is not checked to be a perspective projection.
     #[inline]
-    pub unsafe fn new_with_mat(mat: Mat4<N>) -> PerspMat3<N> {
+    pub unsafe fn new_with_matrix(matrix: Matrix4<N>) -> PerspectiveMatrix3<N> {
-        PerspMat3 {
+        PerspectiveMatrix3 {
-            mat: mat
+            matrix: matrix
         }
     }
 
     /// Returns a reference to the 4D matrix (using homogeneous coordinates) of this projection.
     #[inline]
-    pub fn as_mat<'a>(&'a self) -> &'a Mat4<N> {
+    pub fn as_matrix<'a>(&'a self) -> &'a Matrix4<N> {
-        &self.mat
+        &self.matrix
     }
 
     /// Gets the `width / height` aspect ratio of the view frustrum.
     #[inline]
     pub fn aspect(&self) -> N {
-        self.mat.m22 / self.mat.m11
+        self.matrix.m22 / self.matrix.m11
     }
 
     /// Gets the y field of view of the view frustrum.
@@ -181,7 +181,7 @@ impl<N: BaseFloat> PerspMat3<N> {
         let _1: N = ::one();
         let _2 = _1 + _1;
 
-        (_1 / self.mat.m22).atan() * _2
+        (_1 / self.matrix.m22).atan() * _2
     }
 
     /// Gets the near plane offset of the view frustrum.
@@ -189,9 +189,9 @@ impl<N: BaseFloat> PerspMat3<N> {
     pub fn znear(&self) -> N {
         let _1: N = ::one();
         let _2 = _1 + _1;
-        let ratio = (-self.mat.m33 + _1) / (-self.mat.m33 - _1);
+        let ratio = (-self.matrix.m33 + _1) / (-self.matrix.m33 - _1);
 
-        self.mat.m34 / (_2 * ratio) - self.mat.m34 / _2
+        self.matrix.m34 / (_2 * ratio) - self.matrix.m34 / _2
     }
 
     /// Gets the far plane offset of the view frustrum.
@@ -199,9 +199,9 @@ impl<N: BaseFloat> PerspMat3<N> {
     pub fn zfar(&self) -> N {
         let _1: N = ::one();
         let _2 = _1 + _1;
-        let ratio = (-self.mat.m33 + _1) / (-self.mat.m33 - _1);
+        let ratio = (-self.matrix.m33 + _1) / (-self.matrix.m33 - _1);
 
-        (self.mat.m34 - ratio * self.mat.m34) / _2
+        (self.matrix.m34 - ratio * self.matrix.m34) / _2
     }
 
     // FIXME: add a method to retrieve znear and zfar simultaneously?
@@ -211,7 +211,7 @@ impl<N: BaseFloat> PerspMat3<N> {
     #[inline]
     pub fn set_aspect(&mut self, aspect: N) {
         assert!(!::is_zero(&aspect));
-        self.mat.m11 = self.mat.m22 / aspect;
+        self.matrix.m11 = self.matrix.m22 / aspect;
     }
 
     /// Updates this projection with a new y field of view of the view frustrum.
@@ -220,9 +220,9 @@ impl<N: BaseFloat> PerspMat3<N> {
         let _1: N = ::one();
         let _2 = _1 + _1;
 
-        let old_m22  = self.mat.m22.clone();
+        let old_m22  = self.matrix.m22.clone();
-        self.mat.m22 = _1 / (fovy / _2).tan();
+        self.matrix.m22 = _1 / (fovy / _2).tan();
-        self.mat.m11 = self.mat.m11 * (self.mat.m22 / old_m22);
+        self.matrix.m11 = self.matrix.m11 * (self.matrix.m22 / old_m22);
     }
 
     /// Updates this projection matrix with a new near plane offset of the view frustrum.
@@ -245,47 +245,47 @@ impl<N: BaseFloat> PerspMat3<N> {
         let _1: N = ::one();
         let _2 = _1 + _1;
 
-        self.mat.m33 = (zfar + znear) / (znear - zfar);
+        self.matrix.m33 = (zfar + znear) / (znear - zfar);
-        self.mat.m34 = zfar * znear * _2 / (znear - zfar);
+        self.matrix.m34 = zfar * znear * _2 / (znear - zfar);
     }
 
     /// Projects a point.
     #[inline]
-    pub fn project_pnt(&self, p: &Pnt3<N>) -> Pnt3<N> {
+    pub fn project_point(&self, p: &Point3<N>) -> Point3<N> {
         let _1: N = ::one();
-        let inv_denom = -_1 / p.z;
+        let inverse_denom = -_1 / p.z;
-        Pnt3::new(
+        Point3::new(
-            self.mat.m11 * p.x * inv_denom,
+            self.matrix.m11 * p.x * inverse_denom,
-            self.mat.m22 * p.y * inv_denom,
+            self.matrix.m22 * p.y * inverse_denom,
-            (self.mat.m33 * p.z + self.mat.m34) * inv_denom
+            (self.matrix.m33 * p.z + self.matrix.m34) * inverse_denom
         )
     }
 
     /// Projects a vector.
     #[inline]
-    pub fn project_vec(&self, p: &Vec3<N>) -> Vec3<N> {
+    pub fn project_vector(&self, p: &Vector3<N>) -> Vector3<N> {
         let _1: N = ::one();
-        let inv_denom = -_1 / p.z;
+        let inverse_denom = -_1 / p.z;
-        Vec3::new(
+        Vector3::new(
-            self.mat.m11 * p.x * inv_denom,
+            self.matrix.m11 * p.x * inverse_denom,
-            self.mat.m22 * p.y * inv_denom,
+            self.matrix.m22 * p.y * inverse_denom,
-            self.mat.m33
+            self.matrix.m33
         )
     }
 }
 
-impl<N: BaseFloat + Clone> PerspMat3<N> {
+impl<N: BaseFloat + Clone> PerspectiveMatrix3<N> {
     /// Returns the 4D matrix (using homogeneous coordinates) of this projection.
     #[inline]
-    pub fn to_mat<'a>(&'a self) -> Mat4<N> {
+    pub fn to_matrix<'a>(&'a self) -> Matrix4<N> {
-        self.mat.clone()
+        self.matrix.clone()
     }
 }
 
 #[cfg(feature="arbitrary")]
-impl<N: Arbitrary + BaseFloat> Arbitrary for PerspMat3<N> {
+impl<N: Arbitrary + BaseFloat> Arbitrary for PerspectiveMatrix3<N> {
-    fn arbitrary<G: Gen>(g: &mut G) -> PerspMat3<N> {
+    fn arbitrary<G: Gen>(g: &mut G) -> PerspectiveMatrix3<N> {
-        let x: Persp3<N> = Arbitrary::arbitrary(g);
+        let x: Perspective3<N> = Arbitrary::arbitrary(g);
-        x.to_persp_mat()
+        x.to_perspective_matrix()
     }
 }

src/structs/pnt.rs

@@ -1,309 +0,0 @@
-//! Points with dimension known at compile-time.
-
-use std::mem;
-use std::fmt;
-use std::slice::{Iter, IterMut};
-use std::iter::{Iterator, FromIterator, IntoIterator};
-use std::ops::{Add, Sub, Mul, Div, Neg, AddAssign, SubAssign, MulAssign, DivAssign, Index, IndexMut};
-use rand::{Rand, Rng};
-use num::{Zero, One};
-use traits::operations::{ApproxEq, POrd, POrdering, Axpy};
-use traits::structure::{Cast, Dim, Indexable, Iterable, IterableMut, PntAsVec, Shape,
-                        NumPnt, FloatPnt, BaseFloat, BaseNum, Bounded, Repeat};
-use traits::geometry::{Orig, FromHomogeneous, ToHomogeneous};
-use structs::vec::{Vec1, Vec2, Vec3, Vec4, Vec5, Vec6};
-#[cfg(feature="arbitrary")]
-use quickcheck::{Arbitrary, Gen};
-
-
-/// Point of dimension 1.
-///
-/// The main differance between a point and a vector is that a vector is not affected by
-/// translations.
-#[repr(C)]
-#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
-pub struct Pnt1<N> {
-    /// First component of the point.
-    pub x: N
-}
-
-new_impl!(Pnt1, x);
-orig_impl!(Pnt1, x);
-pord_impl!(Pnt1, x,);
-scalar_mul_impl!(Pnt1, x);
-scalar_div_impl!(Pnt1, x);
-scalar_add_impl!(Pnt1, x);
-scalar_sub_impl!(Pnt1, x);
-vec_cast_impl!(Pnt1, x);
-conversion_impl!(Pnt1, 1);
-index_impl!(Pnt1);
-indexable_impl!(Pnt1, 1);
-at_fast_impl!(Pnt1, 1);
-repeat_impl!(Pnt1, val, x);
-dim_impl!(Pnt1, 1);
-container_impl!(Pnt1);
-pnt_as_vec_impl!(Pnt1, Vec1, x);
-pnt_sub_impl!(Pnt1, Vec1);
-neg_impl!(Pnt1, x);
-pnt_add_vec_impl!(Pnt1, Vec1, x);
-pnt_sub_vec_impl!(Pnt1, Vec1, x);
-approx_eq_impl!(Pnt1, x);
-from_iterator_impl!(Pnt1, iterator);
-bounded_impl!(Pnt1, x);
-axpy_impl!(Pnt1, x);
-iterable_impl!(Pnt1, 1);
-iterable_mut_impl!(Pnt1, 1);
-pnt_to_homogeneous_impl!(Pnt1, Pnt2, y, x);
-pnt_from_homogeneous_impl!(Pnt1, Pnt2, y, x);
-num_float_pnt_impl!(Pnt1, Vec1);
-arbitrary_pnt_impl!(Pnt1, x);
-rand_impl!(Pnt1, x);
-pnt_display_impl!(Pnt1);
-
-/// Point of dimension 2.
-///
-/// The main differance between a point and a vector is that a vector is not affected by
-/// translations.
-#[repr(C)]
-#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
-pub struct Pnt2<N> {
-    /// First component of the point.
-    pub x: N,
-    /// Second component of the point.
-    pub y: N
-}
-
-new_impl!(Pnt2, x, y);
-orig_impl!(Pnt2, x, y);
-pord_impl!(Pnt2, x, y);
-scalar_mul_impl!(Pnt2, x, y);
-scalar_div_impl!(Pnt2, x, y);
-scalar_add_impl!(Pnt2, x, y);
-scalar_sub_impl!(Pnt2, x, y);
-vec_cast_impl!(Pnt2, x, y);
-conversion_impl!(Pnt2, 2);
-index_impl!(Pnt2);
-indexable_impl!(Pnt2, 2);
-at_fast_impl!(Pnt2, 2);
-repeat_impl!(Pnt2, val, x, y);
-dim_impl!(Pnt2, 2);
-container_impl!(Pnt2);
-pnt_as_vec_impl!(Pnt2, Vec2, x, y);
-pnt_sub_impl!(Pnt2, Vec2);
-neg_impl!(Pnt2, x, y);
-pnt_add_vec_impl!(Pnt2, Vec2, x, y);
-pnt_sub_vec_impl!(Pnt2, Vec2, x, y);
-approx_eq_impl!(Pnt2, x, y);
-from_iterator_impl!(Pnt2, iterator, iterator);
-bounded_impl!(Pnt2, x, y);
-axpy_impl!(Pnt2, x, y);
-iterable_impl!(Pnt2, 2);
-iterable_mut_impl!(Pnt2, 2);
-pnt_to_homogeneous_impl!(Pnt2, Pnt3, z, x, y);
-pnt_from_homogeneous_impl!(Pnt2, Pnt3, z, x, y);
-num_float_pnt_impl!(Pnt2, Vec2);
-arbitrary_pnt_impl!(Pnt2, x, y);
-rand_impl!(Pnt2, x, y);
-pnt_display_impl!(Pnt2);
-
-/// Point of dimension 3.
-///
-/// The main differance between a point and a vector is that a vector is not affected by
-/// translations.
-#[repr(C)]
-#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
-pub struct Pnt3<N> {
-    /// First component of the point.
-    pub x: N,
-    /// Second component of the point.
-    pub y: N,
-    /// Third component of the point.
-    pub z: N
-}
-
-new_impl!(Pnt3, x, y, z);
-orig_impl!(Pnt3, x, y, z);
-pord_impl!(Pnt3, x, y, z);
-scalar_mul_impl!(Pnt3, x, y, z);
-scalar_div_impl!(Pnt3, x, y, z);
-scalar_add_impl!(Pnt3, x, y, z);
-scalar_sub_impl!(Pnt3, x, y, z);
-vec_cast_impl!(Pnt3, x, y, z);
-conversion_impl!(Pnt3, 3);
-index_impl!(Pnt3);
-indexable_impl!(Pnt3, 3);
-at_fast_impl!(Pnt3, 3);
-repeat_impl!(Pnt3, val, x, y, z);
-dim_impl!(Pnt3, 3);
-container_impl!(Pnt3);
-pnt_as_vec_impl!(Pnt3, Vec3, x, y, z);
-pnt_sub_impl!(Pnt3, Vec3);
-neg_impl!(Pnt3, x, y, z);
-pnt_add_vec_impl!(Pnt3, Vec3, x, y, z);
-pnt_sub_vec_impl!(Pnt3, Vec3, x, y, z);
-approx_eq_impl!(Pnt3, x, y, z);
-from_iterator_impl!(Pnt3, iterator, iterator, iterator);
-bounded_impl!(Pnt3, x, y, z);
-axpy_impl!(Pnt3, x, y, z);
-iterable_impl!(Pnt3, 3);
-iterable_mut_impl!(Pnt3, 3);
-pnt_to_homogeneous_impl!(Pnt3, Pnt4, w, x, y, z);
-pnt_from_homogeneous_impl!(Pnt3, Pnt4, w, x, y, z);
-num_float_pnt_impl!(Pnt3, Vec3);
-arbitrary_pnt_impl!(Pnt3, x, y, z);
-rand_impl!(Pnt3, x, y, z);
-pnt_display_impl!(Pnt3);
-
-/// Point of dimension 4.
-///
-/// The main differance between a point and a vector is that a vector is not affected by
-/// translations.
-#[repr(C)]
-#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
-pub struct Pnt4<N> {
-    /// First component of the point.
-    pub x: N,
-    /// Second component of the point.
-    pub y: N,
-    /// Third component of the point.
-    pub z: N,
-    /// Fourth component of the point.
-    pub w: N
-}
-
-new_impl!(Pnt4, x, y, z, w);
-orig_impl!(Pnt4, x, y, z, w);
-pord_impl!(Pnt4, x, y, z, w);
-scalar_mul_impl!(Pnt4, x, y, z, w);
-scalar_div_impl!(Pnt4, x, y, z, w);
-scalar_add_impl!(Pnt4, x, y, z, w);
-scalar_sub_impl!(Pnt4, x, y, z, w);
-vec_cast_impl!(Pnt4, x, y, z, w);
-conversion_impl!(Pnt4, 4);
-index_impl!(Pnt4);
-indexable_impl!(Pnt4, 4);
-at_fast_impl!(Pnt4, 4);
-repeat_impl!(Pnt4, val, x, y, z, w);
-dim_impl!(Pnt4, 4);
-container_impl!(Pnt4);
-pnt_as_vec_impl!(Pnt4, Vec4, x, y, z, w);
-pnt_sub_impl!(Pnt4, Vec4);
-neg_impl!(Pnt4, x, y, z, w);
-pnt_add_vec_impl!(Pnt4, Vec4, x, y, z, w);
-pnt_sub_vec_impl!(Pnt4, Vec4, x, y, z, w);
-approx_eq_impl!(Pnt4, x, y, z, w);
-from_iterator_impl!(Pnt4, iterator, iterator, iterator, iterator);
-bounded_impl!(Pnt4, x, y, z, w);
-axpy_impl!(Pnt4, x, y, z, w);
-iterable_impl!(Pnt4, 4);
-iterable_mut_impl!(Pnt4, 4);
-pnt_to_homogeneous_impl!(Pnt4, Pnt5, a, x, y, z, w);
-pnt_from_homogeneous_impl!(Pnt4, Pnt5, a, x, y, z, w);
-num_float_pnt_impl!(Pnt4, Vec4);
-arbitrary_pnt_impl!(Pnt4, x, y, z, w);
-rand_impl!(Pnt4, x, y, z, w);
-pnt_display_impl!(Pnt4);
-
-/// Point of dimension 5.
-///
-/// The main differance between a point and a vector is that a vector is not affected by
-/// translations.
-#[repr(C)]
-#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
-pub struct Pnt5<N> {
-    /// First component of the point.
-    pub x: N,
-    /// Second component of the point.
-    pub y: N,
-    /// Third component of the point.
-    pub z: N,
-    /// Fourth component of the point.
-    pub w: N,
-    /// Fifth of the point.
-    pub a: N
-}
-
-new_impl!(Pnt5, x, y, z, w, a);
-orig_impl!(Pnt5, x, y, z, w, a);
-pord_impl!(Pnt5, x, y, z, w, a);
-scalar_mul_impl!(Pnt5, x, y, z, w, a);
-scalar_div_impl!(Pnt5, x, y, z, w, a);
-scalar_add_impl!(Pnt5, x, y, z, w, a);
-scalar_sub_impl!(Pnt5, x, y, z, w, a);
-vec_cast_impl!(Pnt5, x, y, z, w, a);
-conversion_impl!(Pnt5, 5);
-index_impl!(Pnt5);
-indexable_impl!(Pnt5, 5);
-at_fast_impl!(Pnt5, 5);
-repeat_impl!(Pnt5, val, x, y, z, w, a);
-dim_impl!(Pnt5, 5);
-container_impl!(Pnt5);
-pnt_as_vec_impl!(Pnt5, Vec5, x, y, z, w, a);
-pnt_sub_impl!(Pnt5, Vec5);
-neg_impl!(Pnt5, x, y, z, w, a);
-pnt_add_vec_impl!(Pnt5, Vec5, x, y, z, w, a);
-pnt_sub_vec_impl!(Pnt5, Vec5, x, y, z, w, a);
-approx_eq_impl!(Pnt5, x, y, z, w, a);
-from_iterator_impl!(Pnt5, iterator, iterator, iterator, iterator, iterator);
-bounded_impl!(Pnt5, x, y, z, w, a);
-axpy_impl!(Pnt5, x, y, z, w, a);
-iterable_impl!(Pnt5, 5);
-iterable_mut_impl!(Pnt5, 5);
-pnt_to_homogeneous_impl!(Pnt5, Pnt6, b, x, y, z, w, a);
-pnt_from_homogeneous_impl!(Pnt5, Pnt6, b, x, y, z, w, a);
-num_float_pnt_impl!(Pnt5, Vec5);
-arbitrary_pnt_impl!(Pnt5, x, y, z, w, a);
-rand_impl!(Pnt5, x, y, z, w, a);
-pnt_display_impl!(Pnt5);
-
-/// Point of dimension 6.
-///
-/// The main differance between a point and a vector is that a vector is not affected by
-/// translations.
-#[repr(C)]
-#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
-pub struct Pnt6<N> {
-    /// First component of the point.
-    pub x: N,
-    /// Second component of the point.
-    pub y: N,
-    /// Third component of the point.
-    pub z: N,
-    /// Fourth component of the point.
-    pub w: N,
-    /// Fifth of the point.
-    pub a: N,
-    /// Sixth component of the point.
-    pub b: N
-}
-
-new_impl!(Pnt6, x, y, z, w, a, b);
-orig_impl!(Pnt6, x, y, z, w, a, b);
-pord_impl!(Pnt6, x, y, z, w, a, b);
-scalar_mul_impl!(Pnt6, x, y, z, w, a, b);
-scalar_div_impl!(Pnt6, x, y, z, w, a, b);
-scalar_add_impl!(Pnt6, x, y, z, w, a, b);
-scalar_sub_impl!(Pnt6, x, y, z, w, a, b);
-vec_cast_impl!(Pnt6, x, y, z, w, a, b);
-conversion_impl!(Pnt6, 6);
-index_impl!(Pnt6);
-indexable_impl!(Pnt6, 6);
-at_fast_impl!(Pnt6, 6);
-repeat_impl!(Pnt6, val, x, y, z, w, a, b);
-dim_impl!(Pnt6, 6);
-container_impl!(Pnt6);
-pnt_as_vec_impl!(Pnt6, Vec6, x, y, z, w, a, b);
-pnt_sub_impl!(Pnt6, Vec6);
-neg_impl!(Pnt6, x, y, z, w, a, b);
-pnt_add_vec_impl!(Pnt6, Vec6, x, y, z, w, a, b);
-pnt_sub_vec_impl!(Pnt6, Vec6, x, y, z, w, a, b);
-approx_eq_impl!(Pnt6, x, y, z, w, a, b);
-from_iterator_impl!(Pnt6, iterator, iterator, iterator, iterator, iterator, iterator);
-bounded_impl!(Pnt6, x, y, z, w, a, b);
-axpy_impl!(Pnt6, x, y, z, w, a, b);
-iterable_impl!(Pnt6, 6);
-iterable_mut_impl!(Pnt6, 6);
-num_float_pnt_impl!(Pnt6, Vec6);
-arbitrary_pnt_impl!(Pnt6, x, y, z, w, a, b);
-rand_impl!(Pnt6, x, y, z, w, a, b);
-pnt_display_impl!(Pnt6);

src/structs/point.rs

@@ -0,0 +1,309 @@
+//! Points with dimension known at compile-time.
+
+use std::mem;
+use std::fmt;
+use std::slice::{Iter, IterMut};
+use std::iter::{Iterator, FromIterator, IntoIterator};
+use std::ops::{Add, Sub, Mul, Div, Neg, AddAssign, SubAssign, MulAssign, DivAssign, Index, IndexMut};
+use rand::{Rand, Rng};
+use num::{Zero, One};
+use traits::operations::{ApproxEq, PartialOrder, PartialOrdering, Axpy};
+use traits::structure::{Cast, Dimension, Indexable, Iterable, IterableMut, PointAsVector, Shape,
+                        NumPoint, FloatPoint, BaseFloat, BaseNum, Bounded, Repeat};
+use traits::geometry::{Origin, FromHomogeneous, ToHomogeneous};
+use structs::vector::{Vector1, Vector2, Vector3, Vector4, Vector5, Vector6};
+#[cfg(feature="arbitrary")]
+use quickcheck::{Arbitrary, Gen};
+
+
+/// Point of dimension 1.
+///
+/// The main differance between a point and a vector is that a vector is not affected by
+/// translations.
+#[repr(C)]
+#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
+pub struct Point1<N> {
+    /// First component of the point.
+    pub x: N
+}
+
+new_impl!(Point1, x);
+origin_impl!(Point1, x);
+pord_impl!(Point1, x,);
+scalar_mul_impl!(Point1, x);
+scalar_div_impl!(Point1, x);
+scalar_add_impl!(Point1, x);
+scalar_sub_impl!(Point1, x);
+vec_cast_impl!(Point1, x);
+conversion_impl!(Point1, 1);
+index_impl!(Point1);
+indexable_impl!(Point1, 1);
+at_fast_impl!(Point1, 1);
+repeat_impl!(Point1, val, x);
+dim_impl!(Point1, 1);
+container_impl!(Point1);
+point_as_vec_impl!(Point1, Vector1, x);
+point_sub_impl!(Point1, Vector1);
+neg_impl!(Point1, x);
+point_add_vec_impl!(Point1, Vector1, x);
+point_sub_vec_impl!(Point1, Vector1, x);
+approx_eq_impl!(Point1, x);
+from_iterator_impl!(Point1, iterator);
+bounded_impl!(Point1, x);
+axpy_impl!(Point1, x);
+iterable_impl!(Point1, 1);
+iterable_mut_impl!(Point1, 1);
+point_to_homogeneous_impl!(Point1, Point2, y, x);
+point_from_homogeneous_impl!(Point1, Point2, y, x);
+num_float_point_impl!(Point1, Vector1);
+arbitrary_point_impl!(Point1, x);
+rand_impl!(Point1, x);
+point_display_impl!(Point1);
+
+/// Point of dimension 2.
+///
+/// The main differance between a point and a vector is that a vector is not affected by
+/// translations.
+#[repr(C)]
+#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
+pub struct Point2<N> {
+    /// First component of the point.
+    pub x: N,
+    /// Second component of the point.
+    pub y: N
+}
+
+new_impl!(Point2, x, y);
+origin_impl!(Point2, x, y);
+pord_impl!(Point2, x, y);
+scalar_mul_impl!(Point2, x, y);
+scalar_div_impl!(Point2, x, y);
+scalar_add_impl!(Point2, x, y);
+scalar_sub_impl!(Point2, x, y);
+vec_cast_impl!(Point2, x, y);
+conversion_impl!(Point2, 2);
+index_impl!(Point2);
+indexable_impl!(Point2, 2);
+at_fast_impl!(Point2, 2);
+repeat_impl!(Point2, val, x, y);
+dim_impl!(Point2, 2);
+container_impl!(Point2);
+point_as_vec_impl!(Point2, Vector2, x, y);
+point_sub_impl!(Point2, Vector2);
+neg_impl!(Point2, x, y);
+point_add_vec_impl!(Point2, Vector2, x, y);
+point_sub_vec_impl!(Point2, Vector2, x, y);
+approx_eq_impl!(Point2, x, y);
+from_iterator_impl!(Point2, iterator, iterator);
+bounded_impl!(Point2, x, y);
+axpy_impl!(Point2, x, y);
+iterable_impl!(Point2, 2);
+iterable_mut_impl!(Point2, 2);
+point_to_homogeneous_impl!(Point2, Point3, z, x, y);
+point_from_homogeneous_impl!(Point2, Point3, z, x, y);
+num_float_point_impl!(Point2, Vector2);
+arbitrary_point_impl!(Point2, x, y);
+rand_impl!(Point2, x, y);
+point_display_impl!(Point2);
+
+/// Point of dimension 3.
+///
+/// The main differance between a point and a vector is that a vector is not affected by
+/// translations.
+#[repr(C)]
+#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
+pub struct Point3<N> {
+    /// First component of the point.
+    pub x: N,
+    /// Second component of the point.
+    pub y: N,
+    /// Third component of the point.
+    pub z: N
+}
+
+new_impl!(Point3, x, y, z);
+origin_impl!(Point3, x, y, z);
+pord_impl!(Point3, x, y, z);
+scalar_mul_impl!(Point3, x, y, z);
+scalar_div_impl!(Point3, x, y, z);
+scalar_add_impl!(Point3, x, y, z);
+scalar_sub_impl!(Point3, x, y, z);
+vec_cast_impl!(Point3, x, y, z);
+conversion_impl!(Point3, 3);
+index_impl!(Point3);
+indexable_impl!(Point3, 3);
+at_fast_impl!(Point3, 3);
+repeat_impl!(Point3, val, x, y, z);
+dim_impl!(Point3, 3);
+container_impl!(Point3);
+point_as_vec_impl!(Point3, Vector3, x, y, z);
+point_sub_impl!(Point3, Vector3);
+neg_impl!(Point3, x, y, z);
+point_add_vec_impl!(Point3, Vector3, x, y, z);
+point_sub_vec_impl!(Point3, Vector3, x, y, z);
+approx_eq_impl!(Point3, x, y, z);
+from_iterator_impl!(Point3, iterator, iterator, iterator);
+bounded_impl!(Point3, x, y, z);
+axpy_impl!(Point3, x, y, z);
+iterable_impl!(Point3, 3);
+iterable_mut_impl!(Point3, 3);
+point_to_homogeneous_impl!(Point3, Point4, w, x, y, z);
+point_from_homogeneous_impl!(Point3, Point4, w, x, y, z);
+num_float_point_impl!(Point3, Vector3);
+arbitrary_point_impl!(Point3, x, y, z);
+rand_impl!(Point3, x, y, z);
+point_display_impl!(Point3);
+
+/// Point of dimension 4.
+///
+/// The main differance between a point and a vector is that a vector is not affected by
+/// translations.
+#[repr(C)]
+#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
+pub struct Point4<N> {
+    /// First component of the point.
+    pub x: N,
+    /// Second component of the point.
+    pub y: N,
+    /// Third component of the point.
+    pub z: N,
+    /// Fourth component of the point.
+    pub w: N
+}
+
+new_impl!(Point4, x, y, z, w);
+origin_impl!(Point4, x, y, z, w);
+pord_impl!(Point4, x, y, z, w);
+scalar_mul_impl!(Point4, x, y, z, w);
+scalar_div_impl!(Point4, x, y, z, w);
+scalar_add_impl!(Point4, x, y, z, w);
+scalar_sub_impl!(Point4, x, y, z, w);
+vec_cast_impl!(Point4, x, y, z, w);
+conversion_impl!(Point4, 4);
+index_impl!(Point4);
+indexable_impl!(Point4, 4);
+at_fast_impl!(Point4, 4);
+repeat_impl!(Point4, val, x, y, z, w);
+dim_impl!(Point4, 4);
+container_impl!(Point4);
+point_as_vec_impl!(Point4, Vector4, x, y, z, w);
+point_sub_impl!(Point4, Vector4);
+neg_impl!(Point4, x, y, z, w);
+point_add_vec_impl!(Point4, Vector4, x, y, z, w);
+point_sub_vec_impl!(Point4, Vector4, x, y, z, w);
+approx_eq_impl!(Point4, x, y, z, w);
+from_iterator_impl!(Point4, iterator, iterator, iterator, iterator);
+bounded_impl!(Point4, x, y, z, w);
+axpy_impl!(Point4, x, y, z, w);
+iterable_impl!(Point4, 4);
+iterable_mut_impl!(Point4, 4);
+point_to_homogeneous_impl!(Point4, Point5, a, x, y, z, w);
+point_from_homogeneous_impl!(Point4, Point5, a, x, y, z, w);
+num_float_point_impl!(Point4, Vector4);
+arbitrary_point_impl!(Point4, x, y, z, w);
+rand_impl!(Point4, x, y, z, w);
+point_display_impl!(Point4);
+
+/// Point of dimension 5.
+///
+/// The main differance between a point and a vector is that a vector is not affected by
+/// translations.
+#[repr(C)]
+#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
+pub struct Point5<N> {
+    /// First component of the point.
+    pub x: N,
+    /// Second component of the point.
+    pub y: N,
+    /// Third component of the point.
+    pub z: N,
+    /// Fourth component of the point.
+    pub w: N,
+    /// Fifth of the point.
+    pub a: N
+}
+
+new_impl!(Point5, x, y, z, w, a);
+origin_impl!(Point5, x, y, z, w, a);
+pord_impl!(Point5, x, y, z, w, a);
+scalar_mul_impl!(Point5, x, y, z, w, a);
+scalar_div_impl!(Point5, x, y, z, w, a);
+scalar_add_impl!(Point5, x, y, z, w, a);
+scalar_sub_impl!(Point5, x, y, z, w, a);
+vec_cast_impl!(Point5, x, y, z, w, a);
+conversion_impl!(Point5, 5);
+index_impl!(Point5);
+indexable_impl!(Point5, 5);
+at_fast_impl!(Point5, 5);
+repeat_impl!(Point5, val, x, y, z, w, a);
+dim_impl!(Point5, 5);
+container_impl!(Point5);
+point_as_vec_impl!(Point5, Vector5, x, y, z, w, a);
+point_sub_impl!(Point5, Vector5);
+neg_impl!(Point5, x, y, z, w, a);
+point_add_vec_impl!(Point5, Vector5, x, y, z, w, a);
+point_sub_vec_impl!(Point5, Vector5, x, y, z, w, a);
+approx_eq_impl!(Point5, x, y, z, w, a);
+from_iterator_impl!(Point5, iterator, iterator, iterator, iterator, iterator);
+bounded_impl!(Point5, x, y, z, w, a);
+axpy_impl!(Point5, x, y, z, w, a);
+iterable_impl!(Point5, 5);
+iterable_mut_impl!(Point5, 5);
+point_to_homogeneous_impl!(Point5, Point6, b, x, y, z, w, a);
+point_from_homogeneous_impl!(Point5, Point6, b, x, y, z, w, a);
+num_float_point_impl!(Point5, Vector5);
+arbitrary_point_impl!(Point5, x, y, z, w, a);
+rand_impl!(Point5, x, y, z, w, a);
+point_display_impl!(Point5);
+
+/// Point of dimension 6.
+///
+/// The main differance between a point and a vector is that a vector is not affected by
+/// translations.
+#[repr(C)]
+#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
+pub struct Point6<N> {
+    /// First component of the point.
+    pub x: N,
+    /// Second component of the point.
+    pub y: N,
+    /// Third component of the point.
+    pub z: N,
+    /// Fourth component of the point.
+    pub w: N,
+    /// Fifth of the point.
+    pub a: N,
+    /// Sixth component of the point.
+    pub b: N
+}
+
+new_impl!(Point6, x, y, z, w, a, b);
+origin_impl!(Point6, x, y, z, w, a, b);
+pord_impl!(Point6, x, y, z, w, a, b);
+scalar_mul_impl!(Point6, x, y, z, w, a, b);
+scalar_div_impl!(Point6, x, y, z, w, a, b);
+scalar_add_impl!(Point6, x, y, z, w, a, b);
+scalar_sub_impl!(Point6, x, y, z, w, a, b);
+vec_cast_impl!(Point6, x, y, z, w, a, b);
+conversion_impl!(Point6, 6);
+index_impl!(Point6);
+indexable_impl!(Point6, 6);
+at_fast_impl!(Point6, 6);
+repeat_impl!(Point6, val, x, y, z, w, a, b);
+dim_impl!(Point6, 6);
+container_impl!(Point6);
+point_as_vec_impl!(Point6, Vector6, x, y, z, w, a, b);
+point_sub_impl!(Point6, Vector6);
+neg_impl!(Point6, x, y, z, w, a, b);
+point_add_vec_impl!(Point6, Vector6, x, y, z, w, a, b);
+point_sub_vec_impl!(Point6, Vector6, x, y, z, w, a, b);
+approx_eq_impl!(Point6, x, y, z, w, a, b);
+from_iterator_impl!(Point6, iterator, iterator, iterator, iterator, iterator, iterator);
+bounded_impl!(Point6, x, y, z, w, a, b);
+axpy_impl!(Point6, x, y, z, w, a, b);
+iterable_impl!(Point6, 6);
+iterable_mut_impl!(Point6, 6);
+num_float_point_impl!(Point6, Vector6);
+arbitrary_point_impl!(Point6, x, y, z, w, a, b);
+rand_impl!(Point6, x, y, z, w, a, b);
+point_display_impl!(Point6);

src/structs/point_macros.rs

@@ -1,37 +1,37 @@
 #![macro_use]
 
-macro_rules! orig_impl(
+macro_rules! origin_impl(
     ($t: ident, $($compN: ident),+) => (
-        impl<N: Zero> Orig for $t<N> {
+        impl<N: Zero> Origin for $t<N> {
             #[inline]
-            fn orig() -> $t<N> {
+            fn origin() -> $t<N> {
                 $t {
                     $($compN: ::zero() ),+
                 }
             }
 
             #[inline]
-            fn is_orig(&self) -> bool {
+            fn is_origin(&self) -> bool {
                 $(self.$compN.is_zero() )&&+
             }
         }
     )
 );
 
-macro_rules! pnt_sub_impl(
+macro_rules! point_sub_impl(
     ($t: ident, $tv: ident) => (
         impl<N: Copy + Sub<N, Output = N>> Sub<$t<N>> for $t<N> {
             type Output = $tv<N>;
 
             #[inline]
             fn sub(self, right: $t<N>) -> $tv<N> {
-                *self.as_vec() - *right.as_vec()
+                *self.as_vector() - *right.as_vector()
             }
         }
     )
 );
 
-macro_rules! pnt_add_vec_impl(
+macro_rules! point_add_vec_impl(
     ($t: ident, $tv: ident, $($compN: ident),+) => (
         impl<N: Copy + Add<N, Output = N>> Add<$tv<N>> for $t<N> {
             type Output = $t<N>;
@@ -51,7 +51,7 @@ macro_rules! pnt_add_vec_impl(
     )
 );
 
-macro_rules! pnt_sub_vec_impl(
+macro_rules! point_sub_vec_impl(
     ($t: ident, $tv: ident, $($compN: ident),+) => (
         impl<N: Copy + Sub<N, Output = N>> Sub<$tv<N>> for $t<N> {
             type Output = $t<N>;
@@ -71,12 +71,12 @@ macro_rules! pnt_sub_vec_impl(
     )
 );
 
-macro_rules! pnt_as_vec_impl(
+macro_rules! point_as_vec_impl(
     ($t: ident, $tv: ident, $($compN: ident),+) => (
         impl<N> $t<N> {
             /// Converts this point to its associated vector.
             #[inline]
-            pub fn to_vec(self) -> $tv<N> {
+            pub fn to_vector(self) -> $tv<N> {
                 $tv::new(
                     $(self.$compN),+
                 )
@@ -84,7 +84,7 @@ macro_rules! pnt_as_vec_impl(
 
             /// Converts a reference to this point to a reference to its associated vector.
             #[inline]
-            pub fn as_vec<'a>(&'a self) -> &'a $tv<N> {
+            pub fn as_vector<'a>(&'a self) -> &'a $tv<N> {
                 unsafe {
                     mem::transmute(self)
                 }
@@ -96,17 +96,17 @@ macro_rules! pnt_as_vec_impl(
             }
         }
 
-        impl<N> PntAsVec for $t<N> {
+        impl<N> PointAsVector for $t<N> {
-            type Vec = $tv<N>;
+            type Vector = $tv<N>;
             
             #[inline]
-            fn to_vec(self) -> $tv<N> {
+            fn to_vector(self) -> $tv<N> {
-                self.to_vec()
+                self.to_vector()
             }
 
             #[inline]
-            fn as_vec<'a>(&'a self) -> &'a $tv<N> {
+            fn as_vector<'a>(&'a self) -> &'a $tv<N> {
-                self.as_vec()
+                self.as_vector()
             }
 
             #[inline]
@@ -117,11 +117,11 @@ macro_rules! pnt_as_vec_impl(
     )
 );
 
-macro_rules! pnt_to_homogeneous_impl(
+macro_rules! point_to_homogeneous_impl(
     ($t: ident, $t2: ident, $extra: ident, $($compN: ident),+) => (
         impl<N: Copy + One + Zero> ToHomogeneous<$t2<N>> for $t<N> {
             fn to_homogeneous(&self) -> $t2<N> {
-                let mut res: $t2<N> = Orig::orig();
+                let mut res: $t2<N> = Origin::origin();
 
                 $( res.$compN = self.$compN; )+
                 res.$extra    = ::one();
@@ -132,11 +132,11 @@ macro_rules! pnt_to_homogeneous_impl(
     )
 );
 
-macro_rules! pnt_from_homogeneous_impl(
+macro_rules! point_from_homogeneous_impl(
     ($t: ident, $t2: ident, $extra: ident, $($compN: ident),+) => (
         impl<N: Copy + Div<N, Output = N> + One + Zero> FromHomogeneous<$t2<N>> for $t<N> {
             fn from(v: &$t2<N>) -> $t<N> {
-                let mut res: $t<N> = Orig::orig();
+                let mut res: $t<N> = Origin::origin();
 
                 $( res.$compN = v.$compN / v.$extra; )+
 
@@ -146,19 +146,19 @@ macro_rules! pnt_from_homogeneous_impl(
     )
 );
 
-macro_rules! num_float_pnt_impl(
+macro_rules! num_float_point_impl(
     ($t: ident, $tv: ident) => (
-        impl<N> NumPnt<N> for $t<N>
+        impl<N> NumPoint<N> for $t<N>
             where N: BaseNum {
         }
 
-        impl<N> FloatPnt<N> for $t<N>
+        impl<N> FloatPoint<N> for $t<N>
             where N: BaseFloat + ApproxEq<N> {
         }
     )
 );
 
-macro_rules! arbitrary_pnt_impl(
+macro_rules! arbitrary_point_impl(
     ($t: ident, $($compN: ident),*) => (
         #[cfg(feature="arbitrary")]
         impl<N: Arbitrary> Arbitrary for $t<N> {
@@ -172,7 +172,7 @@ macro_rules! arbitrary_pnt_impl(
     )
 );
 
-macro_rules! pnt_display_impl(
+macro_rules! point_display_impl(
     ($t: ident) => (
         impl<N: fmt::Display> fmt::Display for $t<N> {
             fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {

src/structs/quat.rs

@@ -1,598 +0,0 @@
-//! Quaternion definition.
-
-use std::fmt;
-use std::mem;
-use std::slice::{Iter, IterMut};
-use std::ops::{Add, Sub, Mul, Div, Neg, AddAssign, SubAssign, MulAssign, DivAssign, Index, IndexMut};
-use std::iter::{FromIterator, IntoIterator};
-use rand::{Rand, Rng};
-use num::{Zero, One};
-use structs::{Vec3, Pnt3, Rot3, Mat3};
-use traits::operations::{ApproxEq, Inv, POrd, POrdering, Axpy};
-use traits::structure::{Cast, Indexable, Iterable, IterableMut, Dim, Shape, BaseFloat, BaseNum,
-                        Bounded, Repeat};
-use traits::geometry::{Norm, Rotation, RotationMatrix, Rotate, RotationTo, Transform};
-
-#[cfg(feature="arbitrary")]
-use quickcheck::{Arbitrary, Gen};
-
-
-/// A quaternion.
-#[repr(C)]
-#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
-pub struct Quat<N> {
-    /// The scalar component of the quaternion.
-    pub w: N,
-    /// The first vector component of the quaternion.
-    pub i: N,
-    /// The second vector component of the quaternion.
-    pub j: N,
-    /// The third vector component of the quaternion.
-    pub k: N
-}
-
-impl<N> Quat<N> {
-    /// Creates a new quaternion from its components.
-    #[inline]
-    pub fn new(w: N, i: N, j: N, k: N) -> Quat<N> {
-        Quat {
-            w: w,
-            i: i,
-            j: j,
-            k: k
-        }
-    }
-
-    /// The vector part `(i, j, k)` of this quaternion.
-    #[inline]
-    pub fn vector<'a>(&'a self) -> &'a Vec3<N> {
-        // FIXME: do this require a `repr(C)` ?
-        unsafe {
-            mem::transmute(&self.i)
-        }
-    }
-
-    /// The scalar part `w` of this quaternion.
-    #[inline]
-    pub fn scalar<'a>(&'a self) -> &'a N {
-        &self.w
-    }
-}
-
-impl<N: Neg<Output = N> + Copy> Quat<N> {
-    /// Compute the conjugate of this quaternion.
-    #[inline]
-    pub fn conjugate(&self) -> Quat<N> {
-        Quat { w: self.w, i: -self.i, j: -self.j, k: -self.k }
-    }
-
-    /// Replaces this quaternion by its conjugate.
-    #[inline]
-    pub fn conjugate_mut(&mut self) {
-        self.i = -self.i;
-        self.j = -self.j;
-        self.k = -self.k;
-    }
-}
-
-impl<N: BaseFloat + ApproxEq<N>> Inv for Quat<N> {
-    #[inline]
-    fn inv(&self) -> Option<Quat<N>> {
-        let mut res = *self;
-
-        if res.inv_mut() {
-            Some(res)
-        }
-        else {
-            None
-        }
-    }
-
-    #[inline]
-    fn inv_mut(&mut self) -> bool {
-        let sqnorm = Norm::sqnorm(self);
-
-        if ApproxEq::approx_eq(&sqnorm, &::zero()) {
-            false
-        }
-        else {
-            self.conjugate_mut();
-            self.w = self.w / sqnorm;
-            self.i = self.i / sqnorm;
-            self.j = self.j / sqnorm;
-            self.k = self.k / sqnorm;
-
-            true
-        }
-    }
-}
-
-impl<N: BaseFloat> Norm<N> for Quat<N> {
-    #[inline]
-    fn sqnorm(&self) -> N {
-        self.w * self.w + self.i * self.i + self.j * self.j + self.k * self.k
-    }
-
-    #[inline]
-    fn normalize(&self) -> Quat<N> {
-        let n = self.norm();
-        Quat::new(self.w / n, self.i / n, self.j / n, self.k / n)
-    }
-
-    #[inline]
-    fn normalize_mut(&mut self) -> N {
-        let n = Norm::norm(self);
-
-        self.w = self.w / n;
-        self.i = self.i / n;
-        self.j = self.j / n;
-        self.k = self.k / n;
-
-        n
-    }
-}
-
-impl<N> Mul<Quat<N>> for Quat<N>
-    where N: Copy + Mul<N, Output = N> + Sub<N, Output = N> + Add<N, Output = N> {
-    type Output = Quat<N>;
-
-    #[inline]
-    fn mul(self, right: Quat<N>) -> Quat<N> {
-        Quat::new(
-            self.w * right.w - self.i * right.i - self.j * right.j - self.k * right.k,
-            self.w * right.i + self.i * right.w + self.j * right.k - self.k * right.j,
-            self.w * right.j - self.i * right.k + self.j * right.w + self.k * right.i,
-            self.w * right.k + self.i * right.j - self.j * right.i + self.k * right.w)
-    }
-}
-
-impl<N> MulAssign<Quat<N>> for Quat<N>
-    where N: Copy + Mul<N, Output = N> + Sub<N, Output = N> + Add<N, Output = N> {
-    #[inline]
-    fn mul_assign(&mut self, right: Quat<N>) {
-        *self = *self * right;
-    }
-}
-
-impl<N: ApproxEq<N> + BaseFloat> Div<Quat<N>> for Quat<N> {
-    type Output = Quat<N>;
-
-    #[inline]
-    fn div(self, right: Quat<N>) -> Quat<N> {
-        self * right.inv().expect("Unable to invert the denominator.")
-    }
-}
-
-impl<N: ApproxEq<N> + BaseFloat> DivAssign<Quat<N>> for Quat<N> {
-    #[inline]
-    fn div_assign(&mut self, right: Quat<N>) {
-        *self *= right.inv().expect("Unable to invert the denominator.")
-    }
-}
-
-impl<N: fmt::Display> fmt::Display for Quat<N> {
-    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
-        write!(f, "Quaternion {} − ({}, {}, {})", self.w, self.i, self.j, self.k)
-    }
-}
-
-rand_impl!(Quat, w, i, j, k);
-
-
-/// A unit quaternion that can represent a 3D rotation.
-#[repr(C)]
-#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
-pub struct UnitQuat<N> {
-    q: Quat<N>
-}
-
-impl<N: BaseFloat> UnitQuat<N> {
-    /// Creates a new unit quaternion from the axis-angle representation of a rotation.
-    #[inline]
-    pub fn new(axisangle: Vec3<N>) -> UnitQuat<N> {
-        let sqang = Norm::sqnorm(&axisangle);
-
-        if ::is_zero(&sqang) {
-            ::one()
-        }
-        else {
-            let ang    = sqang.sqrt();
-            let (s, c) = (ang / Cast::from(2.0)).sin_cos();
-
-            let s_ang = s / ang;
-
-            unsafe {
-                UnitQuat::new_with_unit_quat(
-                    Quat::new(
-                        c,
-                        axisangle.x * s_ang,
-                        axisangle.y * s_ang,
-                        axisangle.z * s_ang)
-                )
-            }
-        }
-    }
-
-    /// Creates a new unit quaternion from a quaternion.
-    ///
-    /// The input quaternion will be normalized.
-    #[inline]
-    pub fn new_with_quat(q: Quat<N>) -> UnitQuat<N> {
-        UnitQuat { q: q.normalize() }
-    }
-
-    /// Creates a new unit quaternion from Euler angles.
-    ///
-    /// The primitive rotations are applied in order: 1 roll − 2 pitch − 3 yaw.
-    #[inline]
-    pub fn new_with_euler_angles(roll: N, pitch: N, yaw: N) -> UnitQuat<N> {
-        let _0_5: N  = Cast::from(0.5);
-        let (sr, cr) = (roll * _0_5).sin_cos();
-        let (sp, cp) = (pitch * _0_5).sin_cos();
-        let (sy, cy) = (yaw * _0_5).sin_cos();
-
-        unsafe {
-            UnitQuat::new_with_unit_quat(
-                Quat::new(
-                    cr * cp * cy + sr * sp * sy,
-                    sr * cp * cy - cr * sp * sy,
-                    cr * sp * cy + sr * cp * sy,
-                    cr * cp * sy - sr * sp * cy)
-            )
-        }
-    }
-
-    /// Builds a rotation matrix from this quaternion.
-    pub fn to_rot(&self) -> Rot3<N> {
-        let _2: N = Cast::from(2.0);
-        let ww = self.q.w * self.q.w;
-        let ii = self.q.i * self.q.i;
-        let jj = self.q.j * self.q.j;
-        let kk = self.q.k * self.q.k;
-        let ij = _2 * self.q.i * self.q.j;
-        let wk = _2 * self.q.w * self.q.k;
-        let wj = _2 * self.q.w * self.q.j;
-        let ik = _2 * self.q.i * self.q.k;
-        let jk = _2 * self.q.j * self.q.k;
-        let wi = _2 * self.q.w * self.q.i;
-
-        unsafe {
-            Rot3::new_with_mat(
-                Mat3::new(
-                    ww + ii - jj - kk, ij - wk,           wj + ik,
-                    wk + ij,           ww - ii + jj - kk, jk - wi,
-                    ik - wj,           wi + jk,           ww - ii - jj + kk
-                )
-            )
-        }
-    }
-}
-
-
-impl<N> UnitQuat<N> {
-    /// Creates a new unit quaternion from a quaternion.
-    ///
-    /// This is unsafe because the input quaternion will not be normalized.
-    #[inline]
-    pub unsafe fn new_with_unit_quat(q: Quat<N>) -> UnitQuat<N> {
-        UnitQuat {
-            q: q
-        }
-    }
-
-    /// The `Quat` representation of this unit quaternion.
-    #[inline]
-    pub fn quat<'a>(&'a self) -> &'a Quat<N> {
-        &self.q
-    }
-}
-
-impl<N: BaseNum> One for UnitQuat<N> {
-    #[inline]
-    fn one() -> UnitQuat<N> {
-        unsafe {
-            UnitQuat::new_with_unit_quat(Quat::new(::one(), ::zero(), ::zero(), ::zero()))
-        }
-    }
-}
-
-impl<N: Copy + Neg<Output = N>> Inv for UnitQuat<N> {
-    #[inline]
-    fn inv(&self) -> Option<UnitQuat<N>> {
-        let mut cpy = *self;
-
-        cpy.inv_mut();
-        Some(cpy)
-    }
-
-    #[inline]
-    fn inv_mut(&mut self) -> bool {
-        self.q.conjugate_mut();
-
-        true
-    }
-}
-
-impl<N: Rand + BaseFloat> Rand for UnitQuat<N> {
-    #[inline]
-    fn rand<R: Rng>(rng: &mut R) -> UnitQuat<N> {
-        UnitQuat::new(rng.gen())
-    }
-}
-
-impl<N: ApproxEq<N>> ApproxEq<N> for UnitQuat<N> {
-    #[inline]
-    fn approx_epsilon(_: Option<UnitQuat<N>>) -> N {
-        ApproxEq::approx_epsilon(None::<N>)
-    }
-
-    #[inline]
-    fn approx_ulps(_: Option<UnitQuat<N>>) -> u32 {
-        ApproxEq::approx_ulps(None::<N>)
-    }
-
-    #[inline]
-    fn approx_eq_eps(&self, other: &UnitQuat<N>, eps: &N) -> bool {
-        ApproxEq::approx_eq_eps(&self.q, &other.q, eps)
-    }
-
-    #[inline]
-    fn approx_eq_ulps(&self, other: &UnitQuat<N>, ulps: u32) -> bool {
-        ApproxEq::approx_eq_ulps(&self.q, &other.q, ulps)
-    }
-}
-
-impl<N: BaseFloat + ApproxEq<N>> Div<UnitQuat<N>> for UnitQuat<N> {
-    type Output = UnitQuat<N>;
-
-    #[inline]
-    fn div(self, other: UnitQuat<N>) -> UnitQuat<N> {
-        UnitQuat { q: self.q / other.q }
-    }
-}
-
-impl<N: BaseFloat + ApproxEq<N>> DivAssign<UnitQuat<N>> for UnitQuat<N> {
-    #[inline]
-    fn div_assign(&mut self, other: UnitQuat<N>) {
-        self.q /= other.q
-    }
-}
-
-impl<N: BaseNum> Mul<UnitQuat<N>> for UnitQuat<N> {
-    type Output = UnitQuat<N>;
-
-    #[inline]
-    fn mul(self, right: UnitQuat<N>) -> UnitQuat<N> {
-        UnitQuat { q: self.q * right.q }
-    }
-}
-
-impl<N: BaseNum> MulAssign<UnitQuat<N>> for UnitQuat<N> {
-    #[inline]
-    fn mul_assign(&mut self, right: UnitQuat<N>) {
-        self.q *= right.q
-    }
-}
-
-impl<N: BaseNum> Mul<Vec3<N>> for UnitQuat<N> {
-    type Output = Vec3<N>;
-
-    #[inline]
-    fn mul(self, right: Vec3<N>) -> Vec3<N> {
-        let _2: N = ::one::<N>() + ::one();
-        let mut t = ::cross(self.q.vector(), &right);
-        t.x = t.x * _2;
-        t.y = t.y * _2;
-        t.z = t.z * _2;
-
-        Vec3::new(t.x * self.q.w, t.y * self.q.w, t.z * self.q.w) + ::cross(self.q.vector(), &t) + right
-    }
-}
-
-impl<N: BaseNum> Mul<Pnt3<N>> for UnitQuat<N> {
-    type Output = Pnt3<N>;
-
-    #[inline]
-    fn mul(self, right: Pnt3<N>) -> Pnt3<N> {
-        ::orig::<Pnt3<N>>() + self * *right.as_vec()
-    }
-}
-
-impl<N: BaseNum + Neg<Output = N>> Mul<UnitQuat<N>> for Vec3<N> {
-    type Output = Vec3<N>;
-
-    #[inline]
-    fn mul(self, right: UnitQuat<N>) -> Vec3<N> {
-        let mut inv_quat = right;
-
-        inv_quat.inv_mut();
-
-        inv_quat * self
-    }
-}
-
-impl<N: BaseNum + Neg<Output = N>> Mul<UnitQuat<N>> for Pnt3<N> {
-    type Output = Pnt3<N>;
-
-    #[inline]
-    fn mul(self, right: UnitQuat<N>) -> Pnt3<N> {
-        ::orig::<Pnt3<N>>() + *self.as_vec() * right
-    }
-}
-
-impl<N: BaseNum + Neg<Output = N>> MulAssign<UnitQuat<N>> for Vec3<N> {
-    #[inline]
-    fn mul_assign(&mut self, right: UnitQuat<N>) {
-        *self = *self * right
-    }
-}
-
-impl<N: BaseNum + Neg<Output = N>> MulAssign<UnitQuat<N>> for Pnt3<N> {
-    #[inline]
-    fn mul_assign(&mut self, right: UnitQuat<N>) {
-        *self = *self * right
-    }
-}
-
-impl<N: BaseFloat> Rotation<Vec3<N>> for UnitQuat<N> {
-    #[inline]
-    fn rotation(&self) -> Vec3<N> {
-        let _2 = ::one::<N>() + ::one();
-        let mut v = *self.q.vector();
-        let ang = _2 * v.normalize_mut().atan2(self.q.w);
-
-        if ::is_zero(&ang) {
-            ::zero()
-        }
-        else {
-            Vec3::new(v.x * ang, v.y * ang, v.z * ang)
-        }
-    }
-
-    #[inline]
-    fn inv_rotation(&self) -> Vec3<N> {
-        -self.rotation()
-    }
-
-    #[inline]
-    fn append_rotation_mut(&mut self, amount: &Vec3<N>) {
-        *self = Rotation::append_rotation(self, amount)
-    }
-
-    #[inline]
-    fn append_rotation(&self, amount: &Vec3<N>) -> UnitQuat<N> {
-        *self * UnitQuat::new(*amount)
-    }
-
-    #[inline]
-    fn prepend_rotation_mut(&mut self, amount: &Vec3<N>) {
-        *self = Rotation::prepend_rotation(self, amount)
-    }
-
-    #[inline]
-    fn prepend_rotation(&self, amount: &Vec3<N>) -> UnitQuat<N> {
-        UnitQuat::new(*amount) * *self
-    }
-
-    #[inline]
-    fn set_rotation(&mut self, v: Vec3<N>) {
-        *self = UnitQuat::new(v)
-    }
-}
-
-impl<N: BaseFloat> RotationMatrix<N, Vec3<N>, Vec3<N>> for UnitQuat<N> {
-    type Output = Rot3<N>;
-
-    #[inline]
-    fn to_rot_mat(&self) -> Rot3<N> {
-        self.to_rot()
-    }
-}
-
-impl<N: BaseNum + Neg<Output = N>> Rotate<Vec3<N>> for UnitQuat<N> {
-    #[inline]
-    fn rotate(&self, v: &Vec3<N>) -> Vec3<N> {
-        *self * *v
-    }
-
-    #[inline]
-    fn inv_rotate(&self, v: &Vec3<N>) -> Vec3<N> {
-        *v * *self
-    }
-}
-
-impl<N: BaseNum + Neg<Output = N>> Rotate<Pnt3<N>> for UnitQuat<N> {
-    #[inline]
-    fn rotate(&self, p: &Pnt3<N>) -> Pnt3<N> {
-        *self * *p
-    }
-
-    #[inline]
-    fn inv_rotate(&self, p: &Pnt3<N>) -> Pnt3<N> {
-        *p * *self
-    }
-}
-
-impl<N: BaseFloat + ApproxEq<N>> RotationTo for UnitQuat<N> {
-    type AngleType = N;
-    type DeltaRotationType = UnitQuat<N>;
-
-    #[inline]
-    fn angle_to(&self, other: &Self) -> N {
-        let delta = self.rotation_to(other);
-        let _2    = ::one::<N>() + ::one();
-
-        _2 * delta.q.vector().norm().atan2(delta.q.w)
-    }
-
-    #[inline]
-    fn rotation_to(&self, other: &Self) -> UnitQuat<N> {
-        *other / *self
-    }
-}
-
-impl<N: BaseNum + Neg<Output = N>> Transform<Vec3<N>> for UnitQuat<N> {
-    #[inline]
-    fn transform(&self, v: &Vec3<N>) -> Vec3<N> {
-        *self * *v
-    }
-
-    #[inline]
-    fn inv_transform(&self, v: &Vec3<N>) -> Vec3<N> {
-        *v * *self
-    }
-}
-
-impl<N: BaseNum + Neg<Output = N>> Transform<Pnt3<N>> for UnitQuat<N> {
-    #[inline]
-    fn transform(&self, p: &Pnt3<N>) -> Pnt3<N> {
-        *self * *p
-    }
-
-    #[inline]
-    fn inv_transform(&self, p: &Pnt3<N>) -> Pnt3<N> {
-        *p * *self
-    }
-}
-
-impl<N: fmt::Display> fmt::Display for UnitQuat<N> {
-    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
-        write!(f, "Unit quaternion {} − ({}, {}, {})", self.q.w, self.q.i, self.q.j, self.q.k)
-    }
-}
-
-#[cfg(feature="arbitrary")]
-impl<N: Arbitrary + BaseFloat> Arbitrary for UnitQuat<N> {
-    fn arbitrary<G: Gen>(g: &mut G) -> UnitQuat<N> {
-        UnitQuat::new(Arbitrary::arbitrary(g))
-    }
-}
-
-
-pord_impl!(Quat, w, i, j, k);
-vec_axis_impl!(Quat, w, i, j, k);
-vec_cast_impl!(Quat, w, i, j, k);
-conversion_impl!(Quat, 4);
-index_impl!(Quat);
-indexable_impl!(Quat, 4);
-at_fast_impl!(Quat, 4);
-repeat_impl!(Quat, val, w, i, j, k);
-dim_impl!(Quat, 3);
-container_impl!(Quat);
-add_impl!(Quat, w, i, j, k);
-sub_impl!(Quat, w, i, j, k);
-scalar_add_impl!(Quat, w, i, j, k);
-scalar_sub_impl!(Quat, w, i, j, k);
-scalar_mul_impl!(Quat, w, i, j, k);
-scalar_div_impl!(Quat, w, i, j, k);
-neg_impl!(Quat, w, i, j, k);
-zero_one_impl!(Quat, w, i, j, k);
-approx_eq_impl!(Quat, w, i, j, k);
-from_iterator_impl!(Quat, iterator, iterator, iterator, iterator);
-bounded_impl!(Quat, w, i, j, k);
-axpy_impl!(Quat, w, i, j, k);
-iterable_impl!(Quat, 4);
-iterable_mut_impl!(Quat, 4);
-arbitrary_impl!(Quat, w, i, j, k);
-
-dim_impl!(UnitQuat, 3);

src/structs/quaternion.rs

@@ -0,0 +1,598 @@
+//! Quaternion definition.
+
+use std::fmt;
+use std::mem;
+use std::slice::{Iter, IterMut};
+use std::ops::{Add, Sub, Mul, Div, Neg, AddAssign, SubAssign, MulAssign, DivAssign, Index, IndexMut};
+use std::iter::{FromIterator, IntoIterator};
+use rand::{Rand, Rng};
+use num::{Zero, One};
+use structs::{Vector3, Point3, Rotation3, Matrix3};
+use traits::operations::{ApproxEq, Inverse, PartialOrder, PartialOrdering, Axpy};
+use traits::structure::{Cast, Indexable, Iterable, IterableMut, Dimension, Shape, BaseFloat, BaseNum,
+                        Bounded, Repeat};
+use traits::geometry::{Norm, Rotation, RotationMatrix, Rotate, RotationTo, Transform};
+
+#[cfg(feature="arbitrary")]
+use quickcheck::{Arbitrary, Gen};
+
+
+/// A quaternion. See `UnitQuaternion` for a quaternion that can be used as a rotation.
+#[repr(C)]
+#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
+pub struct Quaternion<N> {
+    /// The scalar component of the quaternion.
+    pub w: N,
+    /// The first vector component of the quaternion.
+    pub i: N,
+    /// The second vector component of the quaternion.
+    pub j: N,
+    /// The third vector component of the quaternion.
+    pub k: N
+}
+
+impl<N> Quaternion<N> {
+    /// Creates a new quaternion from its components.
+    #[inline]
+    pub fn new(w: N, i: N, j: N, k: N) -> Quaternion<N> {
+        Quaternion {
+            w: w,
+            i: i,
+            j: j,
+            k: k
+        }
+    }
+
+    /// The vector part `(i, j, k)` of this quaternion.
+    #[inline]
+    pub fn vector<'a>(&'a self) -> &'a Vector3<N> {
+        // FIXME: do this require a `repr(C)` ?
+        unsafe {
+            mem::transmute(&self.i)
+        }
+    }
+
+    /// The scalar part `w` of this quaternion.
+    #[inline]
+    pub fn scalar<'a>(&'a self) -> &'a N {
+        &self.w
+    }
+}
+
+impl<N: Neg<Output = N> + Copy> Quaternion<N> {
+    /// Compute the conjugate of this quaternion.
+    #[inline]
+    pub fn conjugate(&self) -> Quaternion<N> {
+        Quaternion { w: self.w, i: -self.i, j: -self.j, k: -self.k }
+    }
+
+    /// Replaces this quaternion by its conjugate.
+    #[inline]
+    pub fn conjugate_mut(&mut self) {
+        self.i = -self.i;
+        self.j = -self.j;
+        self.k = -self.k;
+    }
+}
+
+impl<N: BaseFloat + ApproxEq<N>> Inverse for Quaternion<N> {
+    #[inline]
+    fn inverse(&self) -> Option<Quaternion<N>> {
+        let mut res = *self;
+
+        if res.inverse_mut() {
+            Some(res)
+        }
+        else {
+            None
+        }
+    }
+
+    #[inline]
+    fn inverse_mut(&mut self) -> bool {
+        let norm_squared = Norm::norm_squared(self);
+
+        if ApproxEq::approx_eq(&norm_squared, &::zero()) {
+            false
+        }
+        else {
+            self.conjugate_mut();
+            self.w = self.w / norm_squared;
+            self.i = self.i / norm_squared;
+            self.j = self.j / norm_squared;
+            self.k = self.k / norm_squared;
+
+            true
+        }
+    }
+}
+
+impl<N: BaseFloat> Norm<N> for Quaternion<N> {
+    #[inline]
+    fn norm_squared(&self) -> N {
+        self.w * self.w + self.i * self.i + self.j * self.j + self.k * self.k
+    }
+
+    #[inline]
+    fn normalize(&self) -> Quaternion<N> {
+        let n = self.norm();
+        Quaternion::new(self.w / n, self.i / n, self.j / n, self.k / n)
+    }
+
+    #[inline]
+    fn normalize_mut(&mut self) -> N {
+        let n = Norm::norm(self);
+
+        self.w = self.w / n;
+        self.i = self.i / n;
+        self.j = self.j / n;
+        self.k = self.k / n;
+
+        n
+    }
+}
+
+impl<N> Mul<Quaternion<N>> for Quaternion<N>
+    where N: Copy + Mul<N, Output = N> + Sub<N, Output = N> + Add<N, Output = N> {
+    type Output = Quaternion<N>;
+
+    #[inline]
+    fn mul(self, right: Quaternion<N>) -> Quaternion<N> {
+        Quaternion::new(
+            self.w * right.w - self.i * right.i - self.j * right.j - self.k * right.k,
+            self.w * right.i + self.i * right.w + self.j * right.k - self.k * right.j,
+            self.w * right.j - self.i * right.k + self.j * right.w + self.k * right.i,
+            self.w * right.k + self.i * right.j - self.j * right.i + self.k * right.w)
+    }
+}
+
+impl<N> MulAssign<Quaternion<N>> for Quaternion<N>
+    where N: Copy + Mul<N, Output = N> + Sub<N, Output = N> + Add<N, Output = N> {
+    #[inline]
+    fn mul_assign(&mut self, right: Quaternion<N>) {
+        *self = *self * right;
+    }
+}
+
+impl<N: ApproxEq<N> + BaseFloat> Div<Quaternion<N>> for Quaternion<N> {
+    type Output = Quaternion<N>;
+
+    #[inline]
+    fn div(self, right: Quaternion<N>) -> Quaternion<N> {
+        self * right.inverse().expect("Unable to invert the denominator.")
+    }
+}
+
+impl<N: ApproxEq<N> + BaseFloat> DivAssign<Quaternion<N>> for Quaternion<N> {
+    #[inline]
+    fn div_assign(&mut self, right: Quaternion<N>) {
+        *self *= right.inverse().expect("Unable to invert the denominator.")
+    }
+}
+
+impl<N: fmt::Display> fmt::Display for Quaternion<N> {
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        write!(f, "Quaternion {} − ({}, {}, {})", self.w, self.i, self.j, self.k)
+    }
+}
+
+rand_impl!(Quaternion, w, i, j, k);
+
+
+/// A unit quaternion that can represent a 3D rotation.
+#[repr(C)]
+#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
+pub struct UnitQuaternion<N> {
+    q: Quaternion<N>
+}
+
+impl<N: BaseFloat> UnitQuaternion<N> {
+    /// Creates a new unit quaternion from the axis-angle representation of a rotation.
+    #[inline]
+    pub fn new(axisangle: Vector3<N>) -> UnitQuaternion<N> {
+        let sqang = Norm::norm_squared(&axisangle);
+
+        if ::is_zero(&sqang) {
+            ::one()
+        }
+        else {
+            let ang    = sqang.sqrt();
+            let (s, c) = (ang / Cast::from(2.0)).sin_cos();
+
+            let s_ang = s / ang;
+
+            unsafe {
+                UnitQuaternion::new_with_unit_quaternion(
+                    Quaternion::new(
+                        c,
+                        axisangle.x * s_ang,
+                        axisangle.y * s_ang,
+                        axisangle.z * s_ang)
+                )
+            }
+        }
+    }
+
+    /// Creates a new unit quaternion from a quaternion.
+    ///
+    /// The input quaternion will be normalized.
+    #[inline]
+    pub fn new_with_quaternion(q: Quaternion<N>) -> UnitQuaternion<N> {
+        UnitQuaternion { q: q.normalize() }
+    }
+
+    /// Creates a new unit quaternion from Euler angles.
+    ///
+    /// The primitive rotations are applied in order: 1 roll − 2 pitch − 3 yaw.
+    #[inline]
+    pub fn new_with_euler_angles(roll: N, pitch: N, yaw: N) -> UnitQuaternion<N> {
+        let _0_5: N  = Cast::from(0.5);
+        let (sr, cr) = (roll * _0_5).sin_cos();
+        let (sp, cp) = (pitch * _0_5).sin_cos();
+        let (sy, cy) = (yaw * _0_5).sin_cos();
+
+        unsafe {
+            UnitQuaternion::new_with_unit_quaternion(
+                Quaternion::new(
+                    cr * cp * cy + sr * sp * sy,
+                    sr * cp * cy - cr * sp * sy,
+                    cr * sp * cy + sr * cp * sy,
+                    cr * cp * sy - sr * sp * cy)
+            )
+        }
+    }
+
+    /// Builds a rotation matrix from this quaternion.
+    pub fn to_rotation_matrix(&self) -> Rotation3<N> {
+        let _2: N = Cast::from(2.0);
+        let ww = self.q.w * self.q.w;
+        let ii = self.q.i * self.q.i;
+        let jj = self.q.j * self.q.j;
+        let kk = self.q.k * self.q.k;
+        let ij = _2 * self.q.i * self.q.j;
+        let wk = _2 * self.q.w * self.q.k;
+        let wj = _2 * self.q.w * self.q.j;
+        let ik = _2 * self.q.i * self.q.k;
+        let jk = _2 * self.q.j * self.q.k;
+        let wi = _2 * self.q.w * self.q.i;
+
+        unsafe {
+            Rotation3::new_with_matrix(
+                Matrix3::new(
+                    ww + ii - jj - kk, ij - wk,           wj + ik,
+                    wk + ij,           ww - ii + jj - kk, jk - wi,
+                    ik - wj,           wi + jk,           ww - ii - jj + kk
+                )
+            )
+        }
+    }
+}
+
+
+impl<N> UnitQuaternion<N> {
+    /// Creates a new unit quaternion from a quaternion.
+    ///
+    /// This is unsafe because the input quaternion will not be normalized.
+    #[inline]
+    pub unsafe fn new_with_unit_quaternion(q: Quaternion<N>) -> UnitQuaternion<N> {
+        UnitQuaternion {
+            q: q
+        }
+    }
+
+    /// The `Quaternion` representation of this unit quaternion.
+    #[inline]
+    pub fn quaternion<'a>(&'a self) -> &'a Quaternion<N> {
+        &self.q
+    }
+}
+
+impl<N: BaseNum> One for UnitQuaternion<N> {
+    #[inline]
+    fn one() -> UnitQuaternion<N> {
+        unsafe {
+            UnitQuaternion::new_with_unit_quaternion(Quaternion::new(::one(), ::zero(), ::zero(), ::zero()))
+        }
+    }
+}
+
+impl<N: Copy + Neg<Output = N>> Inverse for UnitQuaternion<N> {
+    #[inline]
+    fn inverse(&self) -> Option<UnitQuaternion<N>> {
+        let mut cpy = *self;
+
+        cpy.inverse_mut();
+        Some(cpy)
+    }
+
+    #[inline]
+    fn inverse_mut(&mut self) -> bool {
+        self.q.conjugate_mut();
+
+        true
+    }
+}
+
+impl<N: Rand + BaseFloat> Rand for UnitQuaternion<N> {
+    #[inline]
+    fn rand<R: Rng>(rng: &mut R) -> UnitQuaternion<N> {
+        UnitQuaternion::new(rng.gen())
+    }
+}
+
+impl<N: ApproxEq<N>> ApproxEq<N> for UnitQuaternion<N> {
+    #[inline]
+    fn approx_epsilon(_: Option<UnitQuaternion<N>>) -> N {
+        ApproxEq::approx_epsilon(None::<N>)
+    }
+
+    #[inline]
+    fn approx_ulps(_: Option<UnitQuaternion<N>>) -> u32 {
+        ApproxEq::approx_ulps(None::<N>)
+    }
+
+    #[inline]
+    fn approx_eq_eps(&self, other: &UnitQuaternion<N>, eps: &N) -> bool {
+        ApproxEq::approx_eq_eps(&self.q, &other.q, eps)
+    }
+
+    #[inline]
+    fn approx_eq_ulps(&self, other: &UnitQuaternion<N>, ulps: u32) -> bool {
+        ApproxEq::approx_eq_ulps(&self.q, &other.q, ulps)
+    }
+}
+
+impl<N: BaseFloat + ApproxEq<N>> Div<UnitQuaternion<N>> for UnitQuaternion<N> {
+    type Output = UnitQuaternion<N>;
+
+    #[inline]
+    fn div(self, other: UnitQuaternion<N>) -> UnitQuaternion<N> {
+        UnitQuaternion { q: self.q / other.q }
+    }
+}
+
+impl<N: BaseFloat + ApproxEq<N>> DivAssign<UnitQuaternion<N>> for UnitQuaternion<N> {
+    #[inline]
+    fn div_assign(&mut self, other: UnitQuaternion<N>) {
+        self.q /= other.q
+    }
+}
+
+impl<N: BaseNum> Mul<UnitQuaternion<N>> for UnitQuaternion<N> {
+    type Output = UnitQuaternion<N>;
+
+    #[inline]
+    fn mul(self, right: UnitQuaternion<N>) -> UnitQuaternion<N> {
+        UnitQuaternion { q: self.q * right.q }
+    }
+}
+
+impl<N: BaseNum> MulAssign<UnitQuaternion<N>> for UnitQuaternion<N> {
+    #[inline]
+    fn mul_assign(&mut self, right: UnitQuaternion<N>) {
+        self.q *= right.q
+    }
+}
+
+impl<N: BaseNum> Mul<Vector3<N>> for UnitQuaternion<N> {
+    type Output = Vector3<N>;
+
+    #[inline]
+    fn mul(self, right: Vector3<N>) -> Vector3<N> {
+        let _2: N = ::one::<N>() + ::one();
+        let mut t = ::cross(self.q.vector(), &right);
+        t.x = t.x * _2;
+        t.y = t.y * _2;
+        t.z = t.z * _2;
+
+        Vector3::new(t.x * self.q.w, t.y * self.q.w, t.z * self.q.w) + ::cross(self.q.vector(), &t) + right
+    }
+}
+
+impl<N: BaseNum> Mul<Point3<N>> for UnitQuaternion<N> {
+    type Output = Point3<N>;
+
+    #[inline]
+    fn mul(self, right: Point3<N>) -> Point3<N> {
+        ::origin::<Point3<N>>() + self * *right.as_vector()
+    }
+}
+
+impl<N: BaseNum + Neg<Output = N>> Mul<UnitQuaternion<N>> for Vector3<N> {
+    type Output = Vector3<N>;
+
+    #[inline]
+    fn mul(self, right: UnitQuaternion<N>) -> Vector3<N> {
+        let mut inverse_quaternion = right;
+
+        inverse_quaternion.inverse_mut();
+
+        inverse_quaternion * self
+    }
+}
+
+impl<N: BaseNum + Neg<Output = N>> Mul<UnitQuaternion<N>> for Point3<N> {
+    type Output = Point3<N>;
+
+    #[inline]
+    fn mul(self, right: UnitQuaternion<N>) -> Point3<N> {
+        ::origin::<Point3<N>>() + *self.as_vector() * right
+    }
+}
+
+impl<N: BaseNum + Neg<Output = N>> MulAssign<UnitQuaternion<N>> for Vector3<N> {
+    #[inline]
+    fn mul_assign(&mut self, right: UnitQuaternion<N>) {
+        *self = *self * right
+    }
+}
+
+impl<N: BaseNum + Neg<Output = N>> MulAssign<UnitQuaternion<N>> for Point3<N> {
+    #[inline]
+    fn mul_assign(&mut self, right: UnitQuaternion<N>) {
+        *self = *self * right
+    }
+}
+
+impl<N: BaseFloat> Rotation<Vector3<N>> for UnitQuaternion<N> {
+    #[inline]
+    fn rotation(&self) -> Vector3<N> {
+        let _2 = ::one::<N>() + ::one();
+        let mut v = *self.q.vector();
+        let ang = _2 * v.normalize_mut().atan2(self.q.w);
+
+        if ::is_zero(&ang) {
+            ::zero()
+        }
+        else {
+            Vector3::new(v.x * ang, v.y * ang, v.z * ang)
+        }
+    }
+
+    #[inline]
+    fn inverse_rotation(&self) -> Vector3<N> {
+        -self.rotation()
+    }
+
+    #[inline]
+    fn append_rotation_mut(&mut self, amount: &Vector3<N>) {
+        *self = Rotation::append_rotation(self, amount)
+    }
+
+    #[inline]
+    fn append_rotation(&self, amount: &Vector3<N>) -> UnitQuaternion<N> {
+        *self * UnitQuaternion::new(*amount)
+    }
+
+    #[inline]
+    fn prepend_rotation_mut(&mut self, amount: &Vector3<N>) {
+        *self = Rotation::prepend_rotation(self, amount)
+    }
+
+    #[inline]
+    fn prepend_rotation(&self, amount: &Vector3<N>) -> UnitQuaternion<N> {
+        UnitQuaternion::new(*amount) * *self
+    }
+
+    #[inline]
+    fn set_rotation(&mut self, v: Vector3<N>) {
+        *self = UnitQuaternion::new(v)
+    }
+}
+
+impl<N: BaseFloat> RotationMatrix<N, Vector3<N>, Vector3<N>> for UnitQuaternion<N> {
+    type Output = Rotation3<N>;
+
+    #[inline]
+    fn to_rotation_matrix(&self) -> Rotation3<N> {
+        self.to_rotation_matrix()
+    }
+}
+
+impl<N: BaseNum + Neg<Output = N>> Rotate<Vector3<N>> for UnitQuaternion<N> {
+    #[inline]
+    fn rotate(&self, v: &Vector3<N>) -> Vector3<N> {
+        *self * *v
+    }
+
+    #[inline]
+    fn inverse_rotate(&self, v: &Vector3<N>) -> Vector3<N> {
+        *v * *self
+    }
+}
+
+impl<N: BaseNum + Neg<Output = N>> Rotate<Point3<N>> for UnitQuaternion<N> {
+    #[inline]
+    fn rotate(&self, p: &Point3<N>) -> Point3<N> {
+        *self * *p
+    }
+
+    #[inline]
+    fn inverse_rotate(&self, p: &Point3<N>) -> Point3<N> {
+        *p * *self
+    }
+}
+
+impl<N: BaseFloat + ApproxEq<N>> RotationTo for UnitQuaternion<N> {
+    type AngleType = N;
+    type DeltaRotationType = UnitQuaternion<N>;
+
+    #[inline]
+    fn angle_to(&self, other: &Self) -> N {
+        let delta = self.rotation_to(other);
+        let _2    = ::one::<N>() + ::one();
+
+        _2 * delta.q.vector().norm().atan2(delta.q.w)
+    }
+
+    #[inline]
+    fn rotation_to(&self, other: &Self) -> UnitQuaternion<N> {
+        *other / *self
+    }
+}
+
+impl<N: BaseNum + Neg<Output = N>> Transform<Vector3<N>> for UnitQuaternion<N> {
+    #[inline]
+    fn transform(&self, v: &Vector3<N>) -> Vector3<N> {
+        *self * *v
+    }
+
+    #[inline]
+    fn inverse_transform(&self, v: &Vector3<N>) -> Vector3<N> {
+        *v * *self
+    }
+}
+
+impl<N: BaseNum + Neg<Output = N>> Transform<Point3<N>> for UnitQuaternion<N> {
+    #[inline]
+    fn transform(&self, p: &Point3<N>) -> Point3<N> {
+        *self * *p
+    }
+
+    #[inline]
+    fn inverse_transform(&self, p: &Point3<N>) -> Point3<N> {
+        *p * *self
+    }
+}
+
+impl<N: fmt::Display> fmt::Display for UnitQuaternion<N> {
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        write!(f, "Unit quaternion {} − ({}, {}, {})", self.q.w, self.q.i, self.q.j, self.q.k)
+    }
+}
+
+#[cfg(feature="arbitrary")]
+impl<N: Arbitrary + BaseFloat> Arbitrary for UnitQuaternion<N> {
+    fn arbitrary<G: Gen>(g: &mut G) -> UnitQuaternion<N> {
+        UnitQuaternion::new(Arbitrary::arbitrary(g))
+    }
+}
+
+
+pord_impl!(Quaternion, w, i, j, k);
+vec_axis_impl!(Quaternion, w, i, j, k);
+vec_cast_impl!(Quaternion, w, i, j, k);
+conversion_impl!(Quaternion, 4);
+index_impl!(Quaternion);
+indexable_impl!(Quaternion, 4);
+at_fast_impl!(Quaternion, 4);
+repeat_impl!(Quaternion, val, w, i, j, k);
+dim_impl!(Quaternion, 3);
+container_impl!(Quaternion);
+add_impl!(Quaternion, w, i, j, k);
+sub_impl!(Quaternion, w, i, j, k);
+scalar_add_impl!(Quaternion, w, i, j, k);
+scalar_sub_impl!(Quaternion, w, i, j, k);
+scalar_mul_impl!(Quaternion, w, i, j, k);
+scalar_div_impl!(Quaternion, w, i, j, k);
+neg_impl!(Quaternion, w, i, j, k);
+zero_one_impl!(Quaternion, w, i, j, k);
+approx_eq_impl!(Quaternion, w, i, j, k);
+from_iterator_impl!(Quaternion, iterator, iterator, iterator, iterator);
+bounded_impl!(Quaternion, w, i, j, k);
+axpy_impl!(Quaternion, w, i, j, k);
+iterable_impl!(Quaternion, 4);
+iterable_mut_impl!(Quaternion, 4);
+arbitrary_impl!(Quaternion, w, i, j, k);
+
+dim_impl!(UnitQuaternion, 3);

src/structs/rot.rs

@@ -1,407 +0,0 @@
-//! Rotations matrices.
-
-use std::fmt;
-use std::ops::{Mul, Neg, MulAssign, Index};
-use rand::{Rand, Rng};
-use num::{Zero, One};
-use traits::geometry::{Rotate, Rotation, AbsoluteRotate, RotationMatrix, RotationTo, Transform,
-                       ToHomogeneous, Norm, Cross};
-use traits::structure::{Cast, Dim, Row, Col, BaseFloat, BaseNum, Eye, Diag};
-use traits::operations::{Absolute, Inv, Transpose, ApproxEq};
-use structs::vec::{Vec1, Vec2, Vec3};
-use structs::pnt::{Pnt2, Pnt3};
-use structs::mat::{Mat2, Mat3, Mat4};
-#[cfg(feature="arbitrary")]
-use quickcheck::{Arbitrary, Gen};
-
-
-/// Two dimensional rotation matrix.
-#[repr(C)]
-#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Debug, Hash, Copy)]
-pub struct Rot2<N> {
-    submat: Mat2<N>
-}
-
-impl<N: Clone + BaseFloat + Neg<Output = N>> Rot2<N> {
-    /// Builds a 2 dimensional rotation matrix from an angle in radian.
-    pub fn new(angle: Vec1<N>) -> Rot2<N> {
-        let (sia, coa) = angle.x.sin_cos();
-
-        Rot2 {
-            submat: Mat2::new(coa.clone(), -sia, sia, coa)
-        }
-    }
-}
-
-impl<N: BaseFloat + Clone> Rotation<Vec1<N>> for Rot2<N> {
-    #[inline]
-    fn rotation(&self) -> Vec1<N> {
-        Vec1::new((-self.submat.m12).atan2(self.submat.m11.clone()))
-    }
-
-    #[inline]
-    fn inv_rotation(&self) -> Vec1<N> {
-        -self.rotation()
-    }
-
-    #[inline]
-    fn append_rotation_mut(&mut self, rot: &Vec1<N>) {
-        *self = Rotation::append_rotation(self, rot)
-    }
-
-    #[inline]
-    fn append_rotation(&self, rot: &Vec1<N>) -> Rot2<N> {
-        Rot2::new(rot.clone()) * *self
-    }
-
-    #[inline]
-    fn prepend_rotation_mut(&mut self, rot: &Vec1<N>) {
-        *self = Rotation::prepend_rotation(self, rot)
-    }
-
-    #[inline]
-    fn prepend_rotation(&self, rot: &Vec1<N>) -> Rot2<N> {
-        *self * Rot2::new(rot.clone())
-    }
-
-    #[inline]
-    fn set_rotation(&mut self, rot: Vec1<N>) {
-        *self = Rot2::new(rot)
-    }
-}
-
-impl<N: BaseFloat> RotationTo for Rot2<N> {
-    type AngleType = N;
-    type DeltaRotationType = Rot2<N>;
-
-    #[inline]
-    fn angle_to(&self, other: &Self) -> N {
-        self.rotation_to(other).rotation().norm()
-    }
-
-    #[inline]
-    fn rotation_to(&self, other: &Self) -> Rot2<N> {
-        *other * ::inv(self).unwrap()
-    }
-}
-
-impl<N: Rand + BaseFloat> Rand for Rot2<N> {
-    #[inline]
-    fn rand<R: Rng>(rng: &mut R) -> Rot2<N> {
-        Rot2::new(rng.gen())
-    }
-}
-
-impl<N: BaseFloat> AbsoluteRotate<Vec2<N>> for Rot2<N> {
-    #[inline]
-    fn absolute_rotate(&self, v: &Vec2<N>) -> Vec2<N> {
-        // the matrix is skew-symetric, so we dont need to compute the absolute value of every
-        // component.
-        let m11 = ::abs(&self.submat.m11);
-        let m12 = ::abs(&self.submat.m12);
-        let m22 = ::abs(&self.submat.m22);
-
-        Vec2::new(m11 * v.x + m12 * v.y, m12 * v.x + m22 * v.y)
-    }
-}
-
-#[cfg(feature="arbitrary")]
-impl<N: Arbitrary + Clone + BaseFloat + Neg<Output = N>> Arbitrary for Rot2<N> {
-    fn arbitrary<G: Gen>(g: &mut G) -> Rot2<N> {
-        Rot2::new(Arbitrary::arbitrary(g))
-    }
-}
-
-
-/*
- * 3d rotation
- */
-/// Three dimensional rotation matrix.
-#[repr(C)]
-#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Debug, Hash, Copy)]
-pub struct Rot3<N> {
-    submat: Mat3<N>
-}
-
-
-impl<N: Clone + BaseFloat> Rot3<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(axisangle: Vec3<N>) -> Rot3<N> {
-        if ::is_zero(&Norm::sqnorm(&axisangle)) {
-            ::one()
-        }
-        else {
-            let mut axis   = axisangle;
-            let angle      = axis.normalize_mut();
-            let _1: N      = ::one();
-            let ux         = axis.x.clone();
-            let uy         = axis.y.clone();
-            let uz         = axis.z.clone();
-            let sqx        = ux * ux;
-            let sqy        = uy * uy;
-            let sqz        = uz * uz;
-            let (sin, cos) = angle.sin_cos();
-            let one_m_cos  = _1 - cos;
-
-            Rot3 {
-                submat: Mat3::new(
-                            (sqx + (_1 - sqx) * cos),
-                            (ux * uy * one_m_cos - uz * sin),
-                            (ux * uz * one_m_cos + uy * sin),
-
-                            (ux * uy * one_m_cos + uz * sin),
-                            (sqy + (_1 - sqy) * cos),
-                            (uy * uz * one_m_cos - ux * sin),
-
-                            (ux * uz * one_m_cos - uy * sin),
-                            (uy * uz * one_m_cos + ux * sin),
-                            (sqz + (_1 - sqz) * cos))
-            }
-        }
-    }
-
-    /// Builds a rotation matrix from an orthogonal matrix.
-    ///
-    /// This is unsafe because the orthogonality of `mat` is not checked.
-    pub unsafe fn new_with_mat(mat: Mat3<N>) -> Rot3<N> {
-        Rot3 {
-            submat: mat
-        }
-    }
-
-    /// Creates a new rotation from Euler angles.
-    ///
-    /// The primitive rotations are applied in order: 1 roll − 2 pitch − 3 yaw.
-    pub fn new_with_euler_angles(roll: N, pitch: N, yaw: N) -> Rot3<N> {
-        let (sr, cr) = roll.sin_cos();
-        let (sp, cp) = pitch.sin_cos();
-        let (sy, cy) = yaw.sin_cos();
-
-        unsafe {
-            Rot3::new_with_mat(
-                Mat3::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
-                )
-            )
-        }
-    }
-}
-
-impl<N: Clone + BaseFloat> Rot3<N> {
-    /// Creates a rotation that corresponds to the local frame of an observer standing at the
-    /// origin and looking toward `dir`.
-    ///
-    /// It maps the view direction `dir` to the positive `z` axis.
-    ///
-    /// # Arguments
-    ///   * dir - The look direction, that is, direction the matrix `z` axis will be aligned with.
-    ///   * up - The vertical direction. The only requirement of this parameter is to not be
-    ///   collinear
-    ///   to `dir`. Non-collinearity is not checked.
-    #[inline]
-    pub fn new_observer_frame(dir: &Vec3<N>, up: &Vec3<N>) -> Rot3<N> {
-        let zaxis = Norm::normalize(dir);
-        let xaxis = Norm::normalize(&Cross::cross(up, &zaxis));
-        let yaxis = Norm::normalize(&Cross::cross(&zaxis, &xaxis));
-
-        unsafe {
-            Rot3::new_with_mat(Mat3::new(
-                xaxis.x.clone(), yaxis.x.clone(), zaxis.x.clone(),
-                xaxis.y.clone(), yaxis.y.clone(), zaxis.y.clone(),
-                xaxis.z        , yaxis.z        , zaxis.z))
-        }
-    }
-
-
-    /// Builds a right-handed look-at view matrix without translation.
-    ///
-    /// This conforms to the common notion of right handed look-at matrix from the computer
-    /// graphics community.
-    ///
-    /// # Arguments
-    ///   * eye - The eye position.
-    ///   * target - The target position.
-    ///   * 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(dir: &Vec3<N>, up: &Vec3<N>) -> Rot3<N> {
-        Rot3::new_observer_frame(&(-*dir), up).inv().unwrap()
-    }
-
-    /// Builds a left-handed look-at view matrix without translation.
-    ///
-    /// This conforms to the common notion of left handed look-at matrix from the computer
-    /// graphics community.
-    ///
-    /// # Arguments
-    ///   * eye - The eye position.
-    ///   * target - The target position.
-    ///   * 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(dir: &Vec3<N>, up: &Vec3<N>) -> Rot3<N> {
-        Rot3::new_observer_frame(&(*dir), up).inv().unwrap()
-    }
-}
-
-impl<N: Clone + BaseFloat + Cast<f64>>
-Rotation<Vec3<N>> for Rot3<N> {
-    #[inline]
-    fn rotation(&self) -> Vec3<N> {
-        let angle = ((self.submat.m11 + self.submat.m22 + self.submat.m33 - ::one()) / Cast::from(2.0)).acos();
-
-        if angle != angle {
-            // FIXME: handle that correctly
-            ::zero()
-        }
-        else if ::is_zero(&angle) {
-            ::zero()
-        }
-        else {
-            let m32_m23 = self.submat.m32 - self.submat.m23;
-            let m13_m31 = self.submat.m13 - self.submat.m31;
-            let m21_m12 = self.submat.m21 - self.submat.m12;
-
-            let denom = (m32_m23 * m32_m23 + m13_m31 * m13_m31 + m21_m12 * m21_m12).sqrt();
-
-            if ::is_zero(&denom) {
-                // XXX: handle that properly
-                // panic!("Internal error: singularity.")
-                ::zero()
-            }
-            else {
-                let a_d = angle / denom;
-
-                Vec3::new(m32_m23 * a_d, m13_m31 * a_d, m21_m12 * a_d)
-            }
-        }
-    }
-
-    #[inline]
-    fn inv_rotation(&self) -> Vec3<N> {
-        -self.rotation()
-    }
-
-
-    #[inline]
-    fn append_rotation_mut(&mut self, rot: &Vec3<N>) {
-        *self = Rotation::append_rotation(self, rot)
-    }
-
-    #[inline]
-    fn append_rotation(&self, axisangle: &Vec3<N>) -> Rot3<N> {
-        Rot3::new(axisangle.clone()) * *self
-    }
-
-    #[inline]
-    fn prepend_rotation_mut(&mut self, rot: &Vec3<N>) {
-        *self = Rotation::prepend_rotation(self, rot)
-    }
-
-    #[inline]
-    fn prepend_rotation(&self, axisangle: &Vec3<N>) -> Rot3<N> {
-        *self * Rot3::new(axisangle.clone())
-    }
-
-    #[inline]
-    fn set_rotation(&mut self, axisangle: Vec3<N>) {
-        *self = Rot3::new(axisangle)
-    }
-}
-
-impl<N: BaseFloat> RotationTo for Rot3<N> {
-    type AngleType = N;
-    type DeltaRotationType = Rot3<N>;
-
-    #[inline]
-    fn angle_to(&self, other: &Self) -> N {
-        // FIXME: refactor to avoid the normalization of the rotation axisangle vector.
-        self.rotation_to(other).rotation().norm()
-    }
-
-    #[inline]
-    fn rotation_to(&self, other: &Self) -> Rot3<N> {
-        *other * ::inv(self).unwrap()
-    }
-}
-
-impl<N: Clone + Rand + BaseFloat> Rand for Rot3<N> {
-    #[inline]
-    fn rand<R: Rng>(rng: &mut R) -> Rot3<N> {
-        Rot3::new(rng.gen())
-    }
-}
-
-impl<N: BaseFloat> AbsoluteRotate<Vec3<N>> for Rot3<N> {
-    #[inline]
-    fn absolute_rotate(&self, v: &Vec3<N>) -> Vec3<N> {
-        Vec3::new(
-            ::abs(&self.submat.m11) * v.x + ::abs(&self.submat.m12) * v.y + ::abs(&self.submat.m13) * v.z,
-            ::abs(&self.submat.m21) * v.x + ::abs(&self.submat.m22) * v.y + ::abs(&self.submat.m23) * v.z,
-            ::abs(&self.submat.m31) * v.x + ::abs(&self.submat.m32) * v.y + ::abs(&self.submat.m33) * v.z)
-    }
-}
-
-#[cfg(feature="arbitrary")]
-impl<N: Arbitrary + Clone + BaseFloat> Arbitrary for Rot3<N> {
-    fn arbitrary<G: Gen>(g: &mut G) -> Rot3<N> {
-        Rot3::new(Arbitrary::arbitrary(g))
-    }
-}
-
-
-/*
- * Common implementations.
- */
-
-submat_impl!(Rot2, Mat2);
-rotate_impl!(Rot2, Vec2, Pnt2);
-transform_impl!(Rot2, Vec2, Pnt2);
-dim_impl!(Rot2, 2);
-rot_mul_rot_impl!(Rot2);
-rot_mul_vec_impl!(Rot2, Vec2);
-vec_mul_rot_impl!(Rot2, Vec2);
-rot_mul_pnt_impl!(Rot2, Pnt2);
-pnt_mul_rot_impl!(Rot2, Pnt2);
-one_impl!(Rot2);
-eye_impl!(Rot2);
-rotation_matrix_impl!(Rot2, Vec2, Vec1);
-col_impl!(Rot2, Vec2);
-row_impl!(Rot2, Vec2);
-index_impl!(Rot2);
-absolute_impl!(Rot2, Mat2);
-to_homogeneous_impl!(Rot2, Mat3);
-inv_impl!(Rot2);
-transpose_impl!(Rot2);
-approx_eq_impl!(Rot2);
-diag_impl!(Rot2, Vec2);
-rot_display_impl!(Rot2);
-
-submat_impl!(Rot3, Mat3);
-rotate_impl!(Rot3, Vec3, Pnt3);
-transform_impl!(Rot3, Vec3, Pnt3);
-dim_impl!(Rot3, 3);
-rot_mul_rot_impl!(Rot3);
-rot_mul_vec_impl!(Rot3, Vec3);
-vec_mul_rot_impl!(Rot3, Vec3);
-rot_mul_pnt_impl!(Rot3, Pnt3);
-pnt_mul_rot_impl!(Rot3, Pnt3);
-one_impl!(Rot3);
-eye_impl!(Rot3);
-rotation_matrix_impl!(Rot3, Vec3, Vec3);
-col_impl!(Rot3, Vec3);
-row_impl!(Rot3, Vec3);
-index_impl!(Rot3);
-absolute_impl!(Rot3, Mat3);
-to_homogeneous_impl!(Rot3, Mat4);
-inv_impl!(Rot3);
-transpose_impl!(Rot3);
-approx_eq_impl!(Rot3);
-diag_impl!(Rot3, Vec3);
-rot_display_impl!(Rot3);

src/structs/rotation.rs

@@ -0,0 +1,407 @@
+//! Rotations matrices.
+
+use std::fmt;
+use std::ops::{Mul, Neg, MulAssign, Index};
+use rand::{Rand, Rng};
+use num::{Zero, One};
+use traits::geometry::{Rotate, Rotation, AbsoluteRotate, RotationMatrix, RotationTo, Transform,
+                       ToHomogeneous, Norm, Cross};
+use traits::structure::{Cast, Dimension, Row, Column, BaseFloat, BaseNum, Eye, Diagonal};
+use traits::operations::{Absolute, Inverse, Transpose, ApproxEq};
+use structs::vector::{Vector1, Vector2, Vector3};
+use structs::point::{Point2, Point3};
+use structs::matrix::{Matrix2, Matrix3, Matrix4};
+#[cfg(feature="arbitrary")]
+use quickcheck::{Arbitrary, Gen};
+
+
+/// Two dimensional rotation matrix.
+#[repr(C)]
+#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Debug, Hash, Copy)]
+pub struct Rotation2<N> {
+    submatrix: Matrix2<N>
+}
+
+impl<N: Clone + BaseFloat + Neg<Output = N>> Rotation2<N> {
+    /// Builds a 2 dimensional rotation matrix from an angle in radian.
+    pub fn new(angle: Vector1<N>) -> Rotation2<N> {
+        let (sia, coa) = angle.x.sin_cos();
+
+        Rotation2 {
+            submatrix: Matrix2::new(coa.clone(), -sia, sia, coa)
+        }
+    }
+}
+
+impl<N: BaseFloat + Clone> Rotation<Vector1<N>> for Rotation2<N> {
+    #[inline]
+    fn rotation(&self) -> Vector1<N> {
+        Vector1::new((-self.submatrix.m12).atan2(self.submatrix.m11.clone()))
+    }
+
+    #[inline]
+    fn inverse_rotation(&self) -> Vector1<N> {
+        -self.rotation()
+    }
+
+    #[inline]
+    fn append_rotation_mut(&mut self, rotation: &Vector1<N>) {
+        *self = Rotation::append_rotation(self, rotation)
+    }
+
+    #[inline]
+    fn append_rotation(&self, rotation: &Vector1<N>) -> Rotation2<N> {
+        Rotation2::new(rotation.clone()) * *self
+    }
+
+    #[inline]
+    fn prepend_rotation_mut(&mut self, rotation: &Vector1<N>) {
+        *self = Rotation::prepend_rotation(self, rotation)
+    }
+
+    #[inline]
+    fn prepend_rotation(&self, rotation: &Vector1<N>) -> Rotation2<N> {
+        *self * Rotation2::new(rotation.clone())
+    }
+
+    #[inline]
+    fn set_rotation(&mut self, rotation: Vector1<N>) {
+        *self = Rotation2::new(rotation)
+    }
+}
+
+impl<N: BaseFloat> RotationTo for Rotation2<N> {
+    type AngleType = N;
+    type DeltaRotationType = Rotation2<N>;
+
+    #[inline]
+    fn angle_to(&self, other: &Self) -> N {
+        self.rotation_to(other).rotation().norm()
+    }
+
+    #[inline]
+    fn rotation_to(&self, other: &Self) -> Rotation2<N> {
+        *other * ::inverse(self).unwrap()
+    }
+}
+
+impl<N: Rand + BaseFloat> Rand for Rotation2<N> {
+    #[inline]
+    fn rand<R: Rng>(rng: &mut R) -> Rotation2<N> {
+        Rotation2::new(rng.gen())
+    }
+}
+
+impl<N: BaseFloat> AbsoluteRotate<Vector2<N>> for Rotation2<N> {
+    #[inline]
+    fn absolute_rotate(&self, v: &Vector2<N>) -> Vector2<N> {
+        // the matrix is skew-symetric, so we dont need to compute the absolute value of every
+        // component.
+        let m11 = ::abs(&self.submatrix.m11);
+        let m12 = ::abs(&self.submatrix.m12);
+        let m22 = ::abs(&self.submatrix.m22);
+
+        Vector2::new(m11 * v.x + m12 * v.y, m12 * v.x + m22 * v.y)
+    }
+}
+
+#[cfg(feature="arbitrary")]
+impl<N: Arbitrary + Clone + BaseFloat + Neg<Output = N>> Arbitrary for Rotation2<N> {
+    fn arbitrary<G: Gen>(g: &mut G) -> Rotation2<N> {
+        Rotation2::new(Arbitrary::arbitrary(g))
+    }
+}
+
+
+/*
+ * 3d rotation
+ */
+/// Three dimensional rotation matrix.
+#[repr(C)]
+#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Debug, Hash, Copy)]
+pub struct Rotation3<N> {
+    submatrix: Matrix3<N>
+}
+
+
+impl<N: Clone + BaseFloat> 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(axisangle: Vector3<N>) -> Rotation3<N> {
+        if ::is_zero(&Norm::norm_squared(&axisangle)) {
+            ::one()
+        }
+        else {
+            let mut axis   = axisangle;
+            let angle      = axis.normalize_mut();
+            let _1: N      = ::one();
+            let ux         = axis.x.clone();
+            let uy         = axis.y.clone();
+            let uz         = axis.z.clone();
+            let sqx        = ux * ux;
+            let sqy        = uy * uy;
+            let sqz        = uz * uz;
+            let (sin, cos) = angle.sin_cos();
+            let one_m_cos  = _1 - cos;
+
+            Rotation3 {
+                submatrix: Matrix3::new(
+                            (sqx + (_1 - sqx) * cos),
+                            (ux * uy * one_m_cos - uz * sin),
+                            (ux * uz * one_m_cos + uy * sin),
+
+                            (ux * uy * one_m_cos + uz * sin),
+                            (sqy + (_1 - sqy) * cos),
+                            (uy * uz * one_m_cos - ux * sin),
+
+                            (ux * uz * one_m_cos - uy * sin),
+                            (uy * uz * one_m_cos + ux * sin),
+                            (sqz + (_1 - sqz) * cos))
+            }
+        }
+    }
+
+    /// Builds a rotation matrix from an orthogonal matrix.
+    ///
+    /// This is unsafe because the orthogonality of `matrix` is not checked.
+    pub unsafe fn new_with_matrix(matrix: Matrix3<N>) -> Rotation3<N> {
+        Rotation3 {
+            submatrix: matrix
+        }
+    }
+
+    /// Creates a new rotation from Euler angles.
+    ///
+    /// The primitive rotations are applied in order: 1 roll − 2 pitch − 3 yaw.
+    pub fn new_with_euler_angles(roll: N, pitch: N, yaw: N) -> Rotation3<N> {
+        let (sr, cr) = roll.sin_cos();
+        let (sp, cp) = pitch.sin_cos();
+        let (sy, cy) = yaw.sin_cos();
+
+        unsafe {
+            Rotation3::new_with_matrix(
+                Matrix3::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
+                )
+            )
+        }
+    }
+}
+
+impl<N: Clone + BaseFloat> Rotation3<N> {
+    /// Creates a rotation that corresponds to the local frame of an observer standing at the
+    /// origin and looking toward `dir`.
+    ///
+    /// It maps the view direction `dir` to the positive `z` axis.
+    ///
+    /// # Arguments
+    ///   * dir - The look direction, that is, direction the matrix `z` axis will be aligned with.
+    ///   * up - The vertical direction. The only requirement of this parameter is to not be
+    ///   collinear
+    ///   to `dir`. Non-collinearity is not checked.
+    #[inline]
+    pub fn new_observer_frame(dir: &Vector3<N>, up: &Vector3<N>) -> Rotation3<N> {
+        let zaxis = Norm::normalize(dir);
+        let xaxis = Norm::normalize(&Cross::cross(up, &zaxis));
+        let yaxis = Norm::normalize(&Cross::cross(&zaxis, &xaxis));
+
+        unsafe {
+            Rotation3::new_with_matrix(Matrix3::new(
+                xaxis.x.clone(), yaxis.x.clone(), zaxis.x.clone(),
+                xaxis.y.clone(), yaxis.y.clone(), zaxis.y.clone(),
+                xaxis.z        , yaxis.z        , zaxis.z))
+        }
+    }
+
+
+    /// Builds a right-handed look-at view matrix without translation.
+    ///
+    /// This conforms to the common notion of right handed look-at matrix from the computer
+    /// graphics community.
+    ///
+    /// # Arguments
+    ///   * eye - The eye position.
+    ///   * target - The target position.
+    ///   * 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(dir: &Vector3<N>, up: &Vector3<N>) -> Rotation3<N> {
+        Rotation3::new_observer_frame(&(-*dir), up).inverse().unwrap()
+    }
+
+    /// Builds a left-handed look-at view matrix without translation.
+    ///
+    /// This conforms to the common notion of left handed look-at matrix from the computer
+    /// graphics community.
+    ///
+    /// # Arguments
+    ///   * eye - The eye position.
+    ///   * target - The target position.
+    ///   * 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(dir: &Vector3<N>, up: &Vector3<N>) -> Rotation3<N> {
+        Rotation3::new_observer_frame(&(*dir), up).inverse().unwrap()
+    }
+}
+
+impl<N: Clone + BaseFloat + Cast<f64>>
+Rotation<Vector3<N>> for Rotation3<N> {
+    #[inline]
+    fn rotation(&self) -> Vector3<N> {
+        let angle = ((self.submatrix.m11 + self.submatrix.m22 + self.submatrix.m33 - ::one()) / Cast::from(2.0)).acos();
+
+        if angle != angle {
+            // FIXME: handle that correctly
+            ::zero()
+        }
+        else if ::is_zero(&angle) {
+            ::zero()
+        }
+        else {
+            let m32_m23 = self.submatrix.m32 - self.submatrix.m23;
+            let m13_m31 = self.submatrix.m13 - self.submatrix.m31;
+            let m21_m12 = self.submatrix.m21 - self.submatrix.m12;
+
+            let denom = (m32_m23 * m32_m23 + m13_m31 * m13_m31 + m21_m12 * m21_m12).sqrt();
+
+            if ::is_zero(&denom) {
+                // XXX: handle that properly
+                // panic!("Internal error: singularity.")
+                ::zero()
+            }
+            else {
+                let a_d = angle / denom;
+
+                Vector3::new(m32_m23 * a_d, m13_m31 * a_d, m21_m12 * a_d)
+            }
+        }
+    }
+
+    #[inline]
+    fn inverse_rotation(&self) -> Vector3<N> {
+        -self.rotation()
+    }
+
+
+    #[inline]
+    fn append_rotation_mut(&mut self, rotation: &Vector3<N>) {
+        *self = Rotation::append_rotation(self, rotation)
+    }
+
+    #[inline]
+    fn append_rotation(&self, axisangle: &Vector3<N>) -> Rotation3<N> {
+        Rotation3::new(axisangle.clone()) * *self
+    }
+
+    #[inline]
+    fn prepend_rotation_mut(&mut self, rotation: &Vector3<N>) {
+        *self = Rotation::prepend_rotation(self, rotation)
+    }
+
+    #[inline]
+    fn prepend_rotation(&self, axisangle: &Vector3<N>) -> Rotation3<N> {
+        *self * Rotation3::new(axisangle.clone())
+    }
+
+    #[inline]
+    fn set_rotation(&mut self, axisangle: Vector3<N>) {
+        *self = Rotation3::new(axisangle)
+    }
+}
+
+impl<N: BaseFloat> RotationTo for Rotation3<N> {
+    type AngleType = N;
+    type DeltaRotationType = Rotation3<N>;
+
+    #[inline]
+    fn angle_to(&self, other: &Self) -> N {
+        // FIXME: refactor to avoid the normalization of the rotation axisangle vector.
+        self.rotation_to(other).rotation().norm()
+    }
+
+    #[inline]
+    fn rotation_to(&self, other: &Self) -> Rotation3<N> {
+        *other * ::inverse(self).unwrap()
+    }
+}
+
+impl<N: Clone + Rand + BaseFloat> Rand for Rotation3<N> {
+    #[inline]
+    fn rand<R: Rng>(rng: &mut R) -> Rotation3<N> {
+        Rotation3::new(rng.gen())
+    }
+}
+
+impl<N: BaseFloat> AbsoluteRotate<Vector3<N>> for Rotation3<N> {
+    #[inline]
+    fn absolute_rotate(&self, v: &Vector3<N>) -> Vector3<N> {
+        Vector3::new(
+            ::abs(&self.submatrix.m11) * v.x + ::abs(&self.submatrix.m12) * v.y + ::abs(&self.submatrix.m13) * v.z,
+            ::abs(&self.submatrix.m21) * v.x + ::abs(&self.submatrix.m22) * v.y + ::abs(&self.submatrix.m23) * v.z,
+            ::abs(&self.submatrix.m31) * v.x + ::abs(&self.submatrix.m32) * v.y + ::abs(&self.submatrix.m33) * v.z)
+    }
+}
+
+#[cfg(feature="arbitrary")]
+impl<N: Arbitrary + Clone + BaseFloat> Arbitrary for Rotation3<N> {
+    fn arbitrary<G: Gen>(g: &mut G) -> Rotation3<N> {
+        Rotation3::new(Arbitrary::arbitrary(g))
+    }
+}
+
+
+/*
+ * Common implementations.
+ */
+
+submat_impl!(Rotation2, Matrix2);
+rotate_impl!(Rotation2, Vector2, Point2);
+transform_impl!(Rotation2, Vector2, Point2);
+dim_impl!(Rotation2, 2);
+rotation_mul_rotation_impl!(Rotation2);
+rotation_mul_vec_impl!(Rotation2, Vector2);
+vec_mul_rotation_impl!(Rotation2, Vector2);
+rotation_mul_point_impl!(Rotation2, Point2);
+point_mul_rotation_impl!(Rotation2, Point2);
+one_impl!(Rotation2);
+eye_impl!(Rotation2);
+rotation_matrix_impl!(Rotation2, Vector2, Vector1);
+col_impl!(Rotation2, Vector2);
+row_impl!(Rotation2, Vector2);
+index_impl!(Rotation2);
+absolute_impl!(Rotation2, Matrix2);
+to_homogeneous_impl!(Rotation2, Matrix3);
+inverse_impl!(Rotation2);
+transpose_impl!(Rotation2);
+approx_eq_impl!(Rotation2);
+diag_impl!(Rotation2, Vector2);
+rotation_display_impl!(Rotation2);
+
+submat_impl!(Rotation3, Matrix3);
+rotate_impl!(Rotation3, Vector3, Point3);
+transform_impl!(Rotation3, Vector3, Point3);
+dim_impl!(Rotation3, 3);
+rotation_mul_rotation_impl!(Rotation3);
+rotation_mul_vec_impl!(Rotation3, Vector3);
+vec_mul_rotation_impl!(Rotation3, Vector3);
+rotation_mul_point_impl!(Rotation3, Point3);
+point_mul_rotation_impl!(Rotation3, Point3);
+one_impl!(Rotation3);
+eye_impl!(Rotation3);
+rotation_matrix_impl!(Rotation3, Vector3, Vector3);
+col_impl!(Rotation3, Vector3);
+row_impl!(Rotation3, Vector3);
+index_impl!(Rotation3);
+absolute_impl!(Rotation3, Matrix3);
+to_homogeneous_impl!(Rotation3, Matrix4);
+inverse_impl!(Rotation3);
+transpose_impl!(Rotation3);
+approx_eq_impl!(Rotation3);
+diag_impl!(Rotation3, Vector3);
+rotation_display_impl!(Rotation3);

src/structs/rotation_macros.rs

@@ -1,12 +1,12 @@
 #![macro_use]
 
 macro_rules! submat_impl(
-    ($t: ident, $submat: ident) => (
+    ($t: ident, $submatrix: ident) => (
         impl<N> $t<N> {
             /// This rotation's underlying matrix.
             #[inline]
-            pub fn submat<'r>(&'r self) -> &'r $submat<N> {
+            pub fn submatrix<'r>(&'r self) -> &'r $submatrix<N> {
-                &self.submat
+                &self.submatrix
             }
         }
     )
@@ -21,7 +21,7 @@ macro_rules! rotate_impl(
             }
 
             #[inline]
-            fn inv_rotate(&self, v: &$tv<N>) -> $tv<N> {
+            fn inverse_rotate(&self, v: &$tv<N>) -> $tv<N> {
                 *v * *self
             }
         }
@@ -33,7 +33,7 @@ macro_rules! rotate_impl(
             }
 
             #[inline]
-            fn inv_rotate(&self, p: &$tp<N>) -> $tp<N> {
+            fn inverse_rotate(&self, p: &$tp<N>) -> $tp<N> {
                 *p * *self
             }
         }
@@ -49,8 +49,8 @@ macro_rules! transform_impl(
             }
 
             #[inline]
-            fn inv_transform(&self, v: &$tv<N>) -> $tv<N> {
+            fn inverse_transform(&self, v: &$tv<N>) -> $tv<N> {
-                self.inv_rotate(v)
+                self.inverse_rotate(v)
             }
         }
 
@@ -61,19 +61,19 @@ macro_rules! transform_impl(
             }
 
             #[inline]
-            fn inv_transform(&self, p: &$tp<N>) -> $tp<N> {
+            fn inverse_transform(&self, p: &$tp<N>) -> $tp<N> {
-                self.inv_rotate(p)
+                self.inverse_rotate(p)
             }
         }
     )
 );
 
 macro_rules! dim_impl(
-    ($t: ident, $dim: expr) => (
+    ($t: ident, $dimension: expr) => (
-        impl<N> Dim for $t<N> {
+        impl<N> Dimension for $t<N> {
             #[inline]
-            fn dim(_: Option<$t<N>>) -> usize {
+            fn dimension(_: Option<$t<N>>) -> usize {
-                $dim
+                $dimension
             }
         }
     )
@@ -85,7 +85,7 @@ macro_rules! rotation_matrix_impl(
             type Output = $t<N>;
 
             #[inline]
-            fn to_rot_mat(&self) -> $t<N> {
+            fn to_rotation_matrix(&self) -> $t<N> {
                 self.clone()
             }
         }
@@ -97,7 +97,7 @@ macro_rules! one_impl(
         impl<N: BaseNum> One for $t<N> {
             #[inline]
             fn one() -> $t<N> {
-                $t { submat: ::one() }
+                $t { submatrix: ::one() }
             }
         }
     )
@@ -107,9 +107,9 @@ macro_rules! eye_impl(
     ($t: ident) => (
         impl<N: BaseNum> Eye for $t<N> {
             #[inline]
-            fn new_identity(dim: usize) -> $t<N> {
+            fn new_identity(dimension: usize) -> $t<N> {
-                if dim != ::dim::<$t<N>>() {
+                if dimension != ::dimension::<$t<N>>() {
-                    panic!("Dimension mismatch: should be {}, got {}.", ::dim::<$t<N>>(), dim);
+                    panic!("Dimension mismatch: should be {}, got {}.", ::dimension::<$t<N>>(), dimension);
                 }
                 else {
                     ::one()
@@ -121,90 +121,90 @@ macro_rules! eye_impl(
 
 macro_rules! diag_impl(
     ($t: ident, $tv: ident) => (
-        impl<N: Copy + Zero> Diag<$tv<N>> for $t<N> {
+        impl<N: Copy + Zero> Diagonal<$tv<N>> for $t<N> {
             #[inline]
-            fn from_diag(diag: &$tv<N>) -> $t<N> {
+            fn from_diagonal(diagonal: &$tv<N>) -> $t<N> {
-                $t { submat: Diag::from_diag(diag) }
+                $t { submatrix: Diagonal::from_diagonal(diagonal) }
             }
 
             #[inline]
-            fn diag(&self) -> $tv<N> {
+            fn diagonal(&self) -> $tv<N> {
-                self.submat.diag()
+                self.submatrix.diagonal()
             }
         }
     )
 );
 
-macro_rules! rot_mul_rot_impl(
+macro_rules! rotation_mul_rotation_impl(
     ($t: ident) => (
         impl<N: BaseNum> Mul<$t<N>> for $t<N> {
             type Output = $t<N>;
 
             #[inline]
             fn mul(self, right: $t<N>) -> $t<N> {
-                $t { submat: self.submat * right.submat }
+                $t { submatrix: self.submatrix * right.submatrix }
             }
         }
 
         impl<N: Copy + BaseNum> MulAssign<$t<N>> for $t<N> {
             #[inline]
             fn mul_assign(&mut self, right: $t<N>) {
-                self.submat *= right.submat
+                self.submatrix *= right.submatrix
             }
         }
     )
 );
 
-macro_rules! rot_mul_vec_impl(
+macro_rules! rotation_mul_vec_impl(
     ($t: ident, $tv: ident) => (
         impl<N: BaseNum> Mul<$tv<N>> for $t<N> {
             type Output = $tv<N>;
 
             #[inline]
             fn mul(self, right: $tv<N>) -> $tv<N> {
-                self.submat * right
+                self.submatrix * right
             }
         }
     )
 );
 
-macro_rules! rot_mul_pnt_impl(
+macro_rules! rotation_mul_point_impl(
     ($t: ident, $tv: ident) => (
-        rot_mul_vec_impl!($t, $tv);
+        rotation_mul_vec_impl!($t, $tv);
     )
 );
 
-macro_rules! vec_mul_rot_impl(
+macro_rules! vec_mul_rotation_impl(
     ($t: ident, $tv: ident) => (
         impl<N: BaseNum> Mul<$t<N>> for $tv<N> {
             type Output = $tv<N>;
 
             #[inline]
             fn mul(self, right: $t<N>) -> $tv<N> {
-                self * right.submat
+                self * right.submatrix
             }
         }
 
         impl<N: Copy + BaseNum> MulAssign<$t<N>> for $tv<N> {
             #[inline]
             fn mul_assign(&mut self, right: $t<N>) {
-                *self *= right.submat
+                *self *= right.submatrix
             }
         }
     )
 );
 
-macro_rules! pnt_mul_rot_impl(
+macro_rules! point_mul_rotation_impl(
     ($t: ident, $tv: ident) => (
-        vec_mul_rot_impl!($t, $tv);
+        vec_mul_rotation_impl!($t, $tv);
     )
 );
 
-macro_rules! inv_impl(
+macro_rules! inverse_impl(
     ($t: ident) => (
-        impl<N: Copy> Inv for $t<N> {
+        impl<N: Copy> Inverse for $t<N> {
             #[inline]
-            fn inv_mut(&mut self) -> bool {
+            fn inverse_mut(&mut self) -> bool {
                 self.transpose_mut();
 
                 // always succeed
@@ -212,7 +212,7 @@ macro_rules! inv_impl(
             }
 
             #[inline]
-            fn inv(&self) -> Option<$t<N>> {
+            fn inverse(&self) -> Option<$t<N>> {
                 // always succeed
                 Some(self.transpose())
             }
@@ -225,12 +225,12 @@ macro_rules! transpose_impl(
         impl<N: Copy> Transpose for $t<N> {
             #[inline]
             fn transpose(&self) -> $t<N> {
-                $t { submat: Transpose::transpose(&self.submat) }
+                $t { submatrix: Transpose::transpose(&self.submatrix) }
             }
 
             #[inline]
             fn transpose_mut(&mut self) {
-                self.submat.transpose_mut()
+                self.submatrix.transpose_mut()
             }
         }
     )
@@ -241,16 +241,16 @@ macro_rules! row_impl(
         impl<N: Copy + Zero> Row<$tv<N>> for $t<N> {
             #[inline]
             fn nrows(&self) -> usize {
-                self.submat.nrows()
+                self.submatrix.nrows()
             }
             #[inline]
             fn row(&self, i: usize) -> $tv<N> {
-                self.submat.row(i)
+                self.submatrix.row(i)
             }
 
             #[inline]
             fn set_row(&mut self, i: usize, row: $tv<N>) {
-                self.submat.set_row(i, row);
+                self.submatrix.set_row(i, row);
             }
         }
     )
@@ -258,19 +258,19 @@ macro_rules! row_impl(
 
 macro_rules! col_impl(
     ($t: ident, $tv: ident) => (
-        impl<N: Copy + Zero> Col<$tv<N>> for $t<N> {
+        impl<N: Copy + Zero> Column<$tv<N>> for $t<N> {
             #[inline]
             fn ncols(&self) -> usize {
-                self.submat.ncols()
+                self.submatrix.ncols()
             }
             #[inline]
-            fn col(&self, i: usize) -> $tv<N> {
+            fn column(&self, i: usize) -> $tv<N> {
-                self.submat.col(i)
+                self.submatrix.column(i)
             }
 
             #[inline]
-            fn set_col(&mut self, i: usize, col: $tv<N>) {
+            fn set_col(&mut self, i: usize, column: $tv<N>) {
-                self.submat.set_col(i, col);
+                self.submatrix.set_col(i, column);
             }
         }
     )
@@ -282,7 +282,7 @@ macro_rules! index_impl(
             type Output = N;
 
             fn index(&self, i: (usize, usize)) -> &N {
-                &self.submat[i]
+                &self.submatrix[i]
             }
         }
     )
@@ -293,7 +293,7 @@ macro_rules! to_homogeneous_impl(
         impl<N: BaseNum> ToHomogeneous<$tm<N>> for $t<N> {
             #[inline]
             fn to_homogeneous(&self) -> $tm<N> {
-                self.submat.to_homogeneous()
+                self.submatrix.to_homogeneous()
             }
         }
     )
@@ -314,17 +314,17 @@ macro_rules! approx_eq_impl(
 
             #[inline]
             fn approx_eq(&self, other: &$t<N>) -> bool {
-                ApproxEq::approx_eq(&self.submat, &other.submat)
+                ApproxEq::approx_eq(&self.submatrix, &other.submatrix)
             }
 
             #[inline]
             fn approx_eq_eps(&self, other: &$t<N>, epsilon: &N) -> bool {
-                ApproxEq::approx_eq_eps(&self.submat, &other.submat, epsilon)
+                ApproxEq::approx_eq_eps(&self.submatrix, &other.submatrix, epsilon)
             }
 
             #[inline]
             fn approx_eq_ulps(&self, other: &$t<N>, ulps: u32) -> bool {
-                ApproxEq::approx_eq_ulps(&self.submat, &other.submat, ulps)
+                ApproxEq::approx_eq_ulps(&self.submatrix, &other.submatrix, ulps)
             }
         }
     )
@@ -335,20 +335,20 @@ macro_rules! absolute_impl(
         impl<N: Absolute<N>> Absolute<$tm<N>> for $t<N> {
             #[inline]
             fn abs(m: &$t<N>) -> $tm<N> {
-                Absolute::abs(&m.submat)
+                Absolute::abs(&m.submatrix)
             }
         }
     )
 );
 
-macro_rules! rot_display_impl(
+macro_rules! rotation_display_impl(
     ($t: ident) => (
         impl<N: fmt::Display + BaseFloat> fmt::Display for $t<N> {
             fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
                 let precision = f.precision().unwrap_or(3);
 
                 try!(writeln!(f, "Rotation matrix {{"));
-                try!(write!(f, "{:.*}", precision, self.submat));
+                try!(write!(f, "{:.*}", precision, self.submatrix));
                 writeln!(f, "}}")
             }
         }

src/structs/sim.rs

@@ -1,86 +0,0 @@
-use std::fmt;
-use std::ops::{Mul, Neg, MulAssign};
-
-use rand::{Rand, Rng};
-use num::One;
-use structs::mat::{Mat3, Mat4};
-use traits::structure::{Dim, Col, BaseFloat, BaseNum};
-use traits::operations::{Inv, ApproxEq};
-use traits::geometry::{Rotation, Transform, Transformation, Translation, ToHomogeneous};
-
-use structs::vec::{Vec1, Vec2, Vec3};
-use structs::pnt::{Pnt2, Pnt3};
-use structs::rot::{Rot2, Rot3};
-use structs::iso::{Iso2, Iso3};
-
-#[cfg(feature="arbitrary")]
-use quickcheck::{Arbitrary, Gen};
-
-// FIXME: the name is not explicit at all but coherent with the other tree-letters names…
-/// A two-dimensional similarity transformation.
-///
-/// This is a composition of a uniform scale, followed by a rotation, followed by a translation.
-/// Vectors `Vec2` are not affected by the translational component of this transformation while
-/// points `Pnt2` are.
-/// Similarity transformations conserve angles. Distances are multiplied by some constant (the
-/// scale factor). The scale factor cannot be zero.
-#[repr(C)]
-#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Debug, Copy)]
-pub struct Sim2<N> {
-    /// The uniform scale applicable by this similarity transformation.
-    scale: N,
-    /// The isometry applicable by this similarity transformation.
-    pub isometry: Iso2<N>
-}
-
-/// A three-dimensional similarity transformation.
-///
-/// This is a composition of a scale, followed by a rotation, followed by a translation.
-/// Vectors `Vec3` are not affected by the translational component of this transformation while
-/// points `Pnt3` are.
-/// Similarity transformations conserve angles. Distances are multiplied by some constant (the
-/// scale factor). The scale factor cannot be zero.
-#[repr(C)]
-#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Debug, Copy)]
-pub struct Sim3<N> {
-    /// The uniform scale applicable by this similarity transformation.
-    scale: N,
-    /// The isometry applicable by this similarity transformation.
-    pub isometry: Iso3<N>
-}
-
-sim_impl!(Sim2, Iso2, Rot2, Vec2, Vec1);
-dim_impl!(Sim2, 2);
-sim_scale_impl!(Sim2);
-sim_one_impl!(Sim2);
-sim_mul_sim_impl!(Sim2);
-sim_mul_iso_impl!(Sim2, Iso2);
-sim_mul_rot_impl!(Sim2, Rot2);
-sim_mul_pnt_vec_impl!(Sim2, Pnt2);
-sim_mul_pnt_vec_impl!(Sim2, Vec2);
-transformation_impl!(Sim2);
-sim_transform_impl!(Sim2, Pnt2);
-sim_inv_impl!(Sim2);
-sim_to_homogeneous_impl!(Sim2, Mat3);
-sim_approx_eq_impl!(Sim2);
-sim_rand_impl!(Sim2);
-sim_arbitrary_impl!(Sim2);
-sim_display_impl!(Sim2);
-
-sim_impl!(Sim3, Iso3, Rot3, Vec3, Vec3);
-dim_impl!(Sim3, 3);
-sim_scale_impl!(Sim3);
-sim_one_impl!(Sim3);
-sim_mul_sim_impl!(Sim3);
-sim_mul_iso_impl!(Sim3, Iso3);
-sim_mul_rot_impl!(Sim3, Rot3);
-sim_mul_pnt_vec_impl!(Sim3, Pnt3);
-sim_mul_pnt_vec_impl!(Sim3, Vec3);
-transformation_impl!(Sim3);
-sim_transform_impl!(Sim3, Pnt3);
-sim_inv_impl!(Sim3);
-sim_to_homogeneous_impl!(Sim3, Mat4);
-sim_approx_eq_impl!(Sim3);
-sim_rand_impl!(Sim3);
-sim_arbitrary_impl!(Sim3);
-sim_display_impl!(Sim3);

src/structs/similarity.rs

@@ -0,0 +1,86 @@
+use std::fmt;
+use std::ops::{Mul, Neg, MulAssign};
+
+use rand::{Rand, Rng};
+use num::One;
+use structs::matrix::{Matrix3, Matrix4};
+use traits::structure::{Dimension, Column, BaseFloat, BaseNum};
+use traits::operations::{Inverse, ApproxEq};
+use traits::geometry::{Rotation, Transform, Transformation, Translation, ToHomogeneous};
+
+use structs::vector::{Vector1, Vector2, Vector3};
+use structs::point::{Point2, Point3};
+use structs::rotation::{Rotation2, Rotation3};
+use structs::isometry::{Isometry2, Isometry3};
+
+#[cfg(feature="arbitrary")]
+use quickcheck::{Arbitrary, Gen};
+
+// FIXME: the name is not explicit at all but coherent with the other tree-letters names…
+/// A two-dimensional similarity transformation.
+///
+/// This is a composition of a uniform scale, followed by a rotation, followed by a translation.
+/// Vectors `Vector2` are not affected by the translational component of this transformation while
+/// points `Point2` are.
+/// Similarity transformations conserve angles. Distances are multiplied by some constant (the
+/// scale factor). The scale factor cannot be zero.
+#[repr(C)]
+#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Debug, Copy)]
+pub struct Similarity2<N> {
+    /// The uniform scale applicable by this similarity transformation.
+    scale: N,
+    /// The isometry applicable by this similarity transformation.
+    pub isometry: Isometry2<N>
+}
+
+/// A three-dimensional similarity transformation.
+///
+/// This is a composition of a scale, followed by a rotation, followed by a translation.
+/// Vectors `Vector3` are not affected by the translational component of this transformation while
+/// points `Point3` are.
+/// Similarity transformations conserve angles. Distances are multiplied by some constant (the
+/// scale factor). The scale factor cannot be zero.
+#[repr(C)]
+#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Debug, Copy)]
+pub struct Similarity3<N> {
+    /// The uniform scale applicable by this similarity transformation.
+    scale: N,
+    /// The isometry applicable by this similarity transformation.
+    pub isometry: Isometry3<N>
+}
+
+sim_impl!(Similarity2, Isometry2, Rotation2, Vector2, Vector1);
+dim_impl!(Similarity2, 2);
+sim_scale_impl!(Similarity2);
+sim_one_impl!(Similarity2);
+sim_mul_sim_impl!(Similarity2);
+sim_mul_isometry_impl!(Similarity2, Isometry2);
+sim_mul_rotation_impl!(Similarity2, Rotation2);
+sim_mul_point_vec_impl!(Similarity2, Point2);
+sim_mul_point_vec_impl!(Similarity2, Vector2);
+transformation_impl!(Similarity2);
+sim_transform_impl!(Similarity2, Point2);
+sim_inverse_impl!(Similarity2);
+sim_to_homogeneous_impl!(Similarity2, Matrix3);
+sim_approx_eq_impl!(Similarity2);
+sim_rand_impl!(Similarity2);
+sim_arbitrary_impl!(Similarity2);
+sim_display_impl!(Similarity2);
+
+sim_impl!(Similarity3, Isometry3, Rotation3, Vector3, Vector3);
+dim_impl!(Similarity3, 3);
+sim_scale_impl!(Similarity3);
+sim_one_impl!(Similarity3);
+sim_mul_sim_impl!(Similarity3);
+sim_mul_isometry_impl!(Similarity3, Isometry3);
+sim_mul_rotation_impl!(Similarity3, Rotation3);
+sim_mul_point_vec_impl!(Similarity3, Point3);
+sim_mul_point_vec_impl!(Similarity3, Vector3);
+transformation_impl!(Similarity3);
+sim_transform_impl!(Similarity3, Point3);
+sim_inverse_impl!(Similarity3);
+sim_to_homogeneous_impl!(Similarity3, Matrix4);
+sim_approx_eq_impl!(Similarity3);
+sim_rand_impl!(Similarity3);
+sim_arbitrary_impl!(Similarity3);
+sim_display_impl!(Similarity3);

src/structs/similarity_macros.rs

@@ -1,18 +1,18 @@
 #![macro_use]
 
 macro_rules! sim_impl(
-    ($t: ident, $iso: ident, $rotmat: ident, $subvec: ident, $subrotvec: ident) => (
+    ($t: ident, $isometry: ident, $rotation_matrix: ident, $subvector: ident, $subrotvector: ident) => (
         impl<N: BaseFloat> $t<N> {
             /// Creates a new similarity transformation from a vector, an axis-angle rotation, and a scale factor.
             ///
             /// The scale factor may be negative but not zero.
             #[inline]
-            pub fn new(translation: $subvec<N>, rotation: $subrotvec<N>, scale: N) -> $t<N> {
+            pub fn new(translation: $subvector<N>, rotation: $subrotvector<N>, scale: N) -> $t<N> {
                 assert!(!scale.is_zero(), "A similarity transformation scale factor cannot be zero.");
 
                 $t {
                     scale:    scale,
-                    isometry: $iso::new(translation, rotation)
+                    isometry: $isometry::new(translation, rotation)
                 }
             }
 
@@ -20,12 +20,12 @@ macro_rules! sim_impl(
             ///
             /// The scale factor may be negative but not zero.
             #[inline]
-            pub fn new_with_rotmat(translation: $subvec<N>, rotation: $rotmat<N>, scale: N) -> $t<N> {
+            pub fn new_with_rotation_matrix(translation: $subvector<N>, rotation: $rotation_matrix<N>, scale: N) -> $t<N> {
                 assert!(!scale.is_zero(), "A similarity transformation scale factor cannot be zero.");
 
                 $t {
                     scale:    scale,
-                    isometry: $iso::new_with_rotmat(translation, rotation)
+                    isometry: $isometry::new_with_rotation_matrix(translation, rotation)
                 }
             }
 
@@ -33,7 +33,7 @@ macro_rules! sim_impl(
             ///
             /// The scale factor may be negative but not zero.
             #[inline]
-            pub fn new_with_iso(isometry: $iso<N>, scale: N) -> $t<N> {
+            pub fn new_with_isometry(isometry: $isometry<N>, scale: N) -> $t<N> {
                 assert!(!scale.is_zero(), "A similarity transformation scale factor cannot be zero.");
 
                 $t {
@@ -56,7 +56,7 @@ macro_rules! sim_scale_impl(
 
             /// The inverse scale factor of this similarity transformation.
             #[inline]
-            pub fn inv_scale(&self) -> N {
+            pub fn inverse_scale(&self) -> N {
                 ::one::<N>() / self.scale
             }
 
@@ -72,7 +72,7 @@ macro_rules! sim_scale_impl(
             #[inline]
             pub fn append_scale(&self, s: &N) -> $t<N> {
                 assert!(!s.is_zero(), "Cannot append a zero scale to a similarity transformation.");
-                $t::new_with_rotmat(self.isometry.translation * *s, self.isometry.rotation, self.scale * *s)
+                $t::new_with_rotation_matrix(self.isometry.translation * *s, self.isometry.rotation, self.scale * *s)
             }
 
             /// Prepends in-place a scale to this similarity transformation.
@@ -86,7 +86,7 @@ macro_rules! sim_scale_impl(
             #[inline]
             pub fn prepend_scale(&self, s: &N) -> $t<N> {
                 assert!(!s.is_zero(), "A similarity transformation scale must not be zero.");
-                $t::new_with_iso(self.isometry, self.scale * *s)
+                $t::new_with_isometry(self.isometry, self.scale * *s)
             }
 
             /// Sets the scale of this similarity transformation.
@@ -104,7 +104,7 @@ macro_rules! sim_one_impl(
         impl<N: BaseFloat> One for $t<N> {
             #[inline]
             fn one() -> $t<N> {
-                $t::new_with_iso(::one(), ::one())
+                $t::new_with_isometry(::one(), ::one())
             }
         }
     )
@@ -117,7 +117,7 @@ macro_rules! sim_mul_sim_impl(
 
             #[inline]
             fn mul(self, right: $t<N>) -> $t<N> {
-                $t::new_with_rotmat(
+                $t::new_with_rotation_matrix(
                     self.isometry.translation + self.isometry.rotation * (right.isometry.translation * self.scale),
                     self.isometry.rotation * right.isometry.rotation,
                     self.scale * right.scale)
@@ -135,14 +135,14 @@ macro_rules! sim_mul_sim_impl(
     )
 );
 
-macro_rules! sim_mul_iso_impl(
+macro_rules! sim_mul_isometry_impl(
     ($t: ident, $ti: ident) => (
         impl<N: BaseFloat> Mul<$ti<N>> for $t<N> {
             type Output = $t<N>;
 
             #[inline]
             fn mul(self, right: $ti<N>) -> $t<N> {
-                $t::new_with_rotmat(
+                $t::new_with_rotation_matrix(
                     self.isometry.translation + self.isometry.rotation * (right.translation * self.scale),
                     self.isometry.rotation * right.rotation,
                     self.scale)
@@ -162,7 +162,7 @@ macro_rules! sim_mul_iso_impl(
 
             #[inline]
             fn mul(self, right: $t<N>) -> $t<N> {
-                $t::new_with_rotmat(
+                $t::new_with_rotation_matrix(
                     self.translation + self.rotation * right.isometry.translation,
                     self.rotation * right.isometry.rotation,
                     right.scale)
@@ -171,14 +171,14 @@ macro_rules! sim_mul_iso_impl(
     )
 );
 
-macro_rules! sim_mul_rot_impl(
+macro_rules! sim_mul_rotation_impl(
     ($t: ident, $tr: ident) => (
         impl<N: BaseFloat> Mul<$tr<N>> for $t<N> {
             type Output = $t<N>;
 
             #[inline]
             fn mul(self, right: $tr<N>) -> $t<N> {
-                $t::new_with_rotmat(
+                $t::new_with_rotation_matrix(
                     self.isometry.translation,
                     self.isometry.rotation * right,
                     self.scale)
@@ -197,7 +197,7 @@ macro_rules! sim_mul_rot_impl(
 
             #[inline]
             fn mul(self, right: $t<N>) -> $t<N> {
-                $t::new_with_rotmat(
+                $t::new_with_rotation_matrix(
                     self * right.isometry.translation,
                     self * right.isometry.rotation,
                     right.scale)
@@ -206,7 +206,7 @@ macro_rules! sim_mul_rot_impl(
     )
 );
 
-macro_rules! sim_mul_pnt_vec_impl(
+macro_rules! sim_mul_point_vec_impl(
     ($t: ident, $tv: ident) => (
         impl<N: BaseNum> Mul<$tv<N>> for $t<N> {
             type Output = $tv<N>;
@@ -232,20 +232,20 @@ macro_rules! sim_transform_impl(
             }
 
             #[inline]
-            fn inv_transform(&self, p: &$tp<N>) -> $tp<N> {
+            fn inverse_transform(&self, p: &$tp<N>) -> $tp<N> {
-                self.isometry.inv_transform(p) / self.scale
+                self.isometry.inverse_transform(p) / self.scale
             }
         }
     )
 );
 
-macro_rules! sim_inv_impl(
+macro_rules! sim_inverse_impl(
     ($t: ident) => (
-        impl<N: BaseNum + Neg<Output = N>> Inv for $t<N> {
+        impl<N: BaseNum + Neg<Output = N>> Inverse for $t<N> {
             #[inline]
-            fn inv_mut(&mut self) -> bool {
+            fn inverse_mut(&mut self) -> bool {
                 self.scale = ::one::<N>() / self.scale;
-                self.isometry.inv_mut();
+                self.isometry.inverse_mut();
                 // We multiply (instead of dividing) by self.scale because it has already been
                 // inverted.
                 self.isometry.translation = self.isometry.translation * self.scale;
@@ -255,9 +255,9 @@ macro_rules! sim_inv_impl(
             }
 
             #[inline]
-            fn inv(&self) -> Option<$t<N>> {
+            fn inverse(&self) -> Option<$t<N>> {
                 let mut res = *self;
-                res.inv_mut();
+                res.inverse_mut();
 
                 // Always succeed.
                 Some(res)
@@ -270,12 +270,12 @@ macro_rules! sim_to_homogeneous_impl(
     ($t: ident, $th: ident) => (
         impl<N: BaseNum> ToHomogeneous<$th<N>> for $t<N> {
             fn to_homogeneous(&self) -> $th<N> {
-                let mut res = (*self.isometry.rotation.submat() * self.scale).to_homogeneous();
+                let mut res = (*self.isometry.rotation.submatrix() * self.scale).to_homogeneous();
 
                 // copy the translation
-                let dim = Dim::dim(None::<$th<N>>);
+                let dimension = Dimension::dimension(None::<$th<N>>);
 
-                res.set_col(dim - 1, self.isometry.translation.as_pnt().to_homogeneous().to_vec());
+                res.set_col(dimension - 1, self.isometry.translation.as_point().to_homogeneous().to_vector());
 
                 res
             }
@@ -321,7 +321,7 @@ macro_rules! sim_rand_impl(
                     scale = rng.gen();
                 }
 
-                $t::new_with_iso(rng.gen(), scale)
+                $t::new_with_isometry(rng.gen(), scale)
             }
         }
     )
@@ -332,7 +332,7 @@ macro_rules! sim_arbitrary_impl(
         #[cfg(feature="arbitrary")]
         impl<N: Arbitrary + BaseFloat> Arbitrary for $t<N> {
             fn arbitrary<G: Gen>(g: &mut G) -> $t<N> {
-                $t::new_with_iso(
+                $t::new_with_isometry(
                     Arbitrary::arbitrary(g),
                     Arbitrary::arbitrary(g)
                 )
@@ -351,13 +351,13 @@ macro_rules! sim_display_impl(
                     try!(writeln!(f, "... scale factor: {:.*}", precision, self.scale));
                     try!(writeln!(f, "... translation: {:.*}", precision, self.isometry.translation));
                     try!(writeln!(f, "... rotation matrix:"));
-                    try!(write!(f, "{:.*}", precision, *self.isometry.rotation.submat()));
+                    try!(write!(f, "{:.*}", precision, *self.isometry.rotation.submatrix()));
                 }
                 else {
                     try!(writeln!(f, "... scale factor: {}", self.scale));
                     try!(writeln!(f, "... translation: {}", self.isometry.translation));
                     try!(writeln!(f, "... rotation matrix:"));
-                    try!(write!(f, "{}", *self.isometry.rotation.submat()));
+                    try!(write!(f, "{}", *self.isometry.rotation.submatrix()));
                 }
 
                 writeln!(f, "}}")

src/structs/spec/vec.rs

@@ -1,307 +0,0 @@
-use std::ops::{Sub, Mul, Neg};
-use num::{Zero, One};
-use traits::structure::{Cast, Row, Basis, BaseFloat};
-use traits::geometry::{Norm, Cross, CrossMatrix, RotationTo, UniformSphereSample};
-use structs::vec::{Vec1, Vec2, Vec3, Vec4};
-use structs::mat::Mat3;
-use structs::rot::{Rot2, Rot3};
-
-impl<N: BaseFloat> RotationTo for Vec2<N> {
-    type AngleType = N;
-    type DeltaRotationType = Rot2<N>;
-
-    #[inline]
-    fn angle_to(&self, other: &Self) -> N {
-        ::cross(self, other).x.atan2(::dot(self, other))
-    }
-
-    #[inline]
-    fn rotation_to(&self, other: &Self) -> Rot2<N> {
-        Rot2::new(Vec1::new(self.angle_to(other)))
-    }
-}
-
-impl<N: BaseFloat> RotationTo for Vec3<N> {
-    type AngleType = N;
-    type DeltaRotationType = Rot3<N>;
-
-    #[inline]
-    fn angle_to(&self, other: &Self) -> N {
-        ::cross(self, other).norm().atan2(::dot(self, other))
-    }
-
-    #[inline]
-    fn rotation_to(&self, other: &Self) -> Rot3<N> {
-        let mut axis = ::cross(self, other);
-        let norm = axis.normalize_mut();
-
-        if ::is_zero(&norm) {
-            ::one()
-        }
-        else {
-            let axis_angle = axis * norm.atan2(::dot(self, other));
-
-            Rot3::new(axis_angle)
-        }
-    }
-}
-
-impl<N: Copy + Mul<N, Output = N> + Sub<N, Output = N>> Cross for Vec2<N> {
-    type CrossProductType = Vec1<N>;
-
-    #[inline]
-    fn cross(&self, other: &Vec2<N>) -> Vec1<N> {
-        Vec1::new(self.x * other.y - self.y * other.x)
-    }
-}
-
-// FIXME: instead of returning a Vec2, define a Mat2x1 matrix?
-impl<N: Neg<Output = N> + Copy> CrossMatrix<Vec2<N>> for Vec2<N> {
-    #[inline]
-    fn cross_matrix(&self) -> Vec2<N> {
-        Vec2::new(-self.y, self.x)
-    }
-}
-
-impl<N: Copy + Mul<N, Output = N> + Sub<N, Output = N>> Cross for Vec3<N> {
-    type CrossProductType = Vec3<N>;
-
-    #[inline]
-    fn cross(&self, other: &Vec3<N>) -> Vec3<N> {
-        Vec3::new(
-            self.y * other.z - self.z * other.y,
-            self.z * other.x - self.x * other.z,
-            self.x * other.y - self.y * other.x
-        )
-    }
-}
-
-impl<N: Neg<Output = N> + Zero + Copy> CrossMatrix<Mat3<N>> for Vec3<N> {
-    #[inline]
-    fn cross_matrix(&self) -> Mat3<N> {
-        Mat3::new(
-            ::zero(), -self.z,  self.y,
-            self.z,   ::zero(), -self.x,
-            -self.y,  self.x,   ::zero()
-        )
-    }
-}
-
-// FIXME: implement this for all other vectors
-impl<N: Copy> Row<Vec1<N>> for Vec2<N> {
-    #[inline]
-    fn nrows(&self) -> usize {
-        2
-    }
-
-    #[inline]
-    fn row(&self, i: usize) -> Vec1<N> {
-        match i {
-            0 => Vec1::new(self.x),
-            1 => Vec1::new(self.y),
-            _ => panic!(format!("Index out of range: 2d vectors do not have {} rows. ", i))
-        }
-    }
-
-    #[inline]
-    fn set_row(&mut self, i: usize, r: Vec1<N>) {
-        match i {
-            0 => self.x = r.x,
-            1 => self.y = r.x,
-            _ => panic!(format!("Index out of range: 2d vectors do not have {} rows.", i))
-
-        }
-    }
-}
-
-impl<N: One> Basis for Vec1<N> {
-    #[inline(always)]
-    fn canonical_basis<F: FnMut(Vec1<N>) -> bool>(mut f: F) {
-        f(Vec1::new(::one()));
-    }
-
-    #[inline(always)]
-    fn orthonormal_subspace_basis<F: FnMut(Vec1<N>) -> bool>(_: &Vec1<N>, _: F) { }
-
-    #[inline]
-    fn canonical_basis_element(i: usize) -> Option<Vec1<N>> {
-        if i == 0 {
-            Some(Vec1::new(::one()))
-        }
-        else {
-            None
-        }
-    }
-}
-
-impl<N: Copy + One + Zero + Neg<Output = N>> Basis for Vec2<N> {
-    #[inline(always)]
-    fn canonical_basis<F: FnMut(Vec2<N>) -> bool>(mut f: F) {
-        if !f(Vec2::new(::one(), ::zero())) { return };
-        f(Vec2::new(::zero(), ::one()));
-    }
-
-    #[inline]
-    fn orthonormal_subspace_basis<F: FnMut(Vec2<N>) -> bool>(n: &Vec2<N>, mut f: F) {
-        f(Vec2::new(-n.y, n.x));
-    }
-
-    #[inline]
-    fn canonical_basis_element(i: usize) -> Option<Vec2<N>> {
-        if i == 0 {
-            Some(Vec2::new(::one(), ::zero()))
-        }
-        else if i == 1 {
-            Some(Vec2::new(::zero(), ::one()))
-        }
-        else {
-            None
-        }
-    }
-}
-
-impl<N: BaseFloat> Basis for Vec3<N> {
-    #[inline(always)]
-    fn canonical_basis<F: FnMut(Vec3<N>) -> bool>(mut f: F) {
-        if !f(Vec3::new(::one(), ::zero(), ::zero())) { return };
-        if !f(Vec3::new(::zero(), ::one(), ::zero())) { return };
-        f(Vec3::new(::zero(), ::zero(), ::one()));
-    }
-
-    #[inline(always)]
-    fn orthonormal_subspace_basis<F: FnMut(Vec3<N>) -> bool>(n: &Vec3<N>, mut f: F) {
-        let a = 
-            if n.x.abs() > n.y.abs() {
-                Norm::normalize(&Vec3::new(n.z, ::zero(), -n.x))
-            }
-            else {
-                Norm::normalize(&Vec3::new(::zero(), -n.z, n.y))
-            };
-
-        if !f(Cross::cross(&a, n)) { return };
-        f(a);
-    }
-
-    #[inline]
-    fn canonical_basis_element(i: usize) -> Option<Vec3<N>> {
-        if i == 0 {
-            Some(Vec3::new(::one(), ::zero(), ::zero()))
-        }
-        else if i == 1 {
-            Some(Vec3::new(::zero(), ::one(), ::zero()))
-        }
-        else if i == 2 {
-            Some(Vec3::new(::zero(), ::zero(), ::one()))
-        }
-        else {
-            None
-        }
-    }
-}
-
-// FIXME: this bad: this fixes definitly the number of samples…
-static SAMPLES_2_F64: [Vec2<f64>; 21] = [
-    Vec2 { x: 1.0,         y: 0.0         },
-    Vec2 { x: 0.95557281,  y: 0.29475517  },
-    Vec2 { x: 0.82623877,  y: 0.56332006  },
-    Vec2 { x: 0.6234898,   y: 0.78183148  },
-    Vec2 { x: 0.36534102,  y: 0.93087375  },
-    Vec2 { x: 0.07473009,  y: 0.9972038   },
-    Vec2 { x: -0.22252093, y: 0.97492791  },
-    Vec2 { x: -0.5,        y: 0.8660254   },
-    Vec2 { x: -0.73305187, y: 0.68017274  },
-    Vec2 { x: -0.90096887, y: 0.43388374  },
-    Vec2 { x: -0.98883083, y: 0.14904227  },
-    Vec2 { x: -0.98883083, y: -0.14904227 },
-    Vec2 { x: -0.90096887, y: -0.43388374 },
-    Vec2 { x: -0.73305187, y: -0.68017274 },
-    Vec2 { x: -0.5,        y: -0.8660254  },
-    Vec2 { x: -0.22252093, y: -0.97492791 },
-    Vec2 { x: 0.07473009,  y: -0.9972038  },
-    Vec2 { x: 0.36534102,  y: -0.93087375 },
-    Vec2 { x: 0.6234898,   y: -0.78183148 },
-    Vec2 { x: 0.82623877,  y: -0.56332006 },
-    Vec2 { x: 0.95557281,  y: -0.29475517 },
-];
-
-// Those vectors come from bullet 3d
-static SAMPLES_3_F64: [Vec3<f64>; 42] = [
-    Vec3 { x: 0.000000 , y: -0.000000, z: -1.000000 },
-    Vec3 { x: 0.723608 , y: -0.525725, z: -0.447219 },
-    Vec3 { x: -0.276388, y: -0.850649, z: -0.447219 },
-    Vec3 { x: -0.894426, y: -0.000000, z: -0.447216 },
-    Vec3 { x: -0.276388, y: 0.850649 , z: -0.447220 },
-    Vec3 { x: 0.723608 , y: 0.525725 , z: -0.447219 },
-    Vec3 { x: 0.276388 , y: -0.850649, z: 0.447220 },
-    Vec3 { x: -0.723608, y: -0.525725, z: 0.447219 },
-    Vec3 { x: -0.723608, y: 0.525725 , z: 0.447219 },
-    Vec3 { x: 0.276388 , y: 0.850649 , z: 0.447219 },
-    Vec3 { x: 0.894426 , y: 0.000000 , z: 0.447216 },
-    Vec3 { x: -0.000000, y: 0.000000 , z: 1.000000 },
-    Vec3 { x: 0.425323 , y: -0.309011, z: -0.850654 },
-    Vec3 { x: -0.162456, y: -0.499995, z: -0.850654 },
-    Vec3 { x: 0.262869 , y: -0.809012, z: -0.525738 },
-    Vec3 { x: 0.425323 , y: 0.309011 , z: -0.850654 },
-    Vec3 { x: 0.850648 , y: -0.000000, z: -0.525736 },
-    Vec3 { x: -0.525730, y: -0.000000, z: -0.850652 },
-    Vec3 { x: -0.688190, y: -0.499997, z: -0.525736 },
-    Vec3 { x: -0.162456, y: 0.499995 , z: -0.850654 },
-    Vec3 { x: -0.688190, y: 0.499997 , z: -0.525736 },
-    Vec3 { x: 0.262869 , y: 0.809012 , z: -0.525738 },
-    Vec3 { x: 0.951058 , y: 0.309013 , z: 0.000000 },
-    Vec3 { x: 0.951058 , y: -0.309013, z: 0.000000 },
-    Vec3 { x: 0.587786 , y: -0.809017, z: 0.000000 },
-    Vec3 { x: 0.000000 , y: -1.000000, z: 0.000000 },
-    Vec3 { x: -0.587786, y: -0.809017, z: 0.000000 },
-    Vec3 { x: -0.951058, y: -0.309013, z: -0.000000 },
-    Vec3 { x: -0.951058, y: 0.309013 , z: -0.000000 },
-    Vec3 { x: -0.587786, y: 0.809017 , z: -0.000000 },
-    Vec3 { x: -0.000000, y: 1.000000 , z: -0.000000 },
-    Vec3 { x: 0.587786 , y: 0.809017 , z: -0.000000 },
-    Vec3 { x: 0.688190 , y: -0.499997, z: 0.525736 },
-    Vec3 { x: -0.262869, y: -0.809012, z: 0.525738 },
-    Vec3 { x: -0.850648, y: 0.000000 , z: 0.525736 },
-    Vec3 { x: -0.262869, y: 0.809012 , z: 0.525738 },
-    Vec3 { x: 0.688190 , y: 0.499997 , z: 0.525736 },
-    Vec3 { x: 0.525730 , y: 0.000000 , z: 0.850652 },
-    Vec3 { x: 0.162456 , y: -0.499995, z: 0.850654 },
-    Vec3 { x: -0.425323, y: -0.309011, z: 0.850654 },
-    Vec3 { x: -0.425323, y: 0.309011 , z: 0.850654 },
-    Vec3 { x: 0.162456 , y: 0.499995 , z: 0.850654 }
-];
-
-impl<N> UniformSphereSample for Vec1<N>
-    where Vec1<N>: One {
-    #[inline(always)]
-    fn sample<F: FnMut(Vec1<N>)>(mut f: F) {
-        f(::one())
-     }
-}
-
-impl<N: Cast<f64> + Copy> UniformSphereSample for Vec2<N> {
-    #[inline(always)]
-    fn sample<F: FnMut(Vec2<N>)>(mut f: F) {
-         for sample in SAMPLES_2_F64.iter() {
-             f(Cast::from(*sample))
-         }
-     }
-}
-
-impl<N: Cast<f64> + Copy> UniformSphereSample for Vec3<N> {
-    #[inline(always)]
-    fn sample<F: FnMut(Vec3<N>)>(mut f: F) {
-        for sample in SAMPLES_3_F64.iter() {
-            f(Cast::from(*sample))
-        }
-    }
-}
-
-impl<N: Cast<f64> + Copy> UniformSphereSample for Vec4<N> {
-    #[inline(always)]
-    fn sample<F: FnMut(Vec4<N>)>(_: F) {
-        panic!("UniformSphereSample::<Vec4<N>>::sample : Not yet implemented.")
-        // for sample in SAMPLES_3_F32.iter() {
-        //     f(Cast::from(*sample))
-        // }
-    }
-}

src/structs/specializations/complex.rs

@@ -2,8 +2,8 @@
 
 use std::num::Zero;
 use extra::complex::Cmplx;
-use traits::operations::{Absolute, Inv};
+use traits::operations::{Absolute, Inverse};
-use traits::structure::{Dim};
+use traits::structure::{Dimension};
 
 impl<N: Clone + BaseNum> Absolute<Cmplx<N>> for Cmplx<N> {
     #[inline]
@@ -12,7 +12,7 @@ impl<N: Clone + BaseNum> Absolute<Cmplx<N>> for Cmplx<N> {
     }
 }
 
-impl<N: Clone + BaseNum + BaseNumCast + Zero> Inv for Cmplx<N> {
+impl<N: Clone + BaseNum + BaseNumCast + Zero> Inverse for Cmplx<N> {
     #[inline]
     fn inverse(&self) -> Option<Cmplx<N>> {
         if self.is_zero() {
@@ -43,55 +43,55 @@ impl<N: Clone + BaseNum + BaseNumCast + Zero> Inv for Cmplx<N> {
     }
 }
 
-impl<N> Dim for Cmplx<N> {
+impl<N> Dimension for Cmplx<N> {
     #[inline]
-    fn dim(unsused_mut: Option<Cmplx<N>>) -> usize {
+    fn dimension(unsused_mut: Option<Cmplx<N>>) -> usize {
         2
     }
 }
 
-impl<N> Rotation<Vec2<N>> for Cmplx<N> {
+impl<N> Rotation<Vector2<N>> for Cmplx<N> {
     #[inline]
-    fn rotation(&self) -> Vec2<N> {
+    fn rotation(&self) -> Vector2<N> {
     }
 
     #[inline]
-    fn inv_rotation(&self) -> Vec2<N> {
+    fn inverse_rotation(&self) -> Vector2<N> {
         -self.rotation();
     }
 
     #[inline]
-    fn rotate_by(&mut self, rotation: &Vec2<N>) {
+    fn rotate_by(&mut self, rotation: &Vector2<N>) {
     }
 
     #[inline]
-    fn rotated(&self, rotation: &Vec2<N>) -> Cmplx<N> {
+    fn rotated(&self, rotation: &Vector2<N>) -> Cmplx<N> {
     }
 
     #[inline]
-    fn set_rotation(&mut self, rotation: Vec2<N>) {
+    fn set_rotation(&mut self, rotation: Vector2<N>) {
     }
 }
 
-impl<N> Rotate<Vec2<N>> for Cmplx<N> {
+impl<N> Rotate<Vector2<N>> for Cmplx<N> {
     #[inline]
     fn rotate(&self, rotation: &V) -> V {
     }
 
     #[inline]
-    fn inv_rotate(&self, rotation: &V) -> V {
+    fn inverse_rotate(&self, rotation: &V) -> V {
     }
 }
 
-impl<N> RotationMatrix<Vec2<N>, Vec2<N>, Rotmat<Mat2<N>>> for Cmplx<N> {
+impl<N> RotationMatrix<Vector2<N>, Vector2<N>, Rotationmatrix<Matrix2<N>>> for Cmplx<N> {
     #[inline]
-    fn to_rot_mat(&self) -> Rotmat<Mat2<N>> {
+    fn to_rotation_matrix(&self) -> Rotationmatrix<Matrix2<N>> {
     }
 }
 
 impl<N> Norm<N> for Cmplx<N> {
     #[inline]
-    fn sqnorm(&self) -> N {
+    fn norm_squared(&self) -> N {
     }
 
     #[inline]

src/structs/specializations/identity.rs

@@ -1,27 +1,27 @@
 use std::ops::Mul;
 use num::One;
-use structs::mat;
+use structs::matrix::Identity;
-use traits::operations::{Inv, Transpose};
+use traits::operations::{Inverse, Transpose};
 use traits::geometry::{Translate, Rotate, Transform, AbsoluteRotate};
 
-impl One for mat::Identity {
+impl One for Identity {
     #[inline]
-    fn one() -> mat::Identity {
+    fn one() -> Identity {
-        mat::Identity::new()
+        Identity::new()
     }
 }
 
-impl Inv for mat::Identity {
+impl Inverse for Identity {
-    fn inv(&self) -> Option<mat::Identity> {
+    fn inverse(&self) -> Option<Identity> {
-        Some(mat::Identity::new())
+        Some(Identity::new())
     }
 
-    fn inv_mut(&mut self) -> bool {
+    fn inverse_mut(&mut self) -> bool {
         true
     }
 }
 
-impl<T: Clone> Mul<T> for mat::Identity {
+impl<T: Clone> Mul<T> for Identity {
     type Output = T;
 
     #[inline]
@@ -30,10 +30,10 @@ impl<T: Clone> Mul<T> for mat::Identity {
     }
 }
 
-impl Transpose for mat::Identity {
+impl Transpose for Identity {
     #[inline]
-    fn transpose(&self) -> mat::Identity {
+    fn transpose(&self) -> Identity {
-        mat::Identity::new()
+        Identity::new()
     }
 
     #[inline]
@@ -41,45 +41,45 @@ impl Transpose for mat::Identity {
     }
 }
 
-impl<V: Clone> Translate<V> for mat::Identity {
+impl<V: Clone> Translate<V> for Identity {
     #[inline]
     fn translate(&self, v: &V) -> V {
         v.clone()
     }
 
     #[inline]
-    fn inv_translate(&self, v: &V) -> V {
+    fn inverse_translate(&self, v: &V) -> V {
         v.clone()
     }
 }
 
-impl<V: Clone> Rotate<V> for mat::Identity {
+impl<V: Clone> Rotate<V> for Identity {
     #[inline]
     fn rotate(&self, v: &V) -> V {
         v.clone()
     }
 
     #[inline]
-    fn inv_rotate(&self, v: &V) -> V {
+    fn inverse_rotate(&self, v: &V) -> V {
         v.clone()
     }
 }
 
-impl<V: Clone> AbsoluteRotate<V> for mat::Identity {
+impl<V: Clone> AbsoluteRotate<V> for Identity {
     #[inline]
     fn absolute_rotate(&self, v: &V) -> V {
         v.clone()
     }
 }
 
-impl<V: Clone> Transform<V> for mat::Identity {
+impl<V: Clone> Transform<V> for Identity {
     #[inline]
     fn transform(&self, v: &V) -> V {
         v.clone()
     }
 
     #[inline]
-    fn inv_transform(&self, v: &V) -> V {
+    fn inverse_transform(&self, v: &V) -> V {
         v.clone()
     }
 }

src/structs/specializations/matrix.rs

@@ -1,16 +1,16 @@
 use std::ops::{Add, Mul, Neg, MulAssign};
-use structs::vec::{Vec2, Vec3};
+use structs::vector::{Vector2, Vector3};
-use structs::pnt::{Pnt2, Pnt3};
+use structs::point::{Point2, Point3};
-use structs::mat::{Mat1, Mat2, Mat3};
+use structs::matrix::{Matrix1, Matrix2, Matrix3};
-use traits::operations::{Inv, Det, ApproxEq};
+use traits::operations::{Inverse, Determinant, ApproxEq};
-use traits::structure::{Row, Col, BaseNum};
+use traits::structure::{Row, Column, BaseNum};
 
 // some specializations:
-impl<N: BaseNum + ApproxEq<N>> Inv for Mat1<N> {
+impl<N: BaseNum + ApproxEq<N>> Inverse for Matrix1<N> {
     #[inline]
-    fn inv(&self) -> Option<Mat1<N>> {
+    fn inverse(&self) -> Option<Matrix1<N>> {
         let mut res = *self;
-        if res.inv_mut() {
+        if res.inverse_mut() {
             Some(res)
         }
         else {
@@ -19,24 +19,24 @@ impl<N: BaseNum + ApproxEq<N>> Inv for Mat1<N> {
     }
 
     #[inline]
-    fn inv_mut(&mut self) -> bool {
+    fn inverse_mut(&mut self) -> bool {
         if ApproxEq::approx_eq(&self.m11, &::zero()) {
             false
         }
         else {
             let _1: N = ::one();
 
-            self.m11 = _1 / Det::det(self);
+            self.m11 = _1 / Determinant::determinant(self);
             true
         }
     }
 }
 
-impl<N: BaseNum + Neg<Output = N> + ApproxEq<N>> Inv for Mat2<N> {
+impl<N: BaseNum + Neg<Output = N> + ApproxEq<N>> Inverse for Matrix2<N> {
     #[inline]
-    fn inv(&self) -> Option<Mat2<N>> {
+    fn inverse(&self) -> Option<Matrix2<N>> {
         let mut res = *self;
-        if res.inv_mut() {
+        if res.inverse_mut() {
             Some(res)
         }
         else {
@@ -45,28 +45,28 @@ impl<N: BaseNum + Neg<Output = N> + ApproxEq<N>> Inv for Mat2<N> {
     }
 
     #[inline]
-    fn inv_mut(&mut self) -> bool {
+    fn inverse_mut(&mut self) -> bool {
-        let det = Det::det(self);
+        let determinant = Determinant::determinant(self);
 
-        if ApproxEq::approx_eq(&det, &::zero()) {
+        if ApproxEq::approx_eq(&determinant, &::zero()) {
             false
         }
         else {
-            *self = Mat2::new(
+            *self = Matrix2::new(
-                self.m22 / det , -self.m12 / det,
+                self.m22 / determinant , -self.m12 / determinant,
-                -self.m21 / det, self.m11 / det);
+                -self.m21 / determinant, self.m11 / determinant);
 
             true
         }
     }
 }
 
-impl<N: BaseNum + Neg<Output = N> + ApproxEq<N>> Inv for Mat3<N> {
+impl<N: BaseNum + Neg<Output = N> + ApproxEq<N>> Inverse for Matrix3<N> {
     #[inline]
-    fn inv(&self) -> Option<Mat3<N>> {
+    fn inverse(&self) -> Option<Matrix3<N>> {
         let mut res = *self;
 
-        if res.inv_mut() {
+        if res.inverse_mut() {
             Some(res)
         }
         else {
@@ -75,29 +75,29 @@ impl<N: BaseNum + Neg<Output = N> + ApproxEq<N>> Inv for Mat3<N> {
     }
 
     #[inline]
-    fn inv_mut(&mut self) -> bool {
+    fn 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 det = self.m11 * minor_m12_m23 - self.m12 * minor_m11_m23 + self.m13 * minor_m11_m22;
+        let determinant = self.m11 * minor_m12_m23 - self.m12 * minor_m11_m23 + self.m13 * minor_m11_m22;
 
-        if ApproxEq::approx_eq(&det, &::zero()) {
+        if ApproxEq::approx_eq(&determinant, &::zero()) {
             false
         }
         else {
-            *self = Mat3::new(
+            *self = Matrix3::new(
-                (minor_m12_m23 / det),
+                (minor_m12_m23 / determinant),
-                ((self.m13 * self.m32 - self.m33 * self.m12) / det),
+                ((self.m13 * self.m32 - self.m33 * self.m12) / determinant),
-                ((self.m12 * self.m23 - self.m22 * self.m13) / det),
+                ((self.m12 * self.m23 - self.m22 * self.m13) / determinant),
 
-                (-minor_m11_m23 / det),
+                (-minor_m11_m23 / determinant),
-                ((self.m11 * self.m33 - self.m31 * self.m13) / det),
+                ((self.m11 * self.m33 - self.m31 * self.m13) / determinant),
-                ((self.m13 * self.m21 - self.m23 * self.m11) / det),
+                ((self.m13 * self.m21 - self.m23 * self.m11) / determinant),
 
-                (minor_m11_m22  / det),
+                (minor_m11_m22  / determinant),
-                ((self.m12 * self.m31 - self.m32 * self.m11) / det),
+                ((self.m12 * self.m31 - self.m32 * self.m11) / determinant),
-                ((self.m11 * self.m22 - self.m21 * self.m12) / det)
+                ((self.m11 * self.m22 - self.m21 * self.m12) / determinant)
                 );
 
             true
@@ -105,23 +105,23 @@ impl<N: BaseNum + Neg<Output = N> + ApproxEq<N>> Inv for Mat3<N> {
     }
 }
 
-impl<N: BaseNum> Det<N> for Mat1<N> {
+impl<N: BaseNum> Determinant<N> for Matrix1<N> {
     #[inline]
-    fn det(&self) -> N {
+    fn determinant(&self) -> N {
         self.m11
     }
 }
 
-impl<N: BaseNum> Det<N> for Mat2<N> {
+impl<N: BaseNum> Determinant<N> for Matrix2<N> {
     #[inline]
-    fn det(&self) -> N {
+    fn determinant(&self) -> N {
         self.m11 * self.m22 - self.m21 * self.m12
     }
 }
 
-impl<N: BaseNum> Det<N> for Mat3<N> {
+impl<N: BaseNum> Determinant<N> for Matrix3<N> {
     #[inline]
-    fn det(&self) -> N {
+    fn determinant(&self) -> N {
         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;
@@ -130,24 +130,24 @@ impl<N: BaseNum> Det<N> for Mat3<N> {
     }
 }
 
-impl<N: Copy> Row<Vec3<N>> for Mat3<N> {
+impl<N: Copy> Row<Vector3<N>> for Matrix3<N> {
     #[inline]
     fn nrows(&self) -> usize {
         3
     }
 
     #[inline]
-    fn row(&self, i: usize) -> Vec3<N> {
+    fn row(&self, i: usize) -> Vector3<N> {
         match i {
-            0 => Vec3::new(self.m11, self.m12, self.m13),
+            0 => Vector3::new(self.m11, self.m12, self.m13),
-            1 => Vec3::new(self.m21, self.m22, self.m23),
+            1 => Vector3::new(self.m21, self.m22, self.m23),
-            2 => Vec3::new(self.m31, self.m32, self.m33),
+            2 => Vector3::new(self.m31, self.m32, self.m33),
             _ => panic!(format!("Index out of range: 3d matrices do not have {} rows.",  i))
         }
     }
 
     #[inline]
-    fn set_row(&mut self, i: usize, r: Vec3<N>) {
+    fn set_row(&mut self, i: usize, r: Vector3<N>) {
         match i {
             0 => {
                 self.m11 = r.x;
@@ -170,24 +170,24 @@ impl<N: Copy> Row<Vec3<N>> for Mat3<N> {
     }
 }
 
-impl<N: Copy> Col<Vec3<N>> for Mat3<N> {
+impl<N: Copy> Column<Vector3<N>> for Matrix3<N> {
     #[inline]
     fn ncols(&self) -> usize {
         3
     }
 
     #[inline]
-    fn col(&self, i: usize) -> Vec3<N> {
+    fn column(&self, i: usize) -> Vector3<N> {
         match i {
-            0 => Vec3::new(self.m11, self.m21, self.m31),
+            0 => Vector3::new(self.m11, self.m21, self.m31),
-            1 => Vec3::new(self.m12, self.m22, self.m32),
+            1 => Vector3::new(self.m12, self.m22, self.m32),
-            2 => Vec3::new(self.m13, self.m23, self.m33),
+            2 => Vector3::new(self.m13, self.m23, self.m33),
             _ => panic!(format!("Index out of range: 3d matrices do not have {} cols.", i))
         }
     }
 
     #[inline]
-    fn set_col(&mut self, i: usize, r: Vec3<N>) {
+    fn set_col(&mut self, i: usize, r: Vector3<N>) {
         match i {
             0 => {
                 self.m11 = r.x;
@@ -210,12 +210,12 @@ impl<N: Copy> Col<Vec3<N>> for Mat3<N> {
     }
 }
 
-impl<N: Copy + Mul<N, Output = N> + Add<N, Output = N>> Mul<Mat3<N>> for Mat3<N> {
+impl<N: Copy + Mul<N, Output = N> + Add<N, Output = N>> Mul<Matrix3<N>> for Matrix3<N> {
-    type Output = Mat3<N>;
+    type Output = Matrix3<N>;
 
     #[inline]
-    fn mul(self, right: Mat3<N>) -> Mat3<N> {
+    fn mul(self, right: Matrix3<N>) -> Matrix3<N> {
-        Mat3::new(
+        Matrix3::new(
             self.m11 * right.m11 + self.m12 * right.m21 + self.m13 * right.m31,
             self.m11 * right.m12 + self.m12 * right.m22 + self.m13 * right.m32,
             self.m11 * right.m13 + self.m12 * right.m23 + self.m13 * right.m33,
@@ -231,12 +231,12 @@ impl<N: Copy + Mul<N, Output = N> + Add<N, Output = N>> Mul<Mat3<N>> for Mat3<N>
     }
 }
 
-impl<N: Copy + Mul<N, Output = N> + Add<N, Output = N>> Mul<Mat2<N>> for Mat2<N> {
+impl<N: Copy + Mul<N, Output = N> + Add<N, Output = N>> Mul<Matrix2<N>> for Matrix2<N> {
-    type Output = Mat2<N>;
+    type Output = Matrix2<N>;
 
     #[inline(always)]
-    fn mul(self, right: Mat2<N>) -> Mat2<N> {
+    fn mul(self, right: Matrix2<N>) -> Matrix2<N> {
-        Mat2::new(
+        Matrix2::new(
             self.m11 * right.m11 + self.m12 * right.m21,
             self.m11 * right.m12 + self.m12 * right.m22,
 
@@ -246,12 +246,12 @@ impl<N: Copy + Mul<N, Output = N> + Add<N, Output = N>> Mul<Mat2<N>> for Mat2<N>
     }
 }
 
-impl<N: Copy + Mul<N, Output = N> + Add<N, Output = N>> Mul<Vec3<N>> for Mat3<N> {
+impl<N: Copy + Mul<N, Output = N> + Add<N, Output = N>> Mul<Vector3<N>> for Matrix3<N> {
-    type Output = Vec3<N>;
+    type Output = Vector3<N>;
 
     #[inline(always)]
-    fn mul(self, right: Vec3<N>) -> Vec3<N> {
+    fn mul(self, right: Vector3<N>) -> Vector3<N> {
-        Vec3::new(
+        Vector3::new(
             self.m11 * right.x + self.m12 * right.y + self.m13 * right.z,
             self.m21 * right.x + self.m22 * right.y + self.m23 * right.z,
             self.m31 * right.x + self.m32 * right.y + self.m33 * right.z
@@ -259,12 +259,12 @@ impl<N: Copy + Mul<N, Output = N> + Add<N, Output = N>> Mul<Vec3<N>> for Mat3<N>
     }
 }
 
-impl<N: Copy + Mul<N, Output = N> + Add<N, Output = N>> Mul<Mat3<N>> for Vec3<N> {
+impl<N: Copy + Mul<N, Output = N> + Add<N, Output = N>> Mul<Matrix3<N>> for Vector3<N> {
-    type Output = Vec3<N>;
+    type Output = Vector3<N>;
 
     #[inline(always)]
-    fn mul(self, right: Mat3<N>) -> Vec3<N> {
+    fn mul(self, right: Matrix3<N>) -> Vector3<N> {
-        Vec3::new(
+        Vector3::new(
             self.x * right.m11 + self.y * right.m21 + self.z * right.m31,
             self.x * right.m12 + self.y * right.m22 + self.z * right.m32,
             self.x * right.m13 + self.y * right.m23 + self.z * right.m33
@@ -272,36 +272,36 @@ impl<N: Copy + Mul<N, Output = N> + Add<N, Output = N>> Mul<Mat3<N>> for Vec3<N>
     }
 }
 
-impl<N: Copy + Mul<N, Output = N> + Add<N, Output = N>> Mul<Mat2<N>> for Vec2<N> {
+impl<N: Copy + Mul<N, Output = N> + Add<N, Output = N>> Mul<Matrix2<N>> for Vector2<N> {
-    type Output = Vec2<N>;
+    type Output = Vector2<N>;
 
     #[inline(always)]
-    fn mul(self, right: Mat2<N>) -> Vec2<N> {
+    fn mul(self, right: Matrix2<N>) -> Vector2<N> {
-        Vec2::new(
+        Vector2::new(
             self.x * right.m11 + self.y * right.m21,
             self.x * right.m12 + self.y * right.m22
         )
     }
 }
 
-impl<N: Copy + Mul<N, Output = N> + Add<N, Output = N>> Mul<Vec2<N>> for Mat2<N> {
+impl<N: Copy + Mul<N, Output = N> + Add<N, Output = N>> Mul<Vector2<N>> for Matrix2<N> {
-    type Output = Vec2<N>;
+    type Output = Vector2<N>;
 
     #[inline(always)]
-    fn mul(self, right: Vec2<N>) -> Vec2<N> {
+    fn mul(self, right: Vector2<N>) -> Vector2<N> {
-        Vec2::new(
+        Vector2::new(
             self.m11 * right.x + self.m12 * right.y,
             self.m21 * right.x + self.m22 * right.y
         )
     }
 }
 
-impl<N: Copy + Mul<N, Output = N> + Add<N, Output = N>> Mul<Pnt3<N>> for Mat3<N> {
+impl<N: Copy + Mul<N, Output = N> + Add<N, Output = N>> Mul<Point3<N>> for Matrix3<N> {
-    type Output = Pnt3<N>;
+    type Output = Point3<N>;
 
     #[inline(always)]
-    fn mul(self, right: Pnt3<N>) -> Pnt3<N> {
+    fn mul(self, right: Point3<N>) -> Point3<N> {
-        Pnt3::new(
+        Point3::new(
             self.m11 * right.x + self.m12 * right.y + self.m13 * right.z,
             self.m21 * right.x + self.m22 * right.y + self.m23 * right.z,
             self.m31 * right.x + self.m32 * right.y + self.m33 * right.z
@@ -309,12 +309,12 @@ impl<N: Copy + Mul<N, Output = N> + Add<N, Output = N>> Mul<Pnt3<N>> for Mat3<N>
     }
 }
 
-impl<N: Copy + Mul<N, Output = N> + Add<N, Output = N>> Mul<Mat3<N>> for Pnt3<N> {
+impl<N: Copy + Mul<N, Output = N> + Add<N, Output = N>> Mul<Matrix3<N>> for Point3<N> {
-    type Output = Pnt3<N>;
+    type Output = Point3<N>;
 
     #[inline(always)]
-    fn mul(self, right: Mat3<N>) -> Pnt3<N> {
+    fn mul(self, right: Matrix3<N>) -> Point3<N> {
-        Pnt3::new(
+        Point3::new(
             self.x * right.m11 + self.y * right.m21 + self.z * right.m31,
             self.x * right.m12 + self.y * right.m22 + self.z * right.m32,
             self.x * right.m13 + self.y * right.m23 + self.z * right.m33
@@ -322,24 +322,24 @@ impl<N: Copy + Mul<N, Output = N> + Add<N, Output = N>> Mul<Mat3<N>> for Pnt3<N>
     }
 }
 
-impl<N: Copy + Mul<N, Output = N> + Add<N, Output = N>> Mul<Mat2<N>> for Pnt2<N> {
+impl<N: Copy + Mul<N, Output = N> + Add<N, Output = N>> Mul<Matrix2<N>> for Point2<N> {
-    type Output = Pnt2<N>;
+    type Output = Point2<N>;
 
     #[inline(always)]
-    fn mul(self, right: Mat2<N>) -> Pnt2<N> {
+    fn mul(self, right: Matrix2<N>) -> Point2<N> {
-        Pnt2::new(
+        Point2::new(
             self.x * right.m11 + self.y * right.m21,
             self.x * right.m12 + self.y * right.m22
         )
     }
 }
 
-impl<N: Copy + Mul<N, Output = N> + Add<N, Output = N>> Mul<Pnt2<N>> for Mat2<N> {
+impl<N: Copy + Mul<N, Output = N> + Add<N, Output = N>> Mul<Point2<N>> for Matrix2<N> {
-    type Output = Pnt2<N>;
+    type Output = Point2<N>;
 
     #[inline(always)]
-    fn mul(self, right: Pnt2<N>) -> Pnt2<N> {
+    fn mul(self, right: Point2<N>) -> Point2<N> {
-        Pnt2::new(
+        Point2::new(
             self.m11 * right.x + self.m12 * right.y,
             self.m21 * right.x + self.m22 * right.y
         )
@@ -360,10 +360,10 @@ macro_rules! impl_mul_assign_from_mul(
     )
 );
 
-impl_mul_assign_from_mul!(Mat3, Mat3);
+impl_mul_assign_from_mul!(Matrix3, Matrix3);
-impl_mul_assign_from_mul!(Mat2, Mat2);
+impl_mul_assign_from_mul!(Matrix2, Matrix2);
 
-impl_mul_assign_from_mul!(Vec3, Mat3);
+impl_mul_assign_from_mul!(Vector3, Matrix3);
-impl_mul_assign_from_mul!(Vec2, Mat2);
+impl_mul_assign_from_mul!(Vector2, Matrix2);
-impl_mul_assign_from_mul!(Pnt3, Mat3);
+impl_mul_assign_from_mul!(Point3, Matrix3);
-impl_mul_assign_from_mul!(Pnt2, Mat2);
+impl_mul_assign_from_mul!(Point2, Matrix2);

src/structs/specializations/vector.rs

@@ -0,0 +1,307 @@
+use std::ops::{Sub, Mul, Neg};
+use num::{Zero, One};
+use traits::structure::{Cast, Row, Basis, BaseFloat};
+use traits::geometry::{Norm, Cross, CrossMatrix, RotationTo, UniformSphereSample};
+use structs::vector::{Vector1, Vector2, Vector3, Vector4};
+use structs::matrix::Matrix3;
+use structs::rotation::{Rotation2, Rotation3};
+
+impl<N: BaseFloat> RotationTo for Vector2<N> {
+    type AngleType = N;
+    type DeltaRotationType = Rotation2<N>;
+
+    #[inline]
+    fn angle_to(&self, other: &Self) -> N {
+        ::cross(self, other).x.atan2(::dot(self, other))
+    }
+
+    #[inline]
+    fn rotation_to(&self, other: &Self) -> Rotation2<N> {
+        Rotation2::new(Vector1::new(self.angle_to(other)))
+    }
+}
+
+impl<N: BaseFloat> RotationTo for Vector3<N> {
+    type AngleType = N;
+    type DeltaRotationType = Rotation3<N>;
+
+    #[inline]
+    fn angle_to(&self, other: &Self) -> N {
+        ::cross(self, other).norm().atan2(::dot(self, other))
+    }
+
+    #[inline]
+    fn rotation_to(&self, other: &Self) -> Rotation3<N> {
+        let mut axis = ::cross(self, other);
+        let norm = axis.normalize_mut();
+
+        if ::is_zero(&norm) {
+            ::one()
+        }
+        else {
+            let axis_angle = axis * norm.atan2(::dot(self, other));
+
+            Rotation3::new(axis_angle)
+        }
+    }
+}
+
+impl<N: Copy + Mul<N, Output = N> + Sub<N, Output = N>> Cross for Vector2<N> {
+    type CrossProductType = Vector1<N>;
+
+    #[inline]
+    fn cross(&self, other: &Vector2<N>) -> Vector1<N> {
+        Vector1::new(self.x * other.y - self.y * other.x)
+    }
+}
+
+// FIXME: instead of returning a Vector2, define a Matrix2x1 matrix?
+impl<N: Neg<Output = N> + Copy> CrossMatrix<Vector2<N>> for Vector2<N> {
+    #[inline]
+    fn cross_matrix(&self) -> Vector2<N> {
+        Vector2::new(-self.y, self.x)
+    }
+}
+
+impl<N: Copy + Mul<N, Output = N> + Sub<N, Output = N>> Cross for Vector3<N> {
+    type CrossProductType = Vector3<N>;
+
+    #[inline]
+    fn cross(&self, other: &Vector3<N>) -> Vector3<N> {
+        Vector3::new(
+            self.y * other.z - self.z * other.y,
+            self.z * other.x - self.x * other.z,
+            self.x * other.y - self.y * other.x
+        )
+    }
+}
+
+impl<N: Neg<Output = N> + Zero + Copy> CrossMatrix<Matrix3<N>> for Vector3<N> {
+    #[inline]
+    fn cross_matrix(&self) -> Matrix3<N> {
+        Matrix3::new(
+            ::zero(), -self.z,  self.y,
+            self.z,   ::zero(), -self.x,
+            -self.y,  self.x,   ::zero()
+        )
+    }
+}
+
+// FIXME: implement this for all other vectors
+impl<N: Copy> Row<Vector1<N>> for Vector2<N> {
+    #[inline]
+    fn nrows(&self) -> usize {
+        2
+    }
+
+    #[inline]
+    fn row(&self, i: usize) -> Vector1<N> {
+        match i {
+            0 => Vector1::new(self.x),
+            1 => Vector1::new(self.y),
+            _ => panic!(format!("Index out of range: 2d vectors do not have {} rows. ", i))
+        }
+    }
+
+    #[inline]
+    fn set_row(&mut self, i: usize, r: Vector1<N>) {
+        match i {
+            0 => self.x = r.x,
+            1 => self.y = r.x,
+            _ => panic!(format!("Index out of range: 2d vectors do not have {} rows.", i))
+
+        }
+    }
+}
+
+impl<N: One> Basis for Vector1<N> {
+    #[inline(always)]
+    fn canonical_basis<F: FnMut(Vector1<N>) -> bool>(mut f: F) {
+        f(Vector1::new(::one()));
+    }
+
+    #[inline(always)]
+    fn orthonormal_subspace_basis<F: FnMut(Vector1<N>) -> bool>(_: &Vector1<N>, _: F) { }
+
+    #[inline]
+    fn canonical_basis_element(i: usize) -> Option<Vector1<N>> {
+        if i == 0 {
+            Some(Vector1::new(::one()))
+        }
+        else {
+            None
+        }
+    }
+}
+
+impl<N: Copy + One + Zero + Neg<Output = N>> Basis for Vector2<N> {
+    #[inline(always)]
+    fn canonical_basis<F: FnMut(Vector2<N>) -> bool>(mut f: F) {
+        if !f(Vector2::new(::one(), ::zero())) { return };
+        f(Vector2::new(::zero(), ::one()));
+    }
+
+    #[inline]
+    fn orthonormal_subspace_basis<F: FnMut(Vector2<N>) -> bool>(n: &Vector2<N>, mut f: F) {
+        f(Vector2::new(-n.y, n.x));
+    }
+
+    #[inline]
+    fn canonical_basis_element(i: usize) -> Option<Vector2<N>> {
+        if i == 0 {
+            Some(Vector2::new(::one(), ::zero()))
+        }
+        else if i == 1 {
+            Some(Vector2::new(::zero(), ::one()))
+        }
+        else {
+            None
+        }
+    }
+}
+
+impl<N: BaseFloat> Basis for Vector3<N> {
+    #[inline(always)]
+    fn canonical_basis<F: FnMut(Vector3<N>) -> bool>(mut f: F) {
+        if !f(Vector3::new(::one(), ::zero(), ::zero())) { return };
+        if !f(Vector3::new(::zero(), ::one(), ::zero())) { return };
+        f(Vector3::new(::zero(), ::zero(), ::one()));
+    }
+
+    #[inline(always)]
+    fn orthonormal_subspace_basis<F: FnMut(Vector3<N>) -> bool>(n: &Vector3<N>, mut f: F) {
+        let a = 
+            if n.x.abs() > n.y.abs() {
+                Norm::normalize(&Vector3::new(n.z, ::zero(), -n.x))
+            }
+            else {
+                Norm::normalize(&Vector3::new(::zero(), -n.z, n.y))
+            };
+
+        if !f(Cross::cross(&a, n)) { return };
+        f(a);
+    }
+
+    #[inline]
+    fn canonical_basis_element(i: usize) -> Option<Vector3<N>> {
+        if i == 0 {
+            Some(Vector3::new(::one(), ::zero(), ::zero()))
+        }
+        else if i == 1 {
+            Some(Vector3::new(::zero(), ::one(), ::zero()))
+        }
+        else if i == 2 {
+            Some(Vector3::new(::zero(), ::zero(), ::one()))
+        }
+        else {
+            None
+        }
+    }
+}
+
+// FIXME: this bad: this fixes definitly the number of samples…
+static SAMPLES_2_F64: [Vector2<f64>; 21] = [
+    Vector2 { x: 1.0,         y: 0.0         },
+    Vector2 { x: 0.95557281,  y: 0.29475517  },
+    Vector2 { x: 0.82623877,  y: 0.56332006  },
+    Vector2 { x: 0.6234898,   y: 0.78183148  },
+    Vector2 { x: 0.36534102,  y: 0.93087375  },
+    Vector2 { x: 0.07473009,  y: 0.9972038   },
+    Vector2 { x: -0.22252093, y: 0.97492791  },
+    Vector2 { x: -0.5,        y: 0.8660254   },
+    Vector2 { x: -0.73305187, y: 0.68017274  },
+    Vector2 { x: -0.90096887, y: 0.43388374  },
+    Vector2 { x: -0.98883083, y: 0.14904227  },
+    Vector2 { x: -0.98883083, y: -0.14904227 },
+    Vector2 { x: -0.90096887, y: -0.43388374 },
+    Vector2 { x: -0.73305187, y: -0.68017274 },
+    Vector2 { x: -0.5,        y: -0.8660254  },
+    Vector2 { x: -0.22252093, y: -0.97492791 },
+    Vector2 { x: 0.07473009,  y: -0.9972038  },
+    Vector2 { x: 0.36534102,  y: -0.93087375 },
+    Vector2 { x: 0.6234898,   y: -0.78183148 },
+    Vector2 { x: 0.82623877,  y: -0.56332006 },
+    Vector2 { x: 0.95557281,  y: -0.29475517 },
+];
+
+// Those vectors come from bullet 3d
+static SAMPLES_3_F64: [Vector3<f64>; 42] = [
+    Vector3 { x: 0.000000 , y: -0.000000, z: -1.000000 },
+    Vector3 { x: 0.723608 , y: -0.525725, z: -0.447219 },
+    Vector3 { x: -0.276388, y: -0.850649, z: -0.447219 },
+    Vector3 { x: -0.894426, y: -0.000000, z: -0.447216 },
+    Vector3 { x: -0.276388, y: 0.850649 , z: -0.447220 },
+    Vector3 { x: 0.723608 , y: 0.525725 , z: -0.447219 },
+    Vector3 { x: 0.276388 , y: -0.850649, z: 0.447220 },
+    Vector3 { x: -0.723608, y: -0.525725, z: 0.447219 },
+    Vector3 { x: -0.723608, y: 0.525725 , z: 0.447219 },
+    Vector3 { x: 0.276388 , y: 0.850649 , z: 0.447219 },
+    Vector3 { x: 0.894426 , y: 0.000000 , z: 0.447216 },
+    Vector3 { x: -0.000000, y: 0.000000 , z: 1.000000 },
+    Vector3 { x: 0.425323 , y: -0.309011, z: -0.850654 },
+    Vector3 { x: -0.162456, y: -0.499995, z: -0.850654 },
+    Vector3 { x: 0.262869 , y: -0.809012, z: -0.525738 },
+    Vector3 { x: 0.425323 , y: 0.309011 , z: -0.850654 },
+    Vector3 { x: 0.850648 , y: -0.000000, z: -0.525736 },
+    Vector3 { x: -0.525730, y: -0.000000, z: -0.850652 },
+    Vector3 { x: -0.688190, y: -0.499997, z: -0.525736 },
+    Vector3 { x: -0.162456, y: 0.499995 , z: -0.850654 },
+    Vector3 { x: -0.688190, y: 0.499997 , z: -0.525736 },
+    Vector3 { x: 0.262869 , y: 0.809012 , z: -0.525738 },
+    Vector3 { x: 0.951058 , y: 0.309013 , z: 0.000000 },
+    Vector3 { x: 0.951058 , y: -0.309013, z: 0.000000 },
+    Vector3 { x: 0.587786 , y: -0.809017, z: 0.000000 },
+    Vector3 { x: 0.000000 , y: -1.000000, z: 0.000000 },
+    Vector3 { x: -0.587786, y: -0.809017, z: 0.000000 },
+    Vector3 { x: -0.951058, y: -0.309013, z: -0.000000 },
+    Vector3 { x: -0.951058, y: 0.309013 , z: -0.000000 },
+    Vector3 { x: -0.587786, y: 0.809017 , z: -0.000000 },
+    Vector3 { x: -0.000000, y: 1.000000 , z: -0.000000 },
+    Vector3 { x: 0.587786 , y: 0.809017 , z: -0.000000 },
+    Vector3 { x: 0.688190 , y: -0.499997, z: 0.525736 },
+    Vector3 { x: -0.262869, y: -0.809012, z: 0.525738 },
+    Vector3 { x: -0.850648, y: 0.000000 , z: 0.525736 },
+    Vector3 { x: -0.262869, y: 0.809012 , z: 0.525738 },
+    Vector3 { x: 0.688190 , y: 0.499997 , z: 0.525736 },
+    Vector3 { x: 0.525730 , y: 0.000000 , z: 0.850652 },
+    Vector3 { x: 0.162456 , y: -0.499995, z: 0.850654 },
+    Vector3 { x: -0.425323, y: -0.309011, z: 0.850654 },
+    Vector3 { x: -0.425323, y: 0.309011 , z: 0.850654 },
+    Vector3 { x: 0.162456 , y: 0.499995 , z: 0.850654 }
+];
+
+impl<N> UniformSphereSample for Vector1<N>
+    where Vector1<N>: One {
+    #[inline(always)]
+    fn sample<F: FnMut(Vector1<N>)>(mut f: F) {
+        f(::one())
+     }
+}
+
+impl<N: Cast<f64> + Copy> UniformSphereSample for Vector2<N> {
+    #[inline(always)]
+    fn sample<F: FnMut(Vector2<N>)>(mut f: F) {
+         for sample in SAMPLES_2_F64.iter() {
+             f(Cast::from(*sample))
+         }
+     }
+}
+
+impl<N: Cast<f64> + Copy> UniformSphereSample for Vector3<N> {
+    #[inline(always)]
+    fn sample<F: FnMut(Vector3<N>)>(mut f: F) {
+        for sample in SAMPLES_3_F64.iter() {
+            f(Cast::from(*sample))
+        }
+    }
+}
+
+impl<N: Cast<f64> + Copy> UniformSphereSample for Vector4<N> {
+    #[inline(always)]
+    fn sample<F: FnMut(Vector4<N>)>(_: F) {
+        panic!("UniformSphereSample::<Vector4<N>>::sample : Not yet implemented.")
+        // for sample in SAMPLES_3_F32.iter() {
+        //     f(Cast::from(*sample))
+        // }
+    }
+}

src/structs/vec.rs

@@ -1,384 +0,0 @@
-//! Vectors with dimension known at compile-time.
-
-use std::ops::{Add, Sub, Mul, Div, Neg, AddAssign, SubAssign, MulAssign, DivAssign, Index, IndexMut};
-use std::mem;
-use std::slice::{Iter, IterMut};
-use std::iter::{Iterator, FromIterator, IntoIterator};
-use std::fmt;
-use rand::{Rand, Rng};
-use num::{Zero, One};
-use traits::operations::{ApproxEq, POrd, POrdering, Axpy, Absolute, Mean};
-use traits::geometry::{Transform, Rotate, FromHomogeneous, ToHomogeneous, Dot, Norm,
-                       Translation, Translate};
-use traits::structure::{Basis, Cast, Dim, Indexable, Iterable, IterableMut, Shape, NumVec,
-                        FloatVec, BaseFloat, BaseNum, Bounded, Repeat};
-use structs::pnt::{Pnt1, Pnt2, Pnt3, Pnt4, Pnt5, Pnt6};
-
-#[cfg(feature="arbitrary")]
-use quickcheck::{Arbitrary, Gen};
-
-
-/// Vector of dimension 1.
-///
-/// The main differance between a point and a vector is that a vector is not affected by
-/// translations.
-#[repr(C)]
-#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
-pub struct Vec1<N> {
-    /// First component of the vector.
-    pub x: N
-}
-
-new_impl!(Vec1, x);
-pord_impl!(Vec1, x,);
-vec_axis_impl!(Vec1, x);
-vec_cast_impl!(Vec1, x);
-conversion_impl!(Vec1, 1);
-index_impl!(Vec1);
-indexable_impl!(Vec1, 1);
-at_fast_impl!(Vec1, 1);
-repeat_impl!(Vec1, val, x);
-dim_impl!(Vec1, 1);
-container_impl!(Vec1);
-// (specialized); basis_impl!(Vec1, 1);
-add_impl!(Vec1, x);
-sub_impl!(Vec1, x);
-mul_impl!(Vec1, x);
-div_impl!(Vec1, x);
-scalar_add_impl!(Vec1, x);
-scalar_sub_impl!(Vec1, x);
-scalar_mul_impl!(Vec1, x);
-scalar_div_impl!(Vec1, x);
-neg_impl!(Vec1, x);
-dot_impl!(Vec1, x);
-translation_impl!(Vec1);
-norm_impl!(Vec1, x);
-approx_eq_impl!(Vec1, x);
-zero_one_impl!(Vec1, x);
-from_iterator_impl!(Vec1, iterator);
-bounded_impl!(Vec1, x);
-axpy_impl!(Vec1, x);
-iterable_impl!(Vec1, 1);
-iterable_mut_impl!(Vec1, 1);
-vec_to_homogeneous_impl!(Vec1, Vec2, y, x);
-vec_from_homogeneous_impl!(Vec1, Vec2, y, x);
-translate_impl!(Vec1, Pnt1);
-rotate_impl!(Vec1);
-rotate_impl!(Pnt1);
-transform_impl!(Vec1, Pnt1);
-vec_as_pnt_impl!(Vec1, Pnt1, x);
-num_float_vec_impl!(Vec1);
-absolute_vec_impl!(Vec1, x);
-arbitrary_impl!(Vec1, x);
-rand_impl!(Vec1, x);
-mean_impl!(Vec1);
-vec_display_impl!(Vec1);
-
-/// Vector of dimension 2.
-///
-/// The main differance between a point and a vector is that a vector is not affected by
-/// translations.
-#[repr(C)]
-#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
-pub struct Vec2<N> {
-    /// First component of the vector.
-    pub x: N,
-    /// Second component of the vector.
-    pub y: N
-}
-
-new_impl!(Vec2, x, y);
-pord_impl!(Vec2, x, y);
-vec_axis_impl!(Vec2, x, y);
-vec_cast_impl!(Vec2, x, y);
-conversion_impl!(Vec2, 2);
-index_impl!(Vec2);
-indexable_impl!(Vec2, 2);
-at_fast_impl!(Vec2, 2);
-repeat_impl!(Vec2, val, x, y);
-dim_impl!(Vec2, 2);
-container_impl!(Vec2);
-// (specialized); basis_impl!(Vec2, 1);
-add_impl!(Vec2, x, y);
-sub_impl!(Vec2, x, y);
-mul_impl!(Vec2, x, y);
-div_impl!(Vec2, x, y);
-scalar_add_impl!(Vec2, x, y);
-scalar_sub_impl!(Vec2, x, y);
-scalar_mul_impl!(Vec2, x, y);
-scalar_div_impl!(Vec2, x, y);
-neg_impl!(Vec2, x, y);
-dot_impl!(Vec2, x, y);
-translation_impl!(Vec2);
-norm_impl!(Vec2, x, y);
-approx_eq_impl!(Vec2, x, y);
-zero_one_impl!(Vec2, x, y);
-from_iterator_impl!(Vec2, iterator, iterator);
-bounded_impl!(Vec2, x, y);
-axpy_impl!(Vec2, x, y);
-iterable_impl!(Vec2, 2);
-iterable_mut_impl!(Vec2, 2);
-vec_to_homogeneous_impl!(Vec2, Vec3, z, x, y);
-vec_from_homogeneous_impl!(Vec2, Vec3, z, x, y);
-translate_impl!(Vec2, Pnt2);
-rotate_impl!(Vec2);
-rotate_impl!(Pnt2);
-transform_impl!(Vec2, Pnt2);
-vec_as_pnt_impl!(Vec2, Pnt2, x, y);
-num_float_vec_impl!(Vec2);
-absolute_vec_impl!(Vec2, x, y);
-arbitrary_impl!(Vec2, x, y);
-rand_impl!(Vec2, x, y);
-mean_impl!(Vec2);
-vec_display_impl!(Vec2);
-
-/// Vector of dimension 3.
-///
-/// The main differance between a point and a vector is that a vector is not affected by
-/// translations.
-#[repr(C)]
-#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
-pub struct Vec3<N> {
-    /// First component of the vector.
-    pub x: N,
-    /// Second component of the vector.
-    pub y: N,
-    /// Third component of the vector.
-    pub z: N
-}
-
-new_impl!(Vec3, x, y, z);
-pord_impl!(Vec3, x, y, z);
-vec_axis_impl!(Vec3, x, y, z);
-vec_cast_impl!(Vec3, x, y, z);
-conversion_impl!(Vec3, 3);
-index_impl!(Vec3);
-indexable_impl!(Vec3, 3);
-at_fast_impl!(Vec3, 3);
-repeat_impl!(Vec3, val, x, y, z);
-dim_impl!(Vec3, 3);
-container_impl!(Vec3);
-// (specialized); basis_impl!(Vec3, 1);
-add_impl!(Vec3, x, y, z);
-sub_impl!(Vec3, x, y, z);
-mul_impl!(Vec3, x, y, z);
-div_impl!(Vec3, x, y, z);
-scalar_add_impl!(Vec3, x, y, z);
-scalar_sub_impl!(Vec3, x, y, z);
-scalar_mul_impl!(Vec3, x, y, z);
-scalar_div_impl!(Vec3, x, y, z);
-neg_impl!(Vec3, x, y, z);
-dot_impl!(Vec3, x, y, z);
-translation_impl!(Vec3);
-norm_impl!(Vec3, x, y ,z);
-approx_eq_impl!(Vec3, x, y, z);
-zero_one_impl!(Vec3, x, y, z);
-from_iterator_impl!(Vec3, iterator, iterator, iterator);
-bounded_impl!(Vec3, x, y, z);
-axpy_impl!(Vec3, x, y, z);
-iterable_impl!(Vec3, 3);
-iterable_mut_impl!(Vec3, 3);
-vec_to_homogeneous_impl!(Vec3, Vec4, w, x, y, z);
-vec_from_homogeneous_impl!(Vec3, Vec4, w, x, y, z);
-translate_impl!(Vec3, Pnt3);
-rotate_impl!(Vec3);
-rotate_impl!(Pnt3);
-transform_impl!(Vec3, Pnt3);
-vec_as_pnt_impl!(Vec3, Pnt3, x, y, z);
-num_float_vec_impl!(Vec3);
-absolute_vec_impl!(Vec3, x, y, z);
-arbitrary_impl!(Vec3, x, y, z);
-rand_impl!(Vec3, x, y, z);
-mean_impl!(Vec3);
-vec_display_impl!(Vec3);
-
-
-/// Vector of dimension 4.
-///
-/// The main differance between a point and a vector is that a vector is not affected by
-/// translations.
-#[repr(C)]
-#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
-pub struct Vec4<N> {
-    /// First component of the vector.
-    pub x: N,
-    /// Second component of the vector.
-    pub y: N,
-    /// Third component of the vector.
-    pub z: N,
-    /// Fourth component of the vector.
-    pub w: N
-}
-
-new_impl!(Vec4, x, y, z, w);
-pord_impl!(Vec4, x, y, z, w);
-vec_axis_impl!(Vec4, x, y, z, w);
-vec_cast_impl!(Vec4, x, y, z, w);
-conversion_impl!(Vec4, 4);
-index_impl!(Vec4);
-indexable_impl!(Vec4, 4);
-at_fast_impl!(Vec4, 4);
-repeat_impl!(Vec4, val, x, y, z, w);
-dim_impl!(Vec4, 4);
-container_impl!(Vec4);
-basis_impl!(Vec4, 4);
-add_impl!(Vec4, x, y, z, w);
-sub_impl!(Vec4, x, y, z, w);
-mul_impl!(Vec4, x, y, z, w);
-div_impl!(Vec4, x, y, z, w);
-scalar_add_impl!(Vec4, x, y, z, w);
-scalar_sub_impl!(Vec4, x, y, z, w);
-scalar_mul_impl!(Vec4, x, y, z, w);
-scalar_div_impl!(Vec4, x, y, z, w);
-neg_impl!(Vec4, x, y, z, w);
-dot_impl!(Vec4, x, y, z, w);
-translation_impl!(Vec4);
-norm_impl!(Vec4, x, y, z, w);
-approx_eq_impl!(Vec4, x, y, z, w);
-zero_one_impl!(Vec4, x, y, z, w);
-from_iterator_impl!(Vec4, iterator, iterator, iterator, iterator);
-bounded_impl!(Vec4, x, y, z, w);
-axpy_impl!(Vec4, x, y, z, w);
-iterable_impl!(Vec4, 4);
-iterable_mut_impl!(Vec4, 4);
-vec_to_homogeneous_impl!(Vec4, Vec5, a, x, y, z, w);
-vec_from_homogeneous_impl!(Vec4, Vec5, a, x, y, z, w);
-translate_impl!(Vec4, Pnt4);
-rotate_impl!(Vec4);
-rotate_impl!(Pnt4);
-transform_impl!(Vec4, Pnt4);
-vec_as_pnt_impl!(Vec4, Pnt4, x, y, z, w);
-num_float_vec_impl!(Vec4);
-absolute_vec_impl!(Vec4, x, y, z, w);
-arbitrary_impl!(Vec4, x, y, z, w);
-rand_impl!(Vec4, x, y, z, w);
-mean_impl!(Vec4);
-vec_display_impl!(Vec4);
-
-/// Vector of dimension 5.
-///
-/// The main differance between a point and a vector is that a vector is not affected by
-/// translations.
-#[repr(C)]
-#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
-pub struct Vec5<N> {
-    /// First component of the vector.
-    pub x: N,
-    /// Second component of the vector.
-    pub y: N,
-    /// Third component of the vector.
-    pub z: N,
-    /// Fourth component of the vector.
-    pub w: N,
-    /// Fifth of the vector.
-    pub a: N
-}
-
-new_impl!(Vec5, x, y, z, w, a);
-pord_impl!(Vec5, x, y, z, w, a);
-vec_axis_impl!(Vec5, x, y, z, w, a);
-vec_cast_impl!(Vec5, x, y, z, w, a);
-conversion_impl!(Vec5, 5);
-index_impl!(Vec5);
-indexable_impl!(Vec5, 5);
-at_fast_impl!(Vec5, 5);
-repeat_impl!(Vec5, val, x, y, z, w, a);
-dim_impl!(Vec5, 5);
-container_impl!(Vec5);
-basis_impl!(Vec5, 5);
-add_impl!(Vec5, x, y, z, w, a);
-sub_impl!(Vec5, x, y, z, w, a);
-mul_impl!(Vec5, x, y, z, w, a);
-div_impl!(Vec5, x, y, z, w, a);
-scalar_add_impl!(Vec5, x, y, z, w, a);
-scalar_sub_impl!(Vec5, x, y, z, w, a);
-scalar_mul_impl!(Vec5, x, y, z, w, a);
-scalar_div_impl!(Vec5, x, y, z, w, a);
-neg_impl!(Vec5, x, y, z, w, a);
-dot_impl!(Vec5, x, y, z, w, a);
-translation_impl!(Vec5);
-norm_impl!(Vec5, x, y, z, w, a);
-approx_eq_impl!(Vec5, x, y, z, w, a);
-zero_one_impl!(Vec5, x, y, z, w, a);
-from_iterator_impl!(Vec5, iterator, iterator, iterator, iterator, iterator);
-bounded_impl!(Vec5, x, y, z, w, a);
-axpy_impl!(Vec5, x, y, z, w, a);
-iterable_impl!(Vec5, 5);
-iterable_mut_impl!(Vec5, 5);
-vec_to_homogeneous_impl!(Vec5, Vec6, b, x, y, z, w, a);
-vec_from_homogeneous_impl!(Vec5, Vec6, b, x, y, z, w, a);
-translate_impl!(Vec5, Pnt5);
-rotate_impl!(Vec5);
-rotate_impl!(Pnt5);
-transform_impl!(Vec5, Pnt5);
-vec_as_pnt_impl!(Vec5, Pnt5, x, y, z, w, a);
-num_float_vec_impl!(Vec5);
-absolute_vec_impl!(Vec5, x, y, z, w, a);
-arbitrary_impl!(Vec5, x, y, z, w, a);
-rand_impl!(Vec5, x, y, z, w, a);
-mean_impl!(Vec5);
-vec_display_impl!(Vec5);
-
-/// Vector of dimension 6.
-///
-/// The main differance between a point and a vector is that a vector is not affected by
-/// translations.
-#[repr(C)]
-#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
-pub struct Vec6<N> {
-    /// First component of the vector.
-    pub x: N,
-    /// Second component of the vector.
-    pub y: N,
-    /// Third component of the vector.
-    pub z: N,
-    /// Fourth component of the vector.
-    pub w: N,
-    /// Fifth of the vector.
-    pub a: N,
-    /// Sixth component of the vector.
-    pub b: N
-}
-
-new_impl!(Vec6, x, y, z, w, a, b);
-pord_impl!(Vec6, x, y, z, w, a, b);
-vec_axis_impl!(Vec6, x, y, z, w, a, b);
-vec_cast_impl!(Vec6, x, y, z, w, a, b);
-conversion_impl!(Vec6, 6);
-index_impl!(Vec6);
-indexable_impl!(Vec6, 6);
-at_fast_impl!(Vec6, 6);
-repeat_impl!(Vec6, val, x, y, z, w, a, b);
-dim_impl!(Vec6, 6);
-container_impl!(Vec6);
-basis_impl!(Vec6, 6);
-add_impl!(Vec6, x, y, z, w, a, b);
-sub_impl!(Vec6, x, y, z, w, a, b);
-mul_impl!(Vec6, x, y, z, w, a, b);
-div_impl!(Vec6, x, y, z, w, a, b);
-scalar_add_impl!(Vec6, x, y, z, w, a, b);
-scalar_sub_impl!(Vec6, x, y, z, w, a, b);
-scalar_mul_impl!(Vec6, x, y, z, w, a, b);
-scalar_div_impl!(Vec6, x, y, z, w, a, b);
-neg_impl!(Vec6, x, y, z, w, a, b);
-dot_impl!(Vec6, x, y, z, w, a, b);
-translation_impl!(Vec6);
-norm_impl!(Vec6, x, y, z, w, a, b);
-approx_eq_impl!(Vec6, x, y, z, w, a, b);
-zero_one_impl!(Vec6, x, y, z, w, a, b);
-from_iterator_impl!(Vec6, iterator, iterator, iterator, iterator, iterator, iterator);
-bounded_impl!(Vec6, x, y, z, w, a, b);
-axpy_impl!(Vec6, x, y, z, w, a, b);
-iterable_impl!(Vec6, 6);
-iterable_mut_impl!(Vec6, 6);
-translate_impl!(Vec6, Pnt6);
-rotate_impl!(Vec6);
-rotate_impl!(Pnt6);
-transform_impl!(Vec6, Pnt6);
-vec_as_pnt_impl!(Vec6, Pnt6, x, y, z, w, a, b);
-num_float_vec_impl!(Vec6);
-absolute_vec_impl!(Vec6, x, y, z, w, a, b);
-arbitrary_impl!(Vec6, x, y, z, w, a, b);
-rand_impl!(Vec6, x, y, z, w, a, b);
-mean_impl!(Vec6);
-vec_display_impl!(Vec6);

src/structs/vector.rs

@@ -0,0 +1,384 @@
+//! Vectors with dimension known at compile-time.
+
+use std::ops::{Add, Sub, Mul, Div, Neg, AddAssign, SubAssign, MulAssign, DivAssign, Index, IndexMut};
+use std::mem;
+use std::slice::{Iter, IterMut};
+use std::iter::{Iterator, FromIterator, IntoIterator};
+use std::fmt;
+use rand::{Rand, Rng};
+use num::{Zero, One};
+use traits::operations::{ApproxEq, PartialOrder, PartialOrdering, Axpy, Absolute, Mean};
+use traits::geometry::{Transform, Rotate, FromHomogeneous, ToHomogeneous, Dot, Norm,
+                       Translation, Translate};
+use traits::structure::{Basis, Cast, Dimension, Indexable, Iterable, IterableMut, Shape, NumVector,
+                        FloatVector, BaseFloat, BaseNum, Bounded, Repeat};
+use structs::point::{Point1, Point2, Point3, Point4, Point5, Point6};
+
+#[cfg(feature="arbitrary")]
+use quickcheck::{Arbitrary, Gen};
+
+
+/// Vector of dimension 1.
+///
+/// The main differance between a point and a vector is that a vector is not affected by
+/// translations.
+#[repr(C)]
+#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
+pub struct Vector1<N> {
+    /// First component of the vector.
+    pub x: N
+}
+
+new_impl!(Vector1, x);
+pord_impl!(Vector1, x,);
+vec_axis_impl!(Vector1, x);
+vec_cast_impl!(Vector1, x);
+conversion_impl!(Vector1, 1);
+index_impl!(Vector1);
+indexable_impl!(Vector1, 1);
+at_fast_impl!(Vector1, 1);
+repeat_impl!(Vector1, val, x);
+dim_impl!(Vector1, 1);
+container_impl!(Vector1);
+// (specialized); basis_impl!(Vector1, 1);
+add_impl!(Vector1, x);
+sub_impl!(Vector1, x);
+mul_impl!(Vector1, x);
+div_impl!(Vector1, x);
+scalar_add_impl!(Vector1, x);
+scalar_sub_impl!(Vector1, x);
+scalar_mul_impl!(Vector1, x);
+scalar_div_impl!(Vector1, x);
+neg_impl!(Vector1, x);
+dot_impl!(Vector1, x);
+translation_impl!(Vector1);
+norm_impl!(Vector1, x);
+approx_eq_impl!(Vector1, x);
+zero_one_impl!(Vector1, x);
+from_iterator_impl!(Vector1, iterator);
+bounded_impl!(Vector1, x);
+axpy_impl!(Vector1, x);
+iterable_impl!(Vector1, 1);
+iterable_mut_impl!(Vector1, 1);
+vec_to_homogeneous_impl!(Vector1, Vector2, y, x);
+vec_from_homogeneous_impl!(Vector1, Vector2, y, x);
+translate_impl!(Vector1, Point1);
+rotate_impl!(Vector1);
+rotate_impl!(Point1);
+transform_impl!(Vector1, Point1);
+vec_as_point_impl!(Vector1, Point1, x);
+num_float_vec_impl!(Vector1);
+absolute_vec_impl!(Vector1, x);
+arbitrary_impl!(Vector1, x);
+rand_impl!(Vector1, x);
+mean_impl!(Vector1);
+vec_display_impl!(Vector1);
+
+/// Vector of dimension 2.
+///
+/// The main differance between a point and a vector is that a vector is not affected by
+/// translations.
+#[repr(C)]
+#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
+pub struct Vector2<N> {
+    /// First component of the vector.
+    pub x: N,
+    /// Second component of the vector.
+    pub y: N
+}
+
+new_impl!(Vector2, x, y);
+pord_impl!(Vector2, x, y);
+vec_axis_impl!(Vector2, x, y);
+vec_cast_impl!(Vector2, x, y);
+conversion_impl!(Vector2, 2);
+index_impl!(Vector2);
+indexable_impl!(Vector2, 2);
+at_fast_impl!(Vector2, 2);
+repeat_impl!(Vector2, val, x, y);
+dim_impl!(Vector2, 2);
+container_impl!(Vector2);
+// (specialized); basis_impl!(Vector2, 1);
+add_impl!(Vector2, x, y);
+sub_impl!(Vector2, x, y);
+mul_impl!(Vector2, x, y);
+div_impl!(Vector2, x, y);
+scalar_add_impl!(Vector2, x, y);
+scalar_sub_impl!(Vector2, x, y);
+scalar_mul_impl!(Vector2, x, y);
+scalar_div_impl!(Vector2, x, y);
+neg_impl!(Vector2, x, y);
+dot_impl!(Vector2, x, y);
+translation_impl!(Vector2);
+norm_impl!(Vector2, x, y);
+approx_eq_impl!(Vector2, x, y);
+zero_one_impl!(Vector2, x, y);
+from_iterator_impl!(Vector2, iterator, iterator);
+bounded_impl!(Vector2, x, y);
+axpy_impl!(Vector2, x, y);
+iterable_impl!(Vector2, 2);
+iterable_mut_impl!(Vector2, 2);
+vec_to_homogeneous_impl!(Vector2, Vector3, z, x, y);
+vec_from_homogeneous_impl!(Vector2, Vector3, z, x, y);
+translate_impl!(Vector2, Point2);
+rotate_impl!(Vector2);
+rotate_impl!(Point2);
+transform_impl!(Vector2, Point2);
+vec_as_point_impl!(Vector2, Point2, x, y);
+num_float_vec_impl!(Vector2);
+absolute_vec_impl!(Vector2, x, y);
+arbitrary_impl!(Vector2, x, y);
+rand_impl!(Vector2, x, y);
+mean_impl!(Vector2);
+vec_display_impl!(Vector2);
+
+/// Vector of dimension 3.
+///
+/// The main differance between a point and a vector is that a vector is not affected by
+/// translations.
+#[repr(C)]
+#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
+pub struct Vector3<N> {
+    /// First component of the vector.
+    pub x: N,
+    /// Second component of the vector.
+    pub y: N,
+    /// Third component of the vector.
+    pub z: N
+}
+
+new_impl!(Vector3, x, y, z);
+pord_impl!(Vector3, x, y, z);
+vec_axis_impl!(Vector3, x, y, z);
+vec_cast_impl!(Vector3, x, y, z);
+conversion_impl!(Vector3, 3);
+index_impl!(Vector3);
+indexable_impl!(Vector3, 3);
+at_fast_impl!(Vector3, 3);
+repeat_impl!(Vector3, val, x, y, z);
+dim_impl!(Vector3, 3);
+container_impl!(Vector3);
+// (specialized); basis_impl!(Vector3, 1);
+add_impl!(Vector3, x, y, z);
+sub_impl!(Vector3, x, y, z);
+mul_impl!(Vector3, x, y, z);
+div_impl!(Vector3, x, y, z);
+scalar_add_impl!(Vector3, x, y, z);
+scalar_sub_impl!(Vector3, x, y, z);
+scalar_mul_impl!(Vector3, x, y, z);
+scalar_div_impl!(Vector3, x, y, z);
+neg_impl!(Vector3, x, y, z);
+dot_impl!(Vector3, x, y, z);
+translation_impl!(Vector3);
+norm_impl!(Vector3, x, y ,z);
+approx_eq_impl!(Vector3, x, y, z);
+zero_one_impl!(Vector3, x, y, z);
+from_iterator_impl!(Vector3, iterator, iterator, iterator);
+bounded_impl!(Vector3, x, y, z);
+axpy_impl!(Vector3, x, y, z);
+iterable_impl!(Vector3, 3);
+iterable_mut_impl!(Vector3, 3);
+vec_to_homogeneous_impl!(Vector3, Vector4, w, x, y, z);
+vec_from_homogeneous_impl!(Vector3, Vector4, w, x, y, z);
+translate_impl!(Vector3, Point3);
+rotate_impl!(Vector3);
+rotate_impl!(Point3);
+transform_impl!(Vector3, Point3);
+vec_as_point_impl!(Vector3, Point3, x, y, z);
+num_float_vec_impl!(Vector3);
+absolute_vec_impl!(Vector3, x, y, z);
+arbitrary_impl!(Vector3, x, y, z);
+rand_impl!(Vector3, x, y, z);
+mean_impl!(Vector3);
+vec_display_impl!(Vector3);
+
+
+/// Vector of dimension 4.
+///
+/// The main differance between a point and a vector is that a vector is not affected by
+/// translations.
+#[repr(C)]
+#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
+pub struct Vector4<N> {
+    /// First component of the vector.
+    pub x: N,
+    /// Second component of the vector.
+    pub y: N,
+    /// Third component of the vector.
+    pub z: N,
+    /// Fourth component of the vector.
+    pub w: N
+}
+
+new_impl!(Vector4, x, y, z, w);
+pord_impl!(Vector4, x, y, z, w);
+vec_axis_impl!(Vector4, x, y, z, w);
+vec_cast_impl!(Vector4, x, y, z, w);
+conversion_impl!(Vector4, 4);
+index_impl!(Vector4);
+indexable_impl!(Vector4, 4);
+at_fast_impl!(Vector4, 4);
+repeat_impl!(Vector4, val, x, y, z, w);
+dim_impl!(Vector4, 4);
+container_impl!(Vector4);
+basis_impl!(Vector4, 4);
+add_impl!(Vector4, x, y, z, w);
+sub_impl!(Vector4, x, y, z, w);
+mul_impl!(Vector4, x, y, z, w);
+div_impl!(Vector4, x, y, z, w);
+scalar_add_impl!(Vector4, x, y, z, w);
+scalar_sub_impl!(Vector4, x, y, z, w);
+scalar_mul_impl!(Vector4, x, y, z, w);
+scalar_div_impl!(Vector4, x, y, z, w);
+neg_impl!(Vector4, x, y, z, w);
+dot_impl!(Vector4, x, y, z, w);
+translation_impl!(Vector4);
+norm_impl!(Vector4, x, y, z, w);
+approx_eq_impl!(Vector4, x, y, z, w);
+zero_one_impl!(Vector4, x, y, z, w);
+from_iterator_impl!(Vector4, iterator, iterator, iterator, iterator);
+bounded_impl!(Vector4, x, y, z, w);
+axpy_impl!(Vector4, x, y, z, w);
+iterable_impl!(Vector4, 4);
+iterable_mut_impl!(Vector4, 4);
+vec_to_homogeneous_impl!(Vector4, Vector5, a, x, y, z, w);
+vec_from_homogeneous_impl!(Vector4, Vector5, a, x, y, z, w);
+translate_impl!(Vector4, Point4);
+rotate_impl!(Vector4);
+rotate_impl!(Point4);
+transform_impl!(Vector4, Point4);
+vec_as_point_impl!(Vector4, Point4, x, y, z, w);
+num_float_vec_impl!(Vector4);
+absolute_vec_impl!(Vector4, x, y, z, w);
+arbitrary_impl!(Vector4, x, y, z, w);
+rand_impl!(Vector4, x, y, z, w);
+mean_impl!(Vector4);
+vec_display_impl!(Vector4);
+
+/// Vector of dimension 5.
+///
+/// The main differance between a point and a vector is that a vector is not affected by
+/// translations.
+#[repr(C)]
+#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
+pub struct Vector5<N> {
+    /// First component of the vector.
+    pub x: N,
+    /// Second component of the vector.
+    pub y: N,
+    /// Third component of the vector.
+    pub z: N,
+    /// Fourth component of the vector.
+    pub w: N,
+    /// Fifth of the vector.
+    pub a: N
+}
+
+new_impl!(Vector5, x, y, z, w, a);
+pord_impl!(Vector5, x, y, z, w, a);
+vec_axis_impl!(Vector5, x, y, z, w, a);
+vec_cast_impl!(Vector5, x, y, z, w, a);
+conversion_impl!(Vector5, 5);
+index_impl!(Vector5);
+indexable_impl!(Vector5, 5);
+at_fast_impl!(Vector5, 5);
+repeat_impl!(Vector5, val, x, y, z, w, a);
+dim_impl!(Vector5, 5);
+container_impl!(Vector5);
+basis_impl!(Vector5, 5);
+add_impl!(Vector5, x, y, z, w, a);
+sub_impl!(Vector5, x, y, z, w, a);
+mul_impl!(Vector5, x, y, z, w, a);
+div_impl!(Vector5, x, y, z, w, a);
+scalar_add_impl!(Vector5, x, y, z, w, a);
+scalar_sub_impl!(Vector5, x, y, z, w, a);
+scalar_mul_impl!(Vector5, x, y, z, w, a);
+scalar_div_impl!(Vector5, x, y, z, w, a);
+neg_impl!(Vector5, x, y, z, w, a);
+dot_impl!(Vector5, x, y, z, w, a);
+translation_impl!(Vector5);
+norm_impl!(Vector5, x, y, z, w, a);
+approx_eq_impl!(Vector5, x, y, z, w, a);
+zero_one_impl!(Vector5, x, y, z, w, a);
+from_iterator_impl!(Vector5, iterator, iterator, iterator, iterator, iterator);
+bounded_impl!(Vector5, x, y, z, w, a);
+axpy_impl!(Vector5, x, y, z, w, a);
+iterable_impl!(Vector5, 5);
+iterable_mut_impl!(Vector5, 5);
+vec_to_homogeneous_impl!(Vector5, Vector6, b, x, y, z, w, a);
+vec_from_homogeneous_impl!(Vector5, Vector6, b, x, y, z, w, a);
+translate_impl!(Vector5, Point5);
+rotate_impl!(Vector5);
+rotate_impl!(Point5);
+transform_impl!(Vector5, Point5);
+vec_as_point_impl!(Vector5, Point5, x, y, z, w, a);
+num_float_vec_impl!(Vector5);
+absolute_vec_impl!(Vector5, x, y, z, w, a);
+arbitrary_impl!(Vector5, x, y, z, w, a);
+rand_impl!(Vector5, x, y, z, w, a);
+mean_impl!(Vector5);
+vec_display_impl!(Vector5);
+
+/// Vector of dimension 6.
+///
+/// The main differance between a point and a vector is that a vector is not affected by
+/// translations.
+#[repr(C)]
+#[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Hash, Debug, Copy)]
+pub struct Vector6<N> {
+    /// First component of the vector.
+    pub x: N,
+    /// Second component of the vector.
+    pub y: N,
+    /// Third component of the vector.
+    pub z: N,
+    /// Fourth component of the vector.
+    pub w: N,
+    /// Fifth of the vector.
+    pub a: N,
+    /// Sixth component of the vector.
+    pub b: N
+}
+
+new_impl!(Vector6, x, y, z, w, a, b);
+pord_impl!(Vector6, x, y, z, w, a, b);
+vec_axis_impl!(Vector6, x, y, z, w, a, b);
+vec_cast_impl!(Vector6, x, y, z, w, a, b);
+conversion_impl!(Vector6, 6);
+index_impl!(Vector6);
+indexable_impl!(Vector6, 6);
+at_fast_impl!(Vector6, 6);
+repeat_impl!(Vector6, val, x, y, z, w, a, b);
+dim_impl!(Vector6, 6);
+container_impl!(Vector6);
+basis_impl!(Vector6, 6);
+add_impl!(Vector6, x, y, z, w, a, b);
+sub_impl!(Vector6, x, y, z, w, a, b);
+mul_impl!(Vector6, x, y, z, w, a, b);
+div_impl!(Vector6, x, y, z, w, a, b);
+scalar_add_impl!(Vector6, x, y, z, w, a, b);
+scalar_sub_impl!(Vector6, x, y, z, w, a, b);
+scalar_mul_impl!(Vector6, x, y, z, w, a, b);
+scalar_div_impl!(Vector6, x, y, z, w, a, b);
+neg_impl!(Vector6, x, y, z, w, a, b);
+dot_impl!(Vector6, x, y, z, w, a, b);
+translation_impl!(Vector6);
+norm_impl!(Vector6, x, y, z, w, a, b);
+approx_eq_impl!(Vector6, x, y, z, w, a, b);
+zero_one_impl!(Vector6, x, y, z, w, a, b);
+from_iterator_impl!(Vector6, iterator, iterator, iterator, iterator, iterator, iterator);
+bounded_impl!(Vector6, x, y, z, w, a, b);
+axpy_impl!(Vector6, x, y, z, w, a, b);
+iterable_impl!(Vector6, 6);
+iterable_mut_impl!(Vector6, 6);
+translate_impl!(Vector6, Point6);
+rotate_impl!(Vector6);
+rotate_impl!(Point6);
+transform_impl!(Vector6, Point6);
+vec_as_point_impl!(Vector6, Point6, x, y, z, w, a, b);
+num_float_vec_impl!(Vector6);
+absolute_vec_impl!(Vector6, x, y, z, w, a, b);
+arbitrary_impl!(Vector6, x, y, z, w, a, b);
+rand_impl!(Vector6, x, y, z, w, a, b);
+mean_impl!(Vector6);
+vec_display_impl!(Vector6);

src/structs/vector_macros.rs

@@ -15,37 +15,37 @@ macro_rules! new_impl(
 );
 
 macro_rules! conversion_impl(
-    ($t: ident, $dim: expr) => (
+    ($t: ident, $dimension: expr) => (
-        impl<N> AsRef<[N; $dim]> for $t<N> {
+        impl<N> AsRef<[N; $dimension]> for $t<N> {
             #[inline]
-            fn as_ref(&self) -> &[N; $dim] {
+            fn as_ref(&self) -> &[N; $dimension] {
                 unsafe {
                     mem::transmute(self)
                 }
             }
         }
 
-        impl<N> AsMut<[N; $dim]> for $t<N> {
+        impl<N> AsMut<[N; $dimension]> for $t<N> {
             #[inline]
-            fn as_mut(&mut self) -> &mut [N; $dim] {
+            fn as_mut(&mut self) -> &mut [N; $dimension] {
                 unsafe {
                     mem::transmute(self)
                 }
             }
         }
 
-        impl<'a, N> From<&'a [N; $dim]> for &'a $t<N> {
+        impl<'a, N> From<&'a [N; $dimension]> for &'a $t<N> {
             #[inline]
-            fn from(arr: &'a [N; $dim]) -> &'a $t<N> {
+            fn from(arr: &'a [N; $dimension]) -> &'a $t<N> {
                 unsafe {
                     mem::transmute(arr)
                 }
             }
         }
 
-        impl<'a, N> From<&'a mut [N; $dim]> for &'a mut $t<N> {
+        impl<'a, N> From<&'a mut [N; $dimension]> for &'a mut $t<N> {
             #[inline]
-            fn from(arr: &'a mut [N; $dim]) -> &'a mut $t<N> {
+            fn from(arr: &'a mut [N; $dimension]) -> &'a mut $t<N> {
                 unsafe {
                     mem::transmute(arr)
                 }
@@ -55,7 +55,7 @@ macro_rules! conversion_impl(
 );
 
 macro_rules! at_fast_impl(
-    ($t: ident, $dim: expr) => (
+    ($t: ident, $dimension: expr) => (
         impl<N: Copy> $t<N> {
             /// Unsafe read access to a vector element by index.
             #[inline]
@@ -76,7 +76,7 @@ macro_rules! at_fast_impl(
 // However, f32/f64 does not implement Ord…
 macro_rules! pord_impl(
     ($t: ident, $comp0: ident, $($compN: ident),*) => (
-        impl<N: BaseFloat> POrd for $t<N> {
+        impl<N: BaseFloat> PartialOrder for $t<N> {
             #[inline]
             fn inf(&self, other: &$t<N>) -> $t<N> {
                 $t::new(self.$comp0.min(other.$comp0)
@@ -90,24 +90,24 @@ macro_rules! pord_impl(
             }
 
             #[inline]
-            #[allow(unused_mut)] // otherwise there will be a warning for is_eq or Vec1.
+            #[allow(unused_mut)] // otherwise there will be a warning for is_eq or Vector1.
-            fn partial_cmp(&self, other: &$t<N>) -> POrdering {
+            fn partial_cmp(&self, other: &$t<N>) -> PartialOrdering {
                 let is_lt     = self.$comp0 <  other.$comp0;
                 let mut is_eq = self.$comp0 == other.$comp0;
 
                 if is_lt { // <
                     $(
                         if self.$compN > other.$compN {
-                            return POrdering::NotComparable
+                            return PartialOrdering::NotComparable
                         }
                      )*
 
-                    POrdering::PartialLess
+                    PartialOrdering::PartialLess
                 }
                 else { // >=
                     $(
                         if self.$compN < other.$compN {
-                            return POrdering::NotComparable
+                            return PartialOrdering::NotComparable
                         }
                         else if self.$compN > other.$compN {
                             is_eq = false;
@@ -116,10 +116,10 @@ macro_rules! pord_impl(
                      )*
 
                     if is_eq {
-                        POrdering::PartialEqual
+                        PartialOrdering::PartialEqual
                     }
                     else {
-                        POrdering::PartialGreater
+                        PartialOrdering::PartialGreater
                     }
                 }
             }
@@ -177,11 +177,11 @@ macro_rules! vec_cast_impl(
 );
 
 macro_rules! indexable_impl(
-    ($t: ident, $dim: expr) => (
+    ($t: ident, $dimension: expr) => (
         impl<N> Shape<usize> for $t<N> {
             #[inline]
             fn shape(&self) -> usize {
-                $dim
+                $dimension
             }
         }
 
@@ -189,18 +189,18 @@ macro_rules! indexable_impl(
             #[inline]
             fn swap(&mut self, i1: usize, i2: usize) {
                 unsafe {
-                    mem::transmute::<&mut $t<N>, &mut [N; $dim]>(self).swap(i1, i2)
+                    mem::transmute::<&mut $t<N>, &mut [N; $dimension]>(self).swap(i1, i2)
                 }
             }
 
             #[inline]
             unsafe fn unsafe_at(&self, i: usize) -> N {
-                (*mem::transmute::<&$t<N>, &[N; $dim]>(self).get_unchecked(i))
+                (*mem::transmute::<&$t<N>, &[N; $dimension]>(self).get_unchecked(i))
             }
 
             #[inline]
             unsafe fn unsafe_set(&mut self, i: usize, val: N) {
-                (*mem::transmute::<&mut $t<N>, &mut [N; $dim]>(self).get_unchecked_mut(i)) = val
+                (*mem::transmute::<&mut $t<N>, &mut [N; $dimension]>(self).get_unchecked_mut(i)) = val
             }
         }
     )
@@ -239,12 +239,12 @@ macro_rules! repeat_impl(
 );
 
 macro_rules! iterable_impl(
-    ($t: ident, $dim: expr) => (
+    ($t: ident, $dimension: expr) => (
         impl<N> Iterable<N> for $t<N> {
             #[inline]
             fn iter<'l>(&'l self) -> Iter<'l, N> {
                 unsafe {
-                    mem::transmute::<&'l $t<N>, &'l [N; $dim]>(self).iter()
+                    mem::transmute::<&'l $t<N>, &'l [N; $dimension]>(self).iter()
                 }
             }
         }
@@ -252,12 +252,12 @@ macro_rules! iterable_impl(
 );
 
 macro_rules! iterable_mut_impl(
-    ($t: ident, $dim: expr) => (
+    ($t: ident, $dimension: expr) => (
         impl<N> IterableMut<N> for $t<N> {
             #[inline]
             fn iter_mut<'l>(&'l mut self) -> IterMut<'l, N> {
                 unsafe {
-                    mem::transmute::<&'l mut $t<N>, &'l mut [N; $dim]>(self).iter_mut()
+                    mem::transmute::<&'l mut $t<N>, &'l mut [N; $dimension]>(self).iter_mut()
                 }
             }
         }
@@ -265,11 +265,11 @@ macro_rules! iterable_mut_impl(
 );
 
 macro_rules! dim_impl(
-    ($t: ident, $dim: expr) => (
+    ($t: ident, $dimension: expr) => (
-        impl<N> Dim for $t<N> {
+        impl<N> Dimension for $t<N> {
             #[inline]
-            fn dim(_: Option<$t<N>>) -> usize {
+            fn dimension(_: Option<$t<N>>) -> usize {
-                $dim
+                $dimension
             }
         }
     )
@@ -281,18 +281,18 @@ macro_rules! container_impl(
             /// The dimension of this entity.
             #[inline]
             pub fn len(&self) -> usize {
-                Dim::dim(None::<$t<N>>)
+                Dimension::dimension(None::<$t<N>>)
             }
         }
     )
 );
 
 macro_rules! basis_impl(
-    ($t: ident, $dim: expr) => (
+    ($t: ident, $dimension: expr) => (
         impl<N: BaseFloat + ApproxEq<N>> Basis for $t<N> {
             #[inline]
             fn canonical_basis<F: FnMut($t<N>) -> bool>(mut f: F) {
-                for i in 0 .. $dim {
+                for i in 0 .. $dimension {
                     if !f(Basis::canonical_basis_element(i).unwrap()) { return }
                 }
             }
@@ -303,14 +303,14 @@ macro_rules! basis_impl(
                 // orthogonalization algorithm.
                 let mut basis: Vec<$t<N>> = Vec::new();
 
-                for i in 0 .. $dim {
+                for i in 0 .. $dimension {
                     let mut basis_element : $t<N> = ::zero();
 
                     unsafe {
                         basis_element.set_fast(i, ::one());
                     }
 
-                    if basis.len() == $dim - 1 {
+                    if basis.len() == $dimension - 1 {
                         break;
                     }
 
@@ -322,7 +322,7 @@ macro_rules! basis_impl(
                         elt = elt - *v * Dot::dot(&elt, v)
                     };
 
-                    if !ApproxEq::approx_eq(&Norm::sqnorm(&elt), &::zero()) {
+                    if !ApproxEq::approx_eq(&Norm::norm_squared(&elt), &::zero()) {
                         let new_element = Norm::normalize(&elt);
 
                         if !f(new_element) { return };
@@ -334,7 +334,7 @@ macro_rules! basis_impl(
 
             #[inline]
             fn canonical_basis_element(i: usize) -> Option<$t<N>> {
-                if i < $dim {
+                if i < $dimension {
                     let mut basis_element : $t<N> = ::zero();
 
                     unsafe {
@@ -621,7 +621,7 @@ macro_rules! translation_impl(
             }
 
             #[inline]
-            fn inv_translation(&self) -> $t<N> {
+            fn inverse_translation(&self) -> $t<N> {
                 -*self
             }
 
@@ -657,7 +657,7 @@ macro_rules! norm_impl(
     ($t: ident, $($compN: ident),+) => (
         impl<N: BaseFloat> Norm<N> for $t<N> {
             #[inline]
-            fn sqnorm(&self) -> N {
+            fn norm_squared(&self) -> N {
                 Dot::dot(self, self)
             }
 
@@ -816,7 +816,7 @@ macro_rules! translate_impl(
                 *other + *self
             }
 
-            fn inv_translate(&self, other: &$t<N>) -> $t<N> {
+            fn inverse_translate(&self, other: &$t<N>) -> $t<N> {
                 *other - *self
             }
         }
@@ -830,7 +830,7 @@ macro_rules! rotate_impl(
                 *other
             }
 
-            fn inv_rotate(&self, other: &O) -> O {
+            fn inverse_rotate(&self, other: &O) -> O {
                 *other
             }
         }
@@ -844,19 +844,19 @@ macro_rules! transform_impl(
                 self.translate(other)
             }
 
-            fn inv_transform(&self, other: &$t<N>) -> $t<N> {
+            fn inverse_transform(&self, other: &$t<N>) -> $t<N> {
-                self.inv_translate(other)
+                self.inverse_translate(other)
             }
         }
     )
 );
 
-macro_rules! vec_as_pnt_impl(
+macro_rules! vec_as_point_impl(
     ($tv: ident, $t: ident, $($compN: ident),+) => (
         impl<N> $tv<N> {
             /// Converts this vector to a point.
             #[inline]
-            pub fn to_pnt(self) -> $t<N> {
+            pub fn to_point(self) -> $t<N> {
                 $t::new(
                     $(self.$compN),+
                 )
@@ -864,7 +864,7 @@ macro_rules! vec_as_pnt_impl(
 
             /// Reinterprets this vector as a point.
             #[inline]
-            pub fn as_pnt(&self) -> &$t<N> {
+            pub fn as_point(&self) -> &$t<N> {
                 unsafe {
                     mem::transmute(self)
                 }
@@ -875,11 +875,11 @@ macro_rules! vec_as_pnt_impl(
 
 macro_rules! num_float_vec_impl(
     ($t: ident) => (
-        impl<N> NumVec<N> for $t<N>
+        impl<N> NumVector<N> for $t<N>
             where N: BaseNum {
         }
 
-        impl<N> FloatVec<N> for $t<N>
+        impl<N> FloatVector<N> for $t<N>
             where N: BaseFloat + ApproxEq<N> {
         }
     )

src/structs/vectorn.rs

@@ -7,35 +7,35 @@ use num::{Zero, One};
 use generic_array::{GenericArray, ArrayLength};
 use traits::operations::{ApproxEq, Axpy, Mean};
 use traits::geometry::{Dot, Norm};
-use traits::structure::{Iterable, IterableMut, Indexable, Shape, BaseFloat, BaseNum, Cast, Dim};
+use traits::structure::{Iterable, IterableMut, Indexable, Shape, BaseFloat, BaseNum, Cast, Dimension};
 #[cfg(feature="arbitrary")]
 use quickcheck::{Arbitrary, Gen};
 
 /// A static array of arbitrary dimension.
 #[repr(C)]
 #[derive(Eq, PartialEq, Debug)] //  FIXME: Hash, RustcEncodable, RustcDecodable
-pub struct VecN<N, D: ArrayLength<N>> {
+pub struct VectorN<N, D: ArrayLength<N>> {
     /// The underlying data of the vector.
     pub at: GenericArray<N, D>
 }
 
-unsafe impl<N: Send, D: ArrayLength<N>> Send for VecN<N, D> {
+unsafe impl<N: Send, D: ArrayLength<N>> Send for VectorN<N, D> {
 }
 
-impl<N: Clone, D: ArrayLength<N>> Clone for VecN<N, D> {
+impl<N: Clone, D: ArrayLength<N>> Clone for VectorN<N, D> {
-    fn clone(&self) -> VecN<N, D> {
+    fn clone(&self) -> VectorN<N, D> {
-        VecN::new(self.at.clone())
+        VectorN::new(self.at.clone())
     }
 }
 
-impl<N: Copy, D: ArrayLength<N>> Copy for VecN<N, D>
+impl<N: Copy, D: ArrayLength<N>> Copy for VectorN<N, D>
     where D::ArrayType: Copy { }
 
-impl<N, D: ArrayLength<N>> VecN<N, D> {
+impl<N, D: ArrayLength<N>> VectorN<N, D> {
     /// Creates a new vector from a given arbirtarily-sized array.
     #[inline]
-    pub fn new(components: GenericArray<N, D>) -> VecN<N, D> {
+    pub fn new(components: GenericArray<N, D>) -> VectorN<N, D> {
-        VecN {
+        VectorN {
             at: components
         }
     }
@@ -47,31 +47,31 @@ impl<N, D: ArrayLength<N>> VecN<N, D> {
     }
 }
 
-impl<N, D: ArrayLength<N>> Dim for VecN<N, D> {
+impl<N, D: ArrayLength<N>> Dimension for VectorN<N, D> {
-    fn dim(_unused: Option<Self>) -> usize {
+    fn dimension(_unused: Option<Self>) -> usize {
         D::to_usize()
     }
 }
 
-impl<N: Copy, D: ArrayLength<N>> FromIterator<N> for VecN<N, D> {
+impl<N: Copy, D: ArrayLength<N>> FromIterator<N> for VectorN<N, D> {
     #[inline]
-    fn from_iter<I: IntoIterator<Item = N>>(param: I) -> VecN<N, D> {
+    fn from_iter<I: IntoIterator<Item = N>>(param: I) -> VectorN<N, D> {
-        let mut res: VecN<N, D> = unsafe { mem::uninitialized() };
+        let mut res: VectorN<N, D> = unsafe { mem::uninitialized() };
 
         let mut it = param.into_iter();
 
         for e in res.iter_mut() {
-            *e = it.next().expect("Not enough data into the provided iterator to initialize this `VecN`.");
+            *e = it.next().expect("Not enough data into the provided iterator to initialize this `VectorN`.");
         }
 
         res
     }
 }
 
-impl<N: Rand + Zero, D: ArrayLength<N>> Rand for VecN<N, D> {
+impl<N: Rand + Zero, D: ArrayLength<N>> Rand for VectorN<N, D> {
     #[inline]
-    fn rand<R: Rng>(rng: &mut R) -> VecN<N, D> {
+    fn rand<R: Rng>(rng: &mut R) -> VectorN<N, D> {
-        let mut res: VecN<N, D> = unsafe { mem::uninitialized() };
+        let mut res: VectorN<N, D> = unsafe { mem::uninitialized() };
 
         for e in res.iter_mut() {
             *e = Rand::rand(rng)
@@ -81,10 +81,10 @@ impl<N: Rand + Zero, D: ArrayLength<N>> Rand for VecN<N, D> {
     }
 }
 
-impl<N: Copy + One + Zero, D: ArrayLength<N>> One for VecN<N, D> {
+impl<N: Copy + One + Zero, D: ArrayLength<N>> One for VectorN<N, D> {
     #[inline]
-    fn one() -> VecN<N, D> {
+    fn one() -> VectorN<N, D> {
-        let mut res: VecN<N, D> = unsafe { mem::uninitialized() };
+        let mut res: VectorN<N, D> = unsafe { mem::uninitialized() };
 
         for e in res.iter_mut() {
             *e = ::one()
@@ -94,10 +94,10 @@ impl<N: Copy + One + Zero, D: ArrayLength<N>> One for VecN<N, D> {
     }
 }
 
-impl<N: Copy + Zero, D: ArrayLength<N>> Zero for VecN<N, D> {
+impl<N: Copy + Zero, D: ArrayLength<N>> Zero for VectorN<N, D> {
     #[inline]
-    fn zero() -> VecN<N, D> {
+    fn zero() -> VectorN<N, D> {
-        let mut res: VecN<N, D> = unsafe { mem::uninitialized() };
+        let mut res: VectorN<N, D> = unsafe { mem::uninitialized() };
 
         for e in res.iter_mut() {
             *e = ::zero()
@@ -113,11 +113,12 @@ impl<N: Copy + Zero, D: ArrayLength<N>> Zero for VecN<N, D> {
 }
 
 #[cfg(feature="arbitrary")]
-impl<N: Arbitrary + Zero + Copy, D: 'static + ArrayLength<N>> Arbitrary for VecN<N, D> {
+impl<N: Arbitrary + Zero + Copy, D: 'static + ArrayLength<N>> Arbitrary for VectorN<N, D> {
     #[inline]
-    fn arbitrary<G: Gen>(g: &mut G) -> VecN<N, D> {
+    fn arbitrary<G: Gen>(g: &mut G) -> VectorN<N, D> {
         (0 .. D::to_usize()).map(|_| Arbitrary::arbitrary(g)).collect()
     }
 }
 
-vecn_dvec_common_impl!(VecN, D);
+
+vecn_dvec_common_impl!(VectorN, D);

src/structs/vectorn_macros.rs

@@ -163,7 +163,7 @@ macro_rules! vecn_dvec_common_impl(
             }
         }
 
-        impl<N> MulAssign<$vecn<N $(, $param)*>> for $vecn<N $(, $param)*>
+        impl<N $(, $param: ArrayLength<N>)*> MulAssign<$vecn<N $(, $param)*>> for $vecn<N $(, $param)*>
             where N: Copy + MulAssign<N> + Zero $(, $param : ArrayLength<N>)* {
             #[inline]
             fn mul_assign(&mut self, right: $vecn<N $(, $param)*>) {
@@ -175,7 +175,7 @@ macro_rules! vecn_dvec_common_impl(
             }
         }
 
-        impl<N> MulAssign<N> for $vecn<N $(, $param)*>
+        impl<N $(, $param: ArrayLength<N>)*> MulAssign<N> for $vecn<N $(, $param)*>
             where N: Copy + MulAssign<N> + Zero $(, $param : ArrayLength<N>)* {
             #[inline]
             fn mul_assign(&mut self, right: N) {
@@ -185,7 +185,7 @@ macro_rules! vecn_dvec_common_impl(
             }
         }
 
-        impl<$($param : ArrayLength<N>),*> Mul<$vecn<f32 $(, $param)*>> for f32 {
+        impl<$($param : ArrayLength<f32>),*> Mul<$vecn<f32 $(, $param)*>> for f32 {
             type Output = $vecn<f32 $(, $param)*>;
 
             #[inline]
@@ -200,7 +200,7 @@ macro_rules! vecn_dvec_common_impl(
             }
         }
 
-        impl<$($param : ArrayLength<N>),*> Mul<$vecn<f64 $(, $param)*>> for f64 {
+        impl<$($param : ArrayLength<f64>),*> Mul<$vecn<f64 $(, $param)*>> for f64 {
             type Output = $vecn<f64 $(, $param)*>;
 
             #[inline]
@@ -253,7 +253,7 @@ macro_rules! vecn_dvec_common_impl(
             }
         }
 
-        impl<N> DivAssign<$vecn<N $(, $param)*>> for $vecn<N $(, $param)*>
+        impl<N $(, $param: ArrayLength<N>)*> DivAssign<$vecn<N $(, $param)*>> for $vecn<N $(, $param)*>
             where N: Copy + DivAssign<N> + Zero $(, $param : ArrayLength<N>)* {
             #[inline]
             fn div_assign(&mut self, right: $vecn<N $(, $param)*>) {
@@ -265,7 +265,7 @@ macro_rules! vecn_dvec_common_impl(
             }
         }
 
-        impl<N> DivAssign<N> for $vecn<N $(, $param)*>
+        impl<N $(, $param: ArrayLength<N>)*> DivAssign<N> for $vecn<N $(, $param)*>
             where N: Copy + DivAssign<N> + Zero $(, $param : ArrayLength<N>)* {
             #[inline]
             fn div_assign(&mut self, right: N) {
@@ -313,7 +313,7 @@ macro_rules! vecn_dvec_common_impl(
             }
         }
 
-        impl<N> AddAssign<$vecn<N $(, $param)*>> for $vecn<N $(, $param)*>
+        impl<N $(, $param: ArrayLength<N>)*> AddAssign<$vecn<N $(, $param)*>> for $vecn<N $(, $param)*>
             where N: Copy + AddAssign<N> + Zero $(, $param : ArrayLength<N>)* {
             #[inline]
             fn add_assign(&mut self, right: $vecn<N $(, $param)*>) {
@@ -325,7 +325,7 @@ macro_rules! vecn_dvec_common_impl(
             }
         }
 
-        impl<N> AddAssign<N> for $vecn<N $(, $param)*>
+        impl<N $(, $param: ArrayLength<N>)*> AddAssign<N> for $vecn<N $(, $param)*>
             where N: Copy + AddAssign<N> + Zero $(, $param : ArrayLength<N>)* {
             #[inline]
             fn add_assign(&mut self, right: N) {
@@ -403,7 +403,7 @@ macro_rules! vecn_dvec_common_impl(
             }
         }
 
-        impl<N> SubAssign<$vecn<N $(, $param)*>> for $vecn<N $(, $param)*>
+        impl<N $(, $param: ArrayLength<N>)*> SubAssign<$vecn<N $(, $param)*>> for $vecn<N $(, $param)*>
             where N: Copy + SubAssign<N> + Zero $(, $param : ArrayLength<N>)* {
             #[inline]
             fn sub_assign(&mut self, right: $vecn<N $(, $param)*>) {
@@ -415,7 +415,7 @@ macro_rules! vecn_dvec_common_impl(
             }
         }
 
-        impl<N> SubAssign<N> for $vecn<N $(, $param)*>
+        impl<N $(, $param: ArrayLength<N>)*> SubAssign<N> for $vecn<N $(, $param)*>
             where N: Copy + SubAssign<N> + Zero $(, $param : ArrayLength<N>)* {
             #[inline]
             fn sub_assign(&mut self, right: N) {
@@ -497,7 +497,7 @@ macro_rules! vecn_dvec_common_impl(
          */
         impl<N: BaseFloat $(, $param : ArrayLength<N>)*> Norm<N> for $vecn<N $(, $param)*> {
             #[inline]
-            fn sqnorm(&self) -> N {
+            fn norm_squared(&self) -> N {
                 Dot::dot(self, self)
             }
 

src/traits/geometry.rs

@@ -1,7 +1,7 @@
 //! Traits of operations having a well-known or explicit geometric meaning.
 
 use std::ops::{Neg, Mul};
-use traits::structure::{BaseFloat, SquareMat};
+use traits::structure::{BaseFloat, SquareMatrix};
 
 /// Trait of object which represent a translation, and to wich new translation
 /// can be appended.
@@ -11,7 +11,7 @@ pub trait Translation<V> {
     fn translation(&self) -> V;
 
     /// Gets the inverse translation associated with this object.
-    fn inv_translation(&self) -> V;
+    fn inverse_translation(&self) -> V;
 
     /// Appends a translation to this object.
     fn append_translation_mut(&mut self, &V);
@@ -36,7 +36,7 @@ pub trait Translate<V> {
     fn translate(&self, &V) -> V;
 
     /// Apply an inverse translation to an object.
-    fn inv_translate(&self, &V) -> V;
+    fn inverse_translate(&self, &V) -> V;
 }
 
 /// Trait of object which can represent a rotation, and to which new rotations can be appended. A
@@ -46,7 +46,7 @@ pub trait Rotation<V> {
     fn rotation(&self) -> V;
 
     /// Gets the inverse rotation associated with `self`.
-    fn inv_rotation(&self) -> V;
+    fn inverse_rotation(&self) -> V;
 
     /// Appends a rotation to this object.
     fn append_rotation_mut(&mut self, &V);
@@ -88,7 +88,7 @@ pub trait Rotate<V> {
     fn rotate(&self, v: &V) -> V;
 
     /// Applies an inverse rotation to `v`.
-    fn inv_rotate(&self, v: &V) -> V;
+    fn inverse_rotate(&self, v: &V) -> V;
 }
 
 /// Various composition of rotation and translation.
@@ -159,10 +159,10 @@ impl<LV: Neg<Output = LV> + Copy, AV, M: Rotation<AV> + Translation<LV>> Rotatio
 /// be implemented by quaternions to convert them to a rotation matrix.
 pub trait RotationMatrix<N, LV: Mul<Self::Output, Output = LV>, AV> : Rotation<AV> {
     /// The output rotation matrix type.
-    type Output: SquareMat<N, LV> + Rotation<AV>;
+    type Output: SquareMatrix<N, LV> + Rotation<AV>;
 
     /// Gets the rotation matrix represented by `self`.
-    fn to_rot_mat(&self) -> Self::Output;
+    fn to_rotation_matrix(&self) -> Self::Output;
 }
 
 /// Composition of a rotation and an absolute value.
@@ -187,7 +187,7 @@ pub trait Transformation<M> {
     fn transformation(&self) -> M;
 
     /// Gets the inverse transformation of `self`.
-    fn inv_transformation(&self) -> M;
+    fn inverse_transformation(&self) -> M;
 
     /// Appends a transformation to this object.
     fn append_transformation_mut(&mut self, &M);
@@ -213,7 +213,7 @@ pub trait Transform<V> {
     fn transform(&self, &V) -> V;
 
     /// Applies an inverse transformation to `v`.
-    fn inv_transform(&self, &V) -> V;
+    fn inverse_transform(&self, &V) -> V;
 }
 
 /// Traits of objects having a dot product.
@@ -228,13 +228,13 @@ pub trait Norm<N: BaseFloat> {
     /// Computes the norm of `self`.
     #[inline]
     fn norm(&self) -> N {
-        self.sqnorm().sqrt()
+        self.norm_squared().sqrt()
     }
 
     /// Computes the squared norm of `self`.
     ///
     /// This is usually faster than computing the norm itself.
-    fn sqnorm(&self) -> N;
+    fn norm_squared(&self) -> N;
 
     /// Gets the normalized version of a copy of `v`.
     fn normalize(&self) -> Self;
@@ -288,10 +288,10 @@ pub trait UniformSphereSample : Sized {
 }
 
 /// The zero element of a vector space, seen as an element of its embeding affine space.
-// XXX: once associated types are suported, move this to the `AnyPnt` trait.
+// XXX: once associated types are suported, move this to the `AnyPoint` trait.
-pub trait Orig {
+pub trait Origin {
     /// The trivial origin.
-    fn orig() -> Self;
+    fn origin() -> Self;
     /// Returns true if this points is exactly the trivial origin.
-    fn is_orig(&self) -> bool;
+    fn is_origin(&self) -> bool;
 }

src/traits/mod.rs

@@ -1,18 +1,18 @@
-//! Mathematical traits.
+//! Matrixhematical traits.
 
-pub use traits::geometry::{AbsoluteRotate, Cross, CrossMatrix, Dot, FromHomogeneous, Norm, Orig,
+pub use traits::geometry::{AbsoluteRotate, Cross, CrossMatrix, Dot, FromHomogeneous, Norm, Origin,
                            Rotate, Rotation, RotationMatrix, RotationWithTranslation, RotationTo,
                            ToHomogeneous, Transform, Transformation, Translate, Translation,
                            UniformSphereSample};
 
-pub use traits::structure::{FloatVec, FloatPnt, Basis, Cast, Col, Dim, Indexable, Iterable,
+pub use traits::structure::{FloatVector, FloatPoint, Basis, Cast, Column, Dimension, Indexable, Iterable,
-                            IterableMut, Mat, SquareMat, Row, NumVec, NumPnt, PntAsVec, ColSlice,
+                            IterableMut, Matrix, SquareMatrix, Row, NumVector, NumPoint, PointAsVector, ColumnSlice,
-                            RowSlice, Diag, DiagMut, Eye, Repeat, Shape, BaseFloat, BaseNum,
+                            RowSlice, Diagonal, DiagMut, Eye, Repeat, Shape, BaseFloat, BaseNum,
                             Bounded};
 
-pub use traits::operations::{Absolute, ApproxEq, Axpy, Cov, Det, Inv, Mean, Outer, POrd, Transpose,
+pub use traits::operations::{Absolute, ApproxEq, Axpy, Covariance, Determinant, Inverse, Mean, Outer, PartialOrder, Transpose,
                              EigenQR};
-pub use traits::operations::POrdering;
+pub use traits::operations::PartialOrdering;
 
 pub mod geometry;
 pub mod structure;

src/traits/operations.rs

@@ -3,11 +3,11 @@
 use num::{Float, Signed};
 use std::ops::Mul;
 use std::cmp::Ordering;
-use traits::structure::SquareMat;
+use traits::structure::SquareMatrix;
 
 /// Result of a partial ordering.
 #[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Debug, Copy)]
-pub enum POrdering {
+pub enum PartialOrdering {
     /// Result of a strict comparison.
     PartialLess,
     /// Equality relationship.
@@ -18,61 +18,61 @@ pub enum POrdering {
     NotComparable
 }
 
-impl POrdering {
+impl PartialOrdering {
     /// Returns `true` if `self` is equal to `Equal`.
     pub fn is_eq(&self) -> bool {
-        *self == POrdering::PartialEqual
+        *self == PartialOrdering::PartialEqual
     }
 
     /// Returns `true` if `self` is equal to `Less`.
     pub fn is_lt(&self) -> bool {
-        *self == POrdering::PartialLess
+        *self == PartialOrdering::PartialLess
     }
 
     /// Returns `true` if `self` is equal to `Less` or `Equal`.
     pub fn is_le(&self) -> bool {
-        *self == POrdering::PartialLess || *self == POrdering::PartialEqual
+        *self == PartialOrdering::PartialLess || *self == PartialOrdering::PartialEqual
     }
 
     /// Returns `true` if `self` is equal to `Greater`.
     pub fn is_gt(&self) -> bool {
-        *self == POrdering::PartialGreater
+        *self == PartialOrdering::PartialGreater
     }
 
     /// Returns `true` if `self` is equal to `Greater` or `Equal`.
     pub fn is_ge(&self) -> bool {
-        *self == POrdering::PartialGreater || *self == POrdering::PartialEqual
+        *self == PartialOrdering::PartialGreater || *self == PartialOrdering::PartialEqual
     }
 
     /// Returns `true` if `self` is equal to `NotComparable`.
     pub fn is_not_comparable(&self) -> bool {
-        *self == POrdering::NotComparable
+        *self == PartialOrdering::NotComparable
     }
 
-    /// Creates a `POrdering` from an `Ordering`.
+    /// Creates a `PartialOrdering` from an `Ordering`.
-    pub fn from_ordering(ord: Ordering) -> POrdering {
+    pub fn from_ordering(ord: Ordering) -> PartialOrdering {
         match ord {
-            Ordering::Less    => POrdering::PartialLess,
+            Ordering::Less    => PartialOrdering::PartialLess,
-            Ordering::Equal   => POrdering::PartialEqual,
+            Ordering::Equal   => PartialOrdering::PartialEqual,
-            Ordering::Greater => POrdering::PartialGreater
+            Ordering::Greater => PartialOrdering::PartialGreater
         }
     }
 
-    /// Converts this `POrdering` to an `Ordering`.
+    /// Converts this `PartialOrdering` to an `Ordering`.
     ///
     /// Returns `None` if `self` is `NotComparable`.
     pub fn to_ordering(self) -> Option<Ordering> {
         match self {
-            POrdering::PartialLess    => Some(Ordering::Less),
+            PartialOrdering::PartialLess    => Some(Ordering::Less),
-            POrdering::PartialEqual   => Some(Ordering::Equal),
+            PartialOrdering::PartialEqual   => Some(Ordering::Equal),
-            POrdering::PartialGreater => Some(Ordering::Greater),
+            PartialOrdering::PartialGreater => Some(Ordering::Greater),
-            POrdering::NotComparable  => None
+            PartialOrdering::NotComparable  => None
         }
     }
 }
 
 /// Pointwise ordering operations.
-pub trait POrd {
+pub trait PartialOrder {
     /// Returns the infimum of this value and another
     fn inf(&self, other: &Self) -> Self;
 
@@ -80,49 +80,49 @@ pub trait POrd {
     fn sup(&self, other: &Self) -> Self;
 
     /// Compare `self` and `other` using a partial ordering relation.
-    fn partial_cmp(&self, other: &Self) -> POrdering;
+    fn partial_cmp(&self, other: &Self) -> PartialOrdering;
 
     /// Returns `true` iff `self` and `other` are comparable and `self <= other`.
     #[inline]
     fn partial_le(&self, other: &Self) -> bool {
-        POrd::partial_cmp(self, other).is_le()
+        PartialOrder::partial_cmp(self, other).is_le()
     }
 
     /// Returns `true` iff `self` and `other` are comparable and `self < other`.
     #[inline]
     fn partial_lt(&self, other: &Self) -> bool {
-        POrd::partial_cmp(self, other).is_lt()
+        PartialOrder::partial_cmp(self, other).is_lt()
     }
 
     /// Returns `true` iff `self` and `other` are comparable and `self >= other`.
     #[inline]
     fn partial_ge(&self, other: &Self) -> bool {
-        POrd::partial_cmp(self, other).is_ge()
+        PartialOrder::partial_cmp(self, other).is_ge()
     }
 
     /// Returns `true` iff `self` and `other` are comparable and `self > other`.
     #[inline]
     fn partial_gt(&self, other: &Self) -> bool {
-        POrd::partial_cmp(self, other).is_gt()
+        PartialOrder::partial_cmp(self, other).is_gt()
     }
 
     /// Return the minimum of `self` and `other` if they are comparable.
     #[inline]
     fn partial_min<'a>(&'a self, other: &'a Self) -> Option<&'a Self> {
-        match POrd::partial_cmp(self, other) {
+        match PartialOrder::partial_cmp(self, other) {
-            POrdering::PartialLess | POrdering::PartialEqual => Some(self),
+            PartialOrdering::PartialLess | PartialOrdering::PartialEqual => Some(self),
-            POrdering::PartialGreater             => Some(other),
+            PartialOrdering::PartialGreater             => Some(other),
-            POrdering::NotComparable              => None
+            PartialOrdering::NotComparable              => None
         }
     }
 
     /// Return the maximum of `self` and `other` if they are comparable.
     #[inline]
     fn partial_max<'a>(&'a self, other: &'a Self) -> Option<&'a Self> {
-        match POrd::partial_cmp(self, other) {
+        match PartialOrder::partial_cmp(self, other) {
-            POrdering::PartialGreater | POrdering::PartialEqual => Some(self),
+            PartialOrdering::PartialGreater | PartialOrdering::PartialEqual => Some(self),
-            POrdering::PartialLess   => Some(other),
+            PartialOrdering::PartialLess   => Some(other),
-            POrdering::NotComparable => None
+            PartialOrdering::NotComparable => None
         }
     }
 
@@ -276,18 +276,18 @@ pub trait Absolute<A> {
 }
 
 /// Trait of objects having an inverse. Typically used to implement matrix inverse.
-pub trait Inv: Sized {
+pub trait Inverse: Sized {
     /// Returns the inverse of `m`.
-    fn inv(&self) -> Option<Self>;
+    fn inverse(&self) -> Option<Self>;
 
     /// In-place version of `inverse`.
-    fn inv_mut(&mut self) -> bool;
+    fn inverse_mut(&mut self) -> bool;
 }
 
 /// Trait of objects having a determinant. Typically used by square matrices.
-pub trait Det<N> {
+pub trait Determinant<N> {
     /// Returns the determinant of `m`.
-    fn det(&self) -> N;
+    fn determinant(&self) -> N;
 }
 
 /// Trait of objects which can be transposed.
@@ -309,19 +309,19 @@ pub trait Outer {
 }
 
 /// Trait for computing the covariance of a set of data.
-pub trait Cov<M> {
+pub trait Covariance<M> {
     /// Computes the covariance of the obsevations stored by `m`:
     ///
     ///   * For matrices, observations are stored in its rows.
     ///   * For vectors, observations are stored in its components (thus are 1-dimensional).
-    fn cov(&self) -> M;
+    fn covariance(&self) -> M;
 
     /// Computes the covariance of the obsevations stored by `m`:
     ///
     ///   * For matrices, observations are stored in its rows.
     ///   * For vectors, observations are stored in its components (thus are 1-dimensional).
-    fn cov_to(&self, out: &mut M) {
+    fn covariance_to(&self, out: &mut M) {
-        *out = self.cov()
+        *out = self.covariance()
     }
 }
 
@@ -335,7 +335,7 @@ pub trait Mean<N> {
 }
 
 /// Trait for computing the eigenvector and eigenvalues of a square matrix usin the QR algorithm.
-pub trait EigenQR<N, V: Mul<Self, Output = V>>: SquareMat<N, V> {
+pub trait EigenQR<N, V: Mul<Self, Output = V>>: SquareMatrix<N, V> {
     /// Computes the eigenvectors and eigenvalues of this matrix.
     fn eigen_qr(&self, eps: &N, niter: usize) -> (Self, V);
 }

src/traits/structure.rs

@@ -6,8 +6,8 @@ use std::ops::{Add, Sub, Mul, Div, Rem,
                AddAssign, SubAssign, MulAssign, DivAssign, RemAssign,
                Index, IndexMut, Neg};
 use num::{Float, Zero, One};
-use traits::operations::{Axpy, Transpose, Inv, Absolute};
+use traits::operations::{Axpy, Transpose, Inverse, Absolute};
-use traits::geometry::{Dot, Norm, Orig};
+use traits::geometry::{Dot, Norm, Origin};
 
 /// Basic integral numeric trait.
 pub trait BaseNum: Copy + Zero + One +
@@ -64,31 +64,31 @@ pub trait Cast<T> {
 /// Trait of matrices.
 ///
 /// A matrix has rows and columns and are able to multiply them.
-pub trait Mat<N, R, C: Mul<Self, Output = R>>: Sized +
+pub trait Matrix<N, R, C: Mul<Self, Output = R>>: Sized +
-                                               Row<R> + Col<C> + Mul<R, Output = C> +
+                                               Row<R> + Column<C> + Mul<R, Output = C> +
                                                Index<(usize, usize), Output = N>
 { }
 
-impl<N, M, R, C> Mat<N, R, C> for M
+impl<N, M, R, C> Matrix<N, R, C> for M
-    where M: Row<R> + Col<C> + Mul<R, Output = C> + Index<(usize, usize), Output = N>,
+    where M: Row<R> + Column<C> + Mul<R, Output = C> + Index<(usize, usize), Output = N>,
           C: Mul<M, Output = R>,
 { }
 
 /// Trait implemented by square matrices.
-pub trait SquareMat<N, V: Mul<Self, Output = V>>: Mat<N, V, V> +
+pub trait SquareMatrix<N, V: Mul<Self, Output = V>>: Matrix<N, V, V> +
                                                   Mul<Self, Output = Self> +
-                                                  Eye + Transpose + Diag<V> + Inv + Dim + One {
+                                                  Eye + Transpose + Diagonal<V> + Inverse + Dimension + One {
 }
 
-impl<N, V, M> SquareMat<N, V> for M
+impl<N, V, M> SquareMatrix<N, V> for M
-    where M: Mat<N, V, V> + Mul<M, Output = M> + Eye + Transpose + Diag<V> + Inv + Dim + One,
+    where M: Matrix<N, V, V> + Mul<M, Output = M> + Eye + Transpose + Diagonal<V> + Inverse + Dimension + One,
           V: Mul<M, Output = V> {
 }
 
 /// Trait for constructing the identity matrix
 pub trait Eye {
     /// Return the identity matrix of specified dimension
-    fn new_identity(dim: usize) -> Self;
+    fn new_identity(dimension: usize) -> Self;
 }
 
 /// Trait for constructiong an object repeating a value.
@@ -134,12 +134,12 @@ pub trait Row<R> {
 }
 
 /// Trait to access columns of a matrix or vector.
-pub trait Col<C> {
+pub trait Column<C> {
     /// The number of column of this matrix or vector.
     fn ncols(&self) -> usize;
 
     /// Reads the `i`-th column of `self`.
-    fn col(&self, i: usize) -> C;
+    fn column(&self, i: usize) -> C;
 
     /// Writes the `i`-th column of `self`.
     fn set_col(&mut self, i: usize, C);
@@ -149,7 +149,7 @@ pub trait Col<C> {
 }
 
 /// Trait to access part of a column of a matrix
-pub trait ColSlice<C> {
+pub trait ColumnSlice<C> {
     /// Returns a view to a slice of a column of a matrix.
     fn col_slice(&self, col_id: usize, row_start: usize, row_end: usize) -> C;
 }
@@ -161,24 +161,24 @@ pub trait RowSlice<R> {
 }
 
 /// Trait of objects having a spacial dimension known at compile time.
-pub trait Dim: Sized {
+pub trait Dimension: Sized {
     /// The dimension of the object.
-    fn dim(_unused: Option<Self>) -> usize;
+    fn dimension(_unused: Option<Self>) -> usize;
 }
 
 /// Trait to get the diagonal of square matrices.
-pub trait Diag<V> {
+pub trait Diagonal<V> {
     /// Creates a new matrix with the given diagonal.
-    fn from_diag(diag: &V) -> Self;
+    fn from_diagonal(diagonal: &V) -> Self;
 
     /// The diagonal of this matrix.
-    fn diag(&self) -> V;
+    fn diagonal(&self) -> V;
 }
 
 /// Trait to set the diagonal of square matrices.
-pub trait DiagMut<V>: Diag<V> {
+pub trait DiagMut<V>: Diagonal<V> {
     /// Sets the diagonal of this matrix.
-    fn set_diag(&mut self, diag: &V);
+    fn set_diagonal(&mut self, diagonal: &V);
 }
 
 /// The shape of an indexable object.
@@ -223,82 +223,82 @@ pub trait IterableMut<N> {
 }
 
 /*
- * Vec related traits.
+ * Vector related traits.
  */
 /// Trait grouping most common operations on vectors.
-pub trait NumVec<N>: Add<Self, Output = Self> + Sub<Self, Output = Self> +
+pub trait NumVector<N>: Add<Self, Output = Self> + Sub<Self, Output = Self> +
-                     Mul<Self, Output = Self> + Div<Self, Output = Self> +
+                        // Mul<Self, Output = Self> + Div<Self, Output = Self> +
 
-                     Add<N, Output = Self> + Sub<N, Output = Self> + 
+                        // Add<N, Output = Self> + Sub<N, Output = Self> + 
-                     Mul<N, Output = Self> + Div<N, Output = Self> + 
+                        Mul<N, Output = Self> + Div<N, Output = Self> + 
 
-                     AddAssign<Self> + SubAssign<Self> +
+                        AddAssign<Self> + SubAssign<Self> +
-                     MulAssign<Self> + DivAssign<Self> + 
+                        // MulAssign<Self> + DivAssign<Self> + 
 
-                     AddAssign<N> + SubAssign<N> + 
+                        // AddAssign<N> + SubAssign<N> + 
-                     MulAssign<N> + DivAssign<N> + 
+                        MulAssign<N> + DivAssign<N> + 
 
-                     Dim + Index<usize, Output = N> +
+                        Dimension + Index<usize, Output = N> +
-                     Zero + PartialEq + Dot<N> + Axpy<N> {
+                        Zero + PartialEq + Dot<N> + Axpy<N> {
 }
 
 /// Trait of vector with components implementing the `BaseFloat` trait.
-pub trait FloatVec<N: BaseFloat>: NumVec<N> + Norm<N> + Neg<Output = Self> + Basis {
+pub trait FloatVector<N: BaseFloat>: NumVector<N> + Norm<N> + Neg<Output = Self> + Basis {
 }
 
 /*
- * Pnt related traits.
+ * Point related traits.
  */
 /// Trait that relates a point of an affine space to a vector of the associated vector space.
-pub trait PntAsVec {
+pub trait PointAsVector {
     /// The vector type of the vector space associated to this point's affine space.
-    type Vec;
+    type Vector;
     
     /// Converts this point to its associated vector.
-    fn to_vec(self) -> Self::Vec;
+    fn to_vector(self) -> Self::Vector;
 
     /// Converts a reference to this point to a reference to its associated vector.
-    fn as_vec<'a>(&'a self) -> &'a Self::Vec;
+    fn as_vector<'a>(&'a self) -> &'a Self::Vector;
 
     // NOTE: this is used in some places to overcome some limitations untill the trait reform is
     // done on rustc.
     /// Sets the coordinates of this point to match those of a given vector.
-    fn set_coords(&mut self, coords: Self::Vec);
+    fn set_coords(&mut self, coords: Self::Vector);
 }
 
 /// Trait grouping most common operations on points.
 // XXX: the vector space element `V` should be an associated type. Though this would prevent V from
 // having bounds (they are not supported yet). So, for now, we will just use a type parameter.
-pub trait NumPnt<N>:
+pub trait NumPoint<N>:
           Copy +
-          PntAsVec +
+          PointAsVector +
-          Dim +
+          Dimension +
-          Orig +
+          Origin +
           PartialEq +
           Axpy<N> +
-          Sub<Self, Output = <Self as PntAsVec>::Vec> +
+          Sub<Self, Output = <Self as PointAsVector>::Vector> +
 
           Mul<N, Output = Self> + Div<N, Output = Self> +
-          Add<<Self as PntAsVec>::Vec, Output = Self> +
+          Add<<Self as PointAsVector>::Vector, Output = Self> +
 
           MulAssign<N> + DivAssign<N> +
-          AddAssign<<Self as PntAsVec>::Vec> +
+          AddAssign<<Self as PointAsVector>::Vector> +
 
           Index<usize, Output = N> { // FIXME: + Sub<V, Self>
 }
 
 /// Trait of points with components implementing the `BaseFloat` trait.
-pub trait FloatPnt<N: BaseFloat>: NumPnt<N> + Sized
+pub trait FloatPoint<N: BaseFloat>: NumPoint<N> + Sized
-where <Self as PntAsVec>::Vec: Norm<N> {
+    where <Self as PointAsVector>::Vector: Norm<N> {
     /// Computes the square distance between two points.
     #[inline]
-    fn sqdist(&self, other: &Self) -> N {
+    fn distance_squared(&self, other: &Self) -> N {
-        (*self - *other).sqnorm()
+        (*self - *other).norm_squared()
     }
 
     /// Computes the distance between two points.
     #[inline]
-    fn dist(&self, other: &Self) -> N {
+    fn distance(&self, other: &Self) -> N {
         (*self - *other).norm()
     }
 }

tests/arbitrary.rs

@@ -18,47 +18,47 @@ macro_rules! trivial_arb_test(
     )
 );
 
-trivial_arb_test!(Vec1<f64>, arb_vec1);
+trivial_arb_test!(Vector1<f64>, arb_vec1);
-trivial_arb_test!(Vec2<f64>, arb_vec2);
+trivial_arb_test!(Vector2<f64>, arb_vec2);
-trivial_arb_test!(Vec3<f64>, arb_vec3);
+trivial_arb_test!(Vector3<f64>, arb_vec3);
-trivial_arb_test!(Vec4<f64>, arb_vec4);
+trivial_arb_test!(Vector4<f64>, arb_vec4);
-trivial_arb_test!(Vec5<f64>, arb_vec5);
+trivial_arb_test!(Vector5<f64>, arb_vec5);
-trivial_arb_test!(Vec6<f64>, arb_vec6);
+trivial_arb_test!(Vector6<f64>, arb_vec6);
 
-trivial_arb_test!(Pnt1<f64>, arb_pnt1);
+trivial_arb_test!(Point1<f64>, arb_point1);
-trivial_arb_test!(Pnt2<f64>, arb_pnt2);
+trivial_arb_test!(Point2<f64>, arb_point2);
-trivial_arb_test!(Pnt3<f64>, arb_pnt3);
+trivial_arb_test!(Point3<f64>, arb_point3);
-trivial_arb_test!(Pnt4<f64>, arb_pnt4);
+trivial_arb_test!(Point4<f64>, arb_point4);
-trivial_arb_test!(Pnt5<f64>, arb_pnt5);
+trivial_arb_test!(Point5<f64>, arb_point5);
-trivial_arb_test!(Pnt6<f64>, arb_pnt6);
+trivial_arb_test!(Point6<f64>, arb_point6);
 
-trivial_arb_test!(Mat1<f64>, arb_mat1);
+trivial_arb_test!(Matrix1<f64>, arb_mat1);
-trivial_arb_test!(Mat2<f64>, arb_mat2);
+trivial_arb_test!(Matrix2<f64>, arb_mat2);
-trivial_arb_test!(Mat3<f64>, arb_mat3);
+trivial_arb_test!(Matrix3<f64>, arb_mat3);
-trivial_arb_test!(Mat4<f64>, arb_mat4);
+trivial_arb_test!(Matrix4<f64>, arb_mat4);
-trivial_arb_test!(Mat5<f64>, arb_mat5);
+trivial_arb_test!(Matrix5<f64>, arb_mat5);
-trivial_arb_test!(Mat6<f64>, arb_mat6);
+trivial_arb_test!(Matrix6<f64>, arb_mat6);
 
-trivial_arb_test!(DVec1<f64>, arb_dvec1);
+trivial_arb_test!(DVector1<f64>, arb_dvec1);
-trivial_arb_test!(DVec2<f64>, arb_dvec2);
+trivial_arb_test!(DVector2<f64>, arb_dvec2);
-trivial_arb_test!(DVec3<f64>, arb_dvec3);
+trivial_arb_test!(DVector3<f64>, arb_dvec3);
-trivial_arb_test!(DVec4<f64>, arb_dvec4);
+trivial_arb_test!(DVector4<f64>, arb_dvec4);
-trivial_arb_test!(DVec5<f64>, arb_dvec5);
+trivial_arb_test!(DVector5<f64>, arb_dvec5);
-trivial_arb_test!(DVec6<f64>, arb_dvec6);
+trivial_arb_test!(DVector6<f64>, arb_dvec6);
 
-trivial_arb_test!(DMat<f64>, arb_dmat);
+trivial_arb_test!(DMatrix<f64>, arb_dmatrix);
-trivial_arb_test!(DVec<f64>, arb_dvec);
+trivial_arb_test!(DVector<f64>, arb_dvector);
 
-trivial_arb_test!(Quat<f64>, arb_quat);
+trivial_arb_test!(Quaternion<f64>, arb_quaternion);
-trivial_arb_test!(UnitQuat<f64>, arb_unit_quat);
+trivial_arb_test!(UnitQuaternion<f64>, arb_unit_quaternion);
 
-trivial_arb_test!(Iso2<f64>, arb_iso2);
+trivial_arb_test!(Isometry2<f64>, arb_iso2);
-trivial_arb_test!(Iso3<f64>, arb_iso3);
+trivial_arb_test!(Isometry3<f64>, arb_iso3);
 
-trivial_arb_test!(Rot2<f64>, arb_rot2);
+trivial_arb_test!(Rotation2<f64>, arb_rot2);
-trivial_arb_test!(Rot3<f64>, arb_rot3);
+trivial_arb_test!(Rotation3<f64>, arb_rot3);
 
-trivial_arb_test!(Ortho3<f64>, arb_ortho3);
+trivial_arb_test!(Orthographic3<f64>, arb_ortho3);
-trivial_arb_test!(OrthoMat3<f64>, arb_ortho_mat3);
+trivial_arb_test!(OrthographicMatrix3<f64>, arb_ortho_mat3);
-trivial_arb_test!(Persp3<f64>, arb_persp3);
+trivial_arb_test!(Perspective3<f64>, arb_persp3);
-trivial_arb_test!(PerspMat3<f64>, arb_persp_mat3);
+trivial_arb_test!(PerspectiveMatrix3<f64>, arb_perspective_mat3);

tests/assert.rs

@@ -3,7 +3,7 @@
 #[macro_use]
 extern crate nalgebra;
 
-use nalgebra::{ApproxEq, Vec2};
+use nalgebra::{ApproxEq, Vector2};
 
 #[test]
 fn assert_approx_eq_f64() {
@@ -16,8 +16,8 @@ fn assert_approx_eq_f64() {
 #[test]
 #[should_panic]
 fn assert_approx_eq_vec2_f32_fail() {
-    let a = Vec2::new(1.0f32, 0.0);
+    let a = Vector2::new(1.0f32, 0.0);
-    let b = Vec2::new(1.1f32, 0.1);
+    let b = Vector2::new(1.1f32, 0.1);
     assert_approx_eq!(a, b);
 }
 

tests/mat.rs

@@ -2,18 +2,18 @@ extern crate nalgebra as na;
 extern crate rand;
 
 use rand::random;
-use na::{Rot2, Rot3, Iso2, Iso3, Sim2, Sim3, Vec3, Mat1, Mat2, Mat3, Mat4, Mat5, Mat6, DMat, DVec,
+use na::{Rotation2, Rotation3, Isometry2, Isometry3, Similarity2, Similarity3, Vector3, Matrix1, Matrix2, Matrix3, Matrix4, Matrix5, Matrix6, DMatrix, DVector,
-         Row, Col, Diag, Transpose, RowSlice, ColSlice, Shape};
+         Row, Column, Diagonal, Transpose, RowSlice, ColumnSlice, Shape};
 
-macro_rules! test_inv_mat_impl(
+macro_rules! test_inverse_mat_impl(
   ($t: ty) => (
     for _ in 0usize .. 10000 {
-      let randmat : $t = random();
+      let randmatrix : $t = random();
 
-      match na::inv(&randmat) {
+      match na::inverse(&randmatrix) {
           None    => { },
           Some(i) => {
-              assert!(na::approx_eq(&(i * randmat), &na::one()))
+              assert!(na::approx_eq(&(i * randmatrix), &na::one()))
           }
       }
     }
@@ -23,9 +23,9 @@ macro_rules! test_inv_mat_impl(
 macro_rules! test_transpose_mat_impl(
   ($t: ty) => (
     for _ in 0usize .. 10000 {
-      let randmat : $t = random();
+      let randmatrix : $t = random();
 
-      assert!(na::transpose(&na::transpose(&randmat)) == randmat);
+      assert!(na::transpose(&na::transpose(&randmatrix)) == randmatrix);
     }
   );
 );
@@ -33,12 +33,12 @@ macro_rules! test_transpose_mat_impl(
 macro_rules! test_qr_impl(
   ($t: ty) => (
     for _ in 0usize .. 10000 {
-      let randmat : $t = random();
+      let randmatrix : $t = random();
 
-      let (q, r) = na::qr(&randmat);
+      let (q, r) = na::qr(&randmatrix);
       let recomp = q * r;
 
-      assert!(na::approx_eq(&randmat,  &recomp));
+      assert!(na::approx_eq(&randmatrix,  &recomp));
     }
   );
 );
@@ -48,19 +48,19 @@ macro_rules! test_cholesky_impl(
     for _ in 0usize .. 10000 {
       
       // construct symmetric positive definite matrix
-      let mut randmat : $t = random();
+      let mut randmatrix : $t = random();
-      let mut diagmat : $t = Diag::from_diag(&na::diag(&randmat));
+      let mut diagmatrix : $t = Diagonal::from_diagonal(&na::diagonal(&randmatrix));
 
-      diagmat = na::abs(&diagmat) + 1.0;
+      diagmatrix = na::abs(&diagmatrix) + 1.0;
-      randmat = randmat * diagmat * na::transpose(&randmat);
+      randmatrix = randmatrix * diagmatrix * na::transpose(&randmatrix);
 
-      let result = na::cholesky(&randmat);
+      let result = na::cholesky(&randmatrix);
 
       assert!(result.is_ok());
 
       let v = result.unwrap();
       let recomp = v * na::transpose(&v);
-      assert!(na::approx_eq(&randmat,  &recomp));
+      assert!(na::approx_eq(&randmatrix,  &recomp));
     }
   );
 );
@@ -69,9 +69,9 @@ macro_rules! test_hessenberg_impl(
   ($t: ty) => (
     for _ in 0usize .. 10000 {
       
-      let randmat : $t = random();
+      let randmatrix : $t = random();
 
-      let (q, h) = na::hessenberg(&randmat);
+      let (q, h) = na::hessenberg(&randmatrix);
       let recomp = q * h * na::transpose(&q);
 
       let (rows, cols) = h.shape();
@@ -85,7 +85,7 @@ macro_rules! test_hessenberg_impl(
           }
       }
 
-      assert!(na::approx_eq(&randmat,  &recomp));
+      assert!(na::approx_eq(&randmatrix,  &recomp));
     }
   );
 );
@@ -93,138 +93,138 @@ macro_rules! test_hessenberg_impl(
 macro_rules! test_eigen_qr_impl(
     ($t: ty) => {
         for _ in 0usize .. 10000 {
-            let randmat : $t = random();
+            let randmatrix : $t = random();
             // Make it symetric so that we can recompose the matrix to test at the end.
-            let randmat = na::transpose(&randmat) * randmat;
+            let randmatrix = na::transpose(&randmatrix) * randmatrix;
-            let (eigenvectors, eigenvalues) = na::eigen_qr(&randmat, &1e-13, 100);
+            let (eigenvectors, eigenvalues) = na::eigen_qr(&randmatrix, &1e-13, 100);
  
-            let diag: $t = Diag::from_diag(&eigenvalues);
+            let diagonal: $t = Diagonal::from_diagonal(&eigenvalues);
-            let recomp = eigenvectors * diag * na::transpose(&eigenvectors);
+            let recomp = eigenvectors * diagonal * na::transpose(&eigenvectors);
             println!("eigenvalues: {:?}", eigenvalues);
-            println!("   mat: {:?}", randmat);
+            println!("   matrix: {:?}", randmatrix);
             println!("recomp: {:?}", recomp);
 
-            assert!(na::approx_eq_eps(&randmat,  &recomp, &1.0e-2));
+            assert!(na::approx_eq_eps(&randmatrix,  &recomp, &1.0e-2));
         }
 
         for _ in 0usize .. 10000 {
-            let randmat : $t = random();
+            let randmatrix : $t = random();
             // Take only diagonal part
-            let randmat: $t = Diag::from_diag(&randmat.diag());
+            let randmatrix: $t = Diagonal::from_diagonal(&randmatrix.diagonal());
-            let (eigenvectors, eigenvalues) = na::eigen_qr(&randmat, &1e-13, 100);
+            let (eigenvectors, eigenvalues) = na::eigen_qr(&randmatrix, &1e-13, 100);
  
-            let diag: $t = Diag::from_diag(&eigenvalues);
+            let diagonal: $t = Diagonal::from_diagonal(&eigenvalues);
-            let recomp = eigenvectors * diag * na::transpose(&eigenvectors);
+            let recomp = eigenvectors * diagonal * na::transpose(&eigenvectors);
             println!("eigenvalues: {:?}", eigenvalues);
-            println!("   mat: {:?}", randmat);
+            println!("   matrix: {:?}", randmatrix);
             println!("recomp: {:?}", recomp);
 
-            assert!(na::approx_eq_eps(&randmat,  &recomp, &1.0e-2));
+            assert!(na::approx_eq_eps(&randmatrix,  &recomp, &1.0e-2));
         }
     }
 );
 
 #[test]
 fn test_transpose_mat1() {
-    test_transpose_mat_impl!(Mat1<f64>);
+    test_transpose_mat_impl!(Matrix1<f64>);
 }
 
 #[test]
 fn test_transpose_mat2() {
-    test_transpose_mat_impl!(Mat2<f64>);
+    test_transpose_mat_impl!(Matrix2<f64>);
 }
 
 #[test]
 fn test_transpose_mat3() {
-    test_transpose_mat_impl!(Mat3<f64>);
+    test_transpose_mat_impl!(Matrix3<f64>);
 }
 
 #[test]
 fn test_transpose_mat4() {
-    test_transpose_mat_impl!(Mat4<f64>);
+    test_transpose_mat_impl!(Matrix4<f64>);
 }
 
 #[test]
 fn test_transpose_mat5() {
-    test_transpose_mat_impl!(Mat5<f64>);
+    test_transpose_mat_impl!(Matrix5<f64>);
 }
 
 #[test]
 fn test_transpose_mat6() {
-    test_transpose_mat_impl!(Mat6<f64>);
+    test_transpose_mat_impl!(Matrix6<f64>);
 }
 
 #[test]
-fn test_inv_mat1() {
+fn test_inverse_mat1() {
-    test_inv_mat_impl!(Mat1<f64>);
+    test_inverse_mat_impl!(Matrix1<f64>);
 }
 
 #[test]
-fn test_inv_mat2() {
+fn test_inverse_mat2() {
-    test_inv_mat_impl!(Mat2<f64>);
+    test_inverse_mat_impl!(Matrix2<f64>);
 }
 
 #[test]
-fn test_inv_mat3() {
+fn test_inverse_mat3() {
-    test_inv_mat_impl!(Mat3<f64>);
+    test_inverse_mat_impl!(Matrix3<f64>);
 }
 
 #[test]
-fn test_inv_mat4() {
+fn test_inverse_mat4() {
-    test_inv_mat_impl!(Mat4<f64>);
+    test_inverse_mat_impl!(Matrix4<f64>);
 }
 
 #[test]
-fn test_inv_mat5() {
+fn test_inverse_mat5() {
-    test_inv_mat_impl!(Mat5<f64>);
+    test_inverse_mat_impl!(Matrix5<f64>);
 }
 
 #[test]
-fn test_inv_mat6() {
+fn test_inverse_mat6() {
-    test_inv_mat_impl!(Mat6<f64>);
+    test_inverse_mat_impl!(Matrix6<f64>);
 }
 
 #[test]
-fn test_inv_rot2() {
+fn test_inverse_rot2() {
-    test_inv_mat_impl!(Rot2<f64>);
+    test_inverse_mat_impl!(Rotation2<f64>);
 }
 
 #[test]
-fn test_inv_rot3() {
+fn test_inverse_rot3() {
-    test_inv_mat_impl!(Rot3<f64>);
+    test_inverse_mat_impl!(Rotation3<f64>);
 }
 
 #[test]
-fn test_inv_iso2() {
+fn test_inverse_iso2() {
-    test_inv_mat_impl!(Iso2<f64>);
+    test_inverse_mat_impl!(Isometry2<f64>);
 }
 
 #[test]
-fn test_inv_iso3() {
+fn test_inverse_iso3() {
-    test_inv_mat_impl!(Iso3<f64>);
+    test_inverse_mat_impl!(Isometry3<f64>);
 }
 
 #[test]
-fn test_inv_sim2() {
+fn test_inverse_sim2() {
-    test_inv_mat_impl!(Sim2<f64>);
+    test_inverse_mat_impl!(Similarity2<f64>);
 }
 
 #[test]
-fn test_inv_sim3() {
+fn test_inverse_sim3() {
-    test_inv_mat_impl!(Sim3<f64>);
+    test_inverse_mat_impl!(Similarity3<f64>);
 }
 
 #[test]
 fn test_index_mat2() {
-  let mat: Mat2<f64> = random();
+  let matrix: Matrix2<f64> = random();
 
-  assert!(mat[(0, 1)] == na::transpose(&mat)[(1, 0)]);
+  assert!(matrix[(0, 1)] == na::transpose(&matrix)[(1, 0)]);
 }
 
 
 #[test]
-fn test_mean_dmat() {
+fn test_mean_dmatrix() {
-    let mat = DMat::from_row_vec(
+    let matrix = DMatrix::from_row_vector(
         3,
         3,
         &[
@@ -234,12 +234,12 @@ fn test_mean_dmat() {
         ]
     );
 
-    assert!(na::approx_eq(&na::mean(&mat), &DVec::from_slice(3, &[4.0f64, 5.0, 6.0])));
+    assert!(na::approx_eq(&na::mean(&matrix), &DVector::from_slice(3, &[4.0f64, 5.0, 6.0])));
 }
 
 #[test]
-fn test_cov_dmat() {
+fn test_covariance_dmatrix() {
-    let mat = DMat::from_row_vec(
+    let matrix = DMatrix::from_row_vector(
         5,
         3,
         &[
@@ -251,7 +251,7 @@ fn test_cov_dmat() {
         ]
     );
 
-    let expected = DMat::from_row_vec(
+    let expected = DMatrix::from_row_vector(
         3,
         3,
         &[
@@ -261,12 +261,12 @@ fn test_cov_dmat() {
         ]
     );
 
-    assert!(na::approx_eq(&na::cov(&mat), &expected));
+    assert!(na::approx_eq(&na::covariance(&matrix), &expected));
 }
 
 #[test]
-fn test_transpose_dmat() {
+fn test_transpose_dmatrix() {
-    let mat = DMat::from_row_vec(
+    let matrix = DMatrix::from_row_vector(
         8,
         4,
         &[
@@ -281,12 +281,12 @@ fn test_transpose_dmat() {
         ]
     );
 
-    assert!(na::transpose(&na::transpose(&mat)) == mat);
+    assert!(na::transpose(&na::transpose(&matrix)) == matrix);
 }
 
 #[test]
-fn test_row_dmat() {
+fn test_row_dmatrix() {
-    let mat = DMat::from_row_vec(
+    let matrix = DMatrix::from_row_vector(
         8,
         4,
         &[
@@ -301,19 +301,19 @@ fn test_row_dmat() {
         ]
     );
 
-    assert_eq!(&DVec::from_slice(4, &[1u32,  2,  3,  4]),  &mat.row(0));
+    assert_eq!(&DVector::from_slice(4, &[1u32,  2,  3,  4]),  &matrix.row(0));
-    assert_eq!(&DVec::from_slice(4, &[5u32,  6,  7,  8]),  &mat.row(1));
+    assert_eq!(&DVector::from_slice(4, &[5u32,  6,  7,  8]),  &matrix.row(1));
-    assert_eq!(&DVec::from_slice(4, &[9u32,  10, 11, 12]), &mat.row(2));
+    assert_eq!(&DVector::from_slice(4, &[9u32,  10, 11, 12]), &matrix.row(2));
-    assert_eq!(&DVec::from_slice(4, &[13u32, 14, 15, 16]), &mat.row(3));
+    assert_eq!(&DVector::from_slice(4, &[13u32, 14, 15, 16]), &matrix.row(3));
-    assert_eq!(&DVec::from_slice(4, &[17u32, 18, 19, 20]), &mat.row(4));
+    assert_eq!(&DVector::from_slice(4, &[17u32, 18, 19, 20]), &matrix.row(4));
-    assert_eq!(&DVec::from_slice(4, &[21u32, 22, 23, 24]), &mat.row(5));
+    assert_eq!(&DVector::from_slice(4, &[21u32, 22, 23, 24]), &matrix.row(5));
-    assert_eq!(&DVec::from_slice(4, &[25u32, 26, 27, 28]), &mat.row(6));
+    assert_eq!(&DVector::from_slice(4, &[25u32, 26, 27, 28]), &matrix.row(6));
-    assert_eq!(&DVec::from_slice(4, &[29u32, 30, 31, 32]), &mat.row(7));
+    assert_eq!(&DVector::from_slice(4, &[29u32, 30, 31, 32]), &matrix.row(7));
 }
 
 #[test]
-fn test_row_slice_dmat() {
+fn test_row_slice_dmatrix() {
-    let mat = DMat::from_row_vec(
+    let matrix = DMatrix::from_row_vector(
         5,
         4,
         &[
@@ -325,15 +325,15 @@ fn test_row_slice_dmat() {
         ]
     );
 
-    assert_eq!(&DVec::from_slice(4, &[1u32, 2, 3, 4]), &mat.row_slice(0, 0, 4));
+    assert_eq!(&DVector::from_slice(4, &[1u32, 2, 3, 4]), &matrix.row_slice(0, 0, 4));
-    assert_eq!(&DVec::from_slice(2, &[1u32, 2]), &mat.row_slice(0, 0, 2));
+    assert_eq!(&DVector::from_slice(2, &[1u32, 2]), &matrix.row_slice(0, 0, 2));
-    assert_eq!(&DVec::from_slice(2, &[10u32, 11]), &mat.row_slice(2, 1, 3));
+    assert_eq!(&DVector::from_slice(2, &[10u32, 11]), &matrix.row_slice(2, 1, 3));
-    assert_eq!(&DVec::from_slice(2, &[19u32, 20]), &mat.row_slice(4, 2, 4));
+    assert_eq!(&DVector::from_slice(2, &[19u32, 20]), &matrix.row_slice(4, 2, 4));
 }
 
 #[test]
-fn test_col_dmat() {
+fn test_col_dmatrix() {
-    let mat = DMat::from_row_vec(
+    let matrix = DMatrix::from_row_vector(
         8,
         4,
         &[
@@ -348,15 +348,15 @@ fn test_col_dmat() {
         ]
     );
 
-    assert_eq!(&DVec::from_slice(8, &[1u32, 5, 9,  13, 17, 21, 25, 29]), &mat.col(0));
+    assert_eq!(&DVector::from_slice(8, &[1u32, 5, 9,  13, 17, 21, 25, 29]), &matrix.column(0));
-    assert_eq!(&DVec::from_slice(8, &[2u32, 6, 10, 14, 18, 22, 26, 30]), &mat.col(1));
+    assert_eq!(&DVector::from_slice(8, &[2u32, 6, 10, 14, 18, 22, 26, 30]), &matrix.column(1));
-    assert_eq!(&DVec::from_slice(8, &[3u32, 7, 11, 15, 19, 23, 27, 31]), &mat.col(2));
+    assert_eq!(&DVector::from_slice(8, &[3u32, 7, 11, 15, 19, 23, 27, 31]), &matrix.column(2));
-    assert_eq!(&DVec::from_slice(8, &[4u32, 8, 12, 16, 20, 24, 28, 32]), &mat.col(3));
+    assert_eq!(&DVector::from_slice(8, &[4u32, 8, 12, 16, 20, 24, 28, 32]), &matrix.column(3));
 }
 
 #[test]
-fn test_col_slice_dmat() {
+fn test_col_slice_dmatrix() {
-    let mat = DMat::from_row_vec(
+    let matrix = DMatrix::from_row_vector(
         8,
         4,
         &[
@@ -371,15 +371,15 @@ fn test_col_slice_dmat() {
         ]
     );
 
-    assert_eq!(&DVec::from_slice(8, &[1u32, 5, 9, 13, 17, 21, 25, 29]), &mat.col_slice(0, 0, 8));
+    assert_eq!(&DVector::from_slice(8, &[1u32, 5, 9, 13, 17, 21, 25, 29]), &matrix.col_slice(0, 0, 8));
-    assert_eq!(&DVec::from_slice(3, &[1u32, 5, 9]), &mat.col_slice(0, 0, 3));
+    assert_eq!(&DVector::from_slice(3, &[1u32, 5, 9]), &matrix.col_slice(0, 0, 3));
-    assert_eq!(&DVec::from_slice(5, &[11u32, 15, 19, 23, 27]), &mat.col_slice(2, 2, 7));
+    assert_eq!(&DVector::from_slice(5, &[11u32, 15, 19, 23, 27]), &matrix.col_slice(2, 2, 7));
-    assert_eq!(&DVec::from_slice(2, &[28u32, 32]), &mat.col_slice(3, 6, 8));
+    assert_eq!(&DVector::from_slice(2, &[28u32, 32]), &matrix.col_slice(3, 6, 8));
 }
 
 #[test]
-fn test_dmat_from_vec() {
+fn test_dmat_from_vector() {
-    let mat1 = DMat::from_row_vec(
+    let mat1 = DMatrix::from_row_vector(
         8,
         4,
         &[
@@ -394,7 +394,7 @@ fn test_dmat_from_vec() {
         ]
     );
 
-    let mat2 = DMat::from_col_vec(
+    let mat2 = DMatrix::from_col_vector(
         8,
         4,
         &[
@@ -412,7 +412,7 @@ fn test_dmat_from_vec() {
 
 #[test]
 fn test_dmat_addition() {
-    let mat1 = DMat::from_row_vec(
+    let mat1 = DMatrix::from_row_vector(
         2,
         2,
         &[
@@ -421,7 +421,7 @@ fn test_dmat_addition() {
         ]
     );
 
-    let mat2 = DMat::from_row_vec(
+    let mat2 = DMatrix::from_row_vector(
         2,
         2,
         &[
@@ -430,7 +430,7 @@ fn test_dmat_addition() {
         ]
     );
 
-    let res = DMat::from_row_vec(
+    let res = DMatrix::from_row_vector(
         2,
         2,
         &[
@@ -444,7 +444,7 @@ fn test_dmat_addition() {
 
 #[test]
 fn test_dmat_multiplication() {
-   let mat1 = DMat::from_row_vec(
+   let mat1 = DMatrix::from_row_vector(
         2,
         2,
         &[
@@ -453,7 +453,7 @@ fn test_dmat_multiplication() {
         ]
     );
 
-    let mat2 = DMat::from_row_vec(
+    let mat2 = DMatrix::from_row_vector(
         2,
         2,
         &[
@@ -462,7 +462,7 @@ fn test_dmat_multiplication() {
         ]
     );
 
-    let res = DMat::from_row_vec(
+    let res = DMatrix::from_row_vector(
         2,
         2,
         &[
@@ -477,7 +477,7 @@ fn test_dmat_multiplication() {
 // Tests multiplication of rectangular (non-square) matrices.
 #[test]
 fn test_dmat_multiplication_rect() {
-    let mat1 = DMat::from_row_vec(
+    let mat1 = DMatrix::from_row_vector(
         1,
         2,
         &[
@@ -485,7 +485,7 @@ fn test_dmat_multiplication_rect() {
         ]
     );
 
-    let mat2 = DMat::from_row_vec(
+    let mat2 = DMatrix::from_row_vector(
         2,
         3,
         &[
@@ -494,7 +494,7 @@ fn test_dmat_multiplication_rect() {
         ]
     );
 
-    let res = DMat::from_row_vec(
+    let res = DMatrix::from_row_vector(
         1,
         3,
         &[
@@ -510,7 +510,7 @@ fn test_dmat_multiplication_rect() {
 
 #[test]
 fn test_dmat_subtraction() {
-    let mat1 = DMat::from_row_vec(
+    let mat1 = DMatrix::from_row_vector(
         2,
         2,
         &[
@@ -519,7 +519,7 @@ fn test_dmat_subtraction() {
         ]
     );
 
-    let mat2 = DMat::from_row_vec(
+    let mat2 = DMatrix::from_row_vector(
         2,
         2,
         &[
@@ -528,7 +528,7 @@ fn test_dmat_subtraction() {
         ]
     );
 
-    let res = DMat::from_row_vec(
+    let res = DMatrix::from_row_vector(
         2,
         2,
         &[
@@ -542,7 +542,7 @@ fn test_dmat_subtraction() {
 
 #[test]
 fn test_dmat_col() {
-    let mat = DMat::from_row_vec(
+    let matrix = DMatrix::from_row_vector(
         3,
         3,
         &[
@@ -552,12 +552,12 @@ fn test_dmat_col() {
         ]
     );
 
-    assert!(mat.col(1) == DVec::from_slice(3, &[2.0, 5.0, 8.0]));
+    assert!(matrix.column(1) == DVector::from_slice(3, &[2.0, 5.0, 8.0]));
 }
 
 #[test]
 fn test_dmat_set_col() {
-    let mut mat = DMat::from_row_vec(
+    let mut matrix = DMatrix::from_row_vector(
         3,
         3,
         &[
@@ -567,9 +567,9 @@ fn test_dmat_set_col() {
         ]
     );
 
-    mat.set_col(1, DVec::from_slice(3, &[12.0, 15.0, 18.0]));
+    matrix.set_col(1, DVector::from_slice(3, &[12.0, 15.0, 18.0]));
 
-    let expected = DMat::from_row_vec(
+    let expected = DMatrix::from_row_vector(
         3,
         3,
         &[
@@ -579,12 +579,12 @@ fn test_dmat_set_col() {
         ]
     );
 
-    assert!(mat == expected);
+    assert!(matrix == expected);
 }
 
 #[test]
 fn test_dmat_row() {
-    let mat = DMat::from_row_vec(
+    let matrix = DMatrix::from_row_vector(
         3,
         3,
         &[
@@ -594,12 +594,12 @@ fn test_dmat_row() {
         ]
     );
 
-    assert!(mat.row(1) == DVec::from_slice(3, &[4.0, 5.0, 6.0]));
+    assert!(matrix.row(1) == DVector::from_slice(3, &[4.0, 5.0, 6.0]));
 }
 
 #[test]
 fn test_dmat_set_row() {
-    let mut mat = DMat::from_row_vec(
+    let mut matrix = DMatrix::from_row_vector(
         3,
         3,
         &[
@@ -609,9 +609,9 @@ fn test_dmat_set_row() {
         ]
     );
 
-    mat.set_row(1, DVec::from_slice(3, &[14.0, 15.0, 16.0]));
+    matrix.set_row(1, DVector::from_slice(3, &[14.0, 15.0, 16.0]));
 
-    let expected = DMat::from_row_vec(
+    let expected = DMatrix::from_row_vector(
         3,
         3,
         &[
@@ -621,10 +621,10 @@ fn test_dmat_set_row() {
         ]
     );
 
-    assert!(mat == expected);
+    assert!(matrix == expected);
 }
 
-/* FIXME: review qr decomposition to make it work with DMat.
+/* FIXME: review qr decomposition to make it work with DMatrix.
 #[test]
 fn test_qr() {
     for _ in 0usize .. 10 {
@@ -632,79 +632,79 @@ fn test_qr() {
         let dim2: usize = random();
         let rows = min(40, max(dim1, dim2));
         let cols = min(40, min(dim1, dim2));
-        let randmat: DMat<f64> = DMat::new_random(rows, cols);
+        let randmatrix: DMatrix<f64> = DMatrix::new_random(rows, cols);
-        let (q, r) = na::qr(&randmat);
+        let (q, r) = na::qr(&randmatrix);
         let recomp = q * r;
 
-        assert!(na::approx_eq(&randmat,  &recomp));
+        assert!(na::approx_eq(&randmatrix,  &recomp));
     }
 }
 */
 
 #[test]
 fn test_qr_mat1() {
-    test_qr_impl!(Mat1<f64>);
+    test_qr_impl!(Matrix1<f64>);
 }
 
 #[test]
 fn test_qr_mat2() {
-    test_qr_impl!(Mat2<f64>);
+    test_qr_impl!(Matrix2<f64>);
 }
 
 #[test]
 fn test_qr_mat3() {
-    test_qr_impl!(Mat3<f64>);
+    test_qr_impl!(Matrix3<f64>);
 }
 
 #[test]
 fn test_qr_mat4() {
-    test_qr_impl!(Mat4<f64>);
+    test_qr_impl!(Matrix4<f64>);
 }
 
 #[test]
 fn test_qr_mat5() {
-    test_qr_impl!(Mat5<f64>);
+    test_qr_impl!(Matrix5<f64>);
 }
 
 #[test]
 fn test_qr_mat6() {
-    test_qr_impl!(Mat6<f64>);
+    test_qr_impl!(Matrix6<f64>);
 }
 
 #[test]
 fn test_eigen_qr_mat1() {
-    test_eigen_qr_impl!(Mat1<f64>);
+    test_eigen_qr_impl!(Matrix1<f64>);
 }
 
 #[test]
 fn test_eigen_qr_mat2() {
-    test_eigen_qr_impl!(Mat2<f64>);
+    test_eigen_qr_impl!(Matrix2<f64>);
 }
 
 #[test]
 fn test_eigen_qr_mat3() {
-    test_eigen_qr_impl!(Mat3<f64>);
+    test_eigen_qr_impl!(Matrix3<f64>);
 }
 
 #[test]
 fn test_eigen_qr_mat4() {
-    test_eigen_qr_impl!(Mat4<f64>);
+    test_eigen_qr_impl!(Matrix4<f64>);
 }
 
 #[test]
 fn test_eigen_qr_mat5() {
-    test_eigen_qr_impl!(Mat5<f64>);
+    test_eigen_qr_impl!(Matrix5<f64>);
 }
 
 #[test]
 fn test_eigen_qr_mat6() {
-    test_eigen_qr_impl!(Mat6<f64>);
+    test_eigen_qr_impl!(Matrix6<f64>);
 }
 
 #[test]
 fn test_from_fn() {
-    let actual: DMat<usize> = DMat::from_fn(3, 4, |i, j| 10 * i + j);
+    let actual: DMatrix<usize> = DMatrix::from_fn(3, 4, |i, j| 10 * i + j);
-    let expected: DMat<usize> = DMat::from_row_vec(3, 4, 
+    let expected: DMatrix<usize> = DMatrix::from_row_vector(3, 4, 
                                                   &[ 0_0, 0_1, 0_2, 0_3,
                                                      1_0, 1_1, 1_2, 1_3,
                                                      2_0, 2_1, 2_2, 2_3 ]);
@@ -714,21 +714,21 @@ fn test_from_fn() {
 
 #[test]
 fn test_row_3() {
-    let mat = Mat3::new(0.0f32, 1.0, 2.0,
+    let matrix = Matrix3::new(0.0f32, 1.0, 2.0,
                         3.0,    4.0, 5.0,
                         6.0,    7.0, 8.0);
-    let second_row = mat.row(1);
+    let second_row = matrix.row(1);
-    let second_col = mat.col(1);
+    let second_col = matrix.column(1);
 
-    assert!(second_row == Vec3::new(3.0, 4.0, 5.0));
+    assert!(second_row == Vector3::new(3.0, 4.0, 5.0));
-    assert!(second_col == Vec3::new(1.0, 4.0, 7.0));
+    assert!(second_col == Vector3::new(1.0, 4.0, 7.0));
 }
 
 #[test]
 fn test_cholesky_const() {
     
-    let a : Mat3<f64> = Mat3::<f64>::new(1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 1.0, 2.0, 3.0);
+    let a : Matrix3<f64> = Matrix3::<f64>::new(1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 1.0, 2.0, 3.0);
-    let g : Mat3<f64> = Mat3::<f64>::new(1.0, 0.0, 0.0, 1.0, 1.0, 0.0, 1.0, 1.0, 1.0);
+    let g : Matrix3<f64> = Matrix3::<f64>::new(1.0, 0.0, 0.0, 1.0, 1.0, 0.0, 1.0, 1.0, 1.0);
 
     let result = na::cholesky(&a);
 
@@ -744,7 +744,7 @@ fn test_cholesky_const() {
 #[test]
 fn test_cholesky_not_spd() {
     
-    let a : Mat3<f64> = Mat3::<f64>::new(1.0, 2.0, 3.0, 3.0, 2.0, 1.0, 1.0, 1.0, 1.0);
+    let a : Matrix3<f64> = Matrix3::<f64>::new(1.0, 2.0, 3.0, 3.0, 2.0, 1.0, 1.0, 1.0, 1.0);
 
     let result = na::cholesky(&a);
 
@@ -754,7 +754,7 @@ fn test_cholesky_not_spd() {
 #[test]
 fn test_cholesky_not_symmetric() {
     
-    let a : Mat2<f64> = Mat2::<f64>::new(1.0, 1.0, -1.0, 1.0);
+    let a : Matrix2<f64> = Matrix2::<f64>::new(1.0, 1.0, -1.0, 1.0);
 
     let result = na::cholesky(&a);
 
@@ -763,83 +763,83 @@ fn test_cholesky_not_symmetric() {
 
 #[test]
 fn test_cholesky_mat1() {
-    test_cholesky_impl!(Mat1<f64>);
+    test_cholesky_impl!(Matrix1<f64>);
 }
 
 #[test]
 fn test_cholesky_mat2() {
-    test_cholesky_impl!(Mat2<f64>);
+    test_cholesky_impl!(Matrix2<f64>);
 }
 
 #[test]
 fn test_cholesky_mat3() {
-    test_cholesky_impl!(Mat3<f64>);
+    test_cholesky_impl!(Matrix3<f64>);
 }
 
 #[test]
 fn test_cholesky_mat4() {
-    test_cholesky_impl!(Mat4<f64>);
+    test_cholesky_impl!(Matrix4<f64>);
 }
 
 #[test]
 fn test_cholesky_mat5() {
-    test_cholesky_impl!(Mat5<f64>);
+    test_cholesky_impl!(Matrix5<f64>);
 }
 
 #[test]
 fn test_cholesky_mat6() {
-    test_cholesky_impl!(Mat6<f64>);
+    test_cholesky_impl!(Matrix6<f64>);
 }
 
 #[test]
 fn test_hessenberg_mat1() {
-    test_hessenberg_impl!(Mat1<f64>);
+    test_hessenberg_impl!(Matrix1<f64>);
 }
 
 #[test]
 fn test_hessenberg_mat2() {
-    test_hessenberg_impl!(Mat2<f64>);
+    test_hessenberg_impl!(Matrix2<f64>);
 }
 
 #[test]
 fn test_hessenberg_mat3() {
-    test_hessenberg_impl!(Mat3<f64>);
+    test_hessenberg_impl!(Matrix3<f64>);
 }
 
 #[test]
 fn test_hessenberg_mat4() {
-    test_hessenberg_impl!(Mat4<f64>);
+    test_hessenberg_impl!(Matrix4<f64>);
 }
 
 #[test]
 fn test_hessenberg_mat5() {
-    test_hessenberg_impl!(Mat5<f64>);
+    test_hessenberg_impl!(Matrix5<f64>);
 }
 
 #[test]
 fn test_hessenberg_mat6() {
-    test_hessenberg_impl!(Mat6<f64>);
+    test_hessenberg_impl!(Matrix6<f64>);
 }
 
 #[test]
-fn test_transpose_square_mat() {
+fn test_transpose_square_matrix() {
-    let col_major_mat = &[0, 1, 2, 3,
+    let col_major_matrix = &[0, 1, 2, 3,
                           0, 1, 2, 3,
                           0, 1, 2, 3,
                           0, 1, 2, 3];
     let num_rows = 4;
     let num_cols = 4;
-    let mut mat = DMat::from_col_vec(num_rows, num_cols, col_major_mat);
+    let mut matrix = DMatrix::from_col_vector(num_rows, num_cols, col_major_matrix);
-    mat.transpose_mut();
+    matrix.transpose_mut();
     for i in 0..num_rows {
-        assert_eq!(&[0, 1, 2, 3], &mat.row_slice(i, 0, num_cols)[..]);
+        assert_eq!(&[0, 1, 2, 3], &matrix.row_slice(i, 0, num_cols)[..]);
     }
 }
 
 #[test]
-fn test_outer_dvec() {
+fn test_outer_dvector() {
-    let vec = DVec::from_slice(5, &[ 1.0, 2.0, 3.0, 4.0, 5.0 ]);
+    let vector = DVector::from_slice(5, &[ 1.0, 2.0, 3.0, 4.0, 5.0 ]);
-    let row = DMat::from_row_vec(1, 5, &vec[..]);
+    let row = DMatrix::from_row_vector(1, 5, &vector[..]);
 
-    assert_eq!(row.transpose() * row, na::outer(&vec, &vec))
+    assert_eq!(row.transpose() * row, na::outer(&vector, &vector))
 }

tests/op_assign.rs

@@ -3,7 +3,7 @@ extern crate rand;
 
 use std::ops::{Mul, Div, Add, Sub, MulAssign, DivAssign, AddAssign, SubAssign};
 use rand::random;
-use na::{Pnt3, Vec3, Mat3, Rot3, Iso3, Sim3, Quat, UnitQuat};
+use na::{Point3, Vector3, Matrix3, Rotation3, Isometry3, Similarity3, Quaternion, UnitQuaternion};
 
 // NOTE: we test only the 3D version because the others share the same code anyway.
 
@@ -25,52 +25,52 @@ macro_rules! test_op_vs_op_assign(
 );
 
 // Multiplication.
-test_op_vs_op_assign!(test_vec3_f32_mul_assign, Vec3<f32>, f32, mul, mul_assign);
+test_op_vs_op_assign!(test_vec3_f32_mul_assign, Vector3<f32>, f32, mul, mul_assign);
-test_op_vs_op_assign!(test_mat3_f32_mul_assign, Mat3<f32>, f32, mul, mul_assign);
+test_op_vs_op_assign!(test_mat3_f32_mul_assign, Matrix3<f32>, f32, mul, mul_assign);
-test_op_vs_op_assign!(test_quat_f32_mul_assign, Quat<f32>, f32, mul, mul_assign);
+test_op_vs_op_assign!(test_quaternion_f32_mul_assign, Quaternion<f32>, f32, mul, mul_assign);
 
-test_op_vs_op_assign!(test_vec3_vec3_mul_assign, Vec3<f32>, Vec3<f32>, mul, mul_assign);
+test_op_vs_op_assign!(test_vec3_vec3_mul_assign, Vector3<f32>, Vector3<f32>, mul, mul_assign);
-test_op_vs_op_assign!(test_quat_quat_mul_assign, Quat<f32>, Quat<f32>, mul, mul_assign);
+test_op_vs_op_assign!(test_quaternion_quaternion_mul_assign, Quaternion<f32>, Quaternion<f32>, mul, mul_assign);
-test_op_vs_op_assign!(test_unit_quat_unit_quat_mul_assign, UnitQuat<f32>, UnitQuat<f32>, mul, mul_assign);
+test_op_vs_op_assign!(test_unit_quaternion_unit_quaternion_mul_assign, UnitQuaternion<f32>, UnitQuaternion<f32>, mul, mul_assign);
 
-test_op_vs_op_assign!(test_vec3_unit_quat_mul_assign, Vec3<f32>, UnitQuat<f32>, mul, mul_assign);
+test_op_vs_op_assign!(test_vec3_unit_quaternion_mul_assign, Vector3<f32>, UnitQuaternion<f32>, mul, mul_assign);
-test_op_vs_op_assign!(test_pnt3_unit_quat_mul_assign, Pnt3<f32>, UnitQuat<f32>, mul, mul_assign);
+test_op_vs_op_assign!(test_point3_unit_quaternion_mul_assign, Point3<f32>, UnitQuaternion<f32>, mul, mul_assign);
 
-test_op_vs_op_assign!(test_mat3_mat3_mul_assign, Mat3<f32>, Mat3<f32>, mul, mul_assign);
+test_op_vs_op_assign!(test_mat3_mat3_mul_assign, Matrix3<f32>, Matrix3<f32>, mul, mul_assign);
-test_op_vs_op_assign!(test_vec3_mat3_mul_assign, Vec3<f32>, Mat3<f32>, mul, mul_assign);
+test_op_vs_op_assign!(test_vec3_mat3_mul_assign, Vector3<f32>, Matrix3<f32>, mul, mul_assign);
-test_op_vs_op_assign!(test_pnt3_mat3_mul_assign, Pnt3<f32>, Mat3<f32>, mul, mul_assign);
+test_op_vs_op_assign!(test_point3_mat3_mul_assign, Point3<f32>, Matrix3<f32>, mul, mul_assign);
 
-test_op_vs_op_assign!(test_rot3_rot3_mul_assign, Rot3<f32>, Rot3<f32>, mul, mul_assign);
+test_op_vs_op_assign!(test_rot3_rot3_mul_assign, Rotation3<f32>, Rotation3<f32>, mul, mul_assign);
-test_op_vs_op_assign!(test_vec3_rot3_mul_assign, Vec3<f32>, Rot3<f32>, mul, mul_assign);
+test_op_vs_op_assign!(test_vec3_rot3_mul_assign, Vector3<f32>, Rotation3<f32>, mul, mul_assign);
-test_op_vs_op_assign!(test_pnt3_rot3_mul_assign, Pnt3<f32>, Rot3<f32>, mul, mul_assign);
+test_op_vs_op_assign!(test_point3_rot3_mul_assign, Point3<f32>, Rotation3<f32>, mul, mul_assign);
 
-test_op_vs_op_assign!(test_iso3_iso3_mul_assign, Iso3<f32>, Iso3<f32>, mul, mul_assign);
+test_op_vs_op_assign!(test_iso3_iso3_mul_assign, Isometry3<f32>, Isometry3<f32>, mul, mul_assign);
-test_op_vs_op_assign!(test_iso3_rot3_mul_assign, Iso3<f32>, Rot3<f32>, mul, mul_assign);
+test_op_vs_op_assign!(test_iso3_rot3_mul_assign, Isometry3<f32>, Rotation3<f32>, mul, mul_assign);
 
-test_op_vs_op_assign!(test_sim3_sim3_mul_assign, Sim3<f32>, Sim3<f32>, mul, mul_assign);
+test_op_vs_op_assign!(test_sim3_sim3_mul_assign, Similarity3<f32>, Similarity3<f32>, mul, mul_assign);
-test_op_vs_op_assign!(test_sim3_iso3_mul_assign, Sim3<f32>, Iso3<f32>, mul, mul_assign);
+test_op_vs_op_assign!(test_sim3_iso3_mul_assign, Similarity3<f32>, Isometry3<f32>, mul, mul_assign);
-test_op_vs_op_assign!(test_sim3_rot3_mul_assign, Sim3<f32>, Rot3<f32>, mul, mul_assign);
+test_op_vs_op_assign!(test_sim3_rot3_mul_assign, Similarity3<f32>, Rotation3<f32>, mul, mul_assign);
 
 // Division.
-test_op_vs_op_assign!(test_vec3_vec3_div_assign, Vec3<f32>, Vec3<f32>, div, div_assign);
+test_op_vs_op_assign!(test_vec3_vec3_div_assign, Vector3<f32>, Vector3<f32>, div, div_assign);
-test_op_vs_op_assign!(test_quat_quat_div_assign, Quat<f32>, Quat<f32>, div, div_assign);
+test_op_vs_op_assign!(test_quaternion_quaternion_div_assign, Quaternion<f32>, Quaternion<f32>, div, div_assign);
-test_op_vs_op_assign!(test_unit_quat_unit_quat_div_assign, UnitQuat<f32>, UnitQuat<f32>, div, div_assign);
+test_op_vs_op_assign!(test_unit_quaternion_unit_quaternion_div_assign, UnitQuaternion<f32>, UnitQuaternion<f32>, div, div_assign);
 
-test_op_vs_op_assign!(test_vec3_f32_div_assign, Vec3<f32>, f32, div, div_assign);
+test_op_vs_op_assign!(test_vec3_f32_div_assign, Vector3<f32>, f32, div, div_assign);
-test_op_vs_op_assign!(test_mat3_f32_div_assign, Mat3<f32>, f32, div, div_assign);
+test_op_vs_op_assign!(test_mat3_f32_div_assign, Matrix3<f32>, f32, div, div_assign);
 
 // Addition.
-test_op_vs_op_assign!(test_vec3_vec3_add_assign, Vec3<f32>, Vec3<f32>, add, add_assign);
+test_op_vs_op_assign!(test_vec3_vec3_add_assign, Vector3<f32>, Vector3<f32>, add, add_assign);
-test_op_vs_op_assign!(test_mat3_mat3_add_assign, Mat3<f32>, Mat3<f32>, add, add_assign);
+test_op_vs_op_assign!(test_mat3_mat3_add_assign, Matrix3<f32>, Matrix3<f32>, add, add_assign);
-test_op_vs_op_assign!(test_quat_quat_add_assign, Quat<f32>, Quat<f32>, add, add_assign);
+test_op_vs_op_assign!(test_quaternion_quaternion_add_assign, Quaternion<f32>, Quaternion<f32>, add, add_assign);
 
-test_op_vs_op_assign!(test_vec3_f32_add_assign, Vec3<f32>, f32, add, add_assign);
+test_op_vs_op_assign!(test_vec3_f32_add_assign, Vector3<f32>, f32, add, add_assign);
-test_op_vs_op_assign!(test_mat3_f32_add_assign, Mat3<f32>, f32, add, add_assign);
+test_op_vs_op_assign!(test_mat3_f32_add_assign, Matrix3<f32>, f32, add, add_assign);
 
 // Subtraction.
-test_op_vs_op_assign!(test_vec3_vec3_sub_assign, Vec3<f32>, Vec3<f32>, sub, sub_assign);
+test_op_vs_op_assign!(test_vec3_vec3_sub_assign, Vector3<f32>, Vector3<f32>, sub, sub_assign);
-test_op_vs_op_assign!(test_mat3_mat3_sub_assign, Mat3<f32>, Mat3<f32>, sub, sub_assign);
+test_op_vs_op_assign!(test_mat3_mat3_sub_assign, Matrix3<f32>, Matrix3<f32>, sub, sub_assign);
-test_op_vs_op_assign!(test_quat_quat_sub_assign, Quat<f32>, Quat<f32>, sub, sub_assign);
+test_op_vs_op_assign!(test_quaternion_quaternion_sub_assign, Quaternion<f32>, Quaternion<f32>, sub, sub_assign);
 
-test_op_vs_op_assign!(test_vec3_f32_sub_assign, Vec3<f32>, f32, sub, sub_assign);
+test_op_vs_op_assign!(test_vec3_f32_sub_assign, Vector3<f32>, f32, sub, sub_assign);
-test_op_vs_op_assign!(test_mat3_f32_sub_assign, Mat3<f32>, f32, sub, sub_assign);
+test_op_vs_op_assign!(test_mat3_f32_sub_assign, Matrix3<f32>, f32, sub, sub_assign);

tests/quat.rs

@@ -1,57 +1,57 @@
 extern crate nalgebra as na;
 extern crate rand;
 
-use na::{Pnt3, Vec3, Rot3, UnitQuat, Rotation};
+use na::{Point3, Vector3, Rotation3, UnitQuaternion, Rotation};
 use rand::random;
 
 #[test]
-fn test_quat_as_mat() {
+fn test_quaternion_as_matrix() {
     for _ in 0usize .. 10000 {
-        let axis_angle: Vec3<f64> = random();
+        let axis_angle: Vector3<f64> = random();
 
-        assert!(na::approx_eq(&UnitQuat::new(axis_angle).to_rot(), &Rot3::new(axis_angle)))
+        assert!(na::approx_eq(&UnitQuaternion::new(axis_angle).to_rotation_matrix(), &Rotation3::new(axis_angle)))
     }
 }
 
 #[test]
-fn test_quat_mul_vec_or_pnt_as_mat() {
+fn test_quaternion_mul_vec_or_point_as_matrix() {
     for _ in 0usize .. 10000 {
-        let axis_angle: Vec3<f64> = random();
+        let axis_angle: Vector3<f64> = random();
-        let vec: Vec3<f64> = random();
+        let vector: Vector3<f64> = random();
-        let pnt: Pnt3<f64> = random();
+        let point: Point3<f64> = random();
 
-        let mat  = Rot3::new(axis_angle);
+        let matrix  = Rotation3::new(axis_angle);
-        let quat = UnitQuat::new(axis_angle);
+        let quaternion = UnitQuaternion::new(axis_angle);
 
-        assert!(na::approx_eq(&(mat * vec), &(quat * vec)));
+        assert!(na::approx_eq(&(matrix * vector), &(quaternion * vector)));
-        assert!(na::approx_eq(&(mat * pnt), &(quat * pnt)));
+        assert!(na::approx_eq(&(matrix * point), &(quaternion * point)));
-        assert!(na::approx_eq(&(vec * mat), &(vec * quat)));
+        assert!(na::approx_eq(&(vector * matrix), &(vector * quaternion)));
-        assert!(na::approx_eq(&(pnt * mat), &(pnt * quat)));
+        assert!(na::approx_eq(&(point * matrix), &(point * quaternion)));
     }
 }
 
 #[test]
-fn test_quat_div_quat() {
+fn test_quaternion_div_quaternion() {
     for _ in 0usize .. 10000 {
-        let axis_angle1: Vec3<f64> = random();
+        let axis_angle1: Vector3<f64> = random();
-        let axis_angle2: Vec3<f64> = random();
+        let axis_angle2: Vector3<f64> = random();
 
-        let r1 = Rot3::new(axis_angle1);
+        let r1 = Rotation3::new(axis_angle1);
-        let r2 = na::inv(&Rot3::new(axis_angle2)).unwrap();
+        let r2 = na::inverse(&Rotation3::new(axis_angle2)).unwrap();
 
-        let q1 = UnitQuat::new(axis_angle1);
+        let q1 = UnitQuaternion::new(axis_angle1);
-        let q2 = UnitQuat::new(axis_angle2);
+        let q2 = UnitQuaternion::new(axis_angle2);
 
-        assert!(na::approx_eq(&(q1 / q2).to_rot(), &(r1 * r2)))
+        assert!(na::approx_eq(&(q1 / q2).to_rotation_matrix(), &(r1 * r2)))
     }
 }
 
 #[test]
-fn test_quat_to_axis_angle() {
+fn test_quaternion_to_axis_angle() {
     for _ in 0usize .. 10000 {
-        let axis_angle: Vec3<f64> = random();
+        let axis_angle: Vector3<f64> = random();
 
-        let q = UnitQuat::new(axis_angle);
+        let q = UnitQuaternion::new(axis_angle);
 
         println!("{:?} {:?}", q.rotation(), axis_angle);
         assert!(na::approx_eq(&q.rotation(), &axis_angle))
@@ -59,21 +59,21 @@ fn test_quat_to_axis_angle() {
 }
 
 #[test]
-fn test_quat_euler_angles() {
+fn test_quaternion_euler_angles() {
     for _ in 0usize .. 10000 {
-        let angles: Vec3<f64> = random();
+        let angles: Vector3<f64> = random();
 
-        let q = UnitQuat::new_with_euler_angles(angles.x, angles.y, angles.z);
+        let q = UnitQuaternion::new_with_euler_angles(angles.x, angles.y, angles.z);
-        let m = Rot3::new_with_euler_angles(angles.x, angles.y, angles.z);
+        let m = Rotation3::new_with_euler_angles(angles.x, angles.y, angles.z);
 
-        assert!(na::approx_eq(&q.to_rot(), &m))
+        assert!(na::approx_eq(&q.to_rotation_matrix(), &m))
     }
 }
 
 #[test]
-fn test_quat_rotation_between() {
+fn test_quaternion_rotation_between() {
-    let q1: UnitQuat<f64> = random();
+    let q1: UnitQuaternion<f64> = random();
-    let q2: UnitQuat<f64> = random();
+    let q2: UnitQuaternion<f64> = random();
 
     let delta = na::rotation_between(&q1, &q2);
 
@@ -81,9 +81,9 @@ fn test_quat_rotation_between() {
 }
 
 #[test]
-fn test_quat_angle_between() {
+fn test_quaternion_angle_between() {
-    let q1: UnitQuat<f64> = random();
+    let q1: UnitQuaternion<f64> = random();
-    let q2: UnitQuat<f64> = random();
+    let q2: UnitQuaternion<f64> = random();
 
     let delta = na::rotation_between(&q1, &q2);
     let delta_angle = na::angle_between(&q1, &q2);

tests/transforms.rs

@@ -2,35 +2,35 @@ extern crate nalgebra as na;
 extern crate rand;
 
 use rand::random;
-use na::{Pnt2, Pnt3, Vec2, Vec3, Vec1, Rot2, Rot3, Persp3, PerspMat3, Ortho3, OrthoMat3,
+use na::{Point2, Point3, Vector2, Vector3, Vector1, Rotation2, Rotation3, Perspective3, PerspectiveMatrix3, Orthographic3, OrthographicMatrix3,
-         Iso2, Iso3, Sim2, Sim3, BaseFloat, Transform};
+         Isometry2, Isometry3, Similarity2, Similarity3, BaseFloat, Transform};
 
 #[test]
 fn test_rotation2() {
     for _ in 0usize .. 10000 {
-        let randmat: na::Rot2<f64> = na::one();
+        let randmatrix: na::Rotation2<f64> = na::one();
-        let ang    = Vec1::new(na::abs(&random::<f64>()) % <f64 as BaseFloat>::pi());
+        let ang    = Vector1::new(na::abs(&random::<f64>()) % <f64 as BaseFloat>::pi());
 
-        assert!(na::approx_eq(&na::rotation(&na::append_rotation(&randmat, &ang)), &ang));
+        assert!(na::approx_eq(&na::rotation(&na::append_rotation(&randmatrix, &ang)), &ang));
     }
 }
 
 #[test]
-fn test_inv_rotation3() {
+fn test_inverse_rotation3() {
     for _ in 0usize .. 10000 {
-        let randmat: Rot3<f64> = na::one();
+        let randmatrix: Rotation3<f64> = na::one();
-        let dir:     Vec3<f64> = random();
+        let dir:     Vector3<f64> = random();
         let ang            = na::normalize(&dir) * (na::abs(&random::<f64>()) % <f64 as BaseFloat>::pi());
-        let rot            = na::append_rotation(&randmat, &ang);
+        let rotation            = na::append_rotation(&randmatrix, &ang);
 
-        assert!(na::approx_eq(&(na::transpose(&rot) * rot), &na::one()));
+        assert!(na::approx_eq(&(na::transpose(&rotation) * rotation), &na::one()));
     }
 }
 
 #[test]
 fn test_rot3_rotation_between() {
-    let r1: Rot3<f64> = random();
+    let r1: Rotation3<f64> = random();
-    let r2: Rot3<f64> = random();
+    let r2: Rotation3<f64> = random();
 
     let delta = na::rotation_between(&r1, &r2);
 
@@ -39,8 +39,8 @@ fn test_rot3_rotation_between() {
 
 #[test]
 fn test_rot3_angle_between() {
-    let r1: Rot3<f64> = random();
+    let r1: Rotation3<f64> = random();
-    let r2: Rot3<f64> = random();
+    let r2: Rotation3<f64> = random();
 
     let delta = na::rotation_between(&r1, &r2);
     let delta_angle = na::angle_between(&r1, &r2);
@@ -50,8 +50,8 @@ fn test_rot3_angle_between() {
 
 #[test]
 fn test_rot2_rotation_between() {
-    let r1: Rot2<f64> = random();
+    let r1: Rotation2<f64> = random();
-    let r2: Rot2<f64> = random();
+    let r2: Rotation2<f64> = random();
 
     let delta = na::rotation_between(&r1, &r2);
 
@@ -60,8 +60,8 @@ fn test_rot2_rotation_between() {
 
 #[test]
 fn test_rot2_angle_between() {
-    let r1: Rot2<f64> = random();
+    let r1: Rotation2<f64> = random();
-    let r2: Rot2<f64> = random();
+    let r2: Rotation2<f64> = random();
 
     let delta = na::rotation_between(&r1, &r2);
     let delta_angle = na::angle_between(&r1, &r2);
@@ -73,58 +73,58 @@ fn test_rot2_angle_between() {
 #[test]
 fn test_look_at_rh_iso3() {
     for _ in 0usize .. 10000 {
-        let eye     = random::<Pnt3<f64>>();
+        let eye     = random::<Point3<f64>>();
-        let target  = random::<Pnt3<f64>>();
+        let target  = random::<Point3<f64>>();
-        let up      = random::<Vec3<f64>>();
+        let up      = random::<Vector3<f64>>();
-        let viewmat = Iso3::look_at_rh(&eye, &target, &up);
+        let viewmatrix = Isometry3::look_at_rh(&eye, &target, &up);
 
-        let origin: Pnt3<f64> = na::orig();
+        let origin: Point3<f64> = na::origin();
-        assert_eq!(&(viewmat * eye), &origin);
+        assert_eq!(&(viewmatrix * eye), &origin);
-        assert!(na::approx_eq(&na::normalize(&(viewmat * (target - eye))), &-Vec3::z()));
+        assert!(na::approx_eq(&na::normalize(&(viewmatrix * (target - eye))), &-Vector3::z()));
     }
 }
 
 #[test]
 fn test_look_at_rh_rot3() {
     for _ in 0usize .. 10000 {
-        let dir     = random::<Vec3<f64>>();
+        let dir     = random::<Vector3<f64>>();
-        let up      = random::<Vec3<f64>>();
+        let up      = random::<Vector3<f64>>();
-        let viewmat = Rot3::look_at_rh(&dir, &up);
+        let viewmatrix = Rotation3::look_at_rh(&dir, &up);
 
-        println!("found: {}", viewmat * dir);
+        println!("found: {}", viewmatrix * dir);
-        assert!(na::approx_eq(&na::normalize(&(viewmat * dir)), &-Vec3::z()));
+        assert!(na::approx_eq(&na::normalize(&(viewmatrix * dir)), &-Vector3::z()));
     }
 }
 
 #[test]
 fn test_observer_frame_iso3() {
     for _ in 0usize .. 10000 {
-        let eye      = random::<Pnt3<f64>>();
+        let eye      = random::<Point3<f64>>();
-        let target   = random::<Pnt3<f64>>();
+        let target   = random::<Point3<f64>>();
-        let up       = random::<Vec3<f64>>();
+        let up       = random::<Vector3<f64>>();
-        let observer = Iso3::new_observer_frame(&eye, &target, &up);
+        let observer = Isometry3::new_observer_frame(&eye, &target, &up);
 
-        assert_eq!(&(observer * na::orig::<Pnt3<f64>>()), &eye);
+        assert_eq!(&(observer * na::origin::<Point3<f64>>()), &eye);
-        assert!(na::approx_eq(&(observer * Vec3::z()), &na::normalize(&(target - eye))));
+        assert!(na::approx_eq(&(observer * Vector3::z()), &na::normalize(&(target - eye))));
     }
 }
 
 #[test]
 fn test_observer_frame_rot3() {
     for _ in 0usize .. 10000 {
-        let dir      = random::<Vec3<f64>>();
+        let dir      = random::<Vector3<f64>>();
-        let up       = random::<Vec3<f64>>();
+        let up       = random::<Vector3<f64>>();
-        let observer = Rot3::new_observer_frame(&dir, &up);
+        let observer = Rotation3::new_observer_frame(&dir, &up);
 
-        assert!(na::approx_eq(&(observer * Vec3::z()), &na::normalize(&dir)));
+        assert!(na::approx_eq(&(observer * Vector3::z()), &na::normalize(&dir)));
     }
 }
 
 #[test]
 fn test_persp() {
-    let mut p  = Persp3::new(42.0f64, 0.5, 1.5, 10.0);
+    let mut p  = Perspective3::new(42.0f64, 0.5, 1.5, 10.0);
-    let mut pm = PerspMat3::new(42.0f64, 0.5, 1.5, 10.0);
+    let mut pm = PerspectiveMatrix3::new(42.0f64, 0.5, 1.5, 10.0);
-    assert!(p.to_mat() == pm.to_mat());
+    assert!(p.to_matrix() == pm.to_matrix());
     assert!(p.aspect() == 42.0);
     assert!(p.fovy()   == 0.5);
     assert!(p.znear()  == 1.5);
@@ -136,19 +136,19 @@ fn test_persp() {
 
     p.set_fovy(0.1);
     pm.set_fovy(0.1);
-    assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
+    assert!(na::approx_eq(&p.to_matrix(), pm.as_matrix()));
 
     p.set_znear(24.0);
     pm.set_znear(24.0);
-    assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
+    assert!(na::approx_eq(&p.to_matrix(), pm.as_matrix()));
 
     p.set_zfar(61.0);
     pm.set_zfar(61.0);
-    assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
+    assert!(na::approx_eq(&p.to_matrix(), pm.as_matrix()));
 
     p.set_aspect(23.0);
     pm.set_aspect(23.0);
-    assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
+    assert!(na::approx_eq(&p.to_matrix(), pm.as_matrix()));
 
     assert!(p.aspect() == 23.0);
     assert!(p.fovy()   == 0.1);
@@ -162,9 +162,9 @@ fn test_persp() {
 
 #[test]
 fn test_ortho() {
-    let mut p  = Ortho3::new(-0.3, 5.2, -3.9, -1.0, 1.5, 10.0);
+    let mut p  = Orthographic3::new(-0.3, 5.2, -3.9, -1.0, 1.5, 10.0);
-    let mut pm = OrthoMat3::new(-0.3, 5.2, -3.9, -1.0, 1.5, 10.0);
+    let mut pm = OrthographicMatrix3::new(-0.3, 5.2, -3.9, -1.0, 1.5, 10.0);
-    assert!(p.to_mat() == pm.to_mat());
+    assert!(p.to_matrix() == pm.to_matrix());
     assert!(p.left()   == -0.3);
     assert!(p.right()  == 5.2);
     assert!(p.bottom() == -3.9);
@@ -180,27 +180,27 @@ fn test_ortho() {
 
     p.set_left(0.1);
     pm.set_left(0.1);
-    assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
+    assert!(na::approx_eq(&p.to_matrix(), pm.as_matrix()));
 
     p.set_right(10.1);
     pm.set_right(10.1);
-    assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
+    assert!(na::approx_eq(&p.to_matrix(), pm.as_matrix()));
 
     p.set_top(24.0);
     pm.set_top(24.0);
-    assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
+    assert!(na::approx_eq(&p.to_matrix(), pm.as_matrix()));
 
     p.set_bottom(-23.0);
     pm.set_bottom(-23.0);
-    assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
+    assert!(na::approx_eq(&p.to_matrix(), pm.as_matrix()));
 
     p.set_zfar(61.0);
     pm.set_zfar(61.0);
-    assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
+    assert!(na::approx_eq(&p.to_matrix(), pm.as_matrix()));
 
     p.set_znear(21.0);
     pm.set_znear(21.0);
-    assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
+    assert!(na::approx_eq(&p.to_matrix(), pm.as_matrix()));
 
     assert!(p.znear()  == 21.0);
     assert!(p.zfar()   == 61.0);
@@ -208,15 +208,15 @@ fn test_ortho() {
     assert!(na::approx_eq(&pm.zfar(),   &61.0));
 }
 
-macro_rules! test_transform_inv_transform_impl(
+macro_rules! test_transform_inverse_transform_impl(
   ($fnname: ident, $t: ty, $p: ty) => (
     #[test]
     fn $fnname() {
         for _ in 0usize .. 10000 {
-          let randmat: $t = random();
+          let randmatrix: $t = random();
           let expected: $p = random();
     
-          let computed = randmat.inv_transform(&randmat.transform(&expected));
+          let computed = randmatrix.inverse_transform(&randmatrix.transform(&expected));
           println!("computed: {}, expected: {}", computed, expected);
     
           assert!(na::approx_eq(&computed, &expected));
@@ -225,12 +225,12 @@ macro_rules! test_transform_inv_transform_impl(
   );
 );
 
-test_transform_inv_transform_impl!(test_transform_inv_transform_rot2, Rot2<f64>, Pnt2<f64>);
+test_transform_inverse_transform_impl!(test_transform_inverse_transform_rot2, Rotation2<f64>, Point2<f64>);
-test_transform_inv_transform_impl!(test_transform_inv_transform_rot3, Rot3<f64>, Pnt3<f64>);
+test_transform_inverse_transform_impl!(test_transform_inverse_transform_rot3, Rotation3<f64>, Point3<f64>);
-test_transform_inv_transform_impl!(test_transform_inv_transform_iso2, Iso2<f64>, Pnt2<f64>);
+test_transform_inverse_transform_impl!(test_transform_inverse_transform_iso2, Isometry2<f64>, Point2<f64>);
-test_transform_inv_transform_impl!(test_transform_inv_transform_iso3, Iso3<f64>, Pnt3<f64>);
+test_transform_inverse_transform_impl!(test_transform_inverse_transform_iso3, Isometry3<f64>, Point3<f64>);
-test_transform_inv_transform_impl!(test_transform_inv_transform_sim2, Sim2<f64>, Pnt2<f64>);
+test_transform_inverse_transform_impl!(test_transform_inverse_transform_sim2, Similarity2<f64>, Point2<f64>);
-test_transform_inv_transform_impl!(test_transform_inv_transform_sim3, Sim3<f64>, Pnt3<f64>);
+test_transform_inverse_transform_impl!(test_transform_inverse_transform_sim3, Similarity3<f64>, Point3<f64>);
 
 macro_rules! test_transform_mul_assoc(
   ($fnname: ident, $t1: ty, $t2: ty, $p: ty) => (
@@ -253,28 +253,28 @@ macro_rules! test_transform_mul_assoc(
   );
 );
 
-test_transform_mul_assoc!(test_transform_inv_transform_sim3_sim3_pnt3, Sim3<f64>, Sim3<f64>, Pnt3<f64>);
+test_transform_mul_assoc!(test_transform_inverse_transform_sim3_sim3_point3, Similarity3<f64>, Similarity3<f64>, Point3<f64>);
-test_transform_mul_assoc!(test_transform_inv_transform_sim3_iso3_pnt3, Sim3<f64>, Iso3<f64>, Pnt3<f64>);
+test_transform_mul_assoc!(test_transform_inverse_transform_sim3_iso3_point3, Similarity3<f64>, Isometry3<f64>, Point3<f64>);
-test_transform_mul_assoc!(test_transform_inv_transform_sim3_rot3_pnt3, Sim3<f64>, Rot3<f64>, Pnt3<f64>);
+test_transform_mul_assoc!(test_transform_inverse_transform_sim3_rot3_point3, Similarity3<f64>, Rotation3<f64>, Point3<f64>);
-test_transform_mul_assoc!(test_transform_inv_transform_iso3_iso3_pnt3, Iso3<f64>, Iso3<f64>, Pnt3<f64>);
+test_transform_mul_assoc!(test_transform_inverse_transform_iso3_iso3_point3, Isometry3<f64>, Isometry3<f64>, Point3<f64>);
-test_transform_mul_assoc!(test_transform_inv_transform_iso3_rot3_pnt3, Iso3<f64>, Rot3<f64>, Pnt3<f64>);
+test_transform_mul_assoc!(test_transform_inverse_transform_iso3_rot3_point3, Isometry3<f64>, Rotation3<f64>, Point3<f64>);
-test_transform_mul_assoc!(test_transform_inv_transform_rot3_rot3_pnt3, Rot3<f64>, Rot3<f64>, Pnt3<f64>);
+test_transform_mul_assoc!(test_transform_inverse_transform_rot3_rot3_point3, Rotation3<f64>, Rotation3<f64>, Point3<f64>);
-test_transform_mul_assoc!(test_transform_inv_transform_sim3_sim3_vec3, Sim3<f64>, Sim3<f64>, Vec3<f64>);
+test_transform_mul_assoc!(test_transform_inverse_transform_sim3_sim3_vec3, Similarity3<f64>, Similarity3<f64>, Vector3<f64>);
-test_transform_mul_assoc!(test_transform_inv_transform_sim3_iso3_vec3, Sim3<f64>, Iso3<f64>, Vec3<f64>);
+test_transform_mul_assoc!(test_transform_inverse_transform_sim3_iso3_vec3, Similarity3<f64>, Isometry3<f64>, Vector3<f64>);
-test_transform_mul_assoc!(test_transform_inv_transform_sim3_rot3_vec3, Sim3<f64>, Rot3<f64>, Vec3<f64>);
+test_transform_mul_assoc!(test_transform_inverse_transform_sim3_rot3_vec3, Similarity3<f64>, Rotation3<f64>, Vector3<f64>);
-test_transform_mul_assoc!(test_transform_inv_transform_iso3_iso3_vec3, Iso3<f64>, Iso3<f64>, Vec3<f64>);
+test_transform_mul_assoc!(test_transform_inverse_transform_iso3_iso3_vec3, Isometry3<f64>, Isometry3<f64>, Vector3<f64>);
-test_transform_mul_assoc!(test_transform_inv_transform_iso3_rot3_vec3, Iso3<f64>, Rot3<f64>, Vec3<f64>);
+test_transform_mul_assoc!(test_transform_inverse_transform_iso3_rot3_vec3, Isometry3<f64>, Rotation3<f64>, Vector3<f64>);
-test_transform_mul_assoc!(test_transform_inv_transform_rot3_rot3_vec3, Rot3<f64>, Rot3<f64>, Vec3<f64>);
+test_transform_mul_assoc!(test_transform_inverse_transform_rot3_rot3_vec3, Rotation3<f64>, Rotation3<f64>, Vector3<f64>);
 
-test_transform_mul_assoc!(test_transform_inv_transform_sim2_sim2_pnt2, Sim2<f64>, Sim2<f64>, Pnt2<f64>);
+test_transform_mul_assoc!(test_transform_inverse_transform_sim2_sim2_point2, Similarity2<f64>, Similarity2<f64>, Point2<f64>);
-test_transform_mul_assoc!(test_transform_inv_transform_sim2_iso2_pnt2, Sim2<f64>, Iso2<f64>, Pnt2<f64>);
+test_transform_mul_assoc!(test_transform_inverse_transform_sim2_iso2_point2, Similarity2<f64>, Isometry2<f64>, Point2<f64>);
-test_transform_mul_assoc!(test_transform_inv_transform_sim2_rot2_pnt2, Sim2<f64>, Rot2<f64>, Pnt2<f64>);
+test_transform_mul_assoc!(test_transform_inverse_transform_sim2_rot2_point2, Similarity2<f64>, Rotation2<f64>, Point2<f64>);
-test_transform_mul_assoc!(test_transform_inv_transform_iso2_iso2_pnt2, Iso2<f64>, Iso2<f64>, Pnt2<f64>);
+test_transform_mul_assoc!(test_transform_inverse_transform_iso2_iso2_point2, Isometry2<f64>, Isometry2<f64>, Point2<f64>);
-test_transform_mul_assoc!(test_transform_inv_transform_iso2_rot2_pnt2, Iso2<f64>, Rot2<f64>, Pnt2<f64>);
+test_transform_mul_assoc!(test_transform_inverse_transform_iso2_rot2_point2, Isometry2<f64>, Rotation2<f64>, Point2<f64>);
-test_transform_mul_assoc!(test_transform_inv_transform_rot2_rot2_pnt2, Rot2<f64>, Rot2<f64>, Pnt2<f64>);
+test_transform_mul_assoc!(test_transform_inverse_transform_rot2_rot2_point2, Rotation2<f64>, Rotation2<f64>, Point2<f64>);
-test_transform_mul_assoc!(test_transform_inv_transform_sim2_sim2_vec2, Sim2<f64>, Sim2<f64>, Vec2<f64>);
+test_transform_mul_assoc!(test_transform_inverse_transform_sim2_sim2_vec2, Similarity2<f64>, Similarity2<f64>, Vector2<f64>);
-test_transform_mul_assoc!(test_transform_inv_transform_sim2_iso2_vec2, Sim2<f64>, Iso2<f64>, Vec2<f64>);
+test_transform_mul_assoc!(test_transform_inverse_transform_sim2_iso2_vec2, Similarity2<f64>, Isometry2<f64>, Vector2<f64>);
-test_transform_mul_assoc!(test_transform_inv_transform_sim2_rot2_vec2, Sim2<f64>, Rot2<f64>, Vec2<f64>);
+test_transform_mul_assoc!(test_transform_inverse_transform_sim2_rot2_vec2, Similarity2<f64>, Rotation2<f64>, Vector2<f64>);
-test_transform_mul_assoc!(test_transform_inv_transform_iso2_iso2_vec2, Iso2<f64>, Iso2<f64>, Vec2<f64>);
+test_transform_mul_assoc!(test_transform_inverse_transform_iso2_iso2_vec2, Isometry2<f64>, Isometry2<f64>, Vector2<f64>);
-test_transform_mul_assoc!(test_transform_inv_transform_iso2_rot2_vec2, Iso2<f64>, Rot2<f64>, Vec2<f64>);
+test_transform_mul_assoc!(test_transform_inverse_transform_iso2_rot2_vec2, Isometry2<f64>, Rotation2<f64>, Vector2<f64>);
-test_transform_mul_assoc!(test_transform_inv_transform_rot2_rot2_vec2, Rot2<f64>, Rot2<f64>, Vec2<f64>);
+test_transform_mul_assoc!(test_transform_inverse_transform_rot2_rot2_vec2, Rotation2<f64>, Rotation2<f64>, Vector2<f64>);

tests/vec.rs

@@ -4,12 +4,12 @@ extern crate typenum;
 extern crate nalgebra as na;
 
 use rand::random;
-use na::{Vec1, Vec2, Vec3, Vec4, Vec5, Vec6, Mat3, Rot2, Rot3, Iterable, IterableMut};
+use na::{Vector1, Vector2, Vector3, Vector4, Vector5, Vector6, Matrix3, Rotation2, Rotation3, Iterable, IterableMut};
 
 #[cfg(feature="generic_sizes")]
 use typenum::U10;
 #[cfg(feature="generic_sizes")]
-use na::VecN;
+use na::VectorN;
 
 
 macro_rules! test_iterator_impl(
@@ -109,9 +109,9 @@ macro_rules! test_subspace_basis_impl(
 #[test]
 fn test_cross_vec3() {
     for _ in 0usize .. 10000 {
-        let v1 : Vec3<f64> = random();
+        let v1 : Vector3<f64> = random();
-        let v2 : Vec3<f64> = random();
+        let v2 : Vector3<f64> = random();
-        let v3 : Vec3<f64> = na::cross(&v1, &v2);
+        let v3 : Vector3<f64> = na::cross(&v1, &v2);
 
         assert!(na::approx_eq(&na::dot(&v3, &v2), &na::zero()));
         assert!(na::approx_eq(&na::dot(&v3, &v1), &na::zero()));
@@ -120,182 +120,182 @@ fn test_cross_vec3() {
 
 #[test]
 fn test_commut_dot_vec1() {
-    test_commut_dot_impl!(Vec1<f64>);
+    test_commut_dot_impl!(Vector1<f64>);
 }
 
 #[test]
 fn test_commut_dot_vec2() {
-    test_commut_dot_impl!(Vec2<f64>);
+    test_commut_dot_impl!(Vector2<f64>);
 }
 
 #[test]
 fn test_commut_dot_vec3() {
-    test_commut_dot_impl!(Vec3<f64>);
+    test_commut_dot_impl!(Vector3<f64>);
 }
 
 #[test]
 fn test_commut_dot_vec4() {
-    test_commut_dot_impl!(Vec4<f64>);
+    test_commut_dot_impl!(Vector4<f64>);
 }
 
 #[test]
 fn test_commut_dot_vec5() {
-    test_commut_dot_impl!(Vec5<f64>);
+    test_commut_dot_impl!(Vector5<f64>);
 }
 
 #[test]
 fn test_commut_dot_vec6() {
-    test_commut_dot_impl!(Vec6<f64>);
+    test_commut_dot_impl!(Vector6<f64>);
 }
 
 #[test]
 fn test_basis_vec1() {
-    test_basis_impl!(Vec1<f64>);
+    test_basis_impl!(Vector1<f64>);
 }
 
 #[test]
 fn test_basis_vec2() {
-    test_basis_impl!(Vec2<f64>);
+    test_basis_impl!(Vector2<f64>);
 }
 
 #[test]
 fn test_basis_vec3() {
-    test_basis_impl!(Vec3<f64>);
+    test_basis_impl!(Vector3<f64>);
 }
 
 #[test]
 fn test_basis_vec4() {
-    test_basis_impl!(Vec4<f64>);
+    test_basis_impl!(Vector4<f64>);
 }
 
 #[test]
 fn test_basis_vec5() {
-    test_basis_impl!(Vec5<f64>);
+    test_basis_impl!(Vector5<f64>);
 }
 
 #[test]
 fn test_basis_vec6() {
-    test_basis_impl!(Vec6<f64>);
+    test_basis_impl!(Vector6<f64>);
 }
 
 #[test]
 fn test_subspace_basis_vec1() {
-    test_subspace_basis_impl!(Vec1<f64>);
+    test_subspace_basis_impl!(Vector1<f64>);
 }
 
 #[test]
 fn test_subspace_basis_vec2() {
-    test_subspace_basis_impl!(Vec2<f64>);
+    test_subspace_basis_impl!(Vector2<f64>);
 }
 
 #[test]
 fn test_subspace_basis_vec3() {
-    test_subspace_basis_impl!(Vec3<f64>);
+    test_subspace_basis_impl!(Vector3<f64>);
 }
 
 #[test]
 fn test_subspace_basis_vec4() {
-    test_subspace_basis_impl!(Vec4<f64>);
+    test_subspace_basis_impl!(Vector4<f64>);
 }
 
 #[test]
 fn test_subspace_basis_vec5() {
-    test_subspace_basis_impl!(Vec5<f64>);
+    test_subspace_basis_impl!(Vector5<f64>);
 }
 
 #[test]
 fn test_subspace_basis_vec6() {
-    test_subspace_basis_impl!(Vec6<f64>);
+    test_subspace_basis_impl!(Vector6<f64>);
 }
 
 #[test]
 fn test_scalar_op_vec1() {
-    test_scalar_op_impl!(Vec1<f64>, f64);
+    test_scalar_op_impl!(Vector1<f64>, f64);
 }
 
 #[test]
 fn test_scalar_op_vec2() {
-    test_scalar_op_impl!(Vec2<f64>, f64);
+    test_scalar_op_impl!(Vector2<f64>, f64);
 }
 
 #[test]
 fn test_scalar_op_vec3() {
-    test_scalar_op_impl!(Vec3<f64>, f64);
+    test_scalar_op_impl!(Vector3<f64>, f64);
 }
 
 #[test]
 fn test_scalar_op_vec4() {
-    test_scalar_op_impl!(Vec4<f64>, f64);
+    test_scalar_op_impl!(Vector4<f64>, f64);
 }
 
 #[test]
 fn test_scalar_op_vec5() {
-    test_scalar_op_impl!(Vec5<f64>, f64);
+    test_scalar_op_impl!(Vector5<f64>, f64);
 }
 
 #[test]
 fn test_scalar_op_vec6() {
-    test_scalar_op_impl!(Vec6<f64>, f64);
+    test_scalar_op_impl!(Vector6<f64>, f64);
 }
 
 #[test]
 fn test_iterator_vec1() {
-    test_iterator_impl!(Vec1<f64>, f64);
+    test_iterator_impl!(Vector1<f64>, f64);
 }
 
 #[test]
 fn test_iterator_vec2() {
-    test_iterator_impl!(Vec2<f64>, f64);
+    test_iterator_impl!(Vector2<f64>, f64);
 }
 
 #[test]
 fn test_iterator_vec3() {
-    test_iterator_impl!(Vec3<f64>, f64);
+    test_iterator_impl!(Vector3<f64>, f64);
 }
 
 #[test]
 fn test_iterator_vec4() {
-    test_iterator_impl!(Vec4<f64>, f64);
+    test_iterator_impl!(Vector4<f64>, f64);
 }
 
 #[test]
 fn test_iterator_vec5() {
-    test_iterator_impl!(Vec5<f64>, f64);
+    test_iterator_impl!(Vector5<f64>, f64);
 }
 
 #[test]
 fn test_iterator_vec6() {
-    test_iterator_impl!(Vec6<f64>, f64);
+    test_iterator_impl!(Vector6<f64>, f64);
 }
 
 #[test]
 fn test_ord_vec3() {
     // equality
-    assert!(Vec3::new(0.5f64, 0.5, 0.5) == Vec3::new(0.5, 0.5, 0.5));
+    assert!(Vector3::new(0.5f64, 0.5, 0.5) == Vector3::new(0.5, 0.5, 0.5));
-    assert!(!(Vec3::new(1.5f64, 0.5, 0.5) == Vec3::new(0.5, 0.5, 0.5)));
+    assert!(!(Vector3::new(1.5f64, 0.5, 0.5) == Vector3::new(0.5, 0.5, 0.5)));
-    assert!(Vec3::new(1.5f64, 0.5, 0.5) != Vec3::new(0.5, 0.5, 0.5));
+    assert!(Vector3::new(1.5f64, 0.5, 0.5) != Vector3::new(0.5, 0.5, 0.5));
 
     // comparable
-    assert!(na::partial_cmp(&Vec3::new(0.5f64, 0.3, 0.3), &Vec3::new(1.0, 2.0, 1.0)).is_le());
+    assert!(na::partial_cmp(&Vector3::new(0.5f64, 0.3, 0.3), &Vector3::new(1.0, 2.0, 1.0)).is_le());
-    assert!(na::partial_cmp(&Vec3::new(0.5f64, 0.3, 0.3), &Vec3::new(1.0, 2.0, 1.0)).is_lt());
+    assert!(na::partial_cmp(&Vector3::new(0.5f64, 0.3, 0.3), &Vector3::new(1.0, 2.0, 1.0)).is_lt());
-    assert!(na::partial_cmp(&Vec3::new(2.0f64, 4.0, 2.0), &Vec3::new(1.0, 2.0, 1.0)).is_ge());
+    assert!(na::partial_cmp(&Vector3::new(2.0f64, 4.0, 2.0), &Vector3::new(1.0, 2.0, 1.0)).is_ge());
-    assert!(na::partial_cmp(&Vec3::new(2.0f64, 4.0, 2.0), &Vec3::new(1.0, 2.0, 1.0)).is_gt());
+    assert!(na::partial_cmp(&Vector3::new(2.0f64, 4.0, 2.0), &Vector3::new(1.0, 2.0, 1.0)).is_gt());
 
     // not comparable
-    assert!(na::partial_cmp(&Vec3::new(0.0f64, 3.0, 0.0), &Vec3::new(1.0, 2.0, 1.0)).is_not_comparable());
+    assert!(na::partial_cmp(&Vector3::new(0.0f64, 3.0, 0.0), &Vector3::new(1.0, 2.0, 1.0)).is_not_comparable());
 }
 
 #[test]
 fn test_min_max_vec3() {
-    assert_eq!(na::sup(&Vec3::new(1.0f64, 2.0, 3.0), &Vec3::new(3.0, 2.0, 1.0)), Vec3::new(3.0, 2.0, 3.0));
+    assert_eq!(na::sup(&Vector3::new(1.0f64, 2.0, 3.0), &Vector3::new(3.0, 2.0, 1.0)), Vector3::new(3.0, 2.0, 3.0));
-    assert_eq!(na::inf(&Vec3::new(1.0f64, 2.0, 3.0), &Vec3::new(3.0, 2.0, 1.0)), Vec3::new(1.0, 2.0, 1.0));
+    assert_eq!(na::inf(&Vector3::new(1.0f64, 2.0, 3.0), &Vector3::new(3.0, 2.0, 1.0)), Vector3::new(1.0, 2.0, 1.0));
 }
 
 #[test]
 fn test_outer_vec3() {
     assert_eq!(
-        na::outer(&Vec3::new(1.0f64, 2.0, 3.0), &Vec3::new(4.0, 5.0, 6.0)),
+        na::outer(&Vector3::new(1.0f64, 2.0, 3.0), &Vector3::new(4.0, 5.0, 6.0)),
-        Mat3::new(
+        Matrix3::new(
             4.0, 5.0, 6.0,
             8.0, 10.0, 12.0,
             12.0, 15.0, 18.0));
@@ -305,7 +305,7 @@ fn test_outer_vec3() {
 #[test]
 fn test_vecn10_add_mul() {
     for _ in 0usize .. 10000 {
-        let v1: VecN<f64, U10> = random();
+        let v1: VectorN<f64, U10> = random();
 
         assert!(na::approx_eq(&(v1 + v1), &(v1 * 2.0)))
     }
@@ -315,29 +315,29 @@ fn test_vecn10_add_mul() {
 #[test]
 fn test_vec3_rotation_between() {
     for _ in 0usize .. 10000 {
-        let v1: Vec3<f64> = random();
+        let v1: Vector3<f64> = random();
 
-        let mut v2: Vec3<f64> = random();
+        let mut v2: Vector3<f64> = random();
         v2 = na::normalize(&v2) * na::norm(&v1);
 
-        let rot = na::rotation_between(&v1, &v2);
+        let rotation = na::rotation_between(&v1, &v2);
 
-        assert!(na::approx_eq(&(rot * v1), &v2))
+        assert!(na::approx_eq(&(rotation * v1), &v2))
     }
 }
 
 #[test]
 fn test_vec3_angle_between() {
     for _ in 0usize .. 10000 {
-        let vec: Vec3<f64> = random();
+        let vector: Vector3<f64> = random();
-        let other: Vec3<f64> = random();
+        let other: Vector3<f64> = random();
 
-        // Ensure the axis we are using is orthogonal to `vec`.
+        // Ensure the axis we are using is orthogonal to `vector`.
-        let axis_ang = na::cross(&vec, &other);
+        let axis_ang = na::cross(&vector, &other);
         let ang      = na::norm(&axis_ang);
-        let rot      = Rot3::new(axis_ang);
+        let rotation      = Rotation3::new(axis_ang);
 
-        let delta = na::angle_between(&vec, &(rot * vec));
+        let delta = na::angle_between(&vector, &(rotation * vector));
 
         assert!(na::approx_eq(&ang, &delta))
     }
@@ -347,27 +347,27 @@ fn test_vec3_angle_between() {
 #[test]
 fn test_vec2_rotation_between() {
     for _ in 0usize .. 10000 {
-        let v1: Vec2<f64> = random();
+        let v1: Vector2<f64> = random();
 
-        let mut v2: Vec2<f64> = random();
+        let mut v2: Vector2<f64> = random();
         v2 = na::normalize(&v2) * na::norm(&v1);
 
-        let rot = na::rotation_between(&v1, &v2);
+        let rotation = na::rotation_between(&v1, &v2);
 
-        assert!(na::approx_eq(&(rot * v1), &v2))
+        assert!(na::approx_eq(&(rotation * v1), &v2))
     }
 }
 
 #[test]
 fn test_vec2_angle_between() {
     for _ in 0usize .. 10000 {
-        let axis_ang: Vec1<f64> = random();
+        let axis_ang: Vector1<f64> = random();
         let ang = na::norm(&axis_ang);
 
-        let rot: Rot2<f64> = Rot2::new(axis_ang);
+        let rotation: Rotation2<f64> = Rotation2::new(axis_ang);
-        let vec: Vec2<f64> = random();
+        let vector: Vector2<f64> = random();
 
-        let delta = na::angle_between(&vec, &(rot * vec));
+        let delta = na::angle_between(&vector, &(rotation * vector));
 
         assert!(na::approx_eq(&ang, &delta))
     }