From c5dad7f9605021e3efd91f8c5a846d4319ec8afd Mon Sep 17 00:00:00 2001
From: sebcrozet <developer@crozet.re>
Date: Sun, 5 Apr 2020 17:53:27 +0200
Subject: [PATCH] Re-add all the alga trait impls behind a feature.

---
 Cargo.toml                        |   4 +-
 src/base/matrix_alga.rs           | 452 ++++++++++++++++++++++++++++++
 src/base/mod.rs                   |   2 +
 src/geometry/isometry_alga.rs     | 210 ++++++++++++++
 src/geometry/mod.rs               |  16 ++
 src/geometry/point_alga.rs        |  84 ++++++
 src/geometry/quaternion_alga.rs   | 313 +++++++++++++++++++++
 src/geometry/rotation_alga.rs     | 291 +++++++++++++++++++
 src/geometry/similarity_alga.rs   | 196 +++++++++++++
 src/geometry/transform_alga.rs    | 149 ++++++++++
 src/geometry/translation_alga.rs  | 215 ++++++++++++++
 src/geometry/unit_complex_alga.rs | 185 ++++++++++++
 src/sparse/cs_matrix.rs           |  40 ++-
 13 files changed, 2142 insertions(+), 15 deletions(-)
 create mode 100644 src/base/matrix_alga.rs
 create mode 100755 src/geometry/isometry_alga.rs
 create mode 100644 src/geometry/point_alga.rs
 create mode 100755 src/geometry/quaternion_alga.rs
 create mode 100755 src/geometry/rotation_alga.rs
 create mode 100755 src/geometry/similarity_alga.rs
 create mode 100755 src/geometry/transform_alga.rs
 create mode 100755 src/geometry/translation_alga.rs
 create mode 100755 src/geometry/unit_complex_alga.rs

diff --git a/Cargo.toml b/Cargo.toml
index d97581aa..7692ac55 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -40,7 +40,7 @@ num-complex    = { version = "0.2", default-features = false }
 num-rational   = { version = "0.2", default-features = false }
 approx         = { version = "0.3", default-features = false }
 simba          = { version = "0.1", default-features = false }
-#alga           = { version = "0.9", default-features = false }
+alga           = { version = "0.9", default-features = false, optional = true }
 rand_distr     = { version = "0.2", optional = true }
 matrixmultiply = { version = "0.2", optional = true }
 serde          = { version = "1.0", optional = true }
@@ -73,4 +73,4 @@ path = "benches/lib.rs"
 lto = true
 
 #[patch.crates-io]
-#alga = { path = "../alga/alga" }
\ No newline at end of file
+#simba = { path = "../simba" }
\ No newline at end of file
diff --git a/src/base/matrix_alga.rs b/src/base/matrix_alga.rs
new file mode 100644
index 00000000..18182382
--- /dev/null
+++ b/src/base/matrix_alga.rs
@@ -0,0 +1,452 @@
+#[cfg(all(feature = "alloc", not(feature = "std")))]
+use alloc::vec::Vec;
+
+use num::{One, Zero};
+
+use alga::general::{
+    AbstractGroup, AbstractGroupAbelian, AbstractLoop, AbstractMagma, AbstractModule,
+    AbstractMonoid, AbstractQuasigroup, AbstractSemigroup, Additive, ClosedAdd, ClosedMul,
+    ClosedNeg, ComplexField, Field, Identity, JoinSemilattice, Lattice, MeetSemilattice, Module,
+    Multiplicative, RingCommutative, TwoSidedInverse,
+};
+use alga::linear::{
+    FiniteDimInnerSpace, FiniteDimVectorSpace, InnerSpace, NormedSpace, VectorSpace,
+};
+
+use crate::base::allocator::Allocator;
+use crate::base::dimension::{Dim, DimName};
+use crate::base::storage::{Storage, StorageMut};
+use crate::base::{DefaultAllocator, MatrixMN, MatrixN, Scalar};
+
+/*
+ *
+ * Additive structures.
+ *
+ */
+impl<N, R: DimName, C: DimName> Identity<Additive> for MatrixMN<N, R, C>
+where
+    N: Scalar + Zero,
+    DefaultAllocator: Allocator<N, R, C>,
+{
+    #[inline]
+    fn identity() -> Self {
+        Self::from_element(N::zero())
+    }
+}
+
+impl<N, R: DimName, C: DimName> AbstractMagma<Additive> for MatrixMN<N, R, C>
+where
+    N: Scalar + ClosedAdd,
+    DefaultAllocator: Allocator<N, R, C>,
+{
+    #[inline]
+    fn operate(&self, other: &Self) -> Self {
+        self + other
+    }
+}
+
+impl<N, R: DimName, C: DimName> TwoSidedInverse<Additive> for MatrixMN<N, R, C>
+where
+    N: Scalar + ClosedNeg,
+    DefaultAllocator: Allocator<N, R, C>,
+{
+    #[inline]
+    #[must_use = "Did you mean to use two_sided_inverse_mut()?"]
+    fn two_sided_inverse(&self) -> Self {
+        -self
+    }
+
+    #[inline]
+    fn two_sided_inverse_mut(&mut self) {
+        *self = -self.clone()
+    }
+}
+
+macro_rules! inherit_additive_structure(
+    ($($marker: ident<$operator: ident> $(+ $bounds: ident)*),* $(,)*) => {$(
+        impl<N, R: DimName, C: DimName> $marker<$operator> for MatrixMN<N, R, C>
+            where N: Scalar + $marker<$operator> $(+ $bounds)*,
+                  DefaultAllocator: Allocator<N, R, C> { }
+    )*}
+);
+
+inherit_additive_structure!(
+    AbstractSemigroup<Additive> + ClosedAdd,
+    AbstractMonoid<Additive> + Zero + ClosedAdd,
+    AbstractQuasigroup<Additive> + ClosedAdd + ClosedNeg,
+    AbstractLoop<Additive> + Zero + ClosedAdd + ClosedNeg,
+    AbstractGroup<Additive> + Zero + ClosedAdd + ClosedNeg,
+    AbstractGroupAbelian<Additive> + Zero + ClosedAdd + ClosedNeg
+);
+
+impl<N, R: DimName, C: DimName> AbstractModule for MatrixMN<N, R, C>
+where
+    N: Scalar + RingCommutative,
+    DefaultAllocator: Allocator<N, R, C>,
+{
+    type AbstractRing = N;
+
+    #[inline]
+    fn multiply_by(&self, n: N) -> Self {
+        self * n
+    }
+}
+
+impl<N, R: DimName, C: DimName> Module for MatrixMN<N, R, C>
+where
+    N: Scalar + RingCommutative,
+    DefaultAllocator: Allocator<N, R, C>,
+{
+    type Ring = N;
+}
+
+impl<N, R: DimName, C: DimName> VectorSpace for MatrixMN<N, R, C>
+where
+    N: Scalar + Field,
+    DefaultAllocator: Allocator<N, R, C>,
+{
+    type Field = N;
+}
+
+impl<N, R: DimName, C: DimName> FiniteDimVectorSpace for MatrixMN<N, R, C>
+where
+    N: Scalar + Field,
+    DefaultAllocator: Allocator<N, R, C>,
+{
+    #[inline]
+    fn dimension() -> usize {
+        R::dim() * C::dim()
+    }
+
+    #[inline]
+    fn canonical_basis_element(i: usize) -> Self {
+        assert!(i < Self::dimension(), "Index out of bound.");
+
+        let mut res = Self::zero();
+        unsafe {
+            *res.data.get_unchecked_linear_mut(i) = N::one();
+        }
+
+        res
+    }
+
+    #[inline]
+    fn dot(&self, other: &Self) -> N {
+        self.dot(other)
+    }
+
+    #[inline]
+    unsafe fn component_unchecked(&self, i: usize) -> &N {
+        self.data.get_unchecked_linear(i)
+    }
+
+    #[inline]
+    unsafe fn component_unchecked_mut(&mut self, i: usize) -> &mut N {
+        self.data.get_unchecked_linear_mut(i)
+    }
+}
+
+impl<
+        N: ComplexField + simba::scalar::ComplexField<RealField = <N as ComplexField>::RealField>,
+        R: DimName,
+        C: DimName,
+    > NormedSpace for MatrixMN<N, R, C>
+where
+    <N as ComplexField>::RealField: simba::scalar::RealField,
+    DefaultAllocator: Allocator<N, R, C>,
+{
+    type RealField = <N as ComplexField>::RealField;
+    type ComplexField = N;
+
+    #[inline]
+    fn norm_squared(&self) -> <N as ComplexField>::RealField {
+        self.norm_squared()
+    }
+
+    #[inline]
+    fn norm(&self) -> <N as ComplexField>::RealField {
+        self.norm()
+    }
+
+    #[inline]
+    #[must_use = "Did you mean to use normalize_mut()?"]
+    fn normalize(&self) -> Self {
+        self.normalize()
+    }
+
+    #[inline]
+    fn normalize_mut(&mut self) -> <N as ComplexField>::RealField {
+        self.normalize_mut()
+    }
+
+    #[inline]
+    #[must_use = "Did you mean to use try_normalize_mut()?"]
+    fn try_normalize(&self, min_norm: <N as ComplexField>::RealField) -> Option<Self> {
+        self.try_normalize(min_norm)
+    }
+
+    #[inline]
+    fn try_normalize_mut(
+        &mut self,
+        min_norm: <N as ComplexField>::RealField,
+    ) -> Option<<N as ComplexField>::RealField> {
+        self.try_normalize_mut(min_norm)
+    }
+}
+
+impl<
+        N: ComplexField + simba::scalar::ComplexField<RealField = <N as ComplexField>::RealField>,
+        R: DimName,
+        C: DimName,
+    > InnerSpace for MatrixMN<N, R, C>
+where
+    <N as ComplexField>::RealField: simba::scalar::RealField,
+    DefaultAllocator: Allocator<N, R, C>,
+{
+    #[inline]
+    fn angle(&self, other: &Self) -> <N as ComplexField>::RealField {
+        self.angle(other)
+    }
+
+    #[inline]
+    fn inner_product(&self, other: &Self) -> N {
+        self.dotc(other)
+    }
+}
+
+// FIXME: specialization will greatly simplify this implementation in the future.
+// In particular:
+//   − use `x()` instead of `::canonical_basis_element`
+//   − use `::new(x, y, z)` instead of `::from_slice`
+impl<
+        N: ComplexField + simba::scalar::ComplexField<RealField = <N as ComplexField>::RealField>,
+        R: DimName,
+        C: DimName,
+    > FiniteDimInnerSpace for MatrixMN<N, R, C>
+where
+    <N as ComplexField>::RealField: simba::scalar::RealField,
+    DefaultAllocator: Allocator<N, R, C>,
+{
+    #[inline]
+    fn orthonormalize(vs: &mut [Self]) -> usize {
+        let mut nbasis_elements = 0;
+
+        for i in 0..vs.len() {
+            {
+                let (elt, basis) = vs[..i + 1].split_last_mut().unwrap();
+
+                for basis_element in &basis[..nbasis_elements] {
+                    *elt -= &*basis_element * elt.dot(basis_element)
+                }
+            }
+
+            if vs[i]
+                .try_normalize_mut(<N as ComplexField>::RealField::zero())
+                .is_some()
+            {
+                // FIXME: this will be efficient on dynamically-allocated vectors but for
+                // statically-allocated ones, `.clone_from` would be better.
+                vs.swap(nbasis_elements, i);
+                nbasis_elements += 1;
+
+                // All the other vectors will be dependent.
+                if nbasis_elements == Self::dimension() {
+                    break;
+                }
+            }
+        }
+
+        nbasis_elements
+    }
+
+    #[inline]
+    fn orthonormal_subspace_basis<F>(vs: &[Self], mut f: F)
+    where
+        F: FnMut(&Self) -> bool,
+    {
+        // FIXME: is this necessary?
+        assert!(
+            vs.len() <= Self::dimension(),
+            "The given set of vectors has no chance of being a free family."
+        );
+
+        match Self::dimension() {
+            1 => {
+                if vs.len() == 0 {
+                    let _ = f(&Self::canonical_basis_element(0));
+                }
+            }
+            2 => {
+                if vs.len() == 0 {
+                    let _ = f(&Self::canonical_basis_element(0))
+                        && f(&Self::canonical_basis_element(1));
+                } else if vs.len() == 1 {
+                    let v = &vs[0];
+                    let res = Self::from_column_slice(&[-v[1], v[0]]);
+
+                    let _ = f(&res.normalize());
+                }
+
+                // Otherwise, nothing.
+            }
+            3 => {
+                if vs.len() == 0 {
+                    let _ = f(&Self::canonical_basis_element(0))
+                        && f(&Self::canonical_basis_element(1))
+                        && f(&Self::canonical_basis_element(2));
+                } else if vs.len() == 1 {
+                    let v = &vs[0];
+                    let mut a;
+
+                    if ComplexField::norm1(v[0]) > ComplexField::norm1(v[1]) {
+                        a = Self::from_column_slice(&[v[2], N::zero(), -v[0]]);
+                    } else {
+                        a = Self::from_column_slice(&[N::zero(), -v[2], v[1]]);
+                    };
+
+                    let _ = a.normalize_mut();
+
+                    if f(&a.cross(v)) {
+                        let _ = f(&a);
+                    }
+                } else if vs.len() == 2 {
+                    let _ = f(&vs[0].cross(&vs[1]).normalize());
+                }
+            }
+            _ => {
+                #[cfg(any(feature = "std", feature = "alloc"))]
+                {
+                    // XXX: use a GenericArray instead.
+                    let mut known_basis = Vec::new();
+
+                    for v in vs.iter() {
+                        known_basis.push(v.normalize())
+                    }
+
+                    for i in 0..Self::dimension() - vs.len() {
+                        let mut elt = Self::canonical_basis_element(i);
+
+                        for v in &known_basis {
+                            elt -= v * elt.dot(v)
+                        }
+
+                        if let Some(subsp_elt) =
+                            elt.try_normalize(<N as ComplexField>::RealField::zero())
+                        {
+                            if !f(&subsp_elt) {
+                                return;
+                            };
+
+                            known_basis.push(subsp_elt);
+                        }
+                    }
+                }
+                #[cfg(all(not(feature = "std"), not(feature = "alloc")))]
+                {
+                    panic!("Cannot compute the orthogonal subspace basis of a vector with a dimension greater than 3 \
+                            if #![no_std] is enabled and the 'alloc' feature is not enabled.")
+                }
+            }
+        }
+    }
+}
+
+/*
+ *
+ *
+ * Multiplicative structures.
+ *
+ *
+ */
+impl<N, D: DimName> Identity<Multiplicative> for MatrixN<N, D>
+where
+    N: Scalar + Zero + One,
+    DefaultAllocator: Allocator<N, D, D>,
+{
+    #[inline]
+    fn identity() -> Self {
+        Self::identity()
+    }
+}
+
+impl<N, D: DimName> AbstractMagma<Multiplicative> for MatrixN<N, D>
+where
+    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
+    DefaultAllocator: Allocator<N, D, D>,
+{
+    #[inline]
+    fn operate(&self, other: &Self) -> Self {
+        self * other
+    }
+}
+
+macro_rules! impl_multiplicative_structure(
+    ($($marker: ident<$operator: ident> $(+ $bounds: ident)*),* $(,)*) => {$(
+        impl<N, D: DimName> $marker<$operator> for MatrixN<N, D>
+            where N: Scalar + Zero + One + ClosedAdd + ClosedMul + $marker<$operator> $(+ $bounds)*,
+                  DefaultAllocator: Allocator<N, D, D> { }
+    )*}
+);
+
+impl_multiplicative_structure!(
+    AbstractSemigroup<Multiplicative>,
+    AbstractMonoid<Multiplicative> + One
+);
+
+/*
+ *
+ * Ordering
+ *
+ */
+impl<N, R: Dim, C: Dim> MeetSemilattice for MatrixMN<N, R, C>
+where
+    N: Scalar + MeetSemilattice,
+    DefaultAllocator: Allocator<N, R, C>,
+{
+    #[inline]
+    fn meet(&self, other: &Self) -> Self {
+        self.zip_map(other, |a, b| a.meet(&b))
+    }
+}
+
+impl<N, R: Dim, C: Dim> JoinSemilattice for MatrixMN<N, R, C>
+where
+    N: Scalar + JoinSemilattice,
+    DefaultAllocator: Allocator<N, R, C>,
+{
+    #[inline]
+    fn join(&self, other: &Self) -> Self {
+        self.zip_map(other, |a, b| a.join(&b))
+    }
+}
+
+impl<N, R: Dim, C: Dim> Lattice for MatrixMN<N, R, C>
+where
+    N: Scalar + Lattice,
+    DefaultAllocator: Allocator<N, R, C>,
+{
+    #[inline]
+    fn meet_join(&self, other: &Self) -> (Self, Self) {
+        let shape = self.data.shape();
+        assert!(
+            shape == other.data.shape(),
+            "Matrix meet/join error: mismatched dimensions."
+        );
+
+        let mut mres = unsafe { Self::new_uninitialized_generic(shape.0, shape.1) };
+        let mut jres = unsafe { Self::new_uninitialized_generic(shape.0, shape.1) };
+
+        for i in 0..shape.0.value() * shape.1.value() {
+            unsafe {
+                let mj = self
+                    .data
+                    .get_unchecked_linear(i)
+                    .meet_join(other.data.get_unchecked_linear(i));
+                *mres.data.get_unchecked_linear_mut(i) = mj.0;
+                *jres.data.get_unchecked_linear_mut(i) = mj.1;
+            }
+        }
+
+        (mres, jres)
+    }
+}
diff --git a/src/base/mod.rs b/src/base/mod.rs
index 0f380523..0e8ea72d 100644
--- a/src/base/mod.rs
+++ b/src/base/mod.rs
@@ -21,6 +21,8 @@ mod conversion;
 mod edition;
 pub mod indexing;
 mod matrix;
+#[cfg(feature = "alga")]
+mod matrix_alga;
 mod matrix_simba;
 mod matrix_slice;
 mod norm;
diff --git a/src/geometry/isometry_alga.rs b/src/geometry/isometry_alga.rs
new file mode 100755
index 00000000..3cb965a8
--- /dev/null
+++ b/src/geometry/isometry_alga.rs
@@ -0,0 +1,210 @@
+use alga::general::{
+    AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
+    AbstractSemigroup, Id, Identity, Multiplicative, RealField, TwoSidedInverse,
+};
+use alga::linear::Isometry as AlgaIsometry;
+use alga::linear::{
+    AffineTransformation, DirectIsometry, ProjectiveTransformation, Rotation, Similarity,
+    Transformation,
+};
+
+use crate::base::allocator::Allocator;
+use crate::base::dimension::DimName;
+use crate::base::{DefaultAllocator, VectorN};
+
+use crate::geometry::{AbstractRotation, Isometry, Point, Translation};
+
+/*
+ *
+ * Algebraic structures.
+ *
+ */
+impl<N: RealField + simba::scalar::RealField, D: DimName, R> Identity<Multiplicative>
+    for Isometry<N, D, R>
+where
+    R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
+    DefaultAllocator: Allocator<N, D>,
+{
+    #[inline]
+    fn identity() -> Self {
+        Self::identity()
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField, D: DimName, R> TwoSidedInverse<Multiplicative>
+    for Isometry<N, D, R>
+where
+    R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
+    DefaultAllocator: Allocator<N, D>,
+{
+    #[inline]
+    #[must_use = "Did you mean to use two_sided_inverse_mut()?"]
+    fn two_sided_inverse(&self) -> Self {
+        self.inverse()
+    }
+
+    #[inline]
+    fn two_sided_inverse_mut(&mut self) {
+        self.inverse_mut()
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField, D: DimName, R> AbstractMagma<Multiplicative>
+    for Isometry<N, D, R>
+where
+    R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
+    DefaultAllocator: Allocator<N, D>,
+{
+    #[inline]
+    fn operate(&self, rhs: &Self) -> Self {
+        self * rhs
+    }
+}
+
+macro_rules! impl_multiplicative_structures(
+    ($($marker: ident<$operator: ident>),* $(,)*) => {$(
+        impl<N: RealField + simba::scalar::RealField, D: DimName, R> $marker<$operator> for Isometry<N, D, R>
+            where R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
+                  DefaultAllocator: Allocator<N, D> { }
+    )*}
+);
+
+impl_multiplicative_structures!(
+    AbstractSemigroup<Multiplicative>,
+    AbstractMonoid<Multiplicative>,
+    AbstractQuasigroup<Multiplicative>,
+    AbstractLoop<Multiplicative>,
+    AbstractGroup<Multiplicative>
+);
+
+/*
+ *
+ * Transformation groups.
+ *
+ */
+impl<N: RealField + simba::scalar::RealField, D: DimName, R> Transformation<Point<N, D>>
+    for Isometry<N, D, R>
+where
+    R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
+    DefaultAllocator: Allocator<N, D>,
+{
+    #[inline]
+    fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
+        self.transform_point(pt)
+    }
+
+    #[inline]
+    fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+        self.transform_vector(v)
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField, D: DimName, R> ProjectiveTransformation<Point<N, D>>
+    for Isometry<N, D, R>
+where
+    R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
+    DefaultAllocator: Allocator<N, D>,
+{
+    #[inline]
+    fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
+        self.inverse_transform_point(pt)
+    }
+
+    #[inline]
+    fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+        self.inverse_transform_vector(v)
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField, D: DimName, R> AffineTransformation<Point<N, D>>
+    for Isometry<N, D, R>
+where
+    R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
+    DefaultAllocator: Allocator<N, D>,
+{
+    type Rotation = R;
+    type NonUniformScaling = Id;
+    type Translation = Translation<N, D>;
+
+    #[inline]
+    fn decompose(&self) -> (Self::Translation, R, Id, R) {
+        (
+            self.translation.clone(),
+            self.rotation.clone(),
+            Id::new(),
+            <R as AbstractRotation<N, D>>::identity(),
+        )
+    }
+
+    #[inline]
+    fn append_translation(&self, t: &Self::Translation) -> Self {
+        t * self
+    }
+
+    #[inline]
+    fn prepend_translation(&self, t: &Self::Translation) -> Self {
+        self * t
+    }
+
+    #[inline]
+    fn append_rotation(&self, r: &Self::Rotation) -> Self {
+        let shift = Transformation::transform_vector(r, &self.translation.vector);
+        Isometry::from_parts(Translation::from(shift), r.clone() * self.rotation.clone())
+    }
+
+    #[inline]
+    fn prepend_rotation(&self, r: &Self::Rotation) -> Self {
+        Isometry::from_parts(self.translation.clone(), self.rotation.prepend_rotation(r))
+    }
+
+    #[inline]
+    fn append_scaling(&self, _: &Self::NonUniformScaling) -> Self {
+        self.clone()
+    }
+
+    #[inline]
+    fn prepend_scaling(&self, _: &Self::NonUniformScaling) -> Self {
+        self.clone()
+    }
+
+    #[inline]
+    fn append_rotation_wrt_point(&self, r: &Self::Rotation, p: &Point<N, D>) -> Option<Self> {
+        let mut res = self.clone();
+        res.append_rotation_wrt_point_mut(r, p);
+        Some(res)
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField, D: DimName, R> Similarity<Point<N, D>>
+    for Isometry<N, D, R>
+where
+    R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
+    DefaultAllocator: Allocator<N, D>,
+{
+    type Scaling = Id;
+
+    #[inline]
+    fn translation(&self) -> Translation<N, D> {
+        self.translation.clone()
+    }
+
+    #[inline]
+    fn rotation(&self) -> R {
+        self.rotation.clone()
+    }
+
+    #[inline]
+    fn scaling(&self) -> Id {
+        Id::new()
+    }
+}
+
+macro_rules! marker_impl(
+    ($($Trait: ident),*) => {$(
+        impl<N: RealField + simba::scalar::RealField, D: DimName, R> $Trait<Point<N, D>> for Isometry<N, D, R>
+        where R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
+              DefaultAllocator: Allocator<N, D> { }
+    )*}
+);
+
+marker_impl!(AlgaIsometry, DirectIsometry);
diff --git a/src/geometry/mod.rs b/src/geometry/mod.rs
index 28c03edb..6f991f72 100644
--- a/src/geometry/mod.rs
+++ b/src/geometry/mod.rs
@@ -6,6 +6,8 @@ mod op_macros;
 mod abstract_rotation;
 
 mod point;
+#[cfg(feature = "alga")]
+mod point_alga;
 mod point_alias;
 mod point_construction;
 mod point_conversion;
@@ -14,6 +16,8 @@ mod point_ops;
 mod point_simba;
 
 mod rotation;
+#[cfg(feature = "alga")]
+mod rotation_alga;
 mod rotation_alias;
 mod rotation_construction;
 mod rotation_conversion;
@@ -22,6 +26,8 @@ mod rotation_simba; // FIXME: implement Rotation methods.
 mod rotation_specialization;
 
 mod quaternion;
+#[cfg(feature = "alga")]
+mod quaternion_alga;
 mod quaternion_construction;
 mod quaternion_conversion;
 mod quaternion_coordinates;
@@ -29,12 +35,16 @@ mod quaternion_ops;
 mod quaternion_simba;
 
 mod unit_complex;
+#[cfg(feature = "alga")]
+mod unit_complex_alga;
 mod unit_complex_construction;
 mod unit_complex_conversion;
 mod unit_complex_ops;
 mod unit_complex_simba;
 
 mod translation;
+#[cfg(feature = "alga")]
+mod translation_alga;
 mod translation_alias;
 mod translation_construction;
 mod translation_conversion;
@@ -43,6 +53,8 @@ mod translation_ops;
 mod translation_simba;
 
 mod isometry;
+#[cfg(feature = "alga")]
+mod isometry_alga;
 mod isometry_alias;
 mod isometry_construction;
 mod isometry_conversion;
@@ -50,6 +62,8 @@ mod isometry_ops;
 mod isometry_simba;
 
 mod similarity;
+#[cfg(feature = "alga")]
+mod similarity_alga;
 mod similarity_alias;
 mod similarity_construction;
 mod similarity_conversion;
@@ -59,6 +73,8 @@ mod similarity_simba;
 mod swizzle;
 
 mod transform;
+#[cfg(feature = "alga")]
+mod transform_alga;
 mod transform_alias;
 mod transform_construction;
 mod transform_conversion;
diff --git a/src/geometry/point_alga.rs b/src/geometry/point_alga.rs
new file mode 100644
index 00000000..5a7cace5
--- /dev/null
+++ b/src/geometry/point_alga.rs
@@ -0,0 +1,84 @@
+use alga::general::{Field, JoinSemilattice, Lattice, MeetSemilattice, RealField};
+use alga::linear::{AffineSpace, EuclideanSpace};
+
+use crate::base::allocator::Allocator;
+use crate::base::dimension::DimName;
+use crate::base::{DefaultAllocator, Scalar, VectorN};
+
+use crate::geometry::Point;
+
+impl<N: Scalar + Field, D: DimName> AffineSpace for Point<N, D>
+where
+    N: Scalar + Field,
+    DefaultAllocator: Allocator<N, D>,
+{
+    type Translation = VectorN<N, D>;
+}
+
+impl<N: RealField + simba::scalar::RealField, D: DimName> EuclideanSpace for Point<N, D>
+where
+    DefaultAllocator: Allocator<N, D>,
+{
+    type Coordinates = VectorN<N, D>;
+    type RealField = N;
+
+    #[inline]
+    fn origin() -> Self {
+        Self::origin()
+    }
+
+    #[inline]
+    fn coordinates(&self) -> Self::Coordinates {
+        self.coords.clone()
+    }
+
+    #[inline]
+    fn from_coordinates(coords: Self::Coordinates) -> Self {
+        Self::from(coords)
+    }
+
+    #[inline]
+    fn scale_by(&self, n: N) -> Self {
+        self * n
+    }
+}
+
+/*
+ *
+ * Ordering
+ *
+ */
+impl<N, D: DimName> MeetSemilattice for Point<N, D>
+where
+    N: Scalar + MeetSemilattice,
+    DefaultAllocator: Allocator<N, D>,
+{
+    #[inline]
+    fn meet(&self, other: &Self) -> Self {
+        Self::from(self.coords.meet(&other.coords))
+    }
+}
+
+impl<N, D: DimName> JoinSemilattice for Point<N, D>
+where
+    N: Scalar + JoinSemilattice,
+    DefaultAllocator: Allocator<N, D>,
+{
+    #[inline]
+    fn join(&self, other: &Self) -> Self {
+        Self::from(self.coords.join(&other.coords))
+    }
+}
+
+impl<N, D: DimName> Lattice for Point<N, D>
+where
+    N: Scalar + Lattice,
+    DefaultAllocator: Allocator<N, D>,
+{
+    #[inline]
+    fn meet_join(&self, other: &Self) -> (Self, Self) {
+        let (meet, join) = self.coords.meet_join(&other.coords);
+
+        (Self::from(meet), Self::from(join))
+    }
+}
diff --git a/src/geometry/quaternion_alga.rs b/src/geometry/quaternion_alga.rs
new file mode 100755
index 00000000..087c8a58
--- /dev/null
+++ b/src/geometry/quaternion_alga.rs
@@ -0,0 +1,313 @@
+use num::Zero;
+
+use alga::general::{
+    AbstractGroup, AbstractGroupAbelian, AbstractLoop, AbstractMagma, AbstractModule,
+    AbstractMonoid, AbstractQuasigroup, AbstractSemigroup, Additive, Id, Identity, Module,
+    Multiplicative, RealField, TwoSidedInverse,
+};
+use alga::linear::{
+    AffineTransformation, DirectIsometry, FiniteDimVectorSpace, Isometry, NormedSpace,
+    OrthogonalTransformation, ProjectiveTransformation, Rotation, Similarity, Transformation,
+    VectorSpace,
+};
+
+use crate::base::{Vector3, Vector4};
+use crate::geometry::{Point3, Quaternion, UnitQuaternion};
+
+impl<N: RealField + simba::scalar::RealField> Identity<Multiplicative> for Quaternion<N> {
+    #[inline]
+    fn identity() -> Self {
+        Self::identity()
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField> Identity<Additive> for Quaternion<N> {
+    #[inline]
+    fn identity() -> Self {
+        Self::zero()
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField> AbstractMagma<Multiplicative> for Quaternion<N> {
+    #[inline]
+    fn operate(&self, rhs: &Self) -> Self {
+        self * rhs
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField> AbstractMagma<Additive> for Quaternion<N> {
+    #[inline]
+    fn operate(&self, rhs: &Self) -> Self {
+        self + rhs
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField> TwoSidedInverse<Additive> for Quaternion<N> {
+    #[inline]
+    fn two_sided_inverse(&self) -> Self {
+        -self
+    }
+}
+
+macro_rules! impl_structures(
+    ($Quaternion: ident; $($marker: ident<$operator: ident>),* $(,)*) => {$(
+        impl<N: RealField + simba::scalar::RealField> $marker<$operator> for $Quaternion<N> { }
+    )*}
+);
+
+impl_structures!(
+    Quaternion;
+    AbstractSemigroup<Multiplicative>,
+    AbstractMonoid<Multiplicative>,
+
+    AbstractSemigroup<Additive>,
+    AbstractQuasigroup<Additive>,
+    AbstractMonoid<Additive>,
+    AbstractLoop<Additive>,
+    AbstractGroup<Additive>,
+    AbstractGroupAbelian<Additive>
+);
+
+/*
+ *
+ * Vector space.
+ *
+ */
+impl<N: RealField + simba::scalar::RealField> AbstractModule for Quaternion<N> {
+    type AbstractRing = N;
+
+    #[inline]
+    fn multiply_by(&self, n: N) -> Self {
+        self * n
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField> Module for Quaternion<N> {
+    type Ring = N;
+}
+
+impl<N: RealField + simba::scalar::RealField> VectorSpace for Quaternion<N> {
+    type Field = N;
+}
+
+impl<N: RealField + simba::scalar::RealField> FiniteDimVectorSpace for Quaternion<N> {
+    #[inline]
+    fn dimension() -> usize {
+        4
+    }
+
+    #[inline]
+    fn canonical_basis_element(i: usize) -> Self {
+        Self::from(Vector4::canonical_basis_element(i))
+    }
+
+    #[inline]
+    fn dot(&self, other: &Self) -> N {
+        self.coords.dot(&other.coords)
+    }
+
+    #[inline]
+    unsafe fn component_unchecked(&self, i: usize) -> &N {
+        self.coords.component_unchecked(i)
+    }
+
+    #[inline]
+    unsafe fn component_unchecked_mut(&mut self, i: usize) -> &mut N {
+        self.coords.component_unchecked_mut(i)
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField> NormedSpace for Quaternion<N> {
+    type RealField = N;
+    type ComplexField = N;
+
+    #[inline]
+    fn norm_squared(&self) -> N {
+        self.coords.norm_squared()
+    }
+
+    #[inline]
+    fn norm(&self) -> N {
+        self.as_vector().norm()
+    }
+
+    #[inline]
+    fn normalize(&self) -> Self {
+        let v = self.coords.normalize();
+        Self::from(v)
+    }
+
+    #[inline]
+    fn normalize_mut(&mut self) -> N {
+        self.coords.normalize_mut()
+    }
+
+    #[inline]
+    fn try_normalize(&self, min_norm: N) -> Option<Self> {
+        if let Some(v) = self.coords.try_normalize(min_norm) {
+            Some(Self::from(v))
+        } else {
+            None
+        }
+    }
+
+    #[inline]
+    fn try_normalize_mut(&mut self, min_norm: N) -> Option<N> {
+        self.coords.try_normalize_mut(min_norm)
+    }
+}
+
+/*
+ *
+ * Implementations for UnitQuaternion.
+ *
+ */
+impl<N: RealField + simba::scalar::RealField> Identity<Multiplicative> for UnitQuaternion<N> {
+    #[inline]
+    fn identity() -> Self {
+        Self::identity()
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField> AbstractMagma<Multiplicative> for UnitQuaternion<N> {
+    #[inline]
+    fn operate(&self, rhs: &Self) -> Self {
+        self * rhs
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField> TwoSidedInverse<Multiplicative>
+    for UnitQuaternion<N>
+{
+    #[inline]
+    fn two_sided_inverse(&self) -> Self {
+        self.inverse()
+    }
+
+    #[inline]
+    fn two_sided_inverse_mut(&mut self) {
+        self.inverse_mut()
+    }
+}
+
+impl_structures!(
+    UnitQuaternion;
+    AbstractSemigroup<Multiplicative>,
+    AbstractQuasigroup<Multiplicative>,
+    AbstractMonoid<Multiplicative>,
+    AbstractLoop<Multiplicative>,
+    AbstractGroup<Multiplicative>
+);
+
+impl<N: RealField + simba::scalar::RealField> Transformation<Point3<N>> for UnitQuaternion<N> {
+    #[inline]
+    fn transform_point(&self, pt: &Point3<N>) -> Point3<N> {
+        self.transform_point(pt)
+    }
+
+    #[inline]
+    fn transform_vector(&self, v: &Vector3<N>) -> Vector3<N> {
+        self.transform_vector(v)
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField> ProjectiveTransformation<Point3<N>>
+    for UnitQuaternion<N>
+{
+    #[inline]
+    fn inverse_transform_point(&self, pt: &Point3<N>) -> Point3<N> {
+        self.inverse_transform_point(pt)
+    }
+
+    #[inline]
+    fn inverse_transform_vector(&self, v: &Vector3<N>) -> Vector3<N> {
+        self.inverse_transform_vector(v)
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField> AffineTransformation<Point3<N>>
+    for UnitQuaternion<N>
+{
+    type Rotation = Self;
+    type NonUniformScaling = Id;
+    type Translation = Id;
+
+    #[inline]
+    fn decompose(&self) -> (Id, Self, Id, Self) {
+        (Id::new(), self.clone(), Id::new(), Self::identity())
+    }
+
+    #[inline]
+    fn append_translation(&self, _: &Self::Translation) -> Self {
+        self.clone()
+    }
+
+    #[inline]
+    fn prepend_translation(&self, _: &Self::Translation) -> Self {
+        self.clone()
+    }
+
+    #[inline]
+    fn append_rotation(&self, r: &Self::Rotation) -> Self {
+        r * self
+    }
+
+    #[inline]
+    fn prepend_rotation(&self, r: &Self::Rotation) -> Self {
+        self * r
+    }
+
+    #[inline]
+    fn append_scaling(&self, _: &Self::NonUniformScaling) -> Self {
+        self.clone()
+    }
+
+    #[inline]
+    fn prepend_scaling(&self, _: &Self::NonUniformScaling) -> Self {
+        self.clone()
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField> Similarity<Point3<N>> for UnitQuaternion<N> {
+    type Scaling = Id;
+
+    #[inline]
+    fn translation(&self) -> Id {
+        Id::new()
+    }
+
+    #[inline]
+    fn rotation(&self) -> Self {
+        self.clone()
+    }
+
+    #[inline]
+    fn scaling(&self) -> Id {
+        Id::new()
+    }
+}
+
+macro_rules! marker_impl(
+    ($($Trait: ident),*) => {$(
+        impl<N: RealField + simba::scalar::RealField> $Trait<Point3<N>> for UnitQuaternion<N> { }
+    )*}
+);
+
+marker_impl!(Isometry, DirectIsometry, OrthogonalTransformation);
+
+impl<N: RealField + simba::scalar::RealField> Rotation<Point3<N>> for UnitQuaternion<N> {
+    #[inline]
+    fn powf(&self, n: N) -> Option<Self> {
+        Some(self.powf(n))
+    }
+
+    #[inline]
+    fn rotation_between(a: &Vector3<N>, b: &Vector3<N>) -> Option<Self> {
+        Self::rotation_between(a, b)
+    }
+
+    #[inline]
+    fn scaled_rotation_between(a: &Vector3<N>, b: &Vector3<N>, s: N) -> Option<Self> {
+        Self::scaled_rotation_between(a, b, s)
+    }
+}
diff --git a/src/geometry/rotation_alga.rs b/src/geometry/rotation_alga.rs
new file mode 100755
index 00000000..f37ebbd1
--- /dev/null
+++ b/src/geometry/rotation_alga.rs
@@ -0,0 +1,291 @@
+use alga::general::{
+    AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
+    AbstractSemigroup, Id, Identity, Multiplicative, RealField, TwoSidedInverse,
+};
+use alga::linear::{
+    self, AffineTransformation, DirectIsometry, Isometry, OrthogonalTransformation,
+    ProjectiveTransformation, Similarity, Transformation,
+};
+
+use crate::base::allocator::Allocator;
+use crate::base::dimension::DimName;
+use crate::base::{DefaultAllocator, VectorN};
+
+use crate::geometry::{Point, Rotation};
+
+/*
+ *
+ * Algebraic structures.
+ *
+ */
+impl<N: RealField + simba::scalar::RealField, D: DimName> Identity<Multiplicative>
+    for Rotation<N, D>
+where
+    DefaultAllocator: Allocator<N, D, D>,
+{
+    #[inline]
+    fn identity() -> Self {
+        Self::identity()
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField, D: DimName> TwoSidedInverse<Multiplicative>
+    for Rotation<N, D>
+where
+    DefaultAllocator: Allocator<N, D, D>,
+{
+    #[inline]
+    #[must_use = "Did you mean to use two_sided_inverse_mut()?"]
+    fn two_sided_inverse(&self) -> Self {
+        self.transpose()
+    }
+
+    #[inline]
+    fn two_sided_inverse_mut(&mut self) {
+        self.transpose_mut()
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField, D: DimName> AbstractMagma<Multiplicative>
+    for Rotation<N, D>
+where
+    DefaultAllocator: Allocator<N, D, D>,
+{
+    #[inline]
+    fn operate(&self, rhs: &Self) -> Self {
+        self * rhs
+    }
+}
+
+macro_rules! impl_multiplicative_structures(
+    ($($marker: ident<$operator: ident>),* $(,)*) => {$(
+        impl<N: RealField + simba::scalar::RealField, D: DimName> $marker<$operator> for Rotation<N, D>
+            where DefaultAllocator: Allocator<N, D, D> { }
+    )*}
+);
+
+impl_multiplicative_structures!(
+    AbstractSemigroup<Multiplicative>,
+    AbstractMonoid<Multiplicative>,
+    AbstractQuasigroup<Multiplicative>,
+    AbstractLoop<Multiplicative>,
+    AbstractGroup<Multiplicative>
+);
+
+/*
+ *
+ * Transformation groups.
+ *
+ */
+impl<N: RealField + simba::scalar::RealField, D: DimName> Transformation<Point<N, D>>
+    for Rotation<N, D>
+where
+    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
+{
+    #[inline]
+    fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
+        self.transform_point(pt)
+    }
+
+    #[inline]
+    fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+        self.transform_vector(v)
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField, D: DimName> ProjectiveTransformation<Point<N, D>>
+    for Rotation<N, D>
+where
+    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
+{
+    #[inline]
+    fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
+        self.inverse_transform_point(pt)
+    }
+
+    #[inline]
+    fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+        self.inverse_transform_vector(v)
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField, D: DimName> AffineTransformation<Point<N, D>>
+    for Rotation<N, D>
+where
+    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
+{
+    type Rotation = Self;
+    type NonUniformScaling = Id;
+    type Translation = Id;
+
+    #[inline]
+    fn decompose(&self) -> (Id, Self, Id, Self) {
+        (Id::new(), self.clone(), Id::new(), Self::identity())
+    }
+
+    #[inline]
+    fn append_translation(&self, _: &Self::Translation) -> Self {
+        self.clone()
+    }
+
+    #[inline]
+    fn prepend_translation(&self, _: &Self::Translation) -> Self {
+        self.clone()
+    }
+
+    #[inline]
+    fn append_rotation(&self, r: &Self::Rotation) -> Self {
+        r * self
+    }
+
+    #[inline]
+    fn prepend_rotation(&self, r: &Self::Rotation) -> Self {
+        self * r
+    }
+
+    #[inline]
+    fn append_scaling(&self, _: &Self::NonUniformScaling) -> Self {
+        self.clone()
+    }
+
+    #[inline]
+    fn prepend_scaling(&self, _: &Self::NonUniformScaling) -> Self {
+        self.clone()
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField, D: DimName> Similarity<Point<N, D>> for Rotation<N, D>
+where
+    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
+{
+    type Scaling = Id;
+
+    #[inline]
+    fn translation(&self) -> Id {
+        Id::new()
+    }
+
+    #[inline]
+    fn rotation(&self) -> Self {
+        self.clone()
+    }
+
+    #[inline]
+    fn scaling(&self) -> Id {
+        Id::new()
+    }
+}
+
+macro_rules! marker_impl(
+    ($($Trait: ident),*) => {$(
+        impl<N: RealField + simba::scalar::RealField, D: DimName> $Trait<Point<N, D>> for Rotation<N, D>
+        where DefaultAllocator: Allocator<N, D, D> +
+                                Allocator<N, D> { }
+    )*}
+);
+
+marker_impl!(Isometry, DirectIsometry, OrthogonalTransformation);
+
+/// Subgroups of the n-dimensional rotation group `SO(n)`.
+impl<N: RealField + simba::scalar::RealField, D: DimName> linear::Rotation<Point<N, D>>
+    for Rotation<N, D>
+where
+    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
+{
+    #[inline]
+    fn powf(&self, _: N) -> Option<Self> {
+        // XXX: Add the general case.
+        // XXX: Use specialization for 2D and 3D.
+        unimplemented!()
+    }
+
+    #[inline]
+    fn rotation_between(_: &VectorN<N, D>, _: &VectorN<N, D>) -> Option<Self> {
+        // XXX: Add the general case.
+        // XXX: Use specialization for 2D and 3D.
+        unimplemented!()
+    }
+
+    #[inline]
+    fn scaled_rotation_between(_: &VectorN<N, D>, _: &VectorN<N, D>, _: N) -> Option<Self> {
+        // XXX: Add the general case.
+        // XXX: Use specialization for 2D and 3D.
+        unimplemented!()
+    }
+}
+
+/*
+impl<N: RealField + simba::scalar::RealField> Matrix for Rotation<N> {
+    type Field     = N;
+    type Row       = Matrix<N>;
+    type Column    = Matrix<N>;
+    type Transpose = Self;
+
+    #[inline]
+    fn nrows(&self) -> usize {
+        self.submatrix.nrows()
+    }
+
+    #[inline]
+    fn ncolumns(&self) -> usize {
+        self.submatrix.ncolumns()
+    }
+
+    #[inline]
+    fn row(&self, i: usize) -> Self::Row {
+        self.submatrix.row(i)
+    }
+
+    #[inline]
+    fn column(&self, i: usize) -> Self::Column {
+        self.submatrix.column(i)
+    }
+
+    #[inline]
+    fn get(&self, i: usize, j: usize) -> Self::Field {
+        self.submatrix[(i, j)]
+    }
+
+    #[inline]
+    unsafe fn get_unchecked(&self, i: usize, j: usize) -> Self::Field {
+        self.submatrix.at_fast(i, j)
+    }
+
+    #[inline]
+    fn transpose(&self) -> Self::Transpose {
+        Rotation::from_matrix_unchecked(self.submatrix.transpose())
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField> SquareMatrix for Rotation<N> {
+    type Vector = Matrix<N>;
+
+    #[inline]
+    fn diagonal(&self) -> Self::Coordinates {
+        self.submatrix.diagonal()
+    }
+
+    #[inline]
+    fn determinant(&self) -> Self::Field {
+        crate::one()
+    }
+
+    #[inline]
+    fn try_inverse(&self) -> Option<Self> {
+        Some(::transpose(self))
+    }
+
+    #[inline]
+    fn try_inverse_mut(&mut self) -> bool {
+        self.transpose_mut();
+        true
+    }
+
+    #[inline]
+    fn transpose_mut(&mut self) {
+        self.submatrix.transpose_mut()
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField> InversibleSquareMatrix for Rotation<N> { }
+*/
diff --git a/src/geometry/similarity_alga.rs b/src/geometry/similarity_alga.rs
new file mode 100755
index 00000000..58dd4563
--- /dev/null
+++ b/src/geometry/similarity_alga.rs
@@ -0,0 +1,196 @@
+use alga::general::{
+    AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
+    AbstractSemigroup, Identity, Multiplicative, RealField, TwoSidedInverse,
+};
+use alga::linear::Similarity as AlgaSimilarity;
+use alga::linear::{AffineTransformation, ProjectiveTransformation, Rotation, Transformation};
+
+use crate::base::allocator::Allocator;
+use crate::base::dimension::DimName;
+use crate::base::{DefaultAllocator, VectorN};
+
+use crate::geometry::{AbstractRotation, Point, Similarity, Translation};
+
+/*
+ *
+ * Algebraic structures.
+ *
+ */
+impl<N: RealField + simba::scalar::RealField, D: DimName, R> Identity<Multiplicative>
+    for Similarity<N, D, R>
+where
+    R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
+    DefaultAllocator: Allocator<N, D>,
+{
+    #[inline]
+    fn identity() -> Self {
+        Self::identity()
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField, D: DimName, R> TwoSidedInverse<Multiplicative>
+    for Similarity<N, D, R>
+where
+    R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
+    DefaultAllocator: Allocator<N, D>,
+{
+    #[inline]
+    #[must_use = "Did you mean to use two_sided_inverse_mut()?"]
+    fn two_sided_inverse(&self) -> Self {
+        self.inverse()
+    }
+
+    #[inline]
+    fn two_sided_inverse_mut(&mut self) {
+        self.inverse_mut()
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField, D: DimName, R> AbstractMagma<Multiplicative>
+    for Similarity<N, D, R>
+where
+    R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
+    DefaultAllocator: Allocator<N, D>,
+{
+    #[inline]
+    fn operate(&self, rhs: &Self) -> Self {
+        self * rhs
+    }
+}
+
+macro_rules! impl_multiplicative_structures(
+    ($($marker: ident<$operator: ident>),* $(,)*) => {$(
+        impl<N: RealField + simba::scalar::RealField, D: DimName, R> $marker<$operator> for Similarity<N, D, R>
+            where R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
+                  DefaultAllocator: Allocator<N, D> { }
+    )*}
+);
+
+impl_multiplicative_structures!(
+    AbstractSemigroup<Multiplicative>,
+    AbstractMonoid<Multiplicative>,
+    AbstractQuasigroup<Multiplicative>,
+    AbstractLoop<Multiplicative>,
+    AbstractGroup<Multiplicative>
+);
+
+/*
+ *
+ * Transformation groups.
+ *
+ */
+impl<N: RealField + simba::scalar::RealField, D: DimName, R> Transformation<Point<N, D>>
+    for Similarity<N, D, R>
+where
+    R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
+    DefaultAllocator: Allocator<N, D>,
+{
+    #[inline]
+    fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
+        self.transform_point(pt)
+    }
+
+    #[inline]
+    fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+        self.transform_vector(v)
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField, D: DimName, R> ProjectiveTransformation<Point<N, D>>
+    for Similarity<N, D, R>
+where
+    R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
+    DefaultAllocator: Allocator<N, D>,
+{
+    #[inline]
+    fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
+        self.inverse_transform_point(pt)
+    }
+
+    #[inline]
+    fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+        self.inverse_transform_vector(v)
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField, D: DimName, R> AffineTransformation<Point<N, D>>
+    for Similarity<N, D, R>
+where
+    R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
+    DefaultAllocator: Allocator<N, D>,
+{
+    type NonUniformScaling = N;
+    type Rotation = R;
+    type Translation = Translation<N, D>;
+
+    #[inline]
+    fn decompose(&self) -> (Translation<N, D>, R, N, R) {
+        (
+            self.isometry.translation.clone(),
+            self.isometry.rotation.clone(),
+            self.scaling(),
+            <R as AbstractRotation<N, D>>::identity(),
+        )
+    }
+
+    #[inline]
+    fn append_translation(&self, t: &Self::Translation) -> Self {
+        t * self
+    }
+
+    #[inline]
+    fn prepend_translation(&self, t: &Self::Translation) -> Self {
+        self * t
+    }
+
+    #[inline]
+    fn append_rotation(&self, r: &Self::Rotation) -> Self {
+        Similarity::from_isometry(self.isometry.append_rotation(r), self.scaling())
+    }
+
+    #[inline]
+    fn prepend_rotation(&self, r: &Self::Rotation) -> Self {
+        Similarity::from_isometry(self.isometry.prepend_rotation(r), self.scaling())
+    }
+
+    #[inline]
+    fn append_scaling(&self, s: &Self::NonUniformScaling) -> Self {
+        self.append_scaling(*s)
+    }
+
+    #[inline]
+    fn prepend_scaling(&self, s: &Self::NonUniformScaling) -> Self {
+        self.prepend_scaling(*s)
+    }
+
+    #[inline]
+    fn append_rotation_wrt_point(&self, r: &Self::Rotation, p: &Point<N, D>) -> Option<Self> {
+        let mut res = self.clone();
+        res.append_rotation_wrt_point_mut(r, p);
+        Some(res)
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField, D: DimName, R> AlgaSimilarity<Point<N, D>>
+    for Similarity<N, D, R>
+where
+    R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
+    DefaultAllocator: Allocator<N, D>,
+{
+    type Scaling = N;
+
+    #[inline]
+    fn translation(&self) -> Translation<N, D> {
+        self.isometry.translation()
+    }
+
+    #[inline]
+    fn rotation(&self) -> R {
+        self.isometry.rotation()
+    }
+
+    #[inline]
+    fn scaling(&self) -> N {
+        self.scaling()
+    }
+}
diff --git a/src/geometry/transform_alga.rs b/src/geometry/transform_alga.rs
new file mode 100755
index 00000000..3ba6eb7d
--- /dev/null
+++ b/src/geometry/transform_alga.rs
@@ -0,0 +1,149 @@
+use alga::general::{
+    AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
+    AbstractSemigroup, Identity, Multiplicative, RealField, TwoSidedInverse,
+};
+use alga::linear::{ProjectiveTransformation, Transformation};
+
+use crate::base::allocator::Allocator;
+use crate::base::dimension::{DimNameAdd, DimNameSum, U1};
+use crate::base::{DefaultAllocator, VectorN};
+
+use crate::geometry::{Point, SubTCategoryOf, TCategory, TProjective, Transform};
+
+/*
+ *
+ * Algebraic structures.
+ *
+ */
+impl<N: RealField + simba::scalar::RealField, D: DimNameAdd<U1>, C> Identity<Multiplicative>
+    for Transform<N, D, C>
+where
+    C: TCategory,
+    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+{
+    #[inline]
+    fn identity() -> Self {
+        Self::identity()
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField, D: DimNameAdd<U1>, C> TwoSidedInverse<Multiplicative>
+    for Transform<N, D, C>
+where
+    C: SubTCategoryOf<TProjective>,
+    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+{
+    #[inline]
+    #[must_use = "Did you mean to use two_sided_inverse_mut()?"]
+    fn two_sided_inverse(&self) -> Self {
+        self.clone().inverse()
+    }
+
+    #[inline]
+    fn two_sided_inverse_mut(&mut self) {
+        self.inverse_mut()
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField, D: DimNameAdd<U1>, C> AbstractMagma<Multiplicative>
+    for Transform<N, D, C>
+where
+    C: TCategory,
+    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+{
+    #[inline]
+    fn operate(&self, rhs: &Self) -> Self {
+        self * rhs
+    }
+}
+
+macro_rules! impl_multiplicative_structures(
+    ($($marker: ident<$operator: ident>),* $(,)*) => {$(
+        impl<N: RealField + simba::scalar::RealField, D: DimNameAdd<U1>, C> $marker<$operator> for Transform<N, D, C>
+            where C: TCategory,
+                  DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> { }
+    )*}
+);
+
+macro_rules! impl_inversible_multiplicative_structures(
+    ($($marker: ident<$operator: ident>),* $(,)*) => {$(
+        impl<N: RealField + simba::scalar::RealField, D: DimNameAdd<U1>, C> $marker<$operator> for Transform<N, D, C>
+            where C: SubTCategoryOf<TProjective>,
+                  DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> { }
+    )*}
+);
+
+impl_multiplicative_structures!(
+    AbstractSemigroup<Multiplicative>,
+    AbstractMonoid<Multiplicative>,
+);
+
+impl_inversible_multiplicative_structures!(
+    AbstractQuasigroup<Multiplicative>,
+    AbstractLoop<Multiplicative>,
+    AbstractGroup<Multiplicative>
+);
+
+/*
+ *
+ * Transformation groups.
+ *
+ */
+impl<N, D: DimNameAdd<U1>, C> Transformation<Point<N, D>> for Transform<N, D, C>
+where
+    N: RealField + simba::scalar::RealField,
+    C: TCategory,
+    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
+        + Allocator<N, DimNameSum<D, U1>>
+        + Allocator<N, D, D>
+        + Allocator<N, D>,
+{
+    #[inline]
+    fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
+        self.transform_point(pt)
+    }
+
+    #[inline]
+    fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+        self.transform_vector(v)
+    }
+}
+
+impl<N, D: DimNameAdd<U1>, C> ProjectiveTransformation<Point<N, D>> for Transform<N, D, C>
+where
+    N: RealField + simba::scalar::RealField,
+    C: SubTCategoryOf<TProjective>,
+    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
+        + Allocator<N, DimNameSum<D, U1>>
+        + Allocator<N, D, D>
+        + Allocator<N, D>,
+{
+    #[inline]
+    fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
+        self.inverse_transform_point(pt)
+    }
+
+    #[inline]
+    fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+        self.inverse_transform_vector(v)
+    }
+}
+
+// FIXME: we need to implement an SVD for this.
+//
+// impl<N, D: DimNameAdd<U1>, C> AffineTransformation<Point<N, D>> for Transform<N, D, C>
+//     where N:  RealField,
+//           C: SubTCategoryOf<TAffine>,
+//           DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> +
+//                             Allocator<N, D, D> +
+//                             Allocator<N, D> {
+//     type PreRotation       = Rotation<N, D>;
+//     type NonUniformScaling = VectorN<N, D>;
+//     type PostRotation      = Rotation<N, D>;
+//     type Translation       = Translation<N, D>;
+//
+//     #[inline]
+//     fn decompose(&self) -> (Self::Translation, Self::PostRotation, Self::NonUniformScaling, Self::PreRotation) {
+//         unimplemented!()
+//     }
+// }
diff --git a/src/geometry/translation_alga.rs b/src/geometry/translation_alga.rs
new file mode 100755
index 00000000..aba6f1f4
--- /dev/null
+++ b/src/geometry/translation_alga.rs
@@ -0,0 +1,215 @@
+use alga::general::{
+    AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
+    AbstractSemigroup, Id, Identity, Multiplicative, RealField, TwoSidedInverse,
+};
+use alga::linear::Translation as AlgaTranslation;
+use alga::linear::{
+    AffineTransformation, DirectIsometry, Isometry, ProjectiveTransformation, Similarity,
+    Transformation,
+};
+
+use crate::base::allocator::Allocator;
+use crate::base::dimension::DimName;
+use crate::base::{DefaultAllocator, VectorN};
+
+use crate::geometry::{Point, Translation};
+
+/*
+ *
+ * Algebraic structures.
+ *
+ */
+impl<N: RealField + simba::scalar::RealField, D: DimName> Identity<Multiplicative>
+    for Translation<N, D>
+where
+    DefaultAllocator: Allocator<N, D>,
+{
+    #[inline]
+    fn identity() -> Self {
+        Self::identity()
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField, D: DimName> TwoSidedInverse<Multiplicative>
+    for Translation<N, D>
+where
+    DefaultAllocator: Allocator<N, D>,
+{
+    #[inline]
+    #[must_use = "Did you mean to use two_sided_inverse_mut()?"]
+    fn two_sided_inverse(&self) -> Self {
+        self.inverse()
+    }
+
+    #[inline]
+    fn two_sided_inverse_mut(&mut self) {
+        self.inverse_mut()
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField, D: DimName> AbstractMagma<Multiplicative>
+    for Translation<N, D>
+where
+    DefaultAllocator: Allocator<N, D>,
+{
+    #[inline]
+    fn operate(&self, rhs: &Self) -> Self {
+        self * rhs
+    }
+}
+
+macro_rules! impl_multiplicative_structures(
+    ($($marker: ident<$operator: ident>),* $(,)*) => {$(
+        impl<N: RealField + simba::scalar::RealField, D: DimName> $marker<$operator> for Translation<N, D>
+            where DefaultAllocator: Allocator<N, D> { }
+    )*}
+);
+
+impl_multiplicative_structures!(
+    AbstractSemigroup<Multiplicative>,
+    AbstractMonoid<Multiplicative>,
+    AbstractQuasigroup<Multiplicative>,
+    AbstractLoop<Multiplicative>,
+    AbstractGroup<Multiplicative>
+);
+
+/*
+ *
+ * Transformation groups.
+ *
+ */
+impl<N: RealField + simba::scalar::RealField, D: DimName> Transformation<Point<N, D>>
+    for Translation<N, D>
+where
+    DefaultAllocator: Allocator<N, D>,
+{
+    #[inline]
+    fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
+        self.transform_point(pt)
+    }
+
+    #[inline]
+    fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+        v.clone()
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField, D: DimName> ProjectiveTransformation<Point<N, D>>
+    for Translation<N, D>
+where
+    DefaultAllocator: Allocator<N, D>,
+{
+    #[inline]
+    fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
+        self.inverse_transform_point(pt)
+    }
+
+    #[inline]
+    fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+        v.clone()
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField, D: DimName> AffineTransformation<Point<N, D>>
+    for Translation<N, D>
+where
+    DefaultAllocator: Allocator<N, D>,
+{
+    type Rotation = Id;
+    type NonUniformScaling = Id;
+    type Translation = Self;
+
+    #[inline]
+    fn decompose(&self) -> (Self, Id, Id, Id) {
+        (self.clone(), Id::new(), Id::new(), Id::new())
+    }
+
+    #[inline]
+    fn append_translation(&self, t: &Self::Translation) -> Self {
+        t * self
+    }
+
+    #[inline]
+    fn prepend_translation(&self, t: &Self::Translation) -> Self {
+        self * t
+    }
+
+    #[inline]
+    fn append_rotation(&self, _: &Self::Rotation) -> Self {
+        self.clone()
+    }
+
+    #[inline]
+    fn prepend_rotation(&self, _: &Self::Rotation) -> Self {
+        self.clone()
+    }
+
+    #[inline]
+    fn append_scaling(&self, _: &Self::NonUniformScaling) -> Self {
+        self.clone()
+    }
+
+    #[inline]
+    fn prepend_scaling(&self, _: &Self::NonUniformScaling) -> Self {
+        self.clone()
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField, D: DimName> Similarity<Point<N, D>>
+    for Translation<N, D>
+where
+    DefaultAllocator: Allocator<N, D>,
+{
+    type Scaling = Id;
+
+    #[inline]
+    fn translation(&self) -> Self {
+        self.clone()
+    }
+
+    #[inline]
+    fn rotation(&self) -> Id {
+        Id::new()
+    }
+
+    #[inline]
+    fn scaling(&self) -> Id {
+        Id::new()
+    }
+}
+
+macro_rules! marker_impl(
+    ($($Trait: ident),*) => {$(
+        impl<N: RealField + simba::scalar::RealField, D: DimName> $Trait<Point<N, D>> for Translation<N, D>
+            where DefaultAllocator: Allocator<N, D> { }
+    )*}
+);
+
+marker_impl!(Isometry, DirectIsometry);
+
+/// Subgroups of the n-dimensional translation group `T(n)`.
+impl<N: RealField + simba::scalar::RealField, D: DimName> AlgaTranslation<Point<N, D>>
+    for Translation<N, D>
+where
+    DefaultAllocator: Allocator<N, D>,
+{
+    #[inline]
+    fn to_vector(&self) -> VectorN<N, D> {
+        self.vector.clone()
+    }
+
+    #[inline]
+    fn from_vector(v: VectorN<N, D>) -> Option<Self> {
+        Some(Self::from(v))
+    }
+
+    #[inline]
+    fn powf(&self, n: N) -> Option<Self> {
+        Some(Self::from(&self.vector * n))
+    }
+
+    #[inline]
+    fn translation_between(a: &Point<N, D>, b: &Point<N, D>) -> Option<Self> {
+        Some(Self::from(b - a))
+    }
+}
diff --git a/src/geometry/unit_complex_alga.rs b/src/geometry/unit_complex_alga.rs
new file mode 100755
index 00000000..46e30535
--- /dev/null
+++ b/src/geometry/unit_complex_alga.rs
@@ -0,0 +1,185 @@
+use alga::general::{
+    AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
+    AbstractSemigroup, Id, Identity, Multiplicative, RealField, TwoSidedInverse,
+};
+use alga::linear::{
+    AffineTransformation, DirectIsometry, Isometry, OrthogonalTransformation,
+    ProjectiveTransformation, Rotation, Similarity, Transformation,
+};
+
+use crate::base::allocator::Allocator;
+use crate::base::dimension::U2;
+use crate::base::{DefaultAllocator, Vector2};
+use crate::geometry::{Point2, UnitComplex};
+
+/*
+ *
+ * Implementations for UnitComplex.
+ *
+ */
+impl<N: RealField + simba::scalar::RealField> Identity<Multiplicative> for UnitComplex<N> {
+    #[inline]
+    fn identity() -> Self {
+        Self::identity()
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField> AbstractMagma<Multiplicative> for UnitComplex<N> {
+    #[inline]
+    fn operate(&self, rhs: &Self) -> Self {
+        self * rhs
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField> TwoSidedInverse<Multiplicative> for UnitComplex<N> {
+    #[inline]
+    #[must_use = "Did you mean to use two_sided_inverse_mut()?"]
+    fn two_sided_inverse(&self) -> Self {
+        self.inverse()
+    }
+
+    #[inline]
+    fn two_sided_inverse_mut(&mut self) {
+        self.inverse_mut()
+    }
+}
+
+macro_rules! impl_structures(
+    ($($marker: ident<$operator: ident>),* $(,)*) => {$(
+        impl<N: RealField + simba::scalar::RealField> $marker<$operator> for UnitComplex<N> {
+        }
+    )*}
+);
+
+impl_structures!(
+    AbstractSemigroup<Multiplicative>,
+    AbstractQuasigroup<Multiplicative>,
+    AbstractMonoid<Multiplicative>,
+    AbstractLoop<Multiplicative>,
+    AbstractGroup<Multiplicative>
+);
+
+impl<N: RealField + simba::scalar::RealField> Transformation<Point2<N>> for UnitComplex<N>
+where
+    DefaultAllocator: Allocator<N, U2>,
+{
+    #[inline]
+    fn transform_point(&self, pt: &Point2<N>) -> Point2<N> {
+        self.transform_point(pt)
+    }
+
+    #[inline]
+    fn transform_vector(&self, v: &Vector2<N>) -> Vector2<N> {
+        self.transform_vector(v)
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField> ProjectiveTransformation<Point2<N>> for UnitComplex<N>
+where
+    DefaultAllocator: Allocator<N, U2>,
+{
+    #[inline]
+    fn inverse_transform_point(&self, pt: &Point2<N>) -> Point2<N> {
+        self.inverse_transform_point(pt)
+    }
+
+    #[inline]
+    fn inverse_transform_vector(&self, v: &Vector2<N>) -> Vector2<N> {
+        self.inverse_transform_vector(v)
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField> AffineTransformation<Point2<N>> for UnitComplex<N>
+where
+    DefaultAllocator: Allocator<N, U2>,
+{
+    type Rotation = Self;
+    type NonUniformScaling = Id;
+    type Translation = Id;
+
+    #[inline]
+    fn decompose(&self) -> (Id, Self, Id, Self) {
+        (Id::new(), self.clone(), Id::new(), Self::identity())
+    }
+
+    #[inline]
+    fn append_translation(&self, _: &Self::Translation) -> Self {
+        self.clone()
+    }
+
+    #[inline]
+    fn prepend_translation(&self, _: &Self::Translation) -> Self {
+        self.clone()
+    }
+
+    #[inline]
+    fn append_rotation(&self, r: &Self::Rotation) -> Self {
+        r * self
+    }
+
+    #[inline]
+    fn prepend_rotation(&self, r: &Self::Rotation) -> Self {
+        self * r
+    }
+
+    #[inline]
+    fn append_scaling(&self, _: &Self::NonUniformScaling) -> Self {
+        self.clone()
+    }
+
+    #[inline]
+    fn prepend_scaling(&self, _: &Self::NonUniformScaling) -> Self {
+        self.clone()
+    }
+}
+
+impl<N: RealField + simba::scalar::RealField> Similarity<Point2<N>> for UnitComplex<N>
+where
+    DefaultAllocator: Allocator<N, U2>,
+{
+    type Scaling = Id;
+
+    #[inline]
+    fn translation(&self) -> Id {
+        Id::new()
+    }
+
+    #[inline]
+    fn rotation(&self) -> Self {
+        self.clone()
+    }
+
+    #[inline]
+    fn scaling(&self) -> Id {
+        Id::new()
+    }
+}
+
+macro_rules! marker_impl(
+    ($($Trait: ident),*) => {$(
+        impl<N: RealField + simba::scalar::RealField> $Trait<Point2<N>> for UnitComplex<N>
+        where DefaultAllocator: Allocator<N, U2> { }
+    )*}
+);
+
+marker_impl!(Isometry, DirectIsometry, OrthogonalTransformation);
+
+impl<N: RealField + simba::scalar::RealField> Rotation<Point2<N>> for UnitComplex<N>
+where
+    DefaultAllocator: Allocator<N, U2>,
+{
+    #[inline]
+    fn powf(&self, n: N) -> Option<Self> {
+        Some(self.powf(n))
+    }
+
+    #[inline]
+    fn rotation_between(a: &Vector2<N>, b: &Vector2<N>) -> Option<Self> {
+        Some(Self::rotation_between(a, b))
+    }
+
+    #[inline]
+    fn scaled_rotation_between(a: &Vector2<N>, b: &Vector2<N>, s: N) -> Option<Self> {
+        Some(Self::scaled_rotation_between(a, b, s))
+    }
+}
diff --git a/src/sparse/cs_matrix.rs b/src/sparse/cs_matrix.rs
index ffe87e5f..9ff656d4 100644
--- a/src/sparse/cs_matrix.rs
+++ b/src/sparse/cs_matrix.rs
@@ -55,7 +55,6 @@ pub trait CsStorageIter<'a, N, R, C = U1> {
 
     /// Iterates through all the row indices of the j-th column.
     fn column_row_indices(&'a self, j: usize) -> Self::ColumnRowIndices;
-    #[inline(always)]
     /// Iterates through all the entries of the j-th column.
     fn column_entries(&'a self, j: usize) -> Self::ColumnEntries;
 }
@@ -106,7 +105,8 @@ pub trait CsStorageMut<N, R, C = U1>:
 /// A storage of column-compressed sparse matrix based on a Vec.
 #[derive(Clone, Debug, PartialEq)]
 pub struct CsVecStorage<N: Scalar, R: Dim, C: Dim>
-where DefaultAllocator: Allocator<usize, C>
+where
+    DefaultAllocator: Allocator<usize, C>,
 {
     pub(crate) shape: (R, C),
     pub(crate) p: VectorN<usize, C>,
@@ -115,7 +115,8 @@ where DefaultAllocator: Allocator<usize, C>
 }
 
 impl<N: Scalar, R: Dim, C: Dim> CsVecStorage<N, R, C>
-where DefaultAllocator: Allocator<usize, C>
+where
+    DefaultAllocator: Allocator<usize, C>,
 {
     /// The value buffer of this storage.
     pub fn values(&self) -> &[N] {
@@ -136,7 +137,8 @@ where DefaultAllocator: Allocator<usize, C>
 impl<N: Scalar, R: Dim, C: Dim> CsVecStorage<N, R, C> where DefaultAllocator: Allocator<usize, C> {}
 
 impl<'a, N: Scalar, R: Dim, C: Dim> CsStorageIter<'a, N, R, C> for CsVecStorage<N, R, C>
-where DefaultAllocator: Allocator<usize, C>
+where
+    DefaultAllocator: Allocator<usize, C>,
 {
     type ColumnEntries = ColumnEntries<'a, N>;
     type ColumnRowIndices = iter::Cloned<slice::Iter<'a, usize>>;
@@ -155,7 +157,8 @@ where DefaultAllocator: Allocator<usize, C>
 }
 
 impl<N: Scalar, R: Dim, C: Dim> CsStorage<N, R, C> for CsVecStorage<N, R, C>
-where DefaultAllocator: Allocator<usize, C>
+where
+    DefaultAllocator: Allocator<usize, C>,
 {
     #[inline]
     fn shape(&self) -> (R, C) {
@@ -200,7 +203,8 @@ where DefaultAllocator: Allocator<usize, C>
 }
 
 impl<'a, N: Scalar, R: Dim, C: Dim> CsStorageIterMut<'a, N, R, C> for CsVecStorage<N, R, C>
-where DefaultAllocator: Allocator<usize, C>
+where
+    DefaultAllocator: Allocator<usize, C>,
 {
     type ValuesMut = slice::IterMut<'a, N>;
     type ColumnEntriesMut = iter::Zip<iter::Cloned<slice::Iter<'a, usize>>, slice::IterMut<'a, N>>;
@@ -220,8 +224,10 @@ where DefaultAllocator: Allocator<usize, C>
     }
 }
 
-impl<N: Scalar, R: Dim, C: Dim> CsStorageMut<N, R, C> for CsVecStorage<N, R, C> where DefaultAllocator: Allocator<usize, C>
-{}
+impl<N: Scalar, R: Dim, C: Dim> CsStorageMut<N, R, C> for CsVecStorage<N, R, C> where
+    DefaultAllocator: Allocator<usize, C>
+{
+}
 
 /*
 pub struct CsSliceStorage<'a, N: Scalar, R: Dim, C: DimAdd<U1>> {
@@ -247,7 +253,8 @@ pub struct CsMatrix<
 pub type CsVector<N, R = Dynamic, S = CsVecStorage<N, R, U1>> = CsMatrix<N, R, U1, S>;
 
 impl<N: Scalar, R: Dim, C: Dim> CsMatrix<N, R, C>
-where DefaultAllocator: Allocator<usize, C>
+where
+    DefaultAllocator: Allocator<usize, C>,
 {
     /// Creates a new compressed sparse column matrix with the specified dimension and
     /// `nvals` possible non-zero values.
@@ -403,7 +410,9 @@ impl<N: Scalar, R: Dim, C: Dim, S: CsStorage<N, R, C>> CsMatrix<N, R, C, S> {
 
     /// Computes the transpose of this sparse matrix.
     pub fn transpose(&self) -> CsMatrix<N, C, R>
-    where DefaultAllocator: Allocator<usize, R> {
+    where
+        DefaultAllocator: Allocator<usize, R>,
+    {
         let (nrows, ncols) = self.data.shape();
 
         let nvals = self.len();
@@ -442,10 +451,13 @@ impl<N: Scalar, R: Dim, C: Dim, S: CsStorageMut<N, R, C>> CsMatrix<N, R, C, S> {
 }
 
 impl<N: Scalar, R: Dim, C: Dim> CsMatrix<N, R, C>
-where DefaultAllocator: Allocator<usize, C>
+where
+    DefaultAllocator: Allocator<usize, C>,
 {
     pub(crate) fn sort(&mut self)
-    where DefaultAllocator: Allocator<N, R> {
+    where
+        DefaultAllocator: Allocator<N, R>,
+    {
         // Size = R
         let nrows = self.data.shape().0;
         let mut workspace = unsafe { VectorN::new_uninitialized_generic(nrows, U1) };
@@ -477,7 +489,9 @@ where DefaultAllocator: Allocator<usize, C>
 
     // Remove dupliate entries on a sorted CsMatrix.
     pub(crate) fn dedup(&mut self)
-    where N: Zero + ClosedAdd {
+    where
+        N: Zero + ClosedAdd,
+    {
         let mut curr_i = 0;
 
         for j in 0..self.ncols() {