diff --git a/src/base/cg.rs b/src/base/cg.rs
index 8ffec5cf..2464bce1 100644
--- a/src/base/cg.rs
+++ b/src/base/cg.rs
@@ -11,8 +11,8 @@ use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, DimNameDiff, DimNameSub, U1};
 use crate::base::storage::{Storage, StorageMut};
 use crate::base::{
-    DefaultAllocator, Matrix3, Matrix4, MatrixN, Scalar, SquareMatrix, Unit, Vector, Vector2,
-    Vector3, VectorN,
+    Const, DefaultAllocator, Matrix3, Matrix4, MatrixN, Scalar, SquareMatrix, Unit, Vector,
+    Vector2, Vector3, VectorN,
 };
 use crate::geometry::{
     Isometry, IsometryMatrix3, Orthographic3, Perspective3, Point, Point2, Point3, Rotation2,
@@ -411,18 +411,33 @@ where
 
         transform * v
     }
+}
 
+impl<N: RealField, S: Storage<N, Const<3>, Const<3>>> SquareMatrix<N, Const<3>, S> {
     /// Transforms the given point, assuming the matrix `self` uses homogeneous coordinates.
     #[inline]
-    pub fn transform_point(
-        &self,
-        pt: &Point<N, { DimNameDiff::<D, U1>::USIZE }>,
-    ) -> Point<N, { DimNameDiff::<D, U1>::USIZE }> {
-        let transform = self.fixed_slice::<DimNameDiff<D, U1>, DimNameDiff<D, U1>>(0, 0);
-        let translation = self.fixed_slice::<DimNameDiff<D, U1>, U1>(0, D::dim() - 1);
-        let normalizer = self.fixed_slice::<U1, DimNameDiff<D, U1>>(D::dim() - 1, 0);
-        let n = normalizer.tr_dot(&pt.coords)
-            + unsafe { *self.get_unchecked((D::dim() - 1, D::dim() - 1)) };
+    pub fn transform_point(&self, pt: &Point<N, 2>) -> Point<N, 2> {
+        let transform = self.fixed_slice::<Const<2>, Const<2>>(0, 0);
+        let translation = self.fixed_slice::<Const<2>, U1>(0, 2);
+        let normalizer = self.fixed_slice::<U1, Const<2>>(2, 0);
+        let n = normalizer.tr_dot(&pt.coords) + unsafe { *self.get_unchecked((2, 2)) };
+
+        if !n.is_zero() {
+            (transform * pt + translation) / n
+        } else {
+            transform * pt + translation
+        }
+    }
+}
+
+impl<N: RealField, S: Storage<N, Const<4>, Const<4>>> SquareMatrix<N, Const<4>, S> {
+    /// Transforms the given point, assuming the matrix `self` uses homogeneous coordinates.
+    #[inline]
+    pub fn transform_point(&self, pt: &Point<N, 3>) -> Point<N, 3> {
+        let transform = self.fixed_slice::<Const<3>, Const<3>>(0, 0);
+        let translation = self.fixed_slice::<Const<3>, U1>(0, 3);
+        let normalizer = self.fixed_slice::<U1, Const<3>>(3, 0);
+        let n = normalizer.tr_dot(&pt.coords) + unsafe { *self.get_unchecked((3, 3)) };
 
         if !n.is_zero() {
             (transform * pt + translation) / n
diff --git a/src/geometry/abstract_rotation.rs b/src/geometry/abstract_rotation.rs
index 2c44e46d..749d7473 100644
--- a/src/geometry/abstract_rotation.rs
+++ b/src/geometry/abstract_rotation.rs
@@ -39,7 +39,6 @@ pub trait AbstractRotation<N: Scalar, const D: usize>: PartialEq + ClosedMul + C
 impl<N: SimdRealField, const D: usize> AbstractRotation<N, D> for Rotation<N, D>
 where
     N::Element: SimdRealField,
-    // DefaultAllocator: Allocator<N, D, D>,
 {
     #[inline]
     fn identity() -> Self {
diff --git a/src/geometry/isometry.rs b/src/geometry/isometry.rs
index 144f86b9..065800d4 100755
--- a/src/geometry/isometry.rs
+++ b/src/geometry/isometry.rs
@@ -59,14 +59,14 @@ use crate::geometry::{AbstractRotation, Point, Translation};
 #[cfg_attr(
     feature = "serde-serialize",
     serde(bound(serialize = "R: Serialize,
-                     DefaultAllocator: Allocator<N, D>,
-                     Owned<N, D>: Serialize"))
+                     DefaultAllocator: Allocator<N, Const<D>>,
+                     Owned<N, Const<D>>: Serialize"))
 )]
 #[cfg_attr(
     feature = "serde-serialize",
     serde(bound(deserialize = "R: Deserialize<'de>,
-                       DefaultAllocator: Allocator<N, D>,
-                       Owned<N, D>: Deserialize<'de>"))
+                       DefaultAllocator: Allocator<N, Const<D>>,
+                       Owned<N, Const<D>>: Deserialize<'de>"))
 )]
 pub struct Isometry<N: Scalar, R, const D: usize>
 // where
@@ -84,7 +84,6 @@ where
     N: SimdRealField,
     R: Abomonation,
     Translation<N, D>: Abomonation,
-    // DefaultAllocator: Allocator<N, D>,
 {
     unsafe fn entomb<W: Write>(&self, writer: &mut W) -> IOResult<()> {
         self.rotation.entomb(writer)?;
@@ -104,7 +103,6 @@ where
 
 impl<N: Scalar + hash::Hash, R: hash::Hash, const D: usize> hash::Hash for Isometry<N, R, D>
 where
-    // DefaultAllocator: Allocator<N, D>,
     Owned<N, Const<D>>: hash::Hash,
 {
     fn hash<H: hash::Hasher>(&self, state: &mut H) {
@@ -114,7 +112,6 @@ where
 }
 
 impl<N: Scalar + Copy, R: Copy, const D: usize> Copy for Isometry<N, R, D> where
-    // DefaultAllocator: Allocator<N, D>,
     Owned<N, Const<D>>: Copy
 {
 }
@@ -163,7 +160,6 @@ impl<N: Scalar, R: AbstractRotation<N, D>, const D: usize> Isometry<N, R, D>
 impl<N: SimdRealField, R: AbstractRotation<N, D>, const D: usize> Isometry<N, R, D>
 where
     N::Element: SimdRealField,
-    // DefaultAllocator: Allocator<N, D>,
 {
     /// Inverts `self`.
     ///
@@ -318,7 +314,6 @@ where
 impl<N: SimdRealField, R: AbstractRotation<N, D>, const D: usize> Isometry<N, R, D>
 where
     N::Element: SimdRealField,
-    // DefaultAllocator: Allocator<N, D>,
 {
     /// Transform the given point by this isometry.
     ///
@@ -504,14 +499,13 @@ impl<N: SimdRealField, R, const D: usize> Isometry<N, R, D>
 }
 
 impl<N: SimdRealField, R, const D: usize> Eq for Isometry<N, R, D> where
-    R: AbstractRotation<N, D> + Eq // DefaultAllocator: Allocator<N, D>,
+    R: AbstractRotation<N, D> + Eq
 {
 }
 
 impl<N: SimdRealField, R, const D: usize> PartialEq for Isometry<N, R, D>
 where
     R: AbstractRotation<N, D> + PartialEq,
-    // DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     fn eq(&self, right: &Self) -> bool {
@@ -522,7 +516,6 @@ where
 impl<N: RealField, R, const D: usize> AbsDiffEq for Isometry<N, R, D>
 where
     R: AbstractRotation<N, D> + AbsDiffEq<Epsilon = N::Epsilon>,
-    // DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {
     type Epsilon = N::Epsilon;
@@ -542,7 +535,6 @@ where
 impl<N: RealField, R, const D: usize> RelativeEq for Isometry<N, R, D>
 where
     R: AbstractRotation<N, D> + RelativeEq<Epsilon = N::Epsilon>,
-    // DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {
     #[inline]
@@ -568,7 +560,6 @@ where
 impl<N: RealField, R, const D: usize> UlpsEq for Isometry<N, R, D>
 where
     R: AbstractRotation<N, D> + UlpsEq<Epsilon = N::Epsilon>,
-    // DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {
     #[inline]
@@ -592,7 +583,6 @@ where
 impl<N: RealField + fmt::Display, R, const D: usize> fmt::Display for Isometry<N, R, D>
 where
     R: fmt::Display,
-    // DefaultAllocator: Allocator<N, D> + Allocator<usize, D>,
 {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         let precision = f.precision().unwrap_or(3);
diff --git a/src/geometry/isometry_construction.rs b/src/geometry/isometry_construction.rs
index 7a6b870f..60b5f6e2 100644
--- a/src/geometry/isometry_construction.rs
+++ b/src/geometry/isometry_construction.rs
@@ -13,19 +13,17 @@ use rand::{
 use simba::scalar::SupersetOf;
 use simba::simd::SimdRealField;
 
-use crate::base::dimension::U2;
 use crate::base::{Vector2, Vector3};
 
 use crate::{
-    AbstractRotation, Isometry, Isometry2, Isometry3, IsometryMatrix2, IsometryMatrix3, Point,
-    Point3, Rotation, Rotation3, Scalar, Translation, Translation2, Translation3, UnitComplex,
-    UnitQuaternion,
+    AbstractRotation, Const, Isometry, Isometry2, Isometry3, IsometryMatrix2, IsometryMatrix3,
+    Point, Point3, Rotation, Rotation3, Scalar, Translation, Translation2, Translation3,
+    UnitComplex, UnitQuaternion,
 };
 
 impl<N: SimdRealField, R: AbstractRotation<N, D>, const D: usize> Isometry<N, R, D>
 where
     N::Element: SimdRealField,
-    // DefaultAllocator: Allocator<N, D>,
 {
     /// Creates a new identity isometry.
     ///
@@ -73,7 +71,6 @@ where
 impl<N: SimdRealField, R: AbstractRotation<N, D>, const D: usize> One for Isometry<N, R, D>
 where
     N::Element: SimdRealField,
-    // DefaultAllocator: Allocator<N, D>,
 {
     /// Creates a new identity isometry.
     #[inline]
@@ -87,7 +84,6 @@ impl<N: crate::RealField, R, const D: usize> Distribution<Isometry<N, R, D>> for
 where
     R: AbstractRotation<N, D>,
     Standard: Distribution<N> + Distribution<R>,
-    // DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     fn sample<'a, G: Rng + ?Sized>(&self, rng: &'a mut G) -> Isometry<N, R, D> {
@@ -101,8 +97,7 @@ where
     N: SimdRealField + Arbitrary + Send,
     N::Element: SimdRealField,
     R: AbstractRotation<N, D> + Arbitrary + Send,
-    Owned<N, D>: Send,
-    // DefaultAllocator: Allocator<N, D>,
+    Owned<N, Const<D>>: Send,
 {
     #[inline]
     fn arbitrary(rng: &mut Gen) -> Self {
@@ -136,10 +131,7 @@ where
     /// ```
     #[inline]
     pub fn new(translation: Vector2<N>, angle: N) -> Self {
-        Self::from_parts(
-            Translation::from(translation),
-            Rotation::<N, U2>::new(angle),
-        )
+        Self::from_parts(Translation::from(translation), Rotation::<N, 2>::new(angle))
     }
 
     /// Creates a new isometry from the given translation coordinates.
diff --git a/src/geometry/isometry_conversion.rs b/src/geometry/isometry_conversion.rs
index e75570c2..235b120e 100644
--- a/src/geometry/isometry_conversion.rs
+++ b/src/geometry/isometry_conversion.rs
@@ -27,7 +27,6 @@ where
     N2: RealField + SupersetOf<N1>,
     R1: AbstractRotation<N1, D> + SubsetOf<R2>,
     R2: AbstractRotation<N2, D>,
-    // DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
 {
     #[inline]
     fn to_superset(&self) -> Isometry<N2, R2, D> {
@@ -63,7 +62,7 @@ where
     #[inline]
     fn is_in_subset(dq: &UnitDualQuaternion<N2>) -> bool {
         crate::is_convertible::<_, UnitQuaternion<N1>>(&dq.rotation())
-            && crate::is_convertible::<_, Translation<N1, _>>(&dq.translation())
+            && crate::is_convertible::<_, Translation<N1, 3>>(&dq.translation())
     }
 
     #[inline]
@@ -79,7 +78,6 @@ where
     N2: RealField + SupersetOf<N1>,
     R1: AbstractRotation<N1, D> + SubsetOf<R2>,
     R2: AbstractRotation<N2, D>,
-    // DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
 {
     #[inline]
     fn to_superset(&self) -> Similarity<N2, R2, D> {
@@ -154,8 +152,8 @@ where
 
     #[inline]
     fn is_in_subset(m: &MatrixN<N2, DimNameSum<Const<D>, U1>>) -> bool {
-        let rot = m.fixed_slice::<D, D>(0, 0);
-        let bottom = m.fixed_slice::<U1, D>(D, 0);
+        let rot = m.fixed_slice::<Const<D>, Const<D>>(0, 0);
+        let bottom = m.fixed_slice::<U1, Const<D>>(D, 0);
 
         // Scalar types agree.
         m.iter().all(|e| SupersetOf::<N1>::is_in_subset(e)) &&
@@ -167,7 +165,7 @@ where
 
     #[inline]
     fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<Const<D>, U1>>) -> Self {
-        let t = m.fixed_slice::<D, U1>(0, D).into_owned();
+        let t = m.fixed_slice::<Const<D>, U1>(0, D).into_owned();
         let t = Translation {
             vector: crate::convert_unchecked(t),
         };
@@ -208,7 +206,6 @@ where
     R::Element: AbstractRotation<N::Element, D>,
     N::Element: Scalar + Copy,
     R::Element: Scalar + Copy,
-    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     #[inline]
     fn from(arr: [Isometry<N::Element, R::Element, D>; 2]) -> Self {
@@ -227,7 +224,6 @@ where
     R::Element: AbstractRotation<N::Element, D>,
     N::Element: Scalar + Copy,
     R::Element: Scalar + Copy,
-    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     #[inline]
     fn from(arr: [Isometry<N::Element, R::Element, D>; 4]) -> Self {
@@ -256,7 +252,6 @@ where
     R::Element: AbstractRotation<N::Element, D>,
     N::Element: Scalar + Copy,
     R::Element: Scalar + Copy,
-    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     #[inline]
     fn from(arr: [Isometry<N::Element, R::Element, D>; 8]) -> Self {
@@ -293,7 +288,6 @@ where
     R::Element: AbstractRotation<N::Element, D>,
     N::Element: Scalar + Copy,
     R::Element: Scalar + Copy,
-    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     #[inline]
     fn from(arr: [Isometry<N::Element, R::Element, D>; 16]) -> Self {
diff --git a/src/geometry/isometry_ops.rs b/src/geometry/isometry_ops.rs
index ecca9bb2..f6fff378 100644
--- a/src/geometry/isometry_ops.rs
+++ b/src/geometry/isometry_ops.rs
@@ -5,8 +5,8 @@ use simba::scalar::{ClosedAdd, ClosedMul};
 use simba::simd::SimdRealField;
 
 use crate::base::allocator::Allocator;
-use crate::base::dimension::{DimName, U1, U2, U3, U4};
-use crate::base::{DefaultAllocator, Unit, VectorN};
+use crate::base::dimension::{U1, U2, U3};
+use crate::base::{CVectorN, Const, DefaultAllocator, Unit};
 use crate::Scalar;
 
 use crate::geometry::{
@@ -68,10 +68,9 @@ macro_rules! isometry_binop_impl(
     ($Op: ident, $op: ident;
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Output: ty;
      $action: expr; $($lives: tt),*) => {
-        impl<$($lives ,)* N: SimdRealField, D: DimName, R> $Op<$Rhs> for $Lhs
+        impl<$($lives ,)* N: SimdRealField, R, const D: usize> $Op<$Rhs> for $Lhs
             where N::Element: SimdRealField,
-                  R: AbstractRotation<N, D>,
-                  DefaultAllocator: Allocator<N, D> {
+                  R: AbstractRotation<N, D>, {
             type Output = $Output;
 
             #[inline]
@@ -116,20 +115,18 @@ macro_rules! isometry_binop_assign_impl_all(
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty;
      [val] => $action_val: expr;
      [ref] => $action_ref: expr;) => {
-        impl<N: SimdRealField, D: DimName, R> $OpAssign<$Rhs> for $Lhs
+        impl<N: SimdRealField, R, const D: usize> $OpAssign<$Rhs> for $Lhs
             where N::Element: SimdRealField,
-                  R: AbstractRotation<N, D>,
-                  DefaultAllocator: Allocator<N, D> {
+                  R: AbstractRotation<N, D> {
             #[inline]
             fn $op_assign(&mut $lhs, $rhs: $Rhs) {
                 $action_val
             }
         }
 
-        impl<'b, N: SimdRealField, D: DimName, R> $OpAssign<&'b $Rhs> for $Lhs
+        impl<'b, N: SimdRealField, R, const D: usize> $OpAssign<&'b $Rhs> for $Lhs
             where N::Element: SimdRealField,
-                  R: AbstractRotation<N, D>,
-                  DefaultAllocator: Allocator<N, D> {
+                  R: AbstractRotation<N, D> {
             #[inline]
             fn $op_assign(&mut $lhs, $rhs: &'b $Rhs) {
                 $action_ref
@@ -142,7 +139,7 @@ macro_rules! isometry_binop_assign_impl_all(
 // Isometry ÷ Isometry
 isometry_binop_impl_all!(
     Mul, mul;
-    self: Isometry<N, D, R>, rhs: Isometry<N, D, R>, Output = Isometry<N, D, R>;
+    self: Isometry<N, R, D>, rhs: Isometry<N, R, D>, Output = Isometry<N, R, D>;
     [val val] => &self * &rhs;
     [ref val] => self * &rhs;
     [val ref] => &self * rhs;
@@ -157,7 +154,7 @@ isometry_binop_impl_all!(
 
 isometry_binop_impl_all!(
     Div, div;
-    self: Isometry<N, D, R>, rhs: Isometry<N, D, R>, Output = Isometry<N, D, R>;
+    self: Isometry<N, R, D>, rhs: Isometry<N, R, D>, Output = Isometry<N, R, D>;
     [val val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
     [ref val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
     [val ref] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
@@ -167,7 +164,7 @@ isometry_binop_impl_all!(
 // Isometry ×= Translation
 isometry_binop_assign_impl_all!(
     MulAssign, mul_assign;
-    self: Isometry<N, D, R>, rhs: Translation<N, D>;
+    self: Isometry<N, R, D>, rhs: Translation<N, D>;
     [val] => *self *= &rhs;
     [ref] => #[allow(clippy::suspicious_op_assign_impl)] {
         let shift = self.rotation.transform_vector(&rhs.vector);
@@ -179,7 +176,7 @@ isometry_binop_assign_impl_all!(
 // Isometry ÷= Isometry
 isometry_binop_assign_impl_all!(
     MulAssign, mul_assign;
-    self: Isometry<N, D, R>, rhs: Isometry<N, D, R>;
+    self: Isometry<N, R, D>, rhs: Isometry<N, R, D>;
     [val] => *self *= &rhs;
     [ref] => {
         let shift = self.rotation.transform_vector(&rhs.translation.vector);
@@ -190,7 +187,7 @@ isometry_binop_assign_impl_all!(
 
 isometry_binop_assign_impl_all!(
     DivAssign, div_assign;
-    self: Isometry<N, D, R>, rhs: Isometry<N, D, R>;
+    self: Isometry<N, R, D>, rhs: Isometry<N, R, D>;
     [val] => *self /= &rhs;
     [ref] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
 );
@@ -199,16 +196,18 @@ isometry_binop_assign_impl_all!(
 // Isometry ÷= R
 md_assign_impl_all!(
     MulAssign, mul_assign where N: SimdRealField for N::Element: SimdRealField;
-    (D, U1), (D, D) for D: DimName;
-    self: Isometry<N, D, Rotation<N, D>>, rhs: Rotation<N, D>;
+    (Const<D>, U1), (Const<D>, Const<D>)
+    const D; for; where;
+    self: Isometry<N, Rotation<N, D>, D>, rhs: Rotation<N, D>;
     [val] => self.rotation *= rhs;
     [ref] => self.rotation *= rhs.clone();
 );
 
 md_assign_impl_all!(
     DivAssign, div_assign where N: SimdRealField for N::Element: SimdRealField;
-    (D, U1), (D, D) for D: DimName;
-    self: Isometry<N, D, Rotation<N, D>>, rhs: Rotation<N, D>;
+    (Const<D>, U1), (Const<D>, Const<D>)
+    const D; for; where;
+    self: Isometry<N, Rotation<N, D>, D>, rhs: Rotation<N, D>;
     // TODO: don't invert explicitly?
     [val] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
     [ref] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
@@ -216,16 +215,18 @@ md_assign_impl_all!(
 
 md_assign_impl_all!(
     MulAssign, mul_assign where N: SimdRealField for N::Element: SimdRealField;
-    (U3, U3), (U3, U3) for;
-    self: Isometry<N, U3, UnitQuaternion<N>>, rhs: UnitQuaternion<N>;
+    (U3, U3), (U3, U3)
+    const; for; where;
+    self: Isometry<N, UnitQuaternion<N>, 3>, rhs: UnitQuaternion<N>;
     [val] => self.rotation *= rhs;
     [ref] => self.rotation *= *rhs;
 );
 
 md_assign_impl_all!(
     DivAssign, div_assign where N: SimdRealField for N::Element: SimdRealField;
-    (U3, U3), (U3, U3) for;
-    self: Isometry<N, U3, UnitQuaternion<N>>, rhs: UnitQuaternion<N>;
+    (U3, U3), (U3, U3)
+    const; for; where;
+    self: Isometry<N, UnitQuaternion<N>, 3>, rhs: UnitQuaternion<N>;
     // TODO: don't invert explicitly?
     [val] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
     [ref] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
@@ -233,16 +234,18 @@ md_assign_impl_all!(
 
 md_assign_impl_all!(
     MulAssign, mul_assign where N: SimdRealField for N::Element: SimdRealField;
-    (U2, U2), (U2, U2) for;
-    self: Isometry<N, U2, UnitComplex<N>>, rhs: UnitComplex<N>;
+    (U2, U2), (U2, U2)
+    const; for; where;
+    self: Isometry<N, UnitComplex<N>, 2>, rhs: UnitComplex<N>;
     [val] => self.rotation *= rhs;
     [ref] => self.rotation *= *rhs;
 );
 
 md_assign_impl_all!(
     DivAssign, div_assign where N: SimdRealField for N::Element: SimdRealField;
-    (U2, U2), (U2, U2) for;
-    self: Isometry<N, U2, UnitComplex<N>>, rhs: UnitComplex<N>;
+    (U2, U2), (U2, U2)
+    const; for; where;
+    self: Isometry<N, UnitComplex<N>, 2>, rhs: UnitComplex<N>;
     // TODO: don't invert explicitly?
     [val] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
     [ref] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
@@ -251,7 +254,7 @@ md_assign_impl_all!(
 // Isometry × Point
 isometry_binop_impl_all!(
     Mul, mul;
-    self: Isometry<N, D, R>, right: Point<N, D>, Output = Point<N, D>;
+    self: Isometry<N, R, D>, right: Point<N, D>, Output = Point<N, D>;
     [val val] => self.translation  * self.rotation.transform_point(&right);
     [ref val] => &self.translation * self.rotation.transform_point(&right);
     [val ref] => self.translation  * self.rotation.transform_point(right);
@@ -263,7 +266,7 @@ isometry_binop_impl_all!(
     Mul, mul;
     // TODO: because of `transform_vector`, we cant use a generic storage type for the rhs vector,
     // i.e., right: Vector<N, D, S> where S: Storage<N, D>.
-    self: Isometry<N, D, R>, right: VectorN<N, D>, Output = VectorN<N, D>;
+    self: Isometry<N, R, D>, right: CVectorN<N, D>, Output = CVectorN<N, D>;
     [val val] => self.rotation.transform_vector(&right);
     [ref val] => self.rotation.transform_vector(&right);
     [val ref] => self.rotation.transform_vector(right);
@@ -275,7 +278,7 @@ isometry_binop_impl_all!(
     Mul, mul;
     // TODO: because of `transform_vector`, we cant use a generic storage type for the rhs vector,
     // i.e., right: Vector<N, D, S> where S: Storage<N, D>.
-    self: Isometry<N, D, R>, right: Unit<VectorN<N, D>>, Output = Unit<VectorN<N, D>>;
+    self: Isometry<N, R, D>, right: Unit<CVectorN<N, D>>, Output = Unit<CVectorN<N, D>>;
     [val val] => Unit::new_unchecked(self.rotation.transform_vector(right.as_ref()));
     [ref val] => Unit::new_unchecked(self.rotation.transform_vector(right.as_ref()));
     [val ref] => Unit::new_unchecked(self.rotation.transform_vector(right.as_ref()));
@@ -285,7 +288,7 @@ isometry_binop_impl_all!(
 // Isometry × Translation
 isometry_binop_impl_all!(
     Mul, mul;
-    self: Isometry<N, D, R>, right: Translation<N, D>, Output = Isometry<N, D, R>;
+    self: Isometry<N, R, D>, right: Translation<N, D>, Output = Isometry<N, R, D>;
     [val val] => &self * &right;
     [ref val] => self * &right;
     [val ref] => &self * right;
@@ -299,7 +302,7 @@ isometry_binop_impl_all!(
 // Translation × Isometry
 isometry_binop_impl_all!(
     Mul, mul;
-    self: Translation<N, D>, right: Isometry<N, D, R>, Output = Isometry<N, D, R>;
+    self: Translation<N, D>, right: Isometry<N, R, D>, Output = Isometry<N, R, D>;
     [val val] => Isometry::from_parts(self * right.translation, right.rotation);
     [ref val] => Isometry::from_parts(self * &right.translation, right.rotation);
     [val ref] => Isometry::from_parts(self * &right.translation, right.rotation.clone());
@@ -308,13 +311,11 @@ isometry_binop_impl_all!(
 
 macro_rules! isometry_from_composition_impl(
     ($Op: ident, $op: ident;
-     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) $(for $Dims: ident: $DimsBound: ident),*;
+     $($Dims: ident),*;
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Output: ty;
      $action: expr; $($lives: tt),*) => {
-        impl<$($lives ,)* N: SimdRealField $(, $Dims: $DimsBound)*> $Op<$Rhs> for $Lhs
-            where N::Element: SimdRealField,
-                  DefaultAllocator: Allocator<N, $R1, $C1> +
-                                    Allocator<N, $R2, $C2> {
+        impl<$($lives ,)* N: SimdRealField $(, const $Dims: usize)*> $Op<$Rhs> for $Lhs
+            where N::Element: SimdRealField {
             type Output = $Output;
 
             #[inline]
@@ -327,7 +328,7 @@ macro_rules! isometry_from_composition_impl(
 
 macro_rules! isometry_from_composition_impl_all(
     ($Op: ident, $op: ident;
-     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) $(for $Dims: ident: $DimsBound: ident),*;
+     $($Dims: ident),*;
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Output: ty;
      [val val] => $action_val_val: expr;
      [ref val] => $action_ref_val: expr;
@@ -336,25 +337,25 @@ macro_rules! isometry_from_composition_impl_all(
 
         isometry_from_composition_impl!(
             $Op, $op;
-            ($R1, $C1),($R2, $C2) $(for $Dims: $DimsBound),*;
+            $($Dims),*;
             $lhs: $Lhs, $rhs: $Rhs, Output = $Output;
             $action_val_val; );
 
         isometry_from_composition_impl!(
             $Op, $op;
-            ($R1, $C1),($R2, $C2) $(for $Dims: $DimsBound),*;
+            $($Dims),*;
             $lhs: &'a $Lhs, $rhs: $Rhs, Output = $Output;
             $action_ref_val; 'a);
 
         isometry_from_composition_impl!(
             $Op, $op;
-            ($R1, $C1),($R2, $C2) $(for $Dims: $DimsBound),*;
+            $($Dims),*;
             $lhs: $Lhs, $rhs: &'b $Rhs, Output = $Output;
             $action_val_ref; 'b);
 
         isometry_from_composition_impl!(
             $Op, $op;
-            ($R1, $C1),($R2, $C2) $(for $Dims: $DimsBound),*;
+            $($Dims),*;
             $lhs: &'a $Lhs, $rhs: &'b $Rhs, Output = $Output;
             $action_ref_ref; 'a, 'b);
     }
@@ -363,8 +364,8 @@ macro_rules! isometry_from_composition_impl_all(
 // Rotation × Translation
 isometry_from_composition_impl_all!(
     Mul, mul;
-    (D, D), (D, U1) for D: DimName;
-    self: Rotation<N, D>, right: Translation<N, D>, Output = Isometry<N, D, Rotation<N, D>>;
+    D;
+    self: Rotation<N, D>, right: Translation<N, D>, Output = Isometry<N, Rotation<N, D>, D>;
     [val val] => Isometry::from_parts(Translation::from(&self * right.vector),  self);
     [ref val] => Isometry::from_parts(Translation::from(self * right.vector),   self.clone());
     [val ref] => Isometry::from_parts(Translation::from(&self * &right.vector), self);
@@ -374,9 +375,9 @@ isometry_from_composition_impl_all!(
 // UnitQuaternion × Translation
 isometry_from_composition_impl_all!(
     Mul, mul;
-    (U4, U1), (U3, U1);
-    self: UnitQuaternion<N>, right: Translation<N, U3>,
-    Output = Isometry<N, U3, UnitQuaternion<N>>;
+    ;
+    self: UnitQuaternion<N>, right: Translation<N, 3>,
+    Output = Isometry<N, UnitQuaternion<N>, 3>;
     [val val] => Isometry::from_parts(Translation::from(&self *  right.vector), self);
     [ref val] => Isometry::from_parts(Translation::from( self *  right.vector), *self);
     [val ref] => Isometry::from_parts(Translation::from(&self * &right.vector), self);
@@ -386,9 +387,9 @@ isometry_from_composition_impl_all!(
 // Isometry × Rotation
 isometry_from_composition_impl_all!(
     Mul, mul;
-    (D, D), (D, U1) for D: DimName;
-    self: Isometry<N, D, Rotation<N, D>>, rhs: Rotation<N, D>,
-    Output = Isometry<N, D, Rotation<N, D>>;
+    D;
+    self: Isometry<N, Rotation<N, D>, D>, rhs: Rotation<N, D>,
+    Output = Isometry<N, Rotation<N, D>, D>;
     [val val] => Isometry::from_parts(self.translation, self.rotation * rhs);
     [ref val] => Isometry::from_parts(self.translation.clone(), self.rotation.clone() * rhs); // TODO: do not clone.
     [val ref] => Isometry::from_parts(self.translation, self.rotation * rhs.clone());
@@ -398,9 +399,9 @@ isometry_from_composition_impl_all!(
 // Rotation × Isometry
 isometry_from_composition_impl_all!(
     Mul, mul;
-    (D, D), (D, U1) for D: DimName;
-    self: Rotation<N, D>, right: Isometry<N, D, Rotation<N, D>>,
-    Output = Isometry<N, D, Rotation<N, D>>;
+    D;
+    self: Rotation<N, D>, right: Isometry<N, Rotation<N, D>, D>,
+    Output = Isometry<N, Rotation<N, D>, D>;
     [val val] => &self * &right;
     [ref val] =>  self * &right;
     [val ref] => &self * right;
@@ -413,9 +414,9 @@ isometry_from_composition_impl_all!(
 // Isometry ÷ Rotation
 isometry_from_composition_impl_all!(
     Div, div;
-    (D, D), (D, U1) for D: DimName;
-    self: Isometry<N, D, Rotation<N, D>>, rhs: Rotation<N, D>,
-    Output = Isometry<N, D, Rotation<N, D>>;
+    D;
+    self: Isometry<N, Rotation<N, D>, D>, rhs: Rotation<N, D>,
+    Output = Isometry<N, Rotation<N, D>, D>;
     [val val] => Isometry::from_parts(self.translation, self.rotation / rhs);
     [ref val] => Isometry::from_parts(self.translation.clone(), self.rotation.clone() / rhs); // TODO: do not clone.
     [val ref] => Isometry::from_parts(self.translation, self.rotation / rhs.clone());
@@ -425,9 +426,9 @@ isometry_from_composition_impl_all!(
 // Rotation ÷ Isometry
 isometry_from_composition_impl_all!(
     Div, div;
-    (D, D), (D, U1) for D: DimName;
-    self: Rotation<N, D>, right: Isometry<N, D, Rotation<N, D>>,
-    Output = Isometry<N, D, Rotation<N, D>>;
+    D;
+    self: Rotation<N, D>, right: Isometry<N, Rotation<N, D>, D>,
+    Output = Isometry<N, Rotation<N, D>, D>;
     // TODO: don't call inverse explicitly?
     [val val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * right.inverse() };
     [ref val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * right.inverse() };
@@ -438,9 +439,9 @@ isometry_from_composition_impl_all!(
 // Isometry × UnitQuaternion
 isometry_from_composition_impl_all!(
     Mul, mul;
-    (U4, U1), (U3, U1);
-    self: Isometry<N, U3, UnitQuaternion<N>>, rhs: UnitQuaternion<N>,
-    Output = Isometry<N, U3, UnitQuaternion<N>>;
+    ;
+    self: Isometry<N, UnitQuaternion<N>, 3>, rhs: UnitQuaternion<N>,
+    Output = Isometry<N, UnitQuaternion<N>, 3>;
     [val val] => Isometry::from_parts(self.translation, self.rotation * rhs);
     [ref val] => Isometry::from_parts(self.translation.clone(), self.rotation * rhs); // TODO: do not clone.
     [val ref] => Isometry::from_parts(self.translation, self.rotation * *rhs);
@@ -450,9 +451,9 @@ isometry_from_composition_impl_all!(
 // UnitQuaternion × Isometry
 isometry_from_composition_impl_all!(
     Mul, mul;
-    (U4, U1), (U3, U1);
-    self: UnitQuaternion<N>, right: Isometry<N, U3, UnitQuaternion<N>>,
-    Output = Isometry<N, U3, UnitQuaternion<N>>;
+    ;
+    self: UnitQuaternion<N>, right: Isometry<N, UnitQuaternion<N>, 3>,
+    Output = Isometry<N, UnitQuaternion<N>, 3>;
     [val val] => &self * &right;
     [ref val] =>  self * &right;
     [val ref] => &self * right;
@@ -465,9 +466,9 @@ isometry_from_composition_impl_all!(
 // Isometry ÷ UnitQuaternion
 isometry_from_composition_impl_all!(
     Div, div;
-    (U4, U1), (U3, U1);
-    self: Isometry<N, U3, UnitQuaternion<N>>, rhs: UnitQuaternion<N>,
-    Output = Isometry<N, U3, UnitQuaternion<N>>;
+    ;
+    self: Isometry<N, UnitQuaternion<N>, 3>, rhs: UnitQuaternion<N>,
+    Output = Isometry<N, UnitQuaternion<N>, 3>;
     [val val] => Isometry::from_parts(self.translation, self.rotation / rhs);
     [ref val] => Isometry::from_parts(self.translation.clone(), self.rotation / rhs); // TODO: do not clone.
     [val ref] => Isometry::from_parts(self.translation, self.rotation / *rhs);
@@ -477,9 +478,9 @@ isometry_from_composition_impl_all!(
 // UnitQuaternion ÷ Isometry
 isometry_from_composition_impl_all!(
     Div, div;
-    (U4, U1), (U3, U1);
-    self: UnitQuaternion<N>, right: Isometry<N, U3, UnitQuaternion<N>>,
-    Output = Isometry<N, U3, UnitQuaternion<N>>;
+    ;
+    self: UnitQuaternion<N>, right: Isometry<N, UnitQuaternion<N>, 3>,
+    Output = Isometry<N, UnitQuaternion<N>, 3>;
     // TODO: don't call inverse explicitly?
     [val val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * right.inverse() };
     [ref val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * right.inverse() };
@@ -490,8 +491,8 @@ isometry_from_composition_impl_all!(
 // Translation × Rotation
 isometry_from_composition_impl_all!(
     Mul, mul;
-    (D, D), (D, U1) for D: DimName;
-    self: Translation<N, D>, right: Rotation<N, D>, Output = Isometry<N, D, Rotation<N, D>>;
+    D;
+    self: Translation<N, D>, right: Rotation<N, D>, Output = Isometry<N, Rotation<N, D>, D>;
     [val val] => Isometry::from_parts(self, right);
     [ref val] => Isometry::from_parts(self.clone(), right);
     [val ref] => Isometry::from_parts(self, right.clone());
@@ -501,8 +502,8 @@ isometry_from_composition_impl_all!(
 // Translation × UnitQuaternion
 isometry_from_composition_impl_all!(
     Mul, mul;
-    (U4, U1), (U3, U1);
-    self: Translation<N, U3>, right: UnitQuaternion<N>, Output = Isometry<N, U3, UnitQuaternion<N>>;
+    ;
+    self: Translation<N, 3>, right: UnitQuaternion<N>, Output = Isometry<N, UnitQuaternion<N>, 3>;
     [val val] => Isometry::from_parts(self, right);
     [ref val] => Isometry::from_parts(self.clone(), right);
     [val ref] => Isometry::from_parts(self, *right);
@@ -512,9 +513,9 @@ isometry_from_composition_impl_all!(
 // Isometry × UnitComplex
 isometry_from_composition_impl_all!(
     Mul, mul;
-    (U2, U1), (U2, U1);
-    self: Isometry<N, U2, UnitComplex<N>>, rhs: UnitComplex<N>,
-    Output = Isometry<N, U2, UnitComplex<N>>;
+    ;
+    self: Isometry<N, UnitComplex<N>, 2>, rhs: UnitComplex<N>,
+    Output = Isometry<N, UnitComplex<N>, 2>;
     [val val] => Isometry::from_parts(self.translation, self.rotation * rhs);
     [ref val] => Isometry::from_parts(self.translation.clone(), self.rotation * rhs); // TODO: do not clone.
     [val ref] => Isometry::from_parts(self.translation, self.rotation * *rhs);
@@ -524,9 +525,9 @@ isometry_from_composition_impl_all!(
 // Isometry ÷ UnitComplex
 isometry_from_composition_impl_all!(
     Div, div;
-    (U2, U1), (U2, U1);
-    self: Isometry<N, U2, UnitComplex<N>>, rhs: UnitComplex<N>,
-    Output = Isometry<N, U2, UnitComplex<N>>;
+    ;
+    self: Isometry<N, UnitComplex<N>, 2>, rhs: UnitComplex<N>,
+    Output = Isometry<N, UnitComplex<N>, 2>;
     [val val] => Isometry::from_parts(self.translation, self.rotation / rhs);
     [ref val] => Isometry::from_parts(self.translation.clone(), self.rotation / rhs); // TODO: do not clone.
     [val ref] => Isometry::from_parts(self.translation, self.rotation / *rhs);
diff --git a/src/geometry/isometry_simba.rs b/src/geometry/isometry_simba.rs
index 1db8dd43..1ba8b765 100755
--- a/src/geometry/isometry_simba.rs
+++ b/src/geometry/isometry_simba.rs
@@ -9,7 +9,6 @@ where
     N::Element: SimdRealField,
     R: SimdValue<SimdBool = N::SimdBool> + AbstractRotation<N, D>,
     R::Element: AbstractRotation<N::Element, D>,
-    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     type Element = Isometry<N::Element, R::Element, D>;
     type SimdBool = N::SimdBool;
diff --git a/src/geometry/op_macros.rs b/src/geometry/op_macros.rs
index 5a9cfa00..05194fd2 100644
--- a/src/geometry/op_macros.rs
+++ b/src/geometry/op_macros.rs
@@ -7,21 +7,25 @@ macro_rules! md_impl(
     // Operator, operator method, and scalar bounds.
      $Op: ident, $op: ident $(where N: $($ScalarBounds: ident),*)*;
      // Storage dimensions, and dimension bounds.
-     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) for $($Dims: ident: $DimsBound: ident $(<$($BoundParam: ty),*>)*),+
-     // [Optional] Extra allocator bounds.
-     $(where $ConstraintType: ty: $ConstraintBound: ident<$($ConstraintBoundParams: ty $( = $EqBound: ty )*),*> )*;
+     ($R1: ty, $C1: ty),($R2: ty, $C2: ty)
+     // Const type declaration
+     const $($D: ident),*;
+     // Other generic type declarations.
+     for $($DimsDecl: ident),*;
+     // Where clause.
+     where $($ConstraintType: ty: $ConstraintBound: ident$(<$($ConstraintBoundParams: ty $( = $EqBound: ty )*),*>)*),*;
      // Argument identifiers and types + output.
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Result: ty;
      // Operator actual implementation.
      $action: expr;
      // Lifetime.
      $($lives: tt),*) => {
-        impl<$($lives ,)* N $(, $Dims: $DimsBound $(<$($BoundParam),*>)*)*> $Op<$Rhs> for $Lhs
+        impl<$($lives ,)* N $(, $DimsDecl)* $(, const $D: usize)*> $Op<$Rhs> for $Lhs
             where N: Scalar + Zero + One + ClosedAdd + ClosedMul $($(+ $ScalarBounds)*)*,
                   DefaultAllocator: Allocator<N, $R1, $C1> +
                                     Allocator<N, $R2, $C2> +
                                     Allocator<N, $R1, $C2>,
-                  $( $ConstraintType: $ConstraintBound<$( $ConstraintBoundParams $( = $EqBound )*),*> ),*
+                  $( $ConstraintType: $ConstraintBound$(<$( $ConstraintBoundParams $( = $EqBound )*),*>)* ),*
                    {
             type Output = $Result;
 
@@ -40,9 +44,13 @@ macro_rules! md_impl_all(
      // Operator, operator method, and scalar bounds.
      $Op: ident, $op: ident $(where N: $($ScalarBounds: ident),*)*;
      // Storage dimensions, and dimension bounds.
-     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) for $($Dims: ident: $DimsBound: ident $(<$($BoundParam: ty),*>)*),+
-     // [Optional] Extra allocator bounds.
-     $(where $ConstraintType: ty: $ConstraintBound: ident<$($ConstraintBoundParams: ty $( = $EqBound: ty )*),*> )*;
+     ($R1: ty, $C1: ty),($R2: ty, $C2: ty)
+     // Const type declaration
+     const $($D: ident),*;
+     // Other generic type declarations.
+     for $($DimsDecl: ident),*;
+     // Where clause.
+     where $($ConstraintType: ty: $ConstraintBound: ident$(<$($ConstraintBoundParams: ty $( = $EqBound: ty )*),*>)*),*;
      // Argument identifiers and types + output.
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Result: ty;
      // Operators actual implementations.
@@ -53,29 +61,37 @@ macro_rules! md_impl_all(
 
         md_impl!(
             $Op, $op $(where N: $($ScalarBounds),*)*;
-            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$($BoundParam),*>)*),+
-            $(where $ConstraintType: $ConstraintBound<$($ConstraintBoundParams $( = $EqBound )*),*>)*;
+            ($R1, $C1),($R2, $C2)
+            const $($D),*;
+            for $($DimsDecl),*;
+            where $($ConstraintType: $ConstraintBound$(<$($ConstraintBoundParams $( = $EqBound )*),*>)*),*;
             $lhs: $Lhs, $rhs: $Rhs, Output = $Result;
             $action_val_val; );
 
         md_impl!(
             $Op, $op $(where N: $($ScalarBounds),*)*;
-            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$($BoundParam),*>)*),+
-            $(where $ConstraintType: $ConstraintBound<$($ConstraintBoundParams $( = $EqBound )*),*>)*;
+            ($R1, $C1),($R2, $C2)
+            const $($D),*;
+            for $($DimsDecl),*;
+            where $($ConstraintType: $ConstraintBound$(<$($ConstraintBoundParams $( = $EqBound )*),*>)*),*;
             $lhs: &'a $Lhs, $rhs: $Rhs, Output = $Result;
             $action_ref_val; 'a);
 
         md_impl!(
             $Op, $op $(where N: $($ScalarBounds),*)*;
-            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$($BoundParam),*>)*),+
-            $(where $ConstraintType: $ConstraintBound<$($ConstraintBoundParams $( = $EqBound )*),*>)*;
+            ($R1, $C1),($R2, $C2)
+            const $($D),*;
+            for $($DimsDecl),*;
+            where $($ConstraintType: $ConstraintBound$(<$($ConstraintBoundParams $( = $EqBound )*),*>)*),*;
             $lhs: $Lhs, $rhs: &'b $Rhs, Output = $Result;
             $action_val_ref; 'b);
 
         md_impl!(
             $Op, $op $(where N: $($ScalarBounds),*)*;
-            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$($BoundParam),*>)*),+
-            $(where $ConstraintType: $ConstraintBound<$($ConstraintBoundParams $( = $EqBound )*),*>)*;
+            ($R1, $C1),($R2, $C2)
+            const $($D),*;
+            for $($DimsDecl),*;
+            where $($ConstraintType: $ConstraintBound$(<$($ConstraintBoundParams $( = $EqBound )*),*>)*),*;
             $lhs: &'a $Lhs, $rhs: &'b $Rhs, Output = $Result;
             $action_ref_ref; 'a, 'b);
     }
@@ -85,18 +101,22 @@ macro_rules! md_impl_all(
 macro_rules! md_assign_impl(
     (
      // Operator, operator method, and scalar bounds.
-     $Op: ident, $op: ident $(where N: $($ScalarBounds: ident),*)* $(for N::Element: $ElementBounds: ident)*;
+     $Op: ident, $op: ident $(where N: $($ScalarBounds: ident),*)* $(for N::Element: $($ElementBounds: ident),*)*;
      // Storage dimensions, and dimension bounds.
-     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) for $($Dims: ident: $DimsBound: ident $(<$($BoundParam: ty),*>)*),*
-     // [Optional] Extra allocator bounds.
-     $(where $ConstraintType: ty: $ConstraintBound: ident $(<$($ConstraintBoundParams: ty $( = $EqBound: ty )*),*>)* )*;
+     ($R1: ty, $C1: ty),($R2: ty, $C2: ty)
+     // Const type declaration
+     const $($D: ident),*;
+     // Other generic type declarations.
+     for $($DimsDecl: ident),*;
+     // Where clause.
+     where $($ConstraintType: ty: $ConstraintBound: ident$(<$($ConstraintBoundParams: ty $( = $EqBound: ty )*),*>)*),*;
      // Argument identifiers and types.
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty;
      // Actual implementation and lifetimes.
      $action: expr; $($lives: tt),*) => {
-        impl<$($lives ,)* N $(, $Dims: $DimsBound $(<$($BoundParam),*>)*)*> $Op<$Rhs> for $Lhs
+        impl<$($lives ,)* N $(, $DimsDecl)* $(, const $D: usize)*> $Op<$Rhs> for $Lhs
             where N: Scalar + Zero + One + ClosedAdd + ClosedMul $($(+ $ScalarBounds)*)*,
-                  $(N::Element: $ElementBounds,)*
+                  $($(N::Element: $ElementBounds,)*)*
                   DefaultAllocator: Allocator<N, $R1, $C1> +
                                     Allocator<N, $R2, $C2>,
                   $( $ConstraintType: $ConstraintBound $(<$( $ConstraintBoundParams $( = $EqBound )*),*>)* ),*
@@ -116,9 +136,13 @@ macro_rules! md_assign_impl_all(
      // Operator, operator method, and scalar bounds.
      $Op: ident, $op: ident $(where N: $($ScalarBounds: ident),*)* $(for N::Element: $($ElementBounds: ident),*)*;
      // Storage dimensions, and dimension bounds.
-     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) for $($Dims: ident: $DimsBound: ident $(<$($BoundParam: ty),*>)*),*
-     // [Optional] Extra allocator bounds.
-     $(where $ConstraintType: ty: $ConstraintBound: ident$(<$($ConstraintBoundParams: ty $( = $EqBound: ty )*),*>)* )*;
+     ($R1: ty, $C1: ty),($R2: ty, $C2: ty)
+     // Const type declaration
+     const $($D: ident),*;
+     // Other generic type declarations.
+     for $($DimsDecl: ident),*;
+     // Where clause.
+     where $($ConstraintType: ty: $ConstraintBound: ident$(<$($ConstraintBoundParams: ty $( = $EqBound: ty )*),*>)*),*;
      // Argument identifiers and types.
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty;
      // Actual implementation and lifetimes.
@@ -126,15 +150,19 @@ macro_rules! md_assign_impl_all(
      [ref] => $action_ref: expr;) => {
         md_assign_impl!(
             $Op, $op $(where N: $($ScalarBounds),*)* $(for N::Element: $($ElementBounds),*)*;
-            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$($BoundParam),*>)*),*
-            $(where $ConstraintType: $ConstraintBound $(<$($ConstraintBoundParams $( = $EqBound )*),*>)*)*;
+            ($R1, $C1),($R2, $C2)
+            const $($D),*;
+            for $($DimsDecl),*;
+            where $($ConstraintType: $ConstraintBound$(<$($ConstraintBoundParams $( = $EqBound )*),*>)*),*;
             $lhs: $Lhs, $rhs: $Rhs;
             $action_val; );
 
         md_assign_impl!(
             $Op, $op $(where N: $($ScalarBounds),*)* $(for N::Element: $($ElementBounds),*)*;
-            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$($BoundParam),*>)*),*
-            $(where $ConstraintType: $ConstraintBound $(<$($ConstraintBoundParams $( = $EqBound )*),*>)*)*;
+            ($R1, $C1),($R2, $C2)
+            const $($D),*;
+            for $($DimsDecl),*;
+            where $($ConstraintType: $ConstraintBound$(<$($ConstraintBoundParams $( = $EqBound )*),*>)*),*;
             $lhs: $Lhs, $rhs: &'b $Rhs;
             $action_ref; 'b);
     }
@@ -144,16 +172,23 @@ macro_rules! md_assign_impl_all(
 /// Macro for the implementation of addition and subtraction.
 macro_rules! add_sub_impl(
     ($Op: ident, $op: ident, $bound: ident;
-     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) $(-> ($RRes: ty))* for $($Dims: ident: $DimsBound: ident $(<$($BoundParam: ty),*>)*),+;
+     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) $(-> ($RRes: ty))*
+     // Const type declaration
+     const $($D: ident),*;
+     // Other generic type declarations.
+     for $($DimsDecl: ident),*;
+     // Where clause.
+     where $($ConstraintType: ty: $ConstraintBound: ident$(<$($ConstraintBoundParams: ty $( = $EqBound: ty )*),*>)*),*;
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Result: ty;
      $action: expr; $($lives: tt),*) => {
-        impl<$($lives ,)* N $(, $Dims: $DimsBound $(<$($BoundParam),*>)*)*> $Op<$Rhs> for $Lhs
+        impl<$($lives ,)* N $(, $DimsDecl)* $(, const $D: usize)*> $Op<$Rhs> for $Lhs
             where N: Scalar + $bound,
                   DefaultAllocator: Allocator<N, $R1, $C1> +
                                     Allocator<N, $R2, $C2> +
                                     SameShapeAllocator<N, $R1, $C1, $R2, $C2>,
                   ShapeConstraint: SameNumberOfRows<$R1, $R2 $(, Representative = $RRes)*> +
-                                   SameNumberOfColumns<$C1, $C2> {
+                                   SameNumberOfColumns<$C1, $C2>,
+                  $( $ConstraintType: $ConstraintBound$(<$( $ConstraintBoundParams $( = $EqBound )*),*>)* ),* {
             type Output = $Result;
 
             #[inline]
@@ -168,14 +203,11 @@ macro_rules! add_sub_impl(
 /// Macro for the implementation of assignment-addition and assignment-subtraction.
 macro_rules! add_sub_assign_impl(
     ($Op: ident, $op: ident, $bound: ident;
-     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) for $($Dims: ident: $DimsBound: ident),+;
+    $(const $D: ident),*;
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty;
      $action: expr; $($lives: tt),*) => {
-        impl<$($lives ,)* N $(, $Dims: $DimsBound)*> $Op<$Rhs> for $Lhs
-            where N: Scalar + $bound,
-                  DefaultAllocator: Allocator<N, $R1, $C1> +
-                                    Allocator<N, $R2, $C2>,
-                  ShapeConstraint: SameNumberOfRows<$R1, $R2> + SameNumberOfColumns<$C1, $C2> {
+        impl<$($lives ,)* N $(, const $D: usize),*> $Op<$Rhs> for $Lhs
+            where N: Scalar + $bound {
             #[inline]
             fn $op(&mut $lhs, $rhs: $Rhs) {
                 $action
diff --git a/src/geometry/point.rs b/src/geometry/point.rs
index 307f0b17..4944e158 100644
--- a/src/geometry/point.rs
+++ b/src/geometry/point.rs
@@ -17,7 +17,7 @@ use simba::simd::SimdPartialOrd;
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
 use crate::base::iter::{MatrixIter, MatrixIterMut};
-use crate::base::{Const, DefaultAllocator, Scalar, VectorN};
+use crate::base::{CVectorN, Const, DefaultAllocator, Scalar, VectorN};
 
 /// A point in an euclidean space.
 ///
@@ -64,7 +64,7 @@ impl<N: Scalar + Copy, const D: usize> Copy for Point<N, D>
 
 #[cfg(feature = "bytemuck")]
 unsafe impl<N: Scalar, const D: usize> bytemuck::Zeroable for Point<N, D> where
-    VectorN<N, Const<D>>: bytemuck::Zeroable // DefaultAllocator: Allocator<N, D>,
+    VectorN<N, Const<D>>: bytemuck::Zeroable
 {
 }
 
@@ -73,17 +73,11 @@ unsafe impl<N: Scalar, const D: usize> bytemuck::Pod for Point<N, D>
 where
     N: Copy,
     VectorN<N, Const<D>>: bytemuck::Pod,
-    // DefaultAllocator: Allocator<N, D>,
-    // <DefaultAllocator as Allocator<N, D>>::Buffer: Copy,
 {
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<N: Scalar, const D: usize> Serialize for Point<N, D>
-// where
-//     DefaultAllocator: Allocator<N, D>,
-//     <DefaultAllocator as Allocator<N, D>>::Buffer: Serialize,
-{
+impl<N: Scalar + Serialize, const D: usize> Serialize for Point<N, D> {
     fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
     where
         S: Serializer,
@@ -93,16 +87,12 @@ impl<N: Scalar, const D: usize> Serialize for Point<N, D>
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<'a, N: Scalar, const D: usize> Deserialize<'a> for Point<N, D>
-// where
-//     DefaultAllocator: Allocator<N, D>,
-//     <DefaultAllocator as Allocator<N, D>>::Buffer: Deserialize<'a>,
-{
+impl<'a, N: Scalar + Deserialize<'a>, const D: usize> Deserialize<'a> for Point<N, D> {
     fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
     where
         Des: Deserializer<'a>,
     {
-        let coords = VectorN::<N, D>::deserialize(deserializer)?;
+        let coords = CVectorN::<N, D>::deserialize(deserializer)?;
 
         Ok(Self::from(coords))
     }
@@ -113,7 +103,6 @@ impl<N, const D: usize> Abomonation for Point<N, D>
 where
     N: Scalar,
     VectorN<N, Const<D>>: Abomonation,
-    // DefaultAllocator: Allocator<N, D>,
 {
     unsafe fn entomb<W: Write>(&self, writer: &mut W) -> IOResult<()> {
         self.coords.entomb(writer)
@@ -312,7 +301,6 @@ impl<N: Scalar, const D: usize> Point<N, D>
 
 impl<N: Scalar + AbsDiffEq, const D: usize> AbsDiffEq for Point<N, D>
 where
-    // DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {
     type Epsilon = N::Epsilon;
@@ -330,7 +318,6 @@ where
 
 impl<N: Scalar + RelativeEq, const D: usize> RelativeEq for Point<N, D>
 where
-    // DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {
     #[inline]
@@ -352,7 +339,6 @@ where
 
 impl<N: Scalar + UlpsEq, const D: usize> UlpsEq for Point<N, D>
 where
-    // DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {
     #[inline]
diff --git a/src/geometry/point_construction.rs b/src/geometry/point_construction.rs
index 4ddaf1f9..6d58dd87 100644
--- a/src/geometry/point_construction.rs
+++ b/src/geometry/point_construction.rs
@@ -10,10 +10,10 @@ use rand::{
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimNameAdd, DimNameSum, U1};
-use crate::base::{DefaultAllocator, Scalar, VectorN};
+use crate::base::{CVectorN, DefaultAllocator, Scalar};
 use crate::{
     Const, Point1, Point2, Point3, Point4, Point5, Point6, Vector1, Vector2, Vector3, Vector4,
-    Vector5, Vector6,
+    Vector5, Vector6, VectorN,
 };
 use simba::scalar::{ClosedDiv, SupersetOf};
 
@@ -52,7 +52,7 @@ impl<N: Scalar, const D: usize> Point<N, D>
     where
         N: Zero,
     {
-        Self::from(VectorN::from_element(N::zero()))
+        Self::from(CVectorN::from_element(N::zero()))
     }
 
     /// Creates a new point from a slice.
@@ -71,7 +71,7 @@ impl<N: Scalar, const D: usize> Point<N, D>
     /// ```
     #[inline]
     pub fn from_slice(components: &[N]) -> Self {
-        Self::from(VectorN::from_row_slice(components))
+        Self::from(CVectorN::from_row_slice(components))
     }
 
     /// Creates a new point from its homogeneous vector representation.
@@ -131,7 +131,6 @@ impl<N: Scalar, const D: usize> Point<N, D>
     pub fn cast<To: Scalar>(self) -> Point<To, D>
     where
         Point<To, D>: SupersetOf<Self>,
-        // DefaultAllocator: Allocator<To, D>,
     {
         crate::convert(self)
     }
@@ -148,37 +147,35 @@ impl<N: Scalar + Bounded, const D: usize> Bounded for Point<N, D>
 {
     #[inline]
     fn max_value() -> Self {
-        Self::from(VectorN::max_value())
+        Self::from(CVectorN::max_value())
     }
 
     #[inline]
     fn min_value() -> Self {
-        Self::from(VectorN::min_value())
+        Self::from(CVectorN::min_value())
     }
 }
 
 #[cfg(feature = "rand-no-std")]
 impl<N: Scalar, const D: usize> Distribution<Point<N, D>> for Standard
 where
-    // DefaultAllocator: Allocator<N, D>,
     Standard: Distribution<N>,
 {
      /// Generate a `Point` where each coordinate is an independent variate from `[0, 1)`.
     #[inline]
     fn sample<'a, G: Rng + ?Sized>(&self, rng: &mut G) -> Point<N, D> {
-        Point::from(rng.gen::<VectorN<N, D>>())
+        Point::from(rng.gen::<CVectorN<N, D>>())
     }
 }
 
 #[cfg(feature = "arbitrary")]
 impl<N: Scalar + Arbitrary + Send, const D: usize> Arbitrary for Point<N, D>
 where
-    // DefaultAllocator: Allocator<N, D>,
     <DefaultAllocator as Allocator<N, Const<D>>>::Buffer: Send,
 {
     #[inline]
     fn arbitrary(g: &mut Gen) -> Self {
-        Self::from(VectorN::arbitrary(g))
+        Self::from(CVectorN::arbitrary(g))
     }
 }
 
diff --git a/src/geometry/point_conversion.rs b/src/geometry/point_conversion.rs
index e301f948..43cc7bc7 100644
--- a/src/geometry/point_conversion.rs
+++ b/src/geometry/point_conversion.rs
@@ -20,7 +20,6 @@ impl<N1, N2, const D: usize> SubsetOf<Point<N2, D>> for Point<N1, D>
 where
     N1: Scalar,
     N2: Scalar + SupersetOf<N1>,
-    // DefaultAllocator: Allocator<N2, D> + Allocator<N1, D>,
 {
     #[inline]
     fn to_superset(&self) -> Point<N2, D> {
@@ -58,12 +57,12 @@ where
 
     #[inline]
     fn is_in_subset(v: &VectorN<N2, DimNameSum<Const<D>, U1>>) -> bool {
-        crate::is_convertible::<_, VectorN<N1, DimNameSum<D, U1>>>(v) && !v[D].is_zero()
+        crate::is_convertible::<_, VectorN<N1, DimNameSum<Const<D>, U1>>>(v) && !v[D].is_zero()
     }
 
     #[inline]
     fn from_superset_unchecked(v: &VectorN<N2, DimNameSum<Const<D>, U1>>) -> Self {
-        let coords = v.fixed_slice::<D, U1>(0, 0) / v[D].inlined_clone();
+        let coords = v.fixed_slice::<Const<D>, U1>(0, 0) / v[D].inlined_clone();
         Self {
             coords: crate::convert_unchecked(coords),
         }
@@ -97,7 +96,6 @@ impl<N: Scalar + Copy + PrimitiveSimdValue, const D: usize> From<[Point<N::Eleme
 where
     N: From<[<N as simba::simd::SimdValue>::Element; 2]>,
     N::Element: Scalar + Copy,
-    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
     <DefaultAllocator as Allocator<N::Element, Const<D>>>::Buffer: Copy,
 {
     #[inline]
@@ -111,7 +109,6 @@ impl<N: Scalar + Copy + PrimitiveSimdValue, const D: usize> From<[Point<N::Eleme
 where
     N: From<[<N as simba::simd::SimdValue>::Element; 4]>,
     N::Element: Scalar + Copy,
-    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
     <DefaultAllocator as Allocator<N::Element, Const<D>>>::Buffer: Copy,
 {
     #[inline]
@@ -130,7 +127,6 @@ impl<N: Scalar + Copy + PrimitiveSimdValue, const D: usize> From<[Point<N::Eleme
 where
     N: From<[<N as simba::simd::SimdValue>::Element; 8]>,
     N::Element: Scalar + Copy,
-    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
     <DefaultAllocator as Allocator<N::Element, Const<D>>>::Buffer: Copy,
 {
     #[inline]
@@ -153,7 +149,6 @@ impl<N: Scalar + Copy + PrimitiveSimdValue, const D: usize> From<[Point<N::Eleme
 where
     N: From<[<N as simba::simd::SimdValue>::Element; 16]>,
     N::Element: Scalar + Copy,
-    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
     <DefaultAllocator as Allocator<N::Element, Const<D>>>::Buffer: Copy,
 {
     #[inline]
diff --git a/src/geometry/point_ops.rs b/src/geometry/point_ops.rs
index 48af3a8d..4702b5bb 100644
--- a/src/geometry/point_ops.rs
+++ b/src/geometry/point_ops.rs
@@ -9,7 +9,7 @@ use crate::base::allocator::{Allocator, SameShapeAllocator};
 use crate::base::constraint::{
     AreMultipliable, SameNumberOfColumns, SameNumberOfRows, ShapeConstraint,
 };
-use crate::base::dimension::{Dim, DimName, U1};
+use crate::base::dimension::{Dim, U1};
 use crate::base::storage::Storage;
 use crate::base::{Const, DefaultAllocator, Matrix, Scalar, Vector, VectorSum};
 
@@ -79,74 +79,101 @@ impl<'a, N: Scalar + ClosedNeg, const D: usize> Neg for &'a Point<N, D>
 
 // Point - Point
 add_sub_impl!(Sub, sub, ClosedSub;
-    (D, U1), (D, U1);
-    self: &'a Point<N, D>, right: &'b Point<N, D>, Output = VectorSum<N, D, D>;
+    (Const<D>, U1), (Const<D>, U1)
+    const D; for; where;
+    self: &'a Point<N, D>, right: &'b Point<N, D>, Output = VectorSum<N, Const<D>, Const<D>>;
     &self.coords - &right.coords; 'a, 'b);
 
 add_sub_impl!(Sub, sub, ClosedSub;
-    (D, U1), (D, U1);
-    self: &'a Point<N, D>, right: Point<N, D>, Output = VectorSum<N, D, D>;
+    (Const<D>, U1), (Const<D>, U1)
+    const D; for; where;
+    self: &'a Point<N, D>, right: Point<N, D>, Output = VectorSum<N, Const<D>, Const<D>>;
     &self.coords - right.coords; 'a);
 
 add_sub_impl!(Sub, sub, ClosedSub;
-    (D, U1), (D, U1);
-    self: Point<N, D>, right: &'b Point<N, D>, Output = VectorSum<N, D, D>;
+    (Const<D>, U1), (Const<D>, U1)
+    const D; for; where;
+    self: Point<N, D>, right: &'b Point<N, D>, Output = VectorSum<N, Const<D>, Const<D>>;
     self.coords - &right.coords; 'b);
 
 add_sub_impl!(Sub, sub, ClosedSub;
-    (D, U1), (D, U1);
-    self: Point<N, D>, right: Point<N, D>, Output = VectorSum<N, D, D>;
+    (Const<D>, U1), (Const<D>, U1)
+    const D; for; where;
+    self: Point<N, D>, right: Point<N, D>, Output = VectorSum<N, Const<D>, Const<D>>;
     self.coords - right.coords; );
 
 // Point - Vector
 add_sub_impl!(Sub, sub, ClosedSub;
-    (D1, U1), (D2, U1) -> (D1) for D1: DimName, D2: Dim, SB: Storage<N, D2>;
+    (Const<D1>, U1), (D2, U1) -> (Const<D1>)
+    const D1;
+    for D2, SB;
+    where D2: Dim, SB: Storage<N, D2>;
     self: &'a Point<N, D1>, right: &'b Vector<N, D2, SB>, Output = Point<N, D1>;
     Self::Output::from(&self.coords - right); 'a, 'b);
 
 add_sub_impl!(Sub, sub, ClosedSub;
-    (D1, U1), (D2, U1) -> (D1) for D1: DimName, D2: Dim, SB: Storage<N, D2>;
+    (Const<D1>, U1), (D2, U1) -> (Const<D1>)
+    const D1;
+    for D2, SB;
+    where D2: Dim, SB: Storage<N, D2>;
     self: &'a Point<N, D1>, right: Vector<N, D2, SB>, Output = Point<N, D1>;
     Self::Output::from(&self.coords - &right); 'a); // TODO: should not be a ref to `right`.
 
 add_sub_impl!(Sub, sub, ClosedSub;
-    (D1, U1), (D2, U1) -> (D1) for D1: DimName, D2: Dim, SB: Storage<N, D2>;
+    (Const<D1>, U1), (D2, U1) -> (Const<D1>)
+    const D1;
+    for D2, SB;
+    where D2: Dim, SB: Storage<N, D2>;
     self: Point<N, D1>, right: &'b Vector<N, D2, SB>, Output = Point<N, D1>;
     Self::Output::from(self.coords - right); 'b);
 
 add_sub_impl!(Sub, sub, ClosedSub;
-    (D1, U1), (D2, U1) -> (D1) for D1: DimName, D2: Dim, SB: Storage<N, D2>;
+    (Const<D1>, U1), (D2, U1) -> (Const<D1>)
+    const D1;
+    for D2, SB;
+    where D2: Dim, SB: Storage<N, D2>;
     self: Point<N, D1>, right: Vector<N, D2, SB>, Output = Point<N, D1>;
     Self::Output::from(self.coords - right); );
 
 // Point + Vector
 add_sub_impl!(Add, add, ClosedAdd;
-    (D1, U1), (D2, U1) -> (D1) for D1: DimName, D2: Dim, SB: Storage<N, D2>;
+    (Const<D1>, U1), (D2, U1) -> (Const<D1>)
+    const D1;
+    for D2, SB;
+    where D2: Dim, SB: Storage<N, D2>;
     self: &'a Point<N, D1>, right: &'b Vector<N, D2, SB>, Output = Point<N, D1>;
     Self::Output::from(&self.coords + right); 'a, 'b);
 
 add_sub_impl!(Add, add, ClosedAdd;
-    (D1, U1), (D2, U1) -> (D1) for D1: DimName, D2: Dim, SB: Storage<N, D2>;
+    (Const<D1>, U1), (D2, U1) -> (Const<D1>)
+    const D1;
+    for D2, SB;
+    where D2: Dim, SB: Storage<N, D2>;
     self: &'a Point<N, D1>, right: Vector<N, D2, SB>, Output = Point<N, D1>;
     Self::Output::from(&self.coords + &right); 'a); // TODO: should not be a ref to `right`.
 
 add_sub_impl!(Add, add, ClosedAdd;
-    (D1, U1), (D2, U1) -> (D1) for D1: DimName, D2: Dim, SB: Storage<N, D2>;
+    (Const<D1>, U1), (D2, U1) -> (Const<D1>)
+    const D1;
+    for D2, SB;
+    where D2: Dim, SB: Storage<N, D2>;
     self: Point<N, D1>, right: &'b Vector<N, D2, SB>, Output = Point<N, D1>;
     Self::Output::from(self.coords + right); 'b);
 
 add_sub_impl!(Add, add, ClosedAdd;
-    (D1, U1), (D2, U1) -> (D1) for D1: DimName, D2: Dim, SB: Storage<N, D2>;
+    (Const<D1>, U1), (D2, U1) -> (Const<D1>)
+    const D1;
+    for D2, SB;
+    where D2: Dim, SB: Storage<N, D2>;
     self: Point<N, D1>, right: Vector<N, D2, SB>, Output = Point<N, D1>;
     Self::Output::from(self.coords + right); );
 
-// XXX: replace by the shared macro: add_sub_assign_impl
+// TODO: replace by the shared macro: add_sub_assign_impl?
 macro_rules! op_assign_impl(
     ($($TraitAssign: ident, $method_assign: ident, $bound: ident);* $(;)*) => {$(
         impl<'b, N, D2: Dim, SB, const D1: usize> $TraitAssign<&'b Vector<N, D2, SB>> for Point<N, D1>
             where N: Scalar + $bound,
                   SB: Storage<N, D2>,
-                  // DefaultAllocator: Allocator<N, D1>,
                   ShapeConstraint: SameNumberOfRows<Const<D1>, D2> {
 
             #[inline]
@@ -158,8 +185,7 @@ macro_rules! op_assign_impl(
         impl<N, D2: Dim, SB, const D1: usize> $TraitAssign<Vector<N, D2, SB>> for Point<N, D1>
             where N: Scalar + $bound,
                   SB: Storage<N, D2>,
-                  // DefaultAllocator: Allocator<N, D1>,
-                  ShapeConstraint: SameNumberOfRows<D1, D2> {
+                  ShapeConstraint: SameNumberOfRows<Const<D1>, D2> {
 
             #[inline]
             fn $method_assign(&mut self, right: Vector<N, D2, SB>) {
@@ -181,9 +207,12 @@ op_assign_impl!(
  */
 md_impl_all!(
     Mul, mul;
-    (R1, C1), (D2, U1) for R1: DimName, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>
-    where ShapeConstraint: AreMultipliable<R1, C1, D2, U1>;
-    self: Matrix<N, R1, C1, SA>, right: Point<N, D2>, Output = Point<N, R1>;
+    (Const<R1>, Const<C1>), (Const<D2>, U1)
+    const D2, R1, C1;
+    for SA;
+    where SA: Storage<N, Const<R1>, Const<C1>>,
+          ShapeConstraint: AreMultipliable<Const<R1>, Const<C1>, Const<D2>, U1>;
+    self: Matrix<N, Const<R1>, Const<C1>, SA>, right: Point<N, D2>, Output = Point<N, R1>;
     [val val] => Point::from(self * right.coords);
     [ref val] => Point::from(self * right.coords);
     [val ref] => Point::from(self * &right.coords);
diff --git a/src/geometry/point_simba.rs b/src/geometry/point_simba.rs
index c597d142..b5f25be0 100644
--- a/src/geometry/point_simba.rs
+++ b/src/geometry/point_simba.rs
@@ -7,7 +7,6 @@ use crate::geometry::Point;
 impl<N: Scalar + SimdValue, const D: usize> SimdValue for Point<N, D>
 where
     N::Element: Scalar,
-    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     type Element = Point<N::Element, D>;
     type SimdBool = N::SimdBool;
diff --git a/src/geometry/quaternion_ops.rs b/src/geometry/quaternion_ops.rs
index f9205874..c19984f3 100644
--- a/src/geometry/quaternion_ops.rs
+++ b/src/geometry/quaternion_ops.rs
@@ -54,10 +54,9 @@ use std::ops::{
     Add, AddAssign, Div, DivAssign, Index, IndexMut, Mul, MulAssign, Neg, Sub, SubAssign,
 };
 
-use crate::base::allocator::Allocator;
-use crate::base::dimension::{U1, U3, U4};
+use crate::base::dimension::U3;
 use crate::base::storage::Storage;
-use crate::base::{DefaultAllocator, Scalar, Unit, Vector, Vector3};
+use crate::base::{Const, Scalar, Unit, Vector, Vector3};
 use crate::SimdRealField;
 
 use crate::geometry::{Point3, Quaternion, Rotation, UnitQuaternion};
@@ -80,14 +79,11 @@ impl<N: Scalar> IndexMut<usize> for Quaternion<N> {
 
 macro_rules! quaternion_op_impl(
     ($Op: ident, $op: ident;
-     ($LhsRDim: ident, $LhsCDim: ident), ($RhsRDim: ident, $RhsCDim: ident)
-     $(for $Storage: ident: $StoragesBound: ident $(<$($BoundParam: ty),*>)*),*;
-     $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Result: ty $(=> $VDimA: ty, $VDimB: ty)*;
+     $($Storage: ident: $StoragesBound: ident $(<$($BoundParam: ty),*>)*),*;
+     $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Result: ty;
      $action: expr; $($lives: tt),*) => {
         impl<$($lives ,)* N: SimdRealField $(, $Storage: $StoragesBound $(<$($BoundParam),*>)*)*> $Op<$Rhs> for $Lhs
-            where N::Element: SimdRealField,
-                  DefaultAllocator: Allocator<N, $LhsRDim, $LhsCDim> +
-                                    Allocator<N, $RhsRDim, $RhsCDim> {
+            where N::Element: SimdRealField {
             type Output = $Result;
 
             #[inline]
@@ -101,63 +97,63 @@ macro_rules! quaternion_op_impl(
 // Quaternion + Quaternion
 quaternion_op_impl!(
     Add, add;
-    (U4, U1), (U4, U1);
+    ;
     self: &'a Quaternion<N>, rhs: &'b Quaternion<N>, Output = Quaternion<N>;
     Quaternion::from(&self.coords + &rhs.coords);
     'a, 'b);
 
 quaternion_op_impl!(
     Add, add;
-    (U4, U1), (U4, U1);
+    ;
     self: &'a Quaternion<N>, rhs: Quaternion<N>, Output = Quaternion<N>;
     Quaternion::from(&self.coords + rhs.coords);
     'a);
 
 quaternion_op_impl!(
     Add, add;
-    (U4, U1), (U4, U1);
+    ;
     self: Quaternion<N>, rhs: &'b Quaternion<N>, Output = Quaternion<N>;
     Quaternion::from(self.coords + &rhs.coords);
     'b);
 
 quaternion_op_impl!(
     Add, add;
-    (U4, U1), (U4, U1);
+    ;
     self: Quaternion<N>, rhs: Quaternion<N>, Output = Quaternion<N>;
     Quaternion::from(self.coords + rhs.coords); );
 
 // Quaternion - Quaternion
 quaternion_op_impl!(
     Sub, sub;
-    (U4, U1), (U4, U1);
+    ;
     self: &'a Quaternion<N>, rhs: &'b Quaternion<N>, Output = Quaternion<N>;
     Quaternion::from(&self.coords - &rhs.coords);
     'a, 'b);
 
 quaternion_op_impl!(
     Sub, sub;
-    (U4, U1), (U4, U1);
+    ;
     self: &'a Quaternion<N>, rhs: Quaternion<N>, Output = Quaternion<N>;
     Quaternion::from(&self.coords - rhs.coords);
     'a);
 
 quaternion_op_impl!(
     Sub, sub;
-    (U4, U1), (U4, U1);
+    ;
     self: Quaternion<N>, rhs: &'b Quaternion<N>, Output = Quaternion<N>;
     Quaternion::from(self.coords - &rhs.coords);
     'b);
 
 quaternion_op_impl!(
     Sub, sub;
-    (U4, U1), (U4, U1);
+    ;
     self: Quaternion<N>, rhs: Quaternion<N>, Output = Quaternion<N>;
     Quaternion::from(self.coords - rhs.coords); );
 
 // Quaternion × Quaternion
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U4, U1);
+    ;
     self: &'a Quaternion<N>, rhs: &'b Quaternion<N>, Output = Quaternion<N>;
     Quaternion::new(
         self[3] * rhs[3] - self[0] * rhs[0] - self[1] * rhs[1] - self[2] * rhs[2],
@@ -168,218 +164,218 @@ quaternion_op_impl!(
 
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U4, U1);
+    ;
     self: &'a Quaternion<N>, rhs: Quaternion<N>, Output = Quaternion<N>;
     self * &rhs;
     'a);
 
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U4, U1);
+    ;
     self: Quaternion<N>, rhs: &'b Quaternion<N>, Output = Quaternion<N>;
     &self * rhs;
     'b);
 
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U4, U1);
+    ;
     self: Quaternion<N>, rhs: Quaternion<N>, Output = Quaternion<N>;
     &self * &rhs; );
 
 // UnitQuaternion × UnitQuaternion
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U4, U1);
+    ;
     self: &'a UnitQuaternion<N>, rhs: &'b UnitQuaternion<N>, Output = UnitQuaternion<N>;
     UnitQuaternion::new_unchecked(self.quaternion() * rhs.quaternion());
     'a, 'b);
 
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U4, U1);
+    ;
     self: &'a UnitQuaternion<N>, rhs: UnitQuaternion<N>, Output = UnitQuaternion<N>;
     self * &rhs;
     'a);
 
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U4, U1);
+    ;
     self: UnitQuaternion<N>, rhs: &'b UnitQuaternion<N>, Output = UnitQuaternion<N>;
     &self * rhs;
     'b);
 
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U4, U1);
+    ;
     self: UnitQuaternion<N>, rhs: UnitQuaternion<N>, Output = UnitQuaternion<N>;
     &self * &rhs; );
 
 // UnitQuaternion ÷ UnitQuaternion
 quaternion_op_impl!(
     Div, div;
-    (U4, U1), (U4, U1);
+    ;
     self: &'a UnitQuaternion<N>, rhs: &'b UnitQuaternion<N>, Output = UnitQuaternion<N>;
     #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
     'a, 'b);
 
 quaternion_op_impl!(
     Div, div;
-    (U4, U1), (U4, U1);
+    ;
     self: &'a UnitQuaternion<N>, rhs: UnitQuaternion<N>, Output = UnitQuaternion<N>;
     self / &rhs;
     'a);
 
 quaternion_op_impl!(
     Div, div;
-    (U4, U1), (U4, U1);
+    ;
     self: UnitQuaternion<N>, rhs: &'b UnitQuaternion<N>, Output = UnitQuaternion<N>;
     &self / rhs;
     'b);
 
 quaternion_op_impl!(
     Div, div;
-    (U4, U1), (U4, U1);
+    ;
     self: UnitQuaternion<N>, rhs: UnitQuaternion<N>, Output = UnitQuaternion<N>;
     &self / &rhs; );
 
 // UnitQuaternion × Rotation
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U3, U3);
-    self: &'a UnitQuaternion<N>, rhs: &'b Rotation<N, U3>,
-    Output = UnitQuaternion<N> => U3, U3;
-    // TODO: can we avoid the conversion from a rotation matrix?
+    ;
+    self: &'a UnitQuaternion<N>, rhs: &'b Rotation<N, 3>,
+    Output = UnitQuaternion<N>;
+    // TODO: can we avoid the conversion from a rotation matrix?
     self * UnitQuaternion::<N>::from_rotation_matrix(rhs);
     'a, 'b);
 
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U3, U3);
-    self: &'a UnitQuaternion<N>, rhs: Rotation<N, U3>,
-    Output = UnitQuaternion<N> => U3, U3;
+    ;
+    self: &'a UnitQuaternion<N>, rhs: Rotation<N, 3>,
+    Output = UnitQuaternion<N>;
     self * UnitQuaternion::<N>::from_rotation_matrix(&rhs);
     'a);
 
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U3, U3);
-    self: UnitQuaternion<N>, rhs: &'b Rotation<N, U3>,
-    Output = UnitQuaternion<N> => U3, U3;
+    ;
+    self: UnitQuaternion<N>, rhs: &'b Rotation<N, 3>,
+    Output = UnitQuaternion<N>;
     self * UnitQuaternion::<N>::from_rotation_matrix(rhs);
     'b);
 
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U3, U3);
-    self: UnitQuaternion<N>, rhs: Rotation<N, U3>,
-    Output = UnitQuaternion<N> => U3, U3;
+    ;
+    self: UnitQuaternion<N>, rhs: Rotation<N, 3>,
+    Output = UnitQuaternion<N>;
     self * UnitQuaternion::<N>::from_rotation_matrix(&rhs); );
 
 // UnitQuaternion ÷ Rotation
 quaternion_op_impl!(
     Div, div;
-    (U4, U1), (U3, U3);
-    self: &'a UnitQuaternion<N>, rhs: &'b Rotation<N, U3>,
-    Output = UnitQuaternion<N> => U3, U3;
+    ;
+    self: &'a UnitQuaternion<N>, rhs: &'b Rotation<N, 3>,
+    Output = UnitQuaternion<N>;
     // TODO: can we avoid the conversion to a rotation matrix?
     self / UnitQuaternion::<N>::from_rotation_matrix(rhs);
     'a, 'b);
 
 quaternion_op_impl!(
     Div, div;
-    (U4, U1), (U3, U3);
-    self: &'a UnitQuaternion<N>, rhs: Rotation<N, U3>,
-    Output = UnitQuaternion<N> => U3, U3;
+    ;
+    self: &'a UnitQuaternion<N>, rhs: Rotation<N, 3>,
+    Output = UnitQuaternion<N>;
     self / UnitQuaternion::<N>::from_rotation_matrix(&rhs);
     'a);
 
 quaternion_op_impl!(
     Div, div;
-    (U4, U1), (U3, U3);
-    self: UnitQuaternion<N>, rhs: &'b Rotation<N, U3>,
-    Output = UnitQuaternion<N> => U3, U3;
+    ;
+    self: UnitQuaternion<N>, rhs: &'b Rotation<N, 3>,
+    Output = UnitQuaternion<N>;
     self / UnitQuaternion::<N>::from_rotation_matrix(rhs);
     'b);
 
 quaternion_op_impl!(
     Div, div;
-    (U4, U1), (U3, U3);
-    self: UnitQuaternion<N>, rhs: Rotation<N, U3>,
-    Output = UnitQuaternion<N> => U3, U3;
+    ;
+    self: UnitQuaternion<N>, rhs: Rotation<N, 3>,
+    Output = UnitQuaternion<N>;
     self / UnitQuaternion::<N>::from_rotation_matrix(&rhs); );
 
 // Rotation × UnitQuaternion
 quaternion_op_impl!(
     Mul, mul;
-    (U3, U3), (U4, U1);
-    self: &'a Rotation<N, U3>, rhs: &'b UnitQuaternion<N>,
-    Output = UnitQuaternion<N> => U3, U3;
+    ;
+    self: &'a Rotation<N, 3>, rhs: &'b UnitQuaternion<N>,
+    Output = UnitQuaternion<N>;
     // TODO: can we avoid the conversion from a rotation matrix?
     UnitQuaternion::<N>::from_rotation_matrix(self) * rhs;
     'a, 'b);
 
 quaternion_op_impl!(
     Mul, mul;
-    (U3, U3), (U4, U1);
-    self: &'a Rotation<N, U3>, rhs: UnitQuaternion<N>,
-    Output = UnitQuaternion<N> => U3, U3;
+    ;
+    self: &'a Rotation<N, 3>, rhs: UnitQuaternion<N>,
+    Output = UnitQuaternion<N>;
     UnitQuaternion::<N>::from_rotation_matrix(self) * rhs;
     'a);
 
 quaternion_op_impl!(
     Mul, mul;
-    (U3, U3), (U4, U1);
-    self: Rotation<N, U3>, rhs: &'b UnitQuaternion<N>,
-    Output = UnitQuaternion<N> => U3, U3;
+    ;
+    self: Rotation<N, 3>, rhs: &'b UnitQuaternion<N>,
+    Output = UnitQuaternion<N>;
     UnitQuaternion::<N>::from_rotation_matrix(&self) * rhs;
     'b);
 
 quaternion_op_impl!(
     Mul, mul;
-    (U3, U3), (U4, U1);
-    self: Rotation<N, U3>, rhs: UnitQuaternion<N>,
-    Output = UnitQuaternion<N> => U3, U3;
+    ;
+    self: Rotation<N, 3>, rhs: UnitQuaternion<N>,
+    Output = UnitQuaternion<N>;
     UnitQuaternion::<N>::from_rotation_matrix(&self) * rhs; );
 
 // Rotation ÷ UnitQuaternion
 quaternion_op_impl!(
     Div, div;
-    (U3, U3), (U4, U1);
-    self: &'a Rotation<N, U3>, rhs: &'b UnitQuaternion<N>,
-    Output = UnitQuaternion<N> => U3, U3;
-    // TODO: can we avoid the conversion from a rotation matrix?
+    ;
+    self: &'a Rotation<N, 3>, rhs: &'b UnitQuaternion<N>,
+    Output = UnitQuaternion<N>;
+    // TODO: can we avoid the conversion from a rotation matrix?
     UnitQuaternion::<N>::from_rotation_matrix(self) / rhs;
     'a, 'b);
 
 quaternion_op_impl!(
     Div, div;
-    (U3, U3), (U4, U1);
-    self: &'a Rotation<N, U3>, rhs: UnitQuaternion<N>,
-    Output = UnitQuaternion<N> => U3, U3;
+    ;
+    self: &'a Rotation<N, 3>, rhs: UnitQuaternion<N>,
+    Output = UnitQuaternion<N>;
     UnitQuaternion::<N>::from_rotation_matrix(self) / rhs;
     'a);
 
 quaternion_op_impl!(
     Div, div;
-    (U3, U3), (U4, U1);
-    self: Rotation<N, U3>, rhs: &'b UnitQuaternion<N>,
-    Output = UnitQuaternion<N> => U3, U3;
+    ;
+    self: Rotation<N, 3>, rhs: &'b UnitQuaternion<N>,
+    Output = UnitQuaternion<N>;
     UnitQuaternion::<N>::from_rotation_matrix(&self) / rhs;
     'b);
 
 quaternion_op_impl!(
     Div, div;
-    (U3, U3), (U4, U1);
-    self: Rotation<N, U3>, rhs: UnitQuaternion<N>,
-    Output = UnitQuaternion<N> => U3, U3;
+    ;
+    self: Rotation<N, 3>, rhs: UnitQuaternion<N>,
+    Output = UnitQuaternion<N>;
     UnitQuaternion::<N>::from_rotation_matrix(&self) / rhs; );
 
 // UnitQuaternion × Vector
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U3, U1) for SB: Storage<N, U3> ;
-    self: &'a UnitQuaternion<N>, rhs: &'b Vector<N, U3, SB>,
-    Output = Vector3<N> => U3, U4;
+    SB: Storage<N, Const<3>> ;
+    self: &'a UnitQuaternion<N>, rhs: &'b Vector<N, Const<3>, SB>,
+    Output = Vector3<N>;
     {
         let two: N = crate::convert(2.0f64);
         let t = self.as_ref().vector().cross(rhs) * two;
@@ -391,89 +387,89 @@ quaternion_op_impl!(
 
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U3, U1) for SB: Storage<N, U3> ;
+    SB: Storage<N, Const<3>> ;
     self: &'a UnitQuaternion<N>, rhs: Vector<N, U3, SB>,
-    Output = Vector3<N> => U3, U4;
+    Output = Vector3<N>;
     self * &rhs;
     'a);
 
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U3, U1) for SB: Storage<N, U3> ;
+    SB: Storage<N, Const<3>> ;
     self: UnitQuaternion<N>, rhs: &'b Vector<N, U3, SB>,
-    Output = Vector3<N> => U3, U4;
+    Output = Vector3<N>;
     &self * rhs;
     'b);
 
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U3, U1) for SB: Storage<N, U3> ;
+    SB: Storage<N, Const<3>> ;
     self: UnitQuaternion<N>, rhs: Vector<N, U3, SB>,
-    Output = Vector3<N> => U3, U4;
+    Output = Vector3<N>;
     &self * &rhs; );
 
 // UnitQuaternion × Point
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U3, U1);
+    ;
     self: &'a UnitQuaternion<N>, rhs: &'b Point3<N>,
-    Output = Point3<N> => U3, U4;
+    Output = Point3<N>;
     Point3::from(self * &rhs.coords);
     'a, 'b);
 
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U3, U1);
+    ;
     self: &'a UnitQuaternion<N>, rhs: Point3<N>,
-    Output = Point3<N> => U3, U4;
+    Output = Point3<N>;
     Point3::from(self * rhs.coords);
     'a);
 
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U3, U1);
+    ;
     self: UnitQuaternion<N>, rhs: &'b Point3<N>,
-    Output = Point3<N> => U3, U4;
+    Output = Point3<N>;
     Point3::from(self * &rhs.coords);
     'b);
 
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U3, U1);
+    ;
     self: UnitQuaternion<N>, rhs: Point3<N>,
-    Output = Point3<N> => U3, U4;
+    Output = Point3<N>;
     Point3::from(self * rhs.coords); );
 
 // UnitQuaternion × Unit<Vector>
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U3, U1) for SB: Storage<N, U3> ;
+    SB: Storage<N, Const<3>> ;
     self: &'a UnitQuaternion<N>, rhs: &'b Unit<Vector<N, U3, SB>>,
-    Output = Unit<Vector3<N>> => U3, U4;
+    Output = Unit<Vector3<N>>;
     Unit::new_unchecked(self * rhs.as_ref());
     'a, 'b);
 
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U3, U1) for SB: Storage<N, U3> ;
+    SB: Storage<N, Const<3>> ;
     self: &'a UnitQuaternion<N>, rhs: Unit<Vector<N, U3, SB>>,
-    Output = Unit<Vector3<N>> => U3, U4;
+    Output = Unit<Vector3<N>>;
     Unit::new_unchecked(self * rhs.into_inner());
     'a);
 
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U3, U1) for SB: Storage<N, U3> ;
+    SB: Storage<N, Const<3>> ;
     self: UnitQuaternion<N>, rhs: &'b Unit<Vector<N, U3, SB>>,
-    Output = Unit<Vector3<N>> => U3, U4;
+    Output = Unit<Vector3<N>>;
     Unit::new_unchecked(self * rhs.as_ref());
     'b);
 
 quaternion_op_impl!(
     Mul, mul;
-    (U4, U1), (U3, U1) for SB: Storage<N, U3> ;
+    SB: Storage<N, Const<3>> ;
     self: UnitQuaternion<N>, rhs: Unit<Vector<N, U3, SB>>,
-    Output = Unit<Vector3<N>> => U3, U4;
+    Output = Unit<Vector3<N>>;
     Unit::new_unchecked(self * rhs.into_inner()); );
 
 macro_rules! scalar_op_impl(
@@ -564,13 +560,10 @@ where
 
 macro_rules! quaternion_op_impl(
     ($OpAssign: ident, $op_assign: ident;
-     ($LhsRDim: ident, $LhsCDim: ident), ($RhsRDim: ident, $RhsCDim: ident);
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty $(=> $VDimA: ty, $VDimB: ty)*;
      $action: expr; $($lives: tt),*) => {
         impl<$($lives ,)* N: SimdRealField> $OpAssign<$Rhs> for $Lhs
-            where N::Element: SimdRealField,
-                  DefaultAllocator: Allocator<N, $LhsRDim, $LhsCDim> +
-                                    Allocator<N, $RhsRDim, $RhsCDim> {
+            where N::Element: SimdRealField {
 
             #[inline]
             fn $op_assign(&mut $lhs, $rhs: $Rhs) {
@@ -583,35 +576,30 @@ macro_rules! quaternion_op_impl(
 // Quaternion += Quaternion
 quaternion_op_impl!(
     AddAssign, add_assign;
-    (U4, U1), (U4, U1);
     self: Quaternion<N>, rhs: &'b Quaternion<N>;
     self.coords += &rhs.coords;
     'b);
 
 quaternion_op_impl!(
     AddAssign, add_assign;
-    (U4, U1), (U4, U1);
     self: Quaternion<N>, rhs: Quaternion<N>;
     self.coords += rhs.coords; );
 
 // Quaternion -= Quaternion
 quaternion_op_impl!(
     SubAssign, sub_assign;
-    (U4, U1), (U4, U1);
     self: Quaternion<N>, rhs: &'b Quaternion<N>;
     self.coords -= &rhs.coords;
     'b);
 
 quaternion_op_impl!(
     SubAssign, sub_assign;
-    (U4, U1), (U4, U1);
     self: Quaternion<N>, rhs: Quaternion<N>;
     self.coords -= rhs.coords; );
 
 // Quaternion ×= Quaternion
 quaternion_op_impl!(
     MulAssign, mul_assign;
-    (U4, U1), (U4, U1);
     self: Quaternion<N>, rhs: &'b Quaternion<N>;
     {
         let res = &*self * rhs;
@@ -622,14 +610,12 @@ quaternion_op_impl!(
 
 quaternion_op_impl!(
     MulAssign, mul_assign;
-    (U4, U1), (U4, U1);
     self: Quaternion<N>, rhs: Quaternion<N>;
     *self *= &rhs; );
 
 // UnitQuaternion ×= UnitQuaternion
 quaternion_op_impl!(
     MulAssign, mul_assign;
-    (U4, U1), (U4, U1);
     self: UnitQuaternion<N>, rhs: &'b UnitQuaternion<N>;
     {
         let res = &*self * rhs;
@@ -639,14 +625,12 @@ quaternion_op_impl!(
 
 quaternion_op_impl!(
     MulAssign, mul_assign;
-    (U4, U1), (U4, U1);
     self: UnitQuaternion<N>, rhs: UnitQuaternion<N>;
     *self *= &rhs; );
 
 // UnitQuaternion ÷= UnitQuaternion
 quaternion_op_impl!(
     DivAssign, div_assign;
-    (U4, U1), (U4, U1);
     self: UnitQuaternion<N>, rhs: &'b UnitQuaternion<N>;
     {
         let res = &*self / rhs;
@@ -656,15 +640,13 @@ quaternion_op_impl!(
 
 quaternion_op_impl!(
     DivAssign, div_assign;
-    (U4, U1), (U4, U1);
     self: UnitQuaternion<N>, rhs: UnitQuaternion<N>;
     *self /= &rhs; );
 
 // UnitQuaternion ×= Rotation
 quaternion_op_impl!(
     MulAssign, mul_assign;
-    (U4, U1), (U3, U3);
-    self: UnitQuaternion<N>, rhs: &'b Rotation<N, U3> => U3, U3;
+    self: UnitQuaternion<N>, rhs: &'b Rotation<N, 3>;
     {
         let res = &*self * rhs;
         self.as_mut_unchecked().coords.copy_from(&res.as_ref().coords);
@@ -673,15 +655,13 @@ quaternion_op_impl!(
 
 quaternion_op_impl!(
     MulAssign, mul_assign;
-    (U4, U1), (U3, U3);
-    self: UnitQuaternion<N>, rhs: Rotation<N, U3> => U3, U3;
+    self: UnitQuaternion<N>, rhs: Rotation<N, 3>;
     *self *= &rhs; );
 
 // UnitQuaternion ÷= Rotation
 quaternion_op_impl!(
     DivAssign, div_assign;
-    (U4, U1), (U3, U3);
-    self: UnitQuaternion<N>, rhs: &'b Rotation<N, U3> => U3, U3;
+    self: UnitQuaternion<N>, rhs: &'b Rotation<N, 3>;
     {
         let res = &*self / rhs;
         self.as_mut_unchecked().coords.copy_from(&res.as_ref().coords);
@@ -690,6 +670,5 @@ quaternion_op_impl!(
 
 quaternion_op_impl!(
     DivAssign, div_assign;
-    (U4, U1), (U3, U3);
-    self: UnitQuaternion<N>, rhs: Rotation<N, U3> => U3, U3;
+    self: UnitQuaternion<N>, rhs: Rotation<N, 3>;
     *self /= &rhs; );
diff --git a/src/geometry/rotation.rs b/src/geometry/rotation.rs
index 498886d3..2783f9b1 100755
--- a/src/geometry/rotation.rs
+++ b/src/geometry/rotation.rs
@@ -64,7 +64,6 @@ pub struct Rotation<N: Scalar, const D: usize>
 
 impl<N: Scalar + hash::Hash, const D: usize> hash::Hash for Rotation<N, D>
 where
-    // DefaultAllocator: Allocator<N, D, D>,
     <DefaultAllocator as Allocator<N, Const<D>, Const<D>>>::Buffer: hash::Hash,
 {
     fn hash<H: hash::Hasher>(&self, state: &mut H) {
@@ -73,14 +72,12 @@ where
 }
 
 impl<N: Scalar + Copy, const D: usize> Copy for Rotation<N, D> where
-    // DefaultAllocator: Allocator<N, D, D>,
     <DefaultAllocator as Allocator<N, Const<D>, Const<D>>>::Buffer: Copy
 {
 }
 
 impl<N: Scalar, const D: usize> Clone for Rotation<N, D>
 where
-    // DefaultAllocator: Allocator<N, D, D>,
     <DefaultAllocator as Allocator<N, Const<D>, Const<D>>>::Buffer: Clone,
 {
     #[inline]
@@ -93,8 +90,7 @@ where
 impl<N, const D: usize> Abomonation for Rotation<N, D>
 where
     N: Scalar,
-    CMatrixN<N, Const<D>>: Abomonation,
-    // DefaultAllocator: Allocator<N, D, D>,
+    CMatrixN<N, D>: Abomonation,
 {
     unsafe fn entomb<W: Write>(&self, writer: &mut W) -> IOResult<()> {
         self.matrix.entomb(writer)
@@ -112,8 +108,7 @@ where
 #[cfg(feature = "serde-serialize")]
 impl<N: Scalar, const D: usize> Serialize for Rotation<N, D>
 where
-    // DefaultAllocator: Allocator<N, D, D>,
-    Owned<N, D, D>: Serialize,
+    Owned<N, Const<D>, Const<D>>: Serialize,
 {
     fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
     where
@@ -126,8 +121,7 @@ where
 #[cfg(feature = "serde-serialize")]
 impl<'a, N: Scalar, const D: usize> Deserialize<'a> for Rotation<N, D>
 where
-    // DefaultAllocator: Allocator<N, D, D>,
-    Owned<N, D, D>: Deserialize<'a>,
+    Owned<N, Const<D>, Const<D>>: Deserialize<'a>,
 {
     fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
     where
@@ -286,8 +280,9 @@ impl<N: Scalar, const D: usize> Rotation<N, D>
         // We could use `CMatrixN::to_homogeneous()` here, but that would imply
         // adding the additional traits `DimAdd` and `IsNotStaticOne`. Maybe
         // these things will get nicer once specialization lands in Rust.
-        let mut res = MatrixN::<N, DimNameSum<D, U1>>::identity();
-        res.fixed_slice_mut::<D, D>(0, 0).copy_from(&self.matrix);
+        let mut res = MatrixN::<N, DimNameSum<Const<D>, U1>>::identity();
+        res.fixed_slice_mut::<Const<D>, Const<D>>(0, 0)
+            .copy_from(&self.matrix);
 
         res
     }
@@ -405,7 +400,6 @@ impl<N: Scalar, const D: usize> Rotation<N, D>
 impl<N: SimdRealField, const D: usize> Rotation<N, D>
 where
     N::Element: SimdRealField,
-    // DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
 {
     /// Rotate the given point.
     ///
@@ -521,7 +515,6 @@ impl<N: Scalar + PartialEq, const D: usize> PartialEq for Rotation<N, D>
 impl<N, const D: usize> AbsDiffEq for Rotation<N, D>
 where
     N: Scalar + AbsDiffEq,
-    // DefaultAllocator: Allocator<N, D, D>,
     N::Epsilon: Copy,
 {
     type Epsilon = N::Epsilon;
@@ -540,7 +533,6 @@ where
 impl<N, const D: usize> RelativeEq for Rotation<N, D>
 where
     N: Scalar + RelativeEq,
-    // DefaultAllocator: Allocator<N, D, D>,
     N::Epsilon: Copy,
 {
     #[inline]
@@ -563,7 +555,6 @@ where
 impl<N, const D: usize> UlpsEq for Rotation<N, D>
 where
     N: Scalar + UlpsEq,
-    // DefaultAllocator: Allocator<N, D, D>,
     N::Epsilon: Copy,
 {
     #[inline]
@@ -585,7 +576,6 @@ where
 impl<N, const D: usize> fmt::Display for Rotation<N, D>
 where
     N: RealField + fmt::Display,
-    // DefaultAllocator: Allocator<N, D, D> + Allocator<usize, D, D>,
 {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         let precision = f.precision().unwrap_or(3);
diff --git a/src/geometry/rotation_construction.rs b/src/geometry/rotation_construction.rs
index a144a537..0db4997a 100644
--- a/src/geometry/rotation_construction.rs
+++ b/src/geometry/rotation_construction.rs
@@ -2,7 +2,7 @@ use num::{One, Zero};
 
 use simba::scalar::{ClosedAdd, ClosedMul, SupersetOf};
 
-use crate::base::{MatrixN, Scalar};
+use crate::base::{CMatrixN, Scalar};
 
 use crate::geometry::Rotation;
 
@@ -10,7 +10,6 @@ use crate::geometry::Rotation;
 impl<N, const D: usize> Rotation<N, D>
 where
     N: Scalar + Zero + One,
-    // DefaultAllocator: Allocator<N, D, D>,
 {
     /// Creates a new square identity rotation of the given `dimension`.
     ///
@@ -25,7 +24,7 @@ where
     /// ```
     #[inline]
     pub fn identity() -> Rotation<N, D> {
-        Self::from_matrix_unchecked(MatrixN::<N, D>::identity())
+        Self::from_matrix_unchecked(CMatrixN::<N, D>::identity())
     }
 }
 
@@ -45,7 +44,6 @@ impl<N: Scalar, const D: usize> Rotation<N, D>
     pub fn cast<To: Scalar>(self) -> Rotation<To, D>
     where
         Rotation<To, D>: SupersetOf<Self>,
-        // DefaultAllocator: Allocator<To, D, D>,
     {
         crate::convert(self)
     }
@@ -54,7 +52,6 @@ impl<N: Scalar, const D: usize> Rotation<N, D>
 impl<N, const D: usize> One for Rotation<N, D>
 where
     N: Scalar + Zero + One + ClosedAdd + ClosedMul,
-    // DefaultAllocator: Allocator<N, D, D>,
 {
     #[inline]
     fn one() -> Self {
diff --git a/src/geometry/rotation_conversion.rs b/src/geometry/rotation_conversion.rs
index 14cb296b..02285419 100644
--- a/src/geometry/rotation_conversion.rs
+++ b/src/geometry/rotation_conversion.rs
@@ -5,7 +5,7 @@ use simba::simd::{PrimitiveSimdValue, SimdValue};
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimMin, DimNameAdd, DimNameSum, U1};
-use crate::base::{Const, DefaultAllocator, Matrix2, Matrix3, Matrix4, MatrixN, Scalar};
+use crate::base::{CMatrixN, Const, DefaultAllocator, Matrix2, Matrix3, Matrix4, MatrixN, Scalar};
 
 use crate::geometry::{
     AbstractRotation, Isometry, Rotation, Rotation2, Rotation3, Similarity, SuperTCategoryOf,
@@ -31,7 +31,6 @@ impl<N1, N2, const D: usize> SubsetOf<Rotation<N2, D>> for Rotation<N1, D>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
-    // DefaultAllocator: Allocator<N1, D, D> + Allocator<N2, D, D>,
 {
     #[inline]
     fn to_superset(&self) -> Rotation<N2, D> {
@@ -40,7 +39,7 @@ where
 
     #[inline]
     fn is_in_subset(rot: &Rotation<N2, D>) -> bool {
-        crate::is_convertible::<_, MatrixN<N1, D>>(rot.matrix())
+        crate::is_convertible::<_, CMatrixN<N1, D>>(rot.matrix())
     }
 
     #[inline]
@@ -125,7 +124,6 @@ where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
     R: AbstractRotation<N2, D> + SupersetOf<Self>,
-    // DefaultAllocator: Allocator<N1, D, D> + Allocator<N2, D>,
 {
     #[inline]
     fn to_superset(&self) -> Isometry<N2, R, D> {
@@ -148,7 +146,6 @@ where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
     R: AbstractRotation<N2, D> + SupersetOf<Self>,
-    // DefaultAllocator: Allocator<N1, D, D> + Allocator<N2, D>,
 {
     #[inline]
     fn to_superset(&self) -> Similarity<N2, R, D> {
@@ -213,8 +210,8 @@ where
 
     #[inline]
     fn is_in_subset(m: &MatrixN<N2, DimNameSum<Const<D>, U1>>) -> bool {
-        let rot = m.fixed_slice::<D, D>(0, 0);
-        let bottom = m.fixed_slice::<U1, D>(D, 0);
+        let rot = m.fixed_slice::<Const<D>, Const<D>>(0, 0);
+        let bottom = m.fixed_slice::<U1, Const<D>>(D, 0);
 
         // Scalar types agree.
         m.iter().all(|e| SupersetOf::<N1>::is_in_subset(e)) &&
@@ -226,7 +223,7 @@ where
 
     #[inline]
     fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<Const<D>, U1>>) -> Self {
-        let r = m.fixed_slice::<D, D>(0, 0);
+        let r = m.fixed_slice::<Const<D>, Const<D>>(0, 0);
         Self::from_matrix_unchecked(crate::convert_unchecked(r.into_owned()))
     }
 }
@@ -264,7 +261,6 @@ impl<N: Scalar + PrimitiveSimdValue, const D: usize> From<[Rotation<N::Element,
 where
     N: From<[<N as SimdValue>::Element; 2]>,
     N::Element: Scalar + Copy,
-    // DefaultAllocator: Allocator<N, D, D> + Allocator<N::Element, D, D>,
 {
     #[inline]
     fn from(arr: [Rotation<N::Element, D>; 2]) -> Self {
@@ -280,7 +276,6 @@ impl<N: Scalar + PrimitiveSimdValue, const D: usize> From<[Rotation<N::Element,
 where
     N: From<[<N as SimdValue>::Element; 4]>,
     N::Element: Scalar + Copy,
-    // DefaultAllocator: Allocator<N, D, D> + Allocator<N::Element, D, D>,
 {
     #[inline]
     fn from(arr: [Rotation<N::Element, D>; 4]) -> Self {
@@ -298,7 +293,6 @@ impl<N: Scalar + PrimitiveSimdValue, const D: usize> From<[Rotation<N::Element,
 where
     N: From<[<N as SimdValue>::Element; 8]>,
     N::Element: Scalar + Copy,
-    // DefaultAllocator: Allocator<N, D, D> + Allocator<N::Element, D, D>,
 {
     #[inline]
     fn from(arr: [Rotation<N::Element, D>; 8]) -> Self {
@@ -320,7 +314,6 @@ impl<N: Scalar + PrimitiveSimdValue, const D: usize> From<[Rotation<N::Element,
 where
     N: From<[<N as SimdValue>::Element; 16]>,
     N::Element: Scalar + Copy,
-    // DefaultAllocator: Allocator<N, D, D> + Allocator<N::Element, D, D>,
 {
     #[inline]
     fn from(arr: [Rotation<N::Element, D>; 16]) -> Self {
diff --git a/src/geometry/rotation_ops.rs b/src/geometry/rotation_ops.rs
index ae66c02e..4821328d 100644
--- a/src/geometry/rotation_ops.rs
+++ b/src/geometry/rotation_ops.rs
@@ -24,16 +24,15 @@ use simba::scalar::{ClosedAdd, ClosedMul};
 
 use crate::base::allocator::Allocator;
 use crate::base::constraint::{AreMultipliable, ShapeConstraint};
-use crate::base::dimension::{Dim, DimName, U1};
+use crate::base::dimension::{Dim, U1};
 use crate::base::storage::Storage;
-use crate::base::{DefaultAllocator, Matrix, MatrixMN, Scalar, Unit, Vector, VectorN};
+use crate::base::{
+    CMatrixMN, CVectorN, Const, DefaultAllocator, Matrix, MatrixMN, Scalar, Unit, Vector,
+};
 
 use crate::geometry::{Point, Rotation};
 
-impl<N: Scalar, D: DimName> Index<(usize, usize)> for Rotation<N, D>
-where
-    DefaultAllocator: Allocator<N, D, D>,
-{
+impl<N: Scalar, const D: usize> Index<(usize, usize)> for Rotation<N, D> {
     type Output = N;
 
     #[inline]
@@ -45,7 +44,10 @@ where
 // Rotation × Rotation
 md_impl_all!(
     Mul, mul;
-    (D, D), (D, D) for D: DimName;
+    (Const<D>, Const<D>), (Const<D>, Const<D>)
+    const D;
+    for;
+    where;
     self: Rotation<N, D>, right: Rotation<N, D>, Output = Rotation<N, D>;
     [val val] => Rotation::from_matrix_unchecked(self.into_inner() * right.into_inner());
     [ref val] => Rotation::from_matrix_unchecked(self.matrix() * right.into_inner());
@@ -57,7 +59,10 @@ md_impl_all!(
 // TODO: instead of calling inverse explicitly, could we just add a `mul_tr` or `mul_inv` method?
 md_impl_all!(
     Div, div;
-    (D, D), (D, D) for D: DimName;
+    (Const<D>, Const<D>), (Const<D>, Const<D>)
+    const D;
+    for;
+    where;
     self: Rotation<N, D>, right: Rotation<N, D>, Output = Rotation<N, D>;
     [val val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * right.inverse() };
     [ref val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * right.inverse() };
@@ -68,10 +73,13 @@ md_impl_all!(
 // Rotation × Matrix
 md_impl_all!(
     Mul, mul;
-    (D1, D1), (R2, C2) for D1: DimName, R2: Dim, C2: Dim, SB: Storage<N, R2, C2>
-    where DefaultAllocator: Allocator<N, D1, C2>
-    where ShapeConstraint: AreMultipliable<D1, D1, R2, C2>;
-    self: Rotation<N, D1>, right: Matrix<N, R2, C2, SB>, Output = MatrixMN<N, D1, C2>;
+    (Const<D1>, Const<D1>), (R2, C2)
+    const D1;
+    for R2, C2, SB;
+    where R2: Dim, C2: Dim, SB: Storage<N, R2, C2>,
+          DefaultAllocator: Allocator<N, Const<D1>, C2>,
+          ShapeConstraint: AreMultipliable<Const<D1>, Const<D1>, R2, C2>;
+    self: Rotation<N, D1>, right: Matrix<N, R2, C2, SB>, Output = MatrixMN<N, Const<D1>, C2>;
     [val val] => self.into_inner() * right;
     [ref val] => self.matrix() * right;
     [val ref] => self.into_inner() * right;
@@ -81,10 +89,13 @@ md_impl_all!(
 // Matrix × Rotation
 md_impl_all!(
     Mul, mul;
-    (R1, C1), (D2, D2) for R1: Dim, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>
-    where DefaultAllocator: Allocator<N, R1, D2>
-    where ShapeConstraint:  AreMultipliable<R1, C1, D2, D2>;
-    self: Matrix<N, R1, C1, SA>, right: Rotation<N, D2>, Output = MatrixMN<N, R1, D2>;
+    (R1, C1), (Const<D2>, Const<D2>)
+    const D2;
+    for R1, C1, SA;
+    where R1: Dim, C1: Dim, SA: Storage<N, R1, C1>,
+          DefaultAllocator: Allocator<N, R1, Const<D2>>,
+          ShapeConstraint:  AreMultipliable<R1, C1, Const<D2>, Const<D2>>;
+    self: Matrix<N, R1, C1, SA>, right: Rotation<N, D2>, Output = MatrixMN<N, R1, Const<D2>>;
     [val val] => self * right.into_inner();
     [ref val] => self * right.into_inner();
     [val ref] => self * right.matrix();
@@ -94,10 +105,13 @@ md_impl_all!(
 // Matrix ÷ Rotation
 md_impl_all!(
     Div, div;
-    (R1, C1), (D2, D2) for R1: Dim, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>
-    where DefaultAllocator: Allocator<N, R1, D2>
-    where ShapeConstraint: AreMultipliable<R1, C1, D2, D2>;
-    self: Matrix<N, R1, C1, SA>, right: Rotation<N, D2>, Output = MatrixMN<N, R1, D2>;
+    (R1, C1), (Const<D2>, Const<D2>)
+    const D2;
+    for R1, C1, SA;
+    where R1: Dim, C1: Dim, SA: Storage<N, R1, C1>,
+          DefaultAllocator: Allocator<N, R1, Const<D2>>,
+          ShapeConstraint: AreMultipliable<R1, C1, Const<D2>, Const<D2>>;
+    self: Matrix<N, R1, C1, SA>, right: Rotation<N, D2>, Output = MatrixMN<N, R1, Const<D2>>;
     [val val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * right.inverse() };
     [ref val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * right.inverse() };
     [val ref] => #[allow(clippy::suspicious_arithmetic_impl)] { self * right.inverse() };
@@ -109,9 +123,10 @@ md_impl_all!(
 // behavior?
 md_impl_all!(
     Mul, mul;
-    (D, D), (D, U1) for D: DimName
-    where DefaultAllocator: Allocator<N, D>
-    where ShapeConstraint:  AreMultipliable<D, D, D, U1>;
+    (Const<D>, Const<D>), (Const<D>, U1)
+    const D;
+    for;
+    where ShapeConstraint:  AreMultipliable<Const<D>, Const<D>, Const<D>, U1>;
     self: Rotation<N, D>, right: Point<N, D>, Output = Point<N, D>;
     [val val] => self.into_inner() * right;
     [ref val] => self.matrix() * right;
@@ -122,10 +137,12 @@ md_impl_all!(
 // Rotation × Unit<Vector>
 md_impl_all!(
     Mul, mul;
-    (D, D), (D, U1) for D: DimName, S: Storage<N, D>
-    where DefaultAllocator: Allocator<N, D>
-    where ShapeConstraint:  AreMultipliable<D, D, D, U1>;
-    self: Rotation<N, D>, right: Unit<Vector<N, D, S>>, Output = Unit<VectorN<N, D>>;
+    (Const<D>, Const<D>), (Const<D>, U1)
+    const D;
+    for S;
+    where S: Storage<N, Const<D>>,
+          ShapeConstraint: AreMultipliable<Const<D>, Const<D>, Const<D>, U1>;
+    self: Rotation<N, D>, right: Unit<Vector<N, Const<D>, S>>, Output = Unit<CVectorN<N, D>>;
     [val val] => Unit::new_unchecked(self.into_inner() * right.into_inner());
     [ref val] => Unit::new_unchecked(self.matrix() * right.into_inner());
     [val ref] => Unit::new_unchecked(self.into_inner() * right.as_ref());
@@ -137,7 +154,8 @@ md_impl_all!(
 
 md_assign_impl_all!(
     MulAssign, mul_assign;
-    (D, D), (D, D) for D: DimName;
+    (Const<D>, Const<D>), (Const<D>, Const<D>)
+    const D; for; where;
     self: Rotation<N, D>, right: Rotation<N, D>;
     [val] => self.matrix_mut_unchecked().mul_assign(right.into_inner());
     [ref] => self.matrix_mut_unchecked().mul_assign(right.matrix());
@@ -145,7 +163,8 @@ md_assign_impl_all!(
 
 md_assign_impl_all!(
     DivAssign, div_assign;
-    (D, D), (D, D) for D: DimName;
+    (Const<D>, Const<D>), (Const<D>, Const<D>)
+    const D; for; where;
     self: Rotation<N, D>, right: Rotation<N, D>;
     [val] => self.matrix_mut_unchecked().mul_assign(right.inverse().into_inner());
     [ref] => self.matrix_mut_unchecked().mul_assign(right.inverse().matrix());
@@ -159,16 +178,18 @@ md_assign_impl_all!(
 
 md_assign_impl_all!(
     MulAssign, mul_assign;
-    (R1, C1), (C1, C1) for R1: DimName, C1: DimName;
-    self: MatrixMN<N, R1, C1>, right: Rotation<N, C1>;
+    (Const<R1>, Const<C1>), (Const<C1>, Const<C1>)
+    const R1, C1; for; where;
+    self: CMatrixMN<N, R1, C1>, right: Rotation<N, C1>;
     [val] => self.mul_assign(right.into_inner());
     [ref] => self.mul_assign(right.matrix());
 );
 
 md_assign_impl_all!(
     DivAssign, div_assign;
-    (R1, C1), (C1, C1) for R1: DimName, C1: DimName;
-    self: MatrixMN<N, R1, C1>, right: Rotation<N, C1>;
+    (Const<R1>, Const<C1>), (Const<C1>, Const<C1>)
+    const R1, C1; for; where;
+    self: CMatrixMN<N, R1, C1>, right: Rotation<N, C1>;
     [val] => self.mul_assign(right.inverse().into_inner());
     [ref] => self.mul_assign(right.inverse().matrix());
 );
diff --git a/src/geometry/rotation_simba.rs b/src/geometry/rotation_simba.rs
index 319fcc3c..cb0aa13b 100755
--- a/src/geometry/rotation_simba.rs
+++ b/src/geometry/rotation_simba.rs
@@ -8,7 +8,6 @@ impl<N, const D: usize> SimdValue for Rotation<N, D>
 where
     N: Scalar + SimdValue,
     N::Element: Scalar,
-    // DefaultAllocator: Allocator<N, D, D> + Allocator<N::Element, D, D>,
 {
     type Element = Rotation<N::Element, D>;
     type SimdBool = N::SimdBool;
diff --git a/src/geometry/similarity.rs b/src/geometry/similarity.rs
index 81203fb9..8e813456 100755
--- a/src/geometry/similarity.rs
+++ b/src/geometry/similarity.rs
@@ -29,15 +29,15 @@ use crate::geometry::{AbstractRotation, Isometry, Point, Translation};
     feature = "serde-serialize",
     serde(bound(serialize = "N: Serialize,
                      R: Serialize,
-                     DefaultAllocator: Allocator<N, D>,
-                     Owned<N, D>: Serialize"))
+                     DefaultAllocator: Allocator<N, Const<D>>,
+                     Owned<N, Const<D>>: Serialize"))
 )]
 #[cfg_attr(
     feature = "serde-serialize",
     serde(bound(deserialize = "N: Deserialize<'de>,
                        R: Deserialize<'de>,
-                       DefaultAllocator: Allocator<N, D>,
-                       Owned<N, D>: Deserialize<'de>"))
+                       DefaultAllocator: Allocator<N, Const<D>>,
+                       Owned<N, Const<D>>: Deserialize<'de>"))
 )]
 pub struct Similarity<N: Scalar, R, const D: usize>
 // where
@@ -52,7 +52,6 @@ pub struct Similarity<N: Scalar, R, const D: usize>
 impl<N: Scalar, R, const D: usize> Abomonation for Similarity<N, R, D>
 where
     Isometry<N, R, D>: Abomonation,
-    // DefaultAllocator: Allocator<N, D>,
 {
     unsafe fn entomb<W: Write>(&self, writer: &mut W) -> IOResult<()> {
         self.isometry.entomb(writer)
@@ -69,7 +68,6 @@ where
 
 impl<N: Scalar + hash::Hash, R: hash::Hash, const D: usize> hash::Hash for Similarity<N, R, D>
 where
-    // DefaultAllocator: Allocator<N, D>,
     Owned<N, Const<D>>: hash::Hash,
 {
     fn hash<H: hash::Hasher>(&self, state: &mut H) {
@@ -81,7 +79,6 @@ where
 impl<N: Scalar + Copy + Zero, R: AbstractRotation<N, D> + Copy, const D: usize> Copy
     for Similarity<N, R, D>
 where
-    // DefaultAllocator: Allocator<N, D>,
     Owned<N, Const<D>>: Copy,
 {
 }
@@ -100,7 +97,6 @@ impl<N: Scalar + Zero, R: AbstractRotation<N, D> + Clone, const D: usize> Clone
 impl<N: Scalar + Zero, R, const D: usize> Similarity<N, R, D>
 where
     R: AbstractRotation<N, D>,
-    // DefaultAllocator: Allocator<N, D>,
 {
     /// Creates a new similarity from its rotational and translational parts.
     #[inline]
@@ -143,7 +139,6 @@ impl<N: SimdRealField, R, const D: usize> Similarity<N, R, D>
 where
     N::Element: SimdRealField,
     R: AbstractRotation<N, D>,
-    // DefaultAllocator: Allocator<N, D>,
 {
     /// Creates a new similarity that applies only a scaling factor.
     #[inline]
@@ -345,7 +340,7 @@ impl<N: SimdRealField, R, const D: usize> Similarity<N, R, D>
     {
         let mut res = self.isometry.to_homogeneous();
 
-        for e in res.fixed_slice_mut::<D, D>(0, 0).iter_mut() {
+        for e in res.fixed_slice_mut::<Const<D>, Const<D>>(0, 0).iter_mut() {
             *e *= self.scaling
         }
 
@@ -354,14 +349,13 @@ impl<N: SimdRealField, R, const D: usize> Similarity<N, R, D>
 }
 
 impl<N: SimdRealField, R, const D: usize> Eq for Similarity<N, R, D> where
-    R: AbstractRotation<N, D> + Eq // DefaultAllocator: Allocator<N, D>,
+    R: AbstractRotation<N, D> + Eq
 {
 }
 
 impl<N: SimdRealField, R, const D: usize> PartialEq for Similarity<N, R, D>
 where
     R: AbstractRotation<N, D> + PartialEq,
-    // DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     fn eq(&self, right: &Self) -> bool {
@@ -372,7 +366,6 @@ where
 impl<N: RealField, R, const D: usize> AbsDiffEq for Similarity<N, R, D>
 where
     R: AbstractRotation<N, D> + AbsDiffEq<Epsilon = N::Epsilon>,
-    // DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {
     type Epsilon = N::Epsilon;
@@ -392,7 +385,6 @@ where
 impl<N: RealField, R, const D: usize> RelativeEq for Similarity<N, R, D>
 where
     R: AbstractRotation<N, D> + RelativeEq<Epsilon = N::Epsilon>,
-    // DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {
     #[inline]
@@ -441,7 +433,6 @@ impl<N, R, const D: usize> fmt::Display for Similarity<N, R, D>
 where
     N: RealField + fmt::Display,
     R: AbstractRotation<N, D> + fmt::Display,
-    // DefaultAllocator: Allocator<N, D> + Allocator<usize, D>,
 {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         let precision = f.precision().unwrap_or(3);
diff --git a/src/geometry/similarity_construction.rs b/src/geometry/similarity_construction.rs
index 91e4c228..00847367 100644
--- a/src/geometry/similarity_construction.rs
+++ b/src/geometry/similarity_construction.rs
@@ -16,7 +16,7 @@ use simba::simd::SimdRealField;
 use crate::base::{Vector2, Vector3};
 
 use crate::{
-    AbstractRotation, Isometry, Point, Point3, Rotation2, Rotation3, Scalar, Similarity,
+    AbstractRotation, Const, Isometry, Point, Point3, Rotation2, Rotation3, Scalar, Similarity,
     Translation, UnitComplex, UnitQuaternion,
 };
 
@@ -24,7 +24,6 @@ impl<N: SimdRealField, R, const D: usize> Similarity<N, R, D>
 where
     N::Element: SimdRealField,
     R: AbstractRotation<N, D>,
-    // DefaultAllocator: Allocator<N, D>,
 {
     /// Creates a new identity similarity.
     ///
@@ -51,7 +50,6 @@ impl<N: SimdRealField, R, const D: usize> One for Similarity<N, R, D>
 where
     N::Element: SimdRealField,
     R: AbstractRotation<N, D>,
-    // DefaultAllocator: Allocator<N, D>,
 {
     /// Creates a new identity similarity.
     #[inline]
@@ -64,7 +62,6 @@ where
 impl<N: crate::RealField, R, const D: usize> Distribution<Similarity<N, R, D>> for Standard
 where
     R: AbstractRotation<N, D>,
-    // DefaultAllocator: Allocator<N, D>,
     Standard: Distribution<N> + Distribution<R>,
 {
     /// Generate an arbitrary random variate for testing purposes.
@@ -83,7 +80,6 @@ impl<N: SimdRealField, R, const D: usize> Similarity<N, R, D>
 where
     N::Element: SimdRealField,
     R: AbstractRotation<N, D>,
-    // DefaultAllocator: Allocator<N, D>,
 {
     /// The similarity that applies the scaling factor `scaling`, followed by the rotation `r` with
     /// its axis passing through the point `p`.
@@ -113,8 +109,7 @@ where
     N: crate::RealField + Arbitrary + Send,
     N::Element: crate::RealField,
     R: AbstractRotation<N, D> + Arbitrary + Send,
-    // DefaultAllocator: Allocator<N, D>,
-    Owned<N, D>: Send,
+    Owned<N, Const<D>>: Send,
 {
     #[inline]
     fn arbitrary(rng: &mut Gen) -> Self {
@@ -394,7 +389,7 @@ macro_rules! similarity_construction_impl(
                               up:      &Vector3<N>,
                               scaling: N)
                               -> Self {
-                Self::from_isometry(Isometry::<_, $Rot<N>, _>::look_at_lh(eye, target, up), scaling)
+                Self::from_isometry(Isometry::<_, $Rot<N>, 3>::look_at_lh(eye, target, up), scaling)
             }
         }
     }
diff --git a/src/geometry/similarity_conversion.rs b/src/geometry/similarity_conversion.rs
index 723d27dd..d22d4e3e 100644
--- a/src/geometry/similarity_conversion.rs
+++ b/src/geometry/similarity_conversion.rs
@@ -26,7 +26,6 @@ where
     N2: RealField + SupersetOf<N1>,
     R1: AbstractRotation<N1, D> + SubsetOf<R2>,
     R2: AbstractRotation<N2, D>,
-    // DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
 {
     #[inline]
     fn to_superset(&self) -> Similarity<N2, R2, D> {
@@ -106,7 +105,7 @@ where
 
     #[inline]
     fn is_in_subset(m: &MatrixN<N2, DimNameSum<Const<D>, U1>>) -> bool {
-        let mut rot = m.fixed_slice::<D, D>(0, 0).clone_owned();
+        let mut rot = m.fixed_slice::<Const<D>, Const<D>>(0, 0).clone_owned();
         if rot
             .fixed_columns_mut::<U1>(0)
             .try_normalize_mut(N2::zero())
@@ -128,7 +127,7 @@ where
                 rot.fixed_columns_mut::<U1>(2).neg_mut();
             }
 
-            let bottom = m.fixed_slice::<U1, D>(D, 0);
+            let bottom = m.fixed_slice::<U1, Const<D>>(D, 0);
             // Scalar types agree.
             m.iter().all(|e| SupersetOf::<N1>::is_in_subset(e)) &&
             // The normalized block part is a rotation.
@@ -143,22 +142,22 @@ where
     #[inline]
     fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<Const<D>, U1>>) -> Self {
         let mut mm = m.clone_owned();
-        let na = mm.fixed_slice_mut::<D, U1>(0, 0).normalize_mut();
-        let nb = mm.fixed_slice_mut::<D, U1>(0, 1).normalize_mut();
-        let nc = mm.fixed_slice_mut::<D, U1>(0, 2).normalize_mut();
+        let na = mm.fixed_slice_mut::<Const<D>, U1>(0, 0).normalize_mut();
+        let nb = mm.fixed_slice_mut::<Const<D>, U1>(0, 1).normalize_mut();
+        let nc = mm.fixed_slice_mut::<Const<D>, U1>(0, 2).normalize_mut();
 
         let mut scale = (na + nb + nc) / crate::convert(3.0); // We take the mean, for robustness.
 
         // TODO: could we avoid the explicit computation of the determinant?
         // (its sign is needed to see if the scaling factor is negative).
-        if mm.fixed_slice::<D, D>(0, 0).determinant() < N2::zero() {
-            mm.fixed_slice_mut::<D, U1>(0, 0).neg_mut();
-            mm.fixed_slice_mut::<D, U1>(0, 1).neg_mut();
-            mm.fixed_slice_mut::<D, U1>(0, 2).neg_mut();
+        if mm.fixed_slice::<Const<D>, Const<D>>(0, 0).determinant() < N2::zero() {
+            mm.fixed_slice_mut::<Const<D>, U1>(0, 0).neg_mut();
+            mm.fixed_slice_mut::<Const<D>, U1>(0, 1).neg_mut();
+            mm.fixed_slice_mut::<Const<D>, U1>(0, 2).neg_mut();
             scale = -scale;
         }
 
-        let t = m.fixed_slice::<D, U1>(0, D).into_owned();
+        let t = m.fixed_slice::<Const<D>, U1>(0, D).into_owned();
         let t = Translation {
             vector: crate::convert_unchecked(t),
         };
@@ -192,7 +191,6 @@ where
     R::Element: AbstractRotation<N::Element, D>,
     N::Element: Scalar + Zero + Copy,
     R::Element: Scalar + Zero + Copy,
-    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     #[inline]
     fn from(arr: [Similarity<N::Element, R::Element, D>; 2]) -> Self {
@@ -211,7 +209,6 @@ where
     R::Element: AbstractRotation<N::Element, D>,
     N::Element: Scalar + Zero + Copy,
     R::Element: Scalar + Zero + Copy,
-    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     #[inline]
     fn from(arr: [Similarity<N::Element, R::Element, D>; 4]) -> Self {
@@ -240,7 +237,6 @@ where
     R::Element: AbstractRotation<N::Element, D>,
     N::Element: Scalar + Zero + Copy,
     R::Element: Scalar + Zero + Copy,
-    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     #[inline]
     fn from(arr: [Similarity<N::Element, R::Element, D>; 8]) -> Self {
@@ -277,7 +273,6 @@ where
     R::Element: AbstractRotation<N::Element, D>,
     N::Element: Scalar + Zero + Copy,
     R::Element: Scalar + Zero + Copy,
-    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     #[inline]
     fn from(arr: [Similarity<N::Element, R::Element, D>; 16]) -> Self {
diff --git a/src/geometry/similarity_ops.rs b/src/geometry/similarity_ops.rs
index 4c821e21..b1818f4a 100644
--- a/src/geometry/similarity_ops.rs
+++ b/src/geometry/similarity_ops.rs
@@ -5,8 +5,8 @@ use simba::scalar::{ClosedAdd, ClosedMul};
 use simba::simd::SimdRealField;
 
 use crate::base::allocator::Allocator;
-use crate::base::dimension::{DimName, U1, U2, U3, U4};
-use crate::base::{DefaultAllocator, Scalar, VectorN};
+use crate::base::dimension::{U1, U2, U3};
+use crate::base::{CVectorN, Const, DefaultAllocator, Scalar};
 
 use crate::geometry::{
     AbstractRotation, Isometry, Point, Rotation, Similarity, Translation, UnitComplex,
@@ -70,10 +70,9 @@ macro_rules! similarity_binop_impl(
     ($Op: ident, $op: ident;
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Output: ty;
      $action: expr; $($lives: tt),*) => {
-        impl<$($lives ,)* N: SimdRealField, D: DimName, R> $Op<$Rhs> for $Lhs
+        impl<$($lives ,)* N: SimdRealField, R, const D: usize> $Op<$Rhs> for $Lhs
             where N::Element: SimdRealField,
-                  R: AbstractRotation<N, D>,
-                  DefaultAllocator: Allocator<N, D> {
+                  R: AbstractRotation<N, D> {
             type Output = $Output;
 
             #[inline]
@@ -118,20 +117,18 @@ macro_rules! similarity_binop_assign_impl_all(
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty;
      [val] => $action_val: expr;
      [ref] => $action_ref: expr;) => {
-        impl<N: SimdRealField, D: DimName, R> $OpAssign<$Rhs> for $Lhs
+        impl<N: SimdRealField, R, const D: usize> $OpAssign<$Rhs> for $Lhs
             where N::Element: SimdRealField,
-                  R: AbstractRotation<N, D>,
-                  DefaultAllocator: Allocator<N, D> {
+                  R: AbstractRotation<N, D>{
             #[inline]
             fn $op_assign(&mut $lhs, $rhs: $Rhs) {
                 $action_val
             }
         }
 
-        impl<'b, N: SimdRealField, D: DimName, R> $OpAssign<&'b $Rhs> for $Lhs
+        impl<'b, N: SimdRealField, R, const D: usize> $OpAssign<&'b $Rhs> for $Lhs
             where N::Element: SimdRealField,
-                  R: AbstractRotation<N, D>,
-                  DefaultAllocator: Allocator<N, D> {
+                  R: AbstractRotation<N, D> {
             #[inline]
             fn $op_assign(&mut $lhs, $rhs: &'b $Rhs) {
                 $action_ref
@@ -220,16 +217,18 @@ similarity_binop_assign_impl_all!(
 // Similarity ÷= R
 md_assign_impl_all!(
     MulAssign, mul_assign where N: SimdRealField for N::Element: SimdRealField;
-    (D, U1), (D, D) for D: DimName;
-    self: Similarity<N, D, Rotation<N, D>>, rhs: Rotation<N, D>;
+    (Const<D>, U1), (Const<D>, Const<D>)
+    const D; for; where;
+    self: Similarity<N, Rotation<N, D>, D>, rhs: Rotation<N, D>;
     [val] => self.isometry.rotation *= rhs;
     [ref] => self.isometry.rotation *= rhs.clone();
 );
 
 md_assign_impl_all!(
     DivAssign, div_assign where N: SimdRealField for N::Element: SimdRealField;
-    (D, U1), (D, D) for D: DimName;
-    self: Similarity<N, D, Rotation<N, D>>, rhs: Rotation<N, D>;
+    (Const<D>, U1), (Const<D>, Const<D>)
+    const D; for; where;
+    self: Similarity<N, Rotation<N, D>, D>, rhs: Rotation<N, D>;
     // TODO: don't invert explicitly?
     [val] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
     [ref] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
@@ -237,7 +236,8 @@ md_assign_impl_all!(
 
 md_assign_impl_all!(
     MulAssign, mul_assign where N: SimdRealField for N::Element: SimdRealField;
-    (U3, U3), (U3, U3) for;
+    (U3, U3), (U3, U3)
+    const; for; where;
     self: Similarity<N, UnitQuaternion<N>, 3>, rhs: UnitQuaternion<N>;
     [val] => self.isometry.rotation *= rhs;
     [ref] => self.isometry.rotation *= *rhs;
@@ -245,7 +245,8 @@ md_assign_impl_all!(
 
 md_assign_impl_all!(
     DivAssign, div_assign where N: SimdRealField for N::Element: SimdRealField;
-    (U3, U3), (U3, U3) for;
+    (U3, U3), (U3, U3)
+    const; for; where;
     self: Similarity<N, UnitQuaternion<N>, 3>, rhs: UnitQuaternion<N>;
     // TODO: don't invert explicitly?
     [val] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
@@ -254,16 +255,18 @@ md_assign_impl_all!(
 
 md_assign_impl_all!(
     MulAssign, mul_assign where N: SimdRealField for N::Element: SimdRealField;
-    (U2, U2), (U2, U2) for;
-    self: Similarity<N, U2, UnitComplex<N>>, rhs: UnitComplex<N>;
+    (U2, U2), (U2, U2)
+    const; for; where;
+    self: Similarity<N, UnitComplex<N>, 2>, rhs: UnitComplex<N>;
     [val] => self.isometry.rotation *= rhs;
     [ref] => self.isometry.rotation *= *rhs;
 );
 
 md_assign_impl_all!(
     DivAssign, div_assign where N: SimdRealField for N::Element: SimdRealField;
-    (U2, U2), (U2, U2) for;
-    self: Similarity<N, U2, UnitComplex<N>>, rhs: UnitComplex<N>;
+    (U2, U2), (U2, U2)
+    const; for; where;
+    self: Similarity<N, UnitComplex<N>, 2>, rhs: UnitComplex<N>;
     // TODO: don't invert explicitly?
     [val] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
     [ref] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
@@ -347,7 +350,7 @@ similarity_binop_impl_all!(
 // Similarity × Vector
 similarity_binop_impl_all!(
     Mul, mul;
-    self: Similarity<N, R, D>, right: VectorN<N, D>, Output = VectorN<N, D>;
+    self: Similarity<N, R, D>, right: CVectorN<N, D>, Output = CVectorN<N, D>;
     [val val] => self.isometry.rotation.transform_vector(&right) * self.scaling();
     [ref val] => self.isometry.rotation.transform_vector(&right) * self.scaling();
     [val ref] => self.isometry.rotation.transform_vector(right) * self.scaling();
@@ -389,13 +392,11 @@ similarity_binop_impl_all!(
 
 macro_rules! similarity_from_composition_impl(
     ($Op: ident, $op: ident;
-     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) $(for $Dims: ident: $DimsBound: ident),*;
+     $($Dims: ident),*;
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Output: ty;
      $action: expr; $($lives: tt),*) => {
-        impl<$($lives ,)* N: SimdRealField $(, $Dims: $DimsBound)*> $Op<$Rhs> for $Lhs
-            where N::Element: SimdRealField,
-                  DefaultAllocator: Allocator<N, $R1, $C1> +
-                                    Allocator<N, $R2, $C2> {
+        impl<$($lives ,)* N: SimdRealField $(, const $Dims: usize)*> $Op<$Rhs> for $Lhs
+            where N::Element: SimdRealField {
             type Output = $Output;
 
             #[inline]
@@ -408,7 +409,7 @@ macro_rules! similarity_from_composition_impl(
 
 macro_rules! similarity_from_composition_impl_all(
     ($Op: ident, $op: ident;
-     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) $(for $Dims: ident: $DimsBound: ident),*;
+     $($Dims: ident),*;
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Output: ty;
      [val val] => $action_val_val: expr;
      [ref val] => $action_ref_val: expr;
@@ -417,25 +418,25 @@ macro_rules! similarity_from_composition_impl_all(
 
         similarity_from_composition_impl!(
             $Op, $op;
-            ($R1, $C1),($R2, $C2) $(for $Dims: $DimsBound),*;
+            $($Dims),*;
             $lhs: $Lhs, $rhs: $Rhs, Output = $Output;
             $action_val_val; );
 
         similarity_from_composition_impl!(
             $Op, $op;
-            ($R1, $C1),($R2, $C2) $(for $Dims: $DimsBound),*;
+            $($Dims),*;
             $lhs: &'a $Lhs, $rhs: $Rhs, Output = $Output;
             $action_ref_val; 'a);
 
         similarity_from_composition_impl!(
             $Op, $op;
-            ($R1, $C1),($R2, $C2) $(for $Dims: $DimsBound),*;
+            $($Dims),*;
             $lhs: $Lhs, $rhs: &'b $Rhs, Output = $Output;
             $action_val_ref; 'b);
 
         similarity_from_composition_impl!(
             $Op, $op;
-            ($R1, $C1),($R2, $C2) $(for $Dims: $DimsBound),*;
+            $($Dims),*;
             $lhs: &'a $Lhs, $rhs: &'b $Rhs, Output = $Output;
             $action_ref_ref; 'a, 'b);
     }
@@ -444,9 +445,9 @@ macro_rules! similarity_from_composition_impl_all(
 // Similarity × Rotation
 similarity_from_composition_impl_all!(
     Mul, mul;
-    (D, D), (D, U1) for D: DimName;
-    self: Similarity<N, D, Rotation<N, D>>, rhs: Rotation<N, D>,
-    Output = Similarity<N, D, Rotation<N, D>>;
+    D;
+    self: Similarity<N, Rotation<N, D>, D>, rhs: Rotation<N, D>,
+    Output = Similarity<N, Rotation<N, D>, D>;
     [val val] => {
         let scaling = self.scaling();
         Similarity::from_isometry(self.isometry * rhs, scaling)
@@ -462,9 +463,9 @@ similarity_from_composition_impl_all!(
 // Rotation × Similarity
 similarity_from_composition_impl_all!(
     Mul, mul;
-    (D, D), (D, U1) for D: DimName;
-    self: Rotation<N, D>, right: Similarity<N, D, Rotation<N, D>>,
-    Output = Similarity<N, D, Rotation<N, D>>;
+    D;
+    self: Rotation<N, D>, right: Similarity<N, Rotation<N, D>, D>,
+    Output = Similarity<N, Rotation<N, D>, D>;
     [val val] => &self * &right;
     [ref val] =>  self * &right;
     [val ref] => &self *  right;
@@ -474,9 +475,9 @@ similarity_from_composition_impl_all!(
 // Similarity ÷ Rotation
 similarity_from_composition_impl_all!(
     Div, div;
-    (D, D), (D, U1) for D: DimName;
-    self: Similarity<N, D, Rotation<N, D>>, rhs: Rotation<N, D>,
-    Output = Similarity<N, D, Rotation<N, D>>;
+    D;
+    self: Similarity<N, Rotation<N, D>, D>, rhs: Rotation<N, D>,
+    Output = Similarity<N, Rotation<N, D>, D>;
     [val val] => {
         let scaling = self.scaling();
         Similarity::from_isometry(self.isometry / rhs, scaling)
@@ -492,9 +493,9 @@ similarity_from_composition_impl_all!(
 // Rotation ÷ Similarity
 similarity_from_composition_impl_all!(
     Div, div;
-    (D, D), (D, U1) for D: DimName;
-    self: Rotation<N, D>, right: Similarity<N, D, Rotation<N, D>>,
-    Output = Similarity<N, D, Rotation<N, D>>;
+    D;
+    self: Rotation<N, D>, right: Similarity<N, Rotation<N, D>, D>,
+    Output = Similarity<N, Rotation<N, D>, D>;
     // TODO: don't call inverse explicitly?
     [val val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * right.inverse() };
     [ref val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * right.inverse() };
@@ -505,7 +506,7 @@ similarity_from_composition_impl_all!(
 // Similarity × UnitQuaternion
 similarity_from_composition_impl_all!(
     Mul, mul;
-    (U4, U1), (U3, U1);
+    ;
     self: Similarity<N, UnitQuaternion<N>, 3>, rhs: UnitQuaternion<N>,
     Output = Similarity<N, UnitQuaternion<N>, 3>;
     [val val] => {
@@ -523,7 +524,7 @@ similarity_from_composition_impl_all!(
 // UnitQuaternion × Similarity
 similarity_from_composition_impl_all!(
     Mul, mul;
-    (U4, U1), (U3, U1);
+    ;
     self: UnitQuaternion<N>, right: Similarity<N, UnitQuaternion<N>, 3>,
     Output = Similarity<N, UnitQuaternion<N>, 3>;
     [val val] => &self * &right;
@@ -535,7 +536,7 @@ similarity_from_composition_impl_all!(
 // Similarity ÷ UnitQuaternion
 similarity_from_composition_impl_all!(
     Div, div;
-    (U4, U1), (U3, U1);
+    ;
     self: Similarity<N, UnitQuaternion<N>, 3>, rhs: UnitQuaternion<N>,
     Output = Similarity<N, UnitQuaternion<N>, 3>;
     [val val] => {
@@ -553,7 +554,7 @@ similarity_from_composition_impl_all!(
 // UnitQuaternion ÷ Similarity
 similarity_from_composition_impl_all!(
     Div, div;
-    (U4, U1), (U3, U1);
+    ;
     self: UnitQuaternion<N>, right: Similarity<N, UnitQuaternion<N>, 3>,
     Output = Similarity<N, UnitQuaternion<N>, 3>;
     // TODO: don't call inverse explicitly?
@@ -566,9 +567,9 @@ similarity_from_composition_impl_all!(
 // Similarity × UnitComplex
 similarity_from_composition_impl_all!(
     Mul, mul;
-    (U2, U1), (U2, U1);
-    self: Similarity<N, U2, UnitComplex<N>>, rhs: UnitComplex<N>,
-    Output = Similarity<N, U2, UnitComplex<N>>;
+    ;
+    self: Similarity<N, UnitComplex<N>, 2>, rhs: UnitComplex<N>,
+    Output = Similarity<N, UnitComplex<N>, 2>;
     [val val] => {
         let scaling = self.scaling();
         Similarity::from_isometry(self.isometry * rhs, scaling)
@@ -584,9 +585,9 @@ similarity_from_composition_impl_all!(
 // Similarity ÷ UnitComplex
 similarity_from_composition_impl_all!(
     Div, div;
-    (U2, U1), (U2, U1);
-    self: Similarity<N, U2, UnitComplex<N>>, rhs: UnitComplex<N>,
-    Output = Similarity<N, U2, UnitComplex<N>>;
+    ;
+    self: Similarity<N, UnitComplex<N>, 2>, rhs: UnitComplex<N>,
+    Output = Similarity<N, UnitComplex<N>, 2>;
     [val val] => {
         let scaling = self.scaling();
         Similarity::from_isometry(self.isometry / rhs, scaling)
diff --git a/src/geometry/similarity_simba.rs b/src/geometry/similarity_simba.rs
index 0436130a..91a9e733 100755
--- a/src/geometry/similarity_simba.rs
+++ b/src/geometry/similarity_simba.rs
@@ -7,7 +7,6 @@ where
     N::Element: SimdRealField,
     R: SimdValue<SimdBool = N::SimdBool> + AbstractRotation<N, D>,
     R::Element: AbstractRotation<N::Element, D>,
-    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     type Element = Similarity<N::Element, R::Element, D>;
     type SimdBool = N::SimdBool;
diff --git a/src/geometry/swizzle.rs b/src/geometry/swizzle.rs
index e0c42eaa..d76464e6 100644
--- a/src/geometry/swizzle.rs
+++ b/src/geometry/swizzle.rs
@@ -21,7 +21,6 @@ macro_rules! impl_swizzle {
 impl<N: Scalar, const D: usize> Point<N, D>
 where
     Const<D>: ToTypenum,
-    // DefaultAllocator: Allocator<N, D>,
 {
     impl_swizzle!(
         where U0: xx()  -> Point2[0, 0],
diff --git a/src/geometry/transform.rs b/src/geometry/transform.rs
index 15b2c939..fceae681 100755
--- a/src/geometry/transform.rs
+++ b/src/geometry/transform.rs
@@ -11,7 +11,7 @@ use simba::scalar::RealField;
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimNameAdd, DimNameSum, U1};
 use crate::base::storage::Owned;
-use crate::base::{CMatrixN, CVectorN, Const, DefaultAllocator, MatrixN};
+use crate::base::{CVectorN, Const, DefaultAllocator, DimName, MatrixN};
 
 use crate::geometry::Point;
 
@@ -28,10 +28,10 @@ pub trait TCategory: Any + Debug + Copy + PartialEq + Send {
 
     /// Checks that the given matrix is a valid homogeneous representation of an element of the
     /// category `Self`.
-    fn check_homogeneous_invariants<N: RealField, const D: usize>(mat: &CMatrixN<N, D>) -> bool
+    fn check_homogeneous_invariants<N: RealField, D: DimName>(mat: &MatrixN<N, D>) -> bool
     where
-        N::Epsilon: Copy;
-    // DefaultAllocator: Allocator<N, D, D>;
+        N::Epsilon: Copy,
+        DefaultAllocator: Allocator<N, D, D>;
 }
 
 /// Traits that gives the `Transform` category that is compatible with the result of the
@@ -71,10 +71,10 @@ pub enum TAffine {}
 
 impl TCategory for TGeneral {
     #[inline]
-    fn check_homogeneous_invariants<N: RealField, const D: usize>(_: &CMatrixN<N, D>) -> bool
+    fn check_homogeneous_invariants<N: RealField, D: DimName>(_: &MatrixN<N, D>) -> bool
     where
         N::Epsilon: Copy,
-        // DefaultAllocator: Allocator<N, D, D>,
+        DefaultAllocator: Allocator<N, D, D>,
     {
         true
     }
@@ -82,10 +82,10 @@ impl TCategory for TGeneral {
 
 impl TCategory for TProjective {
     #[inline]
-    fn check_homogeneous_invariants<N: RealField, const D: usize>(mat: &CMatrixN<N, D>) -> bool
+    fn check_homogeneous_invariants<N: RealField, D: DimName>(mat: &MatrixN<N, D>) -> bool
     where
         N::Epsilon: Copy,
-        // DefaultAllocator: Allocator<N, D, D>,
+        DefaultAllocator: Allocator<N, D, D>,
     {
         mat.is_invertible()
     }
@@ -98,12 +98,12 @@ impl TCategory for TAffine {
     }
 
     #[inline]
-    fn check_homogeneous_invariants<N: RealField, const D: usize>(mat: &CMatrixN<N, D>) -> bool
+    fn check_homogeneous_invariants<N: RealField, D: DimName>(mat: &MatrixN<N, D>) -> bool
     where
         N::Epsilon: Copy,
-        // DefaultAllocator: Allocator<N, D, D>,
+        DefaultAllocator: Allocator<N, D, D>,
     {
-        let last = D - 1;
+        let last = D::dim() - 1;
         mat.is_invertible()
             && mat[(last, last)] == N::one()
             && (0..last).all(|i| mat[(last, i)].is_zero())
diff --git a/src/geometry/transform_ops.rs b/src/geometry/transform_ops.rs
index 9a51bbb4..7a70c546 100644
--- a/src/geometry/transform_ops.rs
+++ b/src/geometry/transform_ops.rs
@@ -4,8 +4,8 @@ use std::ops::{Div, DivAssign, Index, IndexMut, Mul, MulAssign};
 use simba::scalar::{ClosedAdd, ClosedMul, RealField, SubsetOf};
 
 use crate::base::allocator::Allocator;
-use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1, U3, U4};
-use crate::base::{DefaultAllocator, MatrixN, Scalar, VectorN};
+use crate::base::dimension::{DimNameAdd, DimNameSum, U1, U4};
+use crate::base::{CVectorN, Const, DefaultAllocator, MatrixN, Scalar};
 
 use crate::geometry::{
     Isometry, Point, Rotation, Similarity, SubTCategoryOf, SuperTCategoryOf, TAffine, TCategory,
@@ -107,16 +107,19 @@ where
 // Transform × Vector
 md_impl_all!(
     Mul, mul where N: RealField;
-    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategory;
-    self: Transform<N, C, D>, rhs: VectorN<N, D>, Output = VectorN<N, D>;
+    (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>), (Const<D>, U1)
+    const D;
+    for C;
+    where Const<D>: DimNameAdd<U1>, C: TCategory;
+    self: Transform<N, C, D>, rhs: CVectorN<N, D>, Output = CVectorN<N, D>;
     [val val] => &self * &rhs;
     [ref val] =>  self * &rhs;
     [val ref] => &self *  rhs;
     [ref ref] => {
-        let transform = self.matrix().fixed_slice::<D, D>(0, 0);
+        let transform = self.matrix().fixed_slice::<Const<D>, Const<D>>(0, 0);
 
         if C::has_normalizer() {
-            let normalizer = self.matrix().fixed_slice::<U1, D>(D::dim(), 0);
+            let normalizer = self.matrix().fixed_slice::<U1, Const<D>>(D, 0);
             let n = normalizer.tr_dot(&rhs);
 
             if !n.is_zero() {
@@ -131,20 +134,22 @@ md_impl_all!(
 // Transform × Point
 md_impl_all!(
     Mul, mul where N: RealField;
-    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategory
-    where DefaultAllocator: Allocator<N, D, D>;
+    (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>), (Const<D>, U1)
+    const D;
+    for C;
+    where Const<D>: DimNameAdd<U1>, C: TCategory;
     self: Transform<N, C, D>, rhs: Point<N, D>, Output = Point<N, D>;
     [val val] => &self * &rhs;
     [ref val] =>  self * &rhs;
     [val ref] => &self *  rhs;
     [ref ref] => {
-        let transform   = self.matrix().fixed_slice::<D, D>(0, 0);
-        let translation = self.matrix().fixed_slice::<D, U1>(0, D::dim());
+        let transform   = self.matrix().fixed_slice::<Const<D>, Const<D>>(0, 0);
+        let translation = self.matrix().fixed_slice::<Const<D>, U1>(0, D);
 
         if C::has_normalizer() {
-            let normalizer = self.matrix().fixed_slice::<U1, D>(D::dim(), 0);
+            let normalizer = self.matrix().fixed_slice::<U1, Const<D>>(D, 0);
             #[allow(clippy::suspicious_arithmetic_impl)]
-            let n = normalizer.tr_dot(&rhs.coords) + unsafe { *self.matrix().get_unchecked((D::dim(), D::dim())) };
+            let n = normalizer.tr_dot(&rhs.coords) + unsafe { *self.matrix().get_unchecked((D, D)) };
 
             if !n.is_zero() {
                 return (transform * rhs + translation) / n;
@@ -158,8 +163,11 @@ md_impl_all!(
 // Transform × Transform
 md_impl_all!(
     Mul, mul where N: RealField;
-    (DimNameSum<D, U1>, DimNameSum<D, U1>), (DimNameSum<D, U1>, DimNameSum<D, U1>) for D: DimNameAdd<U1>, CA: TCategoryMul<CB>, CB: TCategory;
-    self: Transform<N, D, CA>, rhs: Transform<N, D, CB>, Output = Transform<N, D, CA::Representative>;
+    (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>), (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>)
+    const D;
+    for CA, CB;
+    where Const<D>: DimNameAdd<U1>, CA: TCategoryMul<CB>, CB: TCategory;
+    self: Transform<N, CA, D>, rhs: Transform<N, CB, D>, Output = Transform<N, CA::Representative, D>;
     [val val] => Self::Output::from_matrix_unchecked(self.into_inner() * rhs.into_inner());
     [ref val] => Self::Output::from_matrix_unchecked(self.matrix() * rhs.into_inner());
     [val ref] => Self::Output::from_matrix_unchecked(self.into_inner() * rhs.matrix());
@@ -169,7 +177,10 @@ md_impl_all!(
 // Transform × Rotation
 md_impl_all!(
     Mul, mul where N: RealField;
-    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, D) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
+    (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>), (Const<D>, Const<D>)
+    const D;
+    for C;
+    where Const<D>: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
     self: Transform<N, C, D>, rhs: Rotation<N, D>, Output = Transform<N, C::Representative, D>;
     [val val] => Self::Output::from_matrix_unchecked(self.into_inner() * rhs.to_homogeneous());
     [ref val] => Self::Output::from_matrix_unchecked(self.matrix() * rhs.to_homogeneous());
@@ -180,7 +191,10 @@ md_impl_all!(
 // Rotation × Transform
 md_impl_all!(
     Mul, mul where N: RealField;
-    (D, D), (DimNameSum<D, U1>, DimNameSum<D, U1>) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
+    (Const<D>, Const<D>), (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>)
+    const D;
+    for C;
+    where Const<D>: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
     self: Rotation<N, D>, rhs: Transform<N, C, D>, Output = Transform<N, C::Representative, D>;
     [val val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
     [ref val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
@@ -191,7 +205,10 @@ md_impl_all!(
 // Transform × UnitQuaternion
 md_impl_all!(
     Mul, mul where N: RealField;
-    (U4, U4), (U4, U1) for C: TCategoryMul<TAffine>;
+    (U4, U4), (U4, U1)
+    const;
+    for C;
+    where C: TCategoryMul<TAffine>;
     self: Transform<N, C, 3>, rhs: UnitQuaternion<N>, Output = Transform<N, C::Representative, 3>;
     [val val] => Self::Output::from_matrix_unchecked(self.into_inner() * rhs.to_homogeneous());
     [ref val] => Self::Output::from_matrix_unchecked(self.matrix() * rhs.to_homogeneous());
@@ -202,7 +219,10 @@ md_impl_all!(
 // UnitQuaternion × Transform
 md_impl_all!(
     Mul, mul where N: RealField;
-    (U4, U1), (U4, U4) for C: TCategoryMul<TAffine>;
+    (U4, U1), (U4, U4)
+    const;
+    for C;
+    where C: TCategoryMul<TAffine>;
     self: UnitQuaternion<N>, rhs: Transform<N, C, 3>, Output = Transform<N, C::Representative, 3>;
     [val val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
     [ref val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
@@ -213,8 +233,10 @@ md_impl_all!(
 // Transform × Isometry
 md_impl_all!(
     Mul, mul where N: RealField;
-    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
-    for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
+    (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>), (Const<D>, U1)
+    const D;
+    for C, R;
+    where Const<D>: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<Const<D>, U1>> >;
     self: Transform<N, C, D>, rhs: Isometry<N, R, D>, Output = Transform<N, C::Representative, D>;
     [val val] => Self::Output::from_matrix_unchecked(self.into_inner() * rhs.to_homogeneous());
     [ref val] => Self::Output::from_matrix_unchecked(self.matrix() * rhs.to_homogeneous());
@@ -225,8 +247,10 @@ md_impl_all!(
 // Isometry × Transform
 md_impl_all!(
     Mul, mul where N: RealField;
-    (D, U1), (DimNameSum<D, U1>, DimNameSum<D, U1>)
-    for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
+    (Const<D>, U1), (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>)
+    const D;
+    for C, R;
+    where Const<D>: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<Const<D>, U1>> >;
     self: Isometry<N, R, D>, rhs: Transform<N, C, D>, Output = Transform<N, C::Representative, D>;
     [val val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
     [ref val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
@@ -237,8 +261,10 @@ md_impl_all!(
 // Transform × Similarity
 md_impl_all!(
     Mul, mul where N: RealField;
-    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
-    for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
+    (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>), (Const<D>, U1)
+    const D;
+    for C, R;
+    where Const<D>: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<Const<D>, U1>> >;
     self: Transform<N, C, D>, rhs: Similarity<N, R, D>, Output = Transform<N, C::Representative, D>;
     [val val] => Self::Output::from_matrix_unchecked(self.into_inner() * rhs.to_homogeneous());
     [ref val] => Self::Output::from_matrix_unchecked(self.matrix() * rhs.to_homogeneous());
@@ -249,8 +275,10 @@ md_impl_all!(
 // Similarity × Transform
 md_impl_all!(
     Mul, mul where N: RealField;
-    (D, U1), (DimNameSum<D, U1>, DimNameSum<D, U1>)
-    for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
+    (Const<D>, U1), (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>)
+    const D;
+    for C, R;
+    where Const<D>: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<Const<D>, U1>> >;
     self: Similarity<N, R, D>, rhs: Transform<N, C, D>, Output = Transform<N, C::Representative, D>;
     [val val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
     [ref val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
@@ -269,7 +297,10 @@ md_impl_all!(
 // Transform × Translation
 md_impl_all!(
     Mul, mul where N: RealField;
-    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
+    (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>), (Const<D>, U1)
+    const D;
+    for C;
+    where Const<D>: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
     self: Transform<N, C, D>, rhs: Translation<N, D>, Output = Transform<N, C::Representative, D>;
     [val val] => Self::Output::from_matrix_unchecked(self.into_inner() * rhs.to_homogeneous());
     [ref val] => Self::Output::from_matrix_unchecked(self.matrix() * rhs.to_homogeneous());
@@ -280,8 +311,10 @@ md_impl_all!(
 // Translation × Transform
 md_impl_all!(
     Mul, mul where N: RealField;
-    (D, U1), (DimNameSum<D, U1>, DimNameSum<D, U1>)
-    for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
+    (Const<D>, U1), (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>)
+    const D;
+    for C;
+    where Const<D>: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
     self: Translation<N, D>, rhs: Transform<N, C, D>, Output = Transform<N, C::Representative, D>;
     [val val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
     [ref val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
@@ -292,8 +325,11 @@ md_impl_all!(
 // Transform ÷ Transform
 md_impl_all!(
     Div, div where N: RealField;
-    (DimNameSum<D, U1>, DimNameSum<D, U1>), (DimNameSum<D, U1>, DimNameSum<D, U1>) for D: DimNameAdd<U1>, CA: TCategoryMul<CB>, CB: SubTCategoryOf<TProjective>;
-    self: Transform<N, D, CA>, rhs: Transform<N, D, CB>, Output = Transform<N, D, CA::Representative>;
+    (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>), (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>)
+    const D;
+    for CA, CB;
+    where Const<D>: DimNameAdd<U1>, CA: TCategoryMul<CB>, CB: SubTCategoryOf<TProjective>;
+    self: Transform<N, CA, D>, rhs: Transform<N, CB, D>, Output = Transform<N, CA::Representative, D>;
     [val val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
     [ref val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
     [val ref] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.clone().inverse() };
@@ -303,7 +339,10 @@ md_impl_all!(
 // Transform ÷ Rotation
 md_impl_all!(
     Div, div where N: RealField;
-    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, D) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
+    (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>), (Const<D>, Const<D>)
+    const D;
+    for C;
+    where Const<D>: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
     self: Transform<N, C, D>, rhs: Rotation<N, D>, Output = Transform<N, C::Representative, D>;
     [val val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
     [ref val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
@@ -314,7 +353,10 @@ md_impl_all!(
 // Rotation ÷ Transform
 md_impl_all!(
     Div, div where N: RealField;
-    (D, D), (DimNameSum<D, U1>, DimNameSum<D, U1>) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
+    (Const<D>, Const<D>), (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>)
+    const D;
+    for C;
+    where Const<D>: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
     self: Rotation<N, D>, rhs: Transform<N, C, D>, Output = Transform<N, C::Representative, D>;
     [val val] => #[allow(clippy::suspicious_arithmetic_impl)] { self.inverse() * rhs };
     [ref val] => #[allow(clippy::suspicious_arithmetic_impl)] { self.inverse() * rhs };
@@ -325,7 +367,10 @@ md_impl_all!(
 // Transform ÷ UnitQuaternion
 md_impl_all!(
     Div, div where N: RealField;
-    (U4, U4), (U4, U1) for C: TCategoryMul<TAffine>;
+    (U4, U4), (U4, U1)
+    const;
+    for C;
+    where C: TCategoryMul<TAffine>;
     self: Transform<N, C, 3>, rhs: UnitQuaternion<N>, Output = Transform<N, C::Representative, 3>;
     [val val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
     [ref val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
@@ -336,7 +381,10 @@ md_impl_all!(
 // UnitQuaternion ÷ Transform
 md_impl_all!(
     Div, div where N: RealField;
-    (U4, U1), (U4, U4) for C: TCategoryMul<TAffine>;
+    (U4, U1), (U4, U4)
+    const;
+    for C;
+    where C: TCategoryMul<TAffine>;
     self: UnitQuaternion<N>, rhs: Transform<N, C, 3>, Output = Transform<N, C::Representative, 3>;
     [val val] => #[allow(clippy::suspicious_arithmetic_impl)] { self.inverse() * rhs };
     [ref val] => #[allow(clippy::suspicious_arithmetic_impl)] { self.inverse() * rhs };
@@ -347,9 +395,9 @@ md_impl_all!(
 //      // Transform ÷ Isometry
 //      md_impl_all!(
 //          Div, div where N: RealField;
-//          (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
-//          for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >
-//          where SB::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
+//          (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>), (Const<D>, U1)
+//          for Const<D>: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<Const<D>, U1>> >
+//          where SB::Alloc: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1> >;
 //          self: Transform<N, C, D>, rhs: Isometry<N, R, D>, Output = Transform<N, C::Representative, D>;
 //          [val val] => Self::Output::from_matrix_unchecked(self.into_inner() * rhs.inverse().to_homogeneous());
 //          [ref val] => Self::Output::from_matrix_unchecked(self.matrix() * rhs.inverse().to_homogeneous());
@@ -360,9 +408,9 @@ md_impl_all!(
 //      // Isometry ÷ Transform
 //      md_impl_all!(
 //          Div, div where N: RealField;
-//          (D, U1), (DimNameSum<D, U1>, DimNameSum<D, U1>)
-//          for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >
-//          where SA::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
+//          (Const<D>, U1), (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>)
+//          for Const<D>: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<Const<D>, U1>> >
+//          where SA::Alloc: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1> >;
 //          self: Isometry<N, R, D>, rhs: Transform<N, C, D>, Output = Transform<N, C::Representative, D>;
 //          [val val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
 //          [ref val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
@@ -373,10 +421,10 @@ md_impl_all!(
 //      // Transform ÷ Similarity
 //      md_impl_all!(
 //          Div, div where N: RealField;
-//          (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
-//          for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >
+//          (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>), (Const<D>, U1)
+//          for Const<D>: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<Const<D>, U1>> >
 //          where SB::Alloc: Allocator<N, D, D >
-//          where SB::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
+//          where SB::Alloc: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1> >;
 //          self: Transform<N, C, D>, rhs: Similarity<N, R, D>, Output = Transform<N, C::Representative, D>;
 //          [val val] => Self::Output::from_matrix_unchecked(self.into_inner() * rhs.to_homogeneous());
 //          [ref val] => Self::Output::from_matrix_unchecked(self.matrix() * rhs.to_homogeneous());
@@ -387,10 +435,10 @@ md_impl_all!(
 //      // Similarity ÷ Transform
 //      md_impl_all!(
 //          Div, div where N: RealField;
-//          (D, U1), (DimNameSum<D, U1>, DimNameSum<D, U1>)
-//          for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >
+//          (Const<D>, U1), (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>)
+//          for Const<D>: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<Const<D>, U1>> >
 //          where SA::Alloc: Allocator<N, D, D >
-//          where SA::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
+//          where SA::Alloc: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1> >;
 //          self: Similarity<N, R, D>, rhs: Transform<N, C, D>, Output = Transform<N, C::Representative, D>;
 //          [val val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
 //          [ref val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
@@ -401,7 +449,10 @@ md_impl_all!(
 // Transform ÷ Translation
 md_impl_all!(
     Div, div where N: RealField;
-    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
+    (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>), (Const<D>, U1)
+    const D;
+    for C;
+    where Const<D>: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
     self: Transform<N, C, D>, rhs: Translation<N, D>, Output = Transform<N, C::Representative, D>;
     [val val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
     [ref val] => #[allow(clippy::suspicious_arithmetic_impl)] { self * rhs.inverse() };
@@ -412,8 +463,10 @@ md_impl_all!(
 // Translation ÷ Transform
 md_impl_all!(
     Div, div where N: RealField;
-    (D, U1), (DimNameSum<D, U1>, DimNameSum<D, U1>)
-    for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
+    (Const<D>, U1), (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>)
+    const D;
+    for C;
+    where Const<D>: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
     self: Translation<N, D>, rhs: Transform<N, C, D>, Output = Transform<N, C::Representative, D>;
     [val val] => #[allow(clippy::suspicious_arithmetic_impl)] { self.inverse() * rhs };
     [ref val] => #[allow(clippy::suspicious_arithmetic_impl)] { self.inverse() * rhs };
@@ -424,8 +477,11 @@ md_impl_all!(
 // Transform ×= Transform
 md_assign_impl_all!(
     MulAssign, mul_assign where N: RealField;
-    (DimNameSum<D, U1>, DimNameSum<D, U1>), (DimNameSum<D, U1>, DimNameSum<D, U1>) for D: DimNameAdd<U1>, CA: TCategory, CB: SubTCategoryOf<CA>;
-    self: Transform<N, D, CA>, rhs: Transform<N, D, CB>;
+    (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>), (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>)
+    const D;
+    for CA, CB;
+    where Const<D>: DimNameAdd<U1>, CA: TCategory, CB: SubTCategoryOf<CA>;
+    self: Transform<N, CA, D>, rhs: Transform<N, CB, D>;
     [val] => *self.matrix_mut_unchecked() *= rhs.into_inner();
     [ref] => *self.matrix_mut_unchecked() *= rhs.matrix();
 );
@@ -433,8 +489,10 @@ md_assign_impl_all!(
 // Transform ×= Similarity
 md_assign_impl_all!(
     MulAssign, mul_assign where N: RealField;
-    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
-    for D: DimNameAdd<U1>, C: TCategory, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
+    (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>), (Const<D>, U1)
+    const D;
+    for C, R;
+    where Const<D>: DimNameAdd<U1>, C: TCategory, R: SubsetOf<MatrixN<N, DimNameSum<Const<D>, U1>> >;
     self: Transform<N, C, D>, rhs: Similarity<N, R, D>;
     [val] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
     [ref] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
@@ -443,8 +501,10 @@ md_assign_impl_all!(
 // Transform ×= Isometry
 md_assign_impl_all!(
     MulAssign, mul_assign where N: RealField;
-    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
-    for D: DimNameAdd<U1>, C: TCategory, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
+    (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>), (Const<D>, U1)
+    const D;
+    for C, R;
+    where Const<D>: DimNameAdd<U1>, C: TCategory, R: SubsetOf<MatrixN<N, DimNameSum<Const<D>, U1>> >;
     self: Transform<N, C, D>, rhs: Isometry<N, R, D>;
     [val] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
     [ref] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
@@ -461,7 +521,10 @@ md_assign_impl_all!(
 // Transform ×= Translation
 md_assign_impl_all!(
     MulAssign, mul_assign where N: RealField;
-    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategory;
+    (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>), (Const<D>, U1)
+    const D;
+    for C;
+    where Const<D>: DimNameAdd<U1>, C: TCategory;
     self: Transform<N, C, D>, rhs: Translation<N, D>;
     [val] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
     [ref] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
@@ -470,7 +533,10 @@ md_assign_impl_all!(
 // Transform ×= Rotation
 md_assign_impl_all!(
     MulAssign, mul_assign where N: RealField;
-    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, D) for D: DimNameAdd<U1>, C: TCategory;
+    (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>), (Const<D>, Const<D>)
+    const D;
+    for C;
+    where Const<D>: DimNameAdd<U1>, C: TCategory;
     self: Transform<N, C, D>, rhs: Rotation<N, D>;
     [val] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
     [ref] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
@@ -479,7 +545,10 @@ md_assign_impl_all!(
 // Transform ×= UnitQuaternion
 md_assign_impl_all!(
     MulAssign, mul_assign where N: RealField;
-    (U4, U4), (U4, U1) for C: TCategory;
+    (U4, U4), (U4, U1)
+    const;
+    for C;
+    where C: TCategory;
     self: Transform<N, C, 3>, rhs: UnitQuaternion<N>;
     [val] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
     [ref] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
@@ -488,9 +557,11 @@ md_assign_impl_all!(
 // Transform ÷= Transform
 md_assign_impl_all!(
     DivAssign, div_assign where N: RealField;
-    (DimNameSum<D, U1>, DimNameSum<D, U1>), (DimNameSum<D, U1>, DimNameSum<D, U1>)
-    for D: DimNameAdd<U1>, CA: SuperTCategoryOf<CB>, CB: SubTCategoryOf<TProjective>;
-    self: Transform<N, D, CA>, rhs: Transform<N, D, CB>;
+    (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>), (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>)
+    const D;
+    for CA, CB;
+    where Const<D>: DimNameAdd<U1>, CA: SuperTCategoryOf<CB>, CB: SubTCategoryOf<TProjective>;
+    self: Transform<N, CA, D>, rhs: Transform<N, CB, D>;
     [val] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
     [ref] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.clone().inverse() };
 );
@@ -498,8 +569,8 @@ md_assign_impl_all!(
 //      // Transform ÷= Similarity
 //      md_assign_impl_all!(
 //          DivAssign, div_assign;
-//          (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
-//          for D: DimNameAdd<U1>, C: TCategory, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
+//          (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>), (Const<D>, U1)
+//          for Const<D>: DimNameAdd<U1>, C: TCategory, R: SubsetOf<MatrixN<N, DimNameSum<Const<D>, U1>> >;
 //          self: Transform<N, C, D>, rhs: Similarity<N, R, D>;
 //          [val] => *self *= rhs.inverse();
 //          [ref] => *self *= rhs.inverse();
@@ -509,8 +580,8 @@ md_assign_impl_all!(
 //      // Transform ÷= Isometry
 //      md_assign_impl_all!(
 //          DivAssign, div_assign;
-//          (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
-//          for D: DimNameAdd<U1>, C: TCategory, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
+//          (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>), (Const<D>, U1)
+//          for Const<D>: DimNameAdd<U1>, C: TCategory, R: SubsetOf<MatrixN<N, DimNameSum<Const<D>, U1>> >;
 //          self: Transform<N, C, D>, rhs: Isometry<N, R, D>;
 //          [val] => *self *= rhs.inverse();
 //          [ref] => *self *= rhs.inverse();
@@ -519,7 +590,10 @@ md_assign_impl_all!(
 // Transform ÷= Translation
 md_assign_impl_all!(
     DivAssign, div_assign where N: RealField;
-    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategory;
+    (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>), (Const<D>, U1)
+    const D;
+    for C;
+    where Const<D>: DimNameAdd<U1>, C: TCategory;
     self: Transform<N, C, D>, rhs: Translation<N, D>;
     [val] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
     [ref] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
@@ -528,7 +602,10 @@ md_assign_impl_all!(
 // Transform ÷= Rotation
 md_assign_impl_all!(
     DivAssign, div_assign where N: RealField;
-    (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, D) for D: DimNameAdd<U1>, C: TCategory;
+    (DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>), (Const<D>, Const<D>)
+    const D;
+    for C;
+    where Const<D>: DimNameAdd<U1>, C: TCategory;
     self: Transform<N, C, D>, rhs: Rotation<N, D>;
     [val] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
     [ref] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
@@ -537,7 +614,10 @@ md_assign_impl_all!(
 // Transform ÷= UnitQuaternion
 md_assign_impl_all!(
     DivAssign, div_assign where N: RealField;
-    (U4, U4), (U4, U1) for C: TCategory;
+    (U4, U4), (U4, U1)
+    const;
+    for C;
+    where C: TCategory;
     self: Transform<N, C, 3>, rhs: UnitQuaternion<N>;
     [val] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
     [ref] => #[allow(clippy::suspicious_op_assign_impl)] { *self *= rhs.inverse() };
diff --git a/src/geometry/translation.rs b/src/geometry/translation.rs
index 1ae452bb..0fc450cc 100755
--- a/src/geometry/translation.rs
+++ b/src/geometry/translation.rs
@@ -34,7 +34,6 @@ pub struct Translation<N: Scalar, const D: usize>
 
 impl<N: Scalar + hash::Hash, const D: usize> hash::Hash for Translation<N, D>
 where
-    // DefaultAllocator: Allocator<N, D>,
     Owned<N, Const<D>>: hash::Hash,
 {
     fn hash<H: hash::Hasher>(&self, state: &mut H) {
@@ -42,15 +41,10 @@ where
     }
 }
 
-impl<N: Scalar + Copy, const D: usize> Copy for Translation<N, D> where
-    // DefaultAllocator: Allocator<N, D>,
-    Owned<N, Const<D>>: Copy
-{
-}
+impl<N: Scalar + Copy, const D: usize> Copy for Translation<N, D> where Owned<N, Const<D>>: Copy {}
 
 impl<N: Scalar, const D: usize> Clone for Translation<N, D>
 where
-    // DefaultAllocator: Allocator<N, D>,
     Owned<N, Const<D>>: Clone,
 {
     #[inline]
@@ -60,12 +54,10 @@ where
 }
 
 #[cfg(feature = "abomonation-serialize")]
-impl<N, D> Abomonation for Translation<N, D>
+impl<N, const D: usize> Abomonation for Translation<N, D>
 where
     N: Scalar,
-    D: DimName,
     CVectorN<N, D>: Abomonation,
-    // DefaultAllocator: Allocator<N, D>,
 {
     unsafe fn entomb<W: Write>(&self, writer: &mut W) -> IOResult<()> {
         self.vector.entomb(writer)
@@ -83,8 +75,7 @@ where
 #[cfg(feature = "serde-serialize")]
 impl<N: Scalar, const D: usize> Serialize for Translation<N, D>
 where
-    // DefaultAllocator: Allocator<N, D>,
-    Owned<N, D>: Serialize,
+    Owned<N, Const<D>>: Serialize,
 {
     fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
     where
@@ -97,8 +88,7 @@ where
 #[cfg(feature = "serde-serialize")]
 impl<'a, N: Scalar, const D: usize> Deserialize<'a> for Translation<N, D>
 where
-    // DefaultAllocator: Allocator<N, D>,
-    Owned<N, D>: Deserialize<'a>,
+    Owned<N, Const<D>>: Deserialize<'a>,
 {
     fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
     where
@@ -169,8 +159,9 @@ impl<N: Scalar, const D: usize> Translation<N, D>
         Const<D>: DimNameAdd<U1>,
         DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
     {
-        let mut res = MatrixN::<N, DimNameSum<D, U1>>::identity();
-        res.fixed_slice_mut::<D, U1>(0, D).copy_from(&self.vector);
+        let mut res = MatrixN::<N, DimNameSum<Const<D>, U1>>::identity();
+        res.fixed_slice_mut::<Const<D>, U1>(0, D)
+            .copy_from(&self.vector);
 
         res
     }
@@ -257,7 +248,6 @@ impl<N: Scalar + PartialEq, const D: usize> PartialEq for Translation<N, D>
 
 impl<N: Scalar + AbsDiffEq, const D: usize> AbsDiffEq for Translation<N, D>
 where
-    // DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {
     type Epsilon = N::Epsilon;
@@ -275,7 +265,6 @@ where
 
 impl<N: Scalar + RelativeEq, const D: usize> RelativeEq for Translation<N, D>
 where
-    // DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {
     #[inline]
@@ -297,7 +286,6 @@ where
 
 impl<N: Scalar + UlpsEq, const D: usize> UlpsEq for Translation<N, D>
 where
-    // DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {
     #[inline]
diff --git a/src/geometry/translation_construction.rs b/src/geometry/translation_construction.rs
index cfd441d5..7ee2359c 100644
--- a/src/geometry/translation_construction.rs
+++ b/src/geometry/translation_construction.rs
@@ -12,7 +12,7 @@ use rand::{
 
 use simba::scalar::{ClosedAdd, SupersetOf};
 
-use crate::base::{CVectorN, Scalar};
+use crate::base::{CVectorN, Const, Scalar};
 
 use crate::geometry::Translation;
 
@@ -54,7 +54,6 @@ impl<N: Scalar, const D: usize> Translation<N, D>
     pub fn cast<To: Scalar>(self) -> Translation<To, D>
     where
         Translation<To, D>: SupersetOf<Self>,
-        // DefaultAllocator: Allocator<To, D>,
     {
         crate::convert(self)
     }
@@ -73,7 +72,6 @@ impl<N: Scalar + Zero + ClosedAdd, const D: usize> One for Translation<N, D>
 #[cfg(feature = "rand-no-std")]
 impl<N: Scalar, const D: usize> Distribution<Translation<N, D>> for Standard
 where
-    // DefaultAllocator: Allocator<N, D>,
     Standard: Distribution<N>,
 {
     /// Generate an arbitrary random variate for testing purposes.
@@ -86,8 +84,7 @@ where
 #[cfg(feature = "arbitrary")]
 impl<N: Scalar + Arbitrary + Send, const D: usize> Arbitrary for Translation<N, D>
 where
-    // DefaultAllocator: Allocator<N, D>,
-    Owned<N, D>: Send,
+    Owned<N, Const<D>>: Send,
 {
     #[inline]
     fn arbitrary(rng: &mut Gen) -> Self {
diff --git a/src/geometry/translation_conversion.rs b/src/geometry/translation_conversion.rs
index c49e2735..ca5daa25 100644
--- a/src/geometry/translation_conversion.rs
+++ b/src/geometry/translation_conversion.rs
@@ -5,7 +5,7 @@ use simba::simd::PrimitiveSimdValue;
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimNameAdd, DimNameSum, U1};
-use crate::base::{Const, DefaultAllocator, MatrixN, Scalar, VectorN};
+use crate::base::{CVectorN, Const, DefaultAllocator, MatrixN, Scalar, VectorN};
 
 use crate::geometry::{
     AbstractRotation, Isometry, Similarity, SuperTCategoryOf, TAffine, Transform, Translation,
@@ -28,7 +28,6 @@ impl<N1, N2, const D: usize> SubsetOf<Translation<N2, D>> for Translation<N1, D>
 where
     N1: Scalar,
     N2: Scalar + SupersetOf<N1>,
-    // DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
 {
     #[inline]
     fn to_superset(&self) -> Translation<N2, D> {
@@ -37,7 +36,7 @@ where
 
     #[inline]
     fn is_in_subset(rot: &Translation<N2, D>) -> bool {
-        crate::is_convertible::<_, VectorN<N1, D>>(&rot.vector)
+        crate::is_convertible::<_, CVectorN<N1, D>>(&rot.vector)
     }
 
     #[inline]
@@ -53,7 +52,6 @@ where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
     R: AbstractRotation<N2, D>,
-    // DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
 {
     #[inline]
     fn to_superset(&self) -> Isometry<N2, R, D> {
@@ -84,7 +82,7 @@ where
 
     #[inline]
     fn is_in_subset(dq: &UnitDualQuaternion<N2>) -> bool {
-        crate::is_convertible::<_, Translation<N1, _>>(&dq.translation())
+        crate::is_convertible::<_, Translation<N1, 3>>(&dq.translation())
             && dq.rotation() == UnitQuaternion::identity()
     }
 
@@ -100,7 +98,6 @@ where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
     R: AbstractRotation<N2, D>,
-    // DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
 {
     #[inline]
     fn to_superset(&self) -> Similarity<N2, R, D> {
@@ -160,7 +157,7 @@ where
 
     #[inline]
     fn is_in_subset(m: &MatrixN<N2, DimNameSum<Const<D>, U1>>) -> bool {
-        let id = m.fixed_slice::<DimNameSum<Const<D>, U1>, D>(0, 0);
+        let id = m.fixed_slice::<DimNameSum<Const<D>, U1>, Const<D>>(0, 0);
 
         // Scalar types agree.
         m.iter().all(|e| SupersetOf::<N1>::is_in_subset(e)) &&
@@ -172,7 +169,7 @@ where
 
     #[inline]
     fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<Const<D>, U1>>) -> Self {
-        let t = m.fixed_slice::<D, U1>(0, D);
+        let t = m.fixed_slice::<Const<D>, U1>(0, D);
         Self {
             vector: crate::convert_unchecked(t.into_owned()),
         }
@@ -207,7 +204,6 @@ impl<N: Scalar + PrimitiveSimdValue, const D: usize> From<[Translation<N::Elemen
 where
     N: From<[<N as simba::simd::SimdValue>::Element; 2]>,
     N::Element: Scalar,
-    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     #[inline]
     fn from(arr: [Translation<N::Element, D>; 2]) -> Self {
@@ -223,7 +219,6 @@ impl<N: Scalar + PrimitiveSimdValue, const D: usize> From<[Translation<N::Elemen
 where
     N: From<[<N as simba::simd::SimdValue>::Element; 4]>,
     N::Element: Scalar,
-    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     #[inline]
     fn from(arr: [Translation<N::Element, D>; 4]) -> Self {
@@ -241,7 +236,6 @@ impl<N: Scalar + PrimitiveSimdValue, const D: usize> From<[Translation<N::Elemen
 where
     N: From<[<N as simba::simd::SimdValue>::Element; 8]>,
     N::Element: Scalar,
-    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     #[inline]
     fn from(arr: [Translation<N::Element, D>; 8]) -> Self {
@@ -263,7 +257,6 @@ impl<N: Scalar + PrimitiveSimdValue, const D: usize> From<[Translation<N::Elemen
 where
     N: From<[<N as simba::simd::SimdValue>::Element; 16]>,
     N::Element: Scalar,
-    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     #[inline]
     fn from(arr: [Translation<N::Element, D>; 16]) -> Self {
diff --git a/src/geometry/translation_ops.rs b/src/geometry/translation_ops.rs
index fc53b1e6..11d18469 100644
--- a/src/geometry/translation_ops.rs
+++ b/src/geometry/translation_ops.rs
@@ -4,57 +4,65 @@ use simba::scalar::{ClosedAdd, ClosedSub};
 
 use crate::base::allocator::{Allocator, SameShapeAllocator};
 use crate::base::constraint::{SameNumberOfColumns, SameNumberOfRows, ShapeConstraint};
-use crate::base::dimension::{DimName, U1};
-use crate::base::{DefaultAllocator, Scalar};
+use crate::base::dimension::U1;
+use crate::base::{Const, DefaultAllocator, Scalar};
 
 use crate::geometry::{Point, Translation};
 
 // Translation × Translation
 add_sub_impl!(Mul, mul, ClosedAdd;
-    (D, U1), (D, U1) -> (D) for D: DimName;
+    (Const<D>, U1), (Const<D>, U1) -> (Const<D>)
+    const D; for; where;
     self: &'a Translation<N, D>, right: &'b Translation<N, D>, Output = Translation<N, D>;
     #[allow(clippy::suspicious_arithmetic_impl)] { Translation::from(&self.vector + &right.vector) };
     'a, 'b);
 
 add_sub_impl!(Mul, mul, ClosedAdd;
-    (D, U1), (D, U1) -> (D) for D: DimName;
+    (Const<D>, U1), (Const<D>, U1) -> (Const<D>)
+    const D; for; where;
     self: &'a Translation<N, D>, right: Translation<N, D>, Output = Translation<N, D>;
     #[allow(clippy::suspicious_arithmetic_impl)] { Translation::from(&self.vector + right.vector) };
     'a);
 
 add_sub_impl!(Mul, mul, ClosedAdd;
-    (D, U1), (D, U1) -> (D) for D: DimName;
+    (Const<D>, U1), (Const<D>, U1) -> (Const<D>)
+    const D; for; where;
     self: Translation<N, D>, right: &'b Translation<N, D>, Output = Translation<N, D>;
     #[allow(clippy::suspicious_arithmetic_impl)] { Translation::from(self.vector + &right.vector) };
     'b);
 
 add_sub_impl!(Mul, mul, ClosedAdd;
-    (D, U1), (D, U1) -> (D) for D: DimName;
+    (Const<D>, U1), (Const<D>, U1) -> (Const<D>)
+    const D; for; where;
     self: Translation<N, D>, right: Translation<N, D>, Output = Translation<N, D>;
     #[allow(clippy::suspicious_arithmetic_impl)] { Translation::from(self.vector + right.vector) }; );
 
 // Translation ÷ Translation
 // TODO: instead of calling inverse explicitly, could we just add a `mul_tr` or `mul_inv` method?
 add_sub_impl!(Div, div, ClosedSub;
-    (D, U1), (D, U1) -> (D) for D: DimName;
+    (Const<D>, U1), (Const<D>, U1) -> (Const<D>)
+    const D; for; where;
     self: &'a Translation<N, D>, right: &'b Translation<N, D>, Output = Translation<N, D>;
     #[allow(clippy::suspicious_arithmetic_impl)] { Translation::from(&self.vector - &right.vector) };
     'a, 'b);
 
 add_sub_impl!(Div, div, ClosedSub;
-    (D, U1), (D, U1) -> (D) for D: DimName;
+    (Const<D>, U1), (Const<D>, U1) -> (Const<D>)
+    const D; for; where;
     self: &'a Translation<N, D>, right: Translation<N, D>, Output = Translation<N, D>;
     #[allow(clippy::suspicious_arithmetic_impl)] { Translation::from(&self.vector - right.vector) };
     'a);
 
 add_sub_impl!(Div, div, ClosedSub;
-    (D, U1), (D, U1) -> (D) for D: DimName;
+    (Const<D>, U1), (Const<D>, U1) -> (Const<D>)
+    const D; for; where;
     self: Translation<N, D>, right: &'b Translation<N, D>, Output = Translation<N, D>;
     #[allow(clippy::suspicious_arithmetic_impl)] { Translation::from(self.vector - &right.vector) };
     'b);
 
 add_sub_impl!(Div, div, ClosedSub;
-    (D, U1), (D, U1) -> (D) for D: DimName;
+    (Const<D>, U1), (Const<D>, U1) -> (Const<D>)
+    const D; for; where;
     self: Translation<N, D>, right: Translation<N, D>, Output = Translation<N, D>;
     #[allow(clippy::suspicious_arithmetic_impl)] { Translation::from(self.vector - right.vector) }; );
 
@@ -62,47 +70,51 @@ add_sub_impl!(Div, div, ClosedSub;
 // TODO: we don't handle properly non-zero origins here. Do we want this to be the intended
 // behavior?
 add_sub_impl!(Mul, mul, ClosedAdd;
-    (D, U1), (D, U1) -> (D) for D: DimName;
+    (Const<D>, U1), (Const<D>, U1) -> (Const<D>)
+    const D; for; where;
     self: &'a Translation<N, D>, right: &'b Point<N, D>, Output = Point<N, D>;
     #[allow(clippy::suspicious_arithmetic_impl)] { right + &self.vector };
     'a, 'b);
 
 add_sub_impl!(Mul, mul, ClosedAdd;
-    (D, U1), (D, U1) -> (D) for D: DimName;
+    (Const<D>, U1), (Const<D>, U1) -> (Const<D>)
+    const D; for; where;
     self: &'a Translation<N, D>, right: Point<N, D>, Output = Point<N, D>;
     #[allow(clippy::suspicious_arithmetic_impl)] { right + &self.vector };
     'a);
 
 add_sub_impl!(Mul, mul, ClosedAdd;
-    (D, U1), (D, U1) -> (D) for D: DimName;
+    (Const<D>, U1), (Const<D>, U1) -> (Const<D>)
+    const D; for; where;
     self: Translation<N, D>, right: &'b Point<N, D>, Output = Point<N, D>;
     #[allow(clippy::suspicious_arithmetic_impl)] { right + self.vector };
     'b);
 
 add_sub_impl!(Mul, mul, ClosedAdd;
-    (D, U1), (D, U1) -> (D) for D: DimName;
+    (Const<D>, U1), (Const<D>, U1) -> (Const<D>)
+    const D; for; where;
     self: Translation<N, D>, right: Point<N, D>, Output = Point<N, D>;
     #[allow(clippy::suspicious_arithmetic_impl)] { right + self.vector }; );
 
 // Translation *= Translation
 add_sub_assign_impl!(MulAssign, mul_assign, ClosedAdd;
-    (D, U1), (D, U1) for D: DimName;
+    const D;
     self: Translation<N, D>, right: &'b Translation<N, D>;
     #[allow(clippy::suspicious_op_assign_impl)] { self.vector += &right.vector };
     'b);
 
 add_sub_assign_impl!(MulAssign, mul_assign, ClosedAdd;
-    (D, U1), (D, U1) for D: DimName;
+    const D;
     self: Translation<N, D>, right: Translation<N, D>;
     #[allow(clippy::suspicious_op_assign_impl)] { self.vector += right.vector }; );
 
 add_sub_assign_impl!(DivAssign, div_assign, ClosedSub;
-    (D, U1), (D, U1) for D: DimName;
+    const D;
     self: Translation<N, D>, right: &'b Translation<N, D>;
     #[allow(clippy::suspicious_op_assign_impl)] { self.vector -= &right.vector };
     'b);
 
 add_sub_assign_impl!(DivAssign, div_assign, ClosedSub;
-    (D, U1), (D, U1) for D: DimName;
+    const D;
     self: Translation<N, D>, right: Translation<N, D>;
     #[allow(clippy::suspicious_op_assign_impl)] { self.vector -= right.vector }; );
diff --git a/src/geometry/translation_simba.rs b/src/geometry/translation_simba.rs
index 6d96618f..60d6e53f 100755
--- a/src/geometry/translation_simba.rs
+++ b/src/geometry/translation_simba.rs
@@ -8,7 +8,6 @@ use crate::geometry::Translation;
 impl<N: Scalar + SimdValue, const D: usize> SimdValue for Translation<N, D>
 where
     N::Element: Scalar,
-    // DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
 {
     type Element = Translation<N::Element, D>;
     type SimdBool = N::SimdBool;
diff --git a/src/geometry/unit_complex_ops.rs b/src/geometry/unit_complex_ops.rs
index ef227023..621dd46a 100644
--- a/src/geometry/unit_complex_ops.rs
+++ b/src/geometry/unit_complex_ops.rs
@@ -1,9 +1,7 @@
 use std::ops::{Div, DivAssign, Mul, MulAssign};
 
-use crate::base::allocator::Allocator;
-use crate::base::dimension::{U1, U2};
 use crate::base::storage::Storage;
-use crate::base::{DefaultAllocator, Unit, Vector, Vector2};
+use crate::base::{Const, Unit, Vector, Vector2};
 use crate::geometry::{Isometry, Point2, Rotation, Similarity, Translation, UnitComplex};
 use simba::simd::SimdRealField;
 
@@ -142,12 +140,11 @@ where
 
 macro_rules! complex_op_impl(
     ($Op: ident, $op: ident;
-     ($RDim: ident, $CDim: ident) $(for $Storage: ident: $StoragesBound: ident $(<$($BoundParam: ty),*>)*),*;
+     $($Storage: ident: $StoragesBound: ident $(<$($BoundParam: ty),*>)*),*;
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Result: ty;
      $action: expr; $($lives: tt),*) => {
         impl<$($lives ,)* N: SimdRealField $(, $Storage: $StoragesBound $(<$($BoundParam),*>)*)*> $Op<$Rhs> for $Lhs
-            where N::Element: SimdRealField,
-                  DefaultAllocator: Allocator<N, $RDim, $CDim> {
+            where N::Element: SimdRealField {
             type Output = $Result;
 
             #[inline]
@@ -160,7 +157,7 @@ macro_rules! complex_op_impl(
 
 macro_rules! complex_op_impl_all(
     ($Op: ident, $op: ident;
-     ($RDim: ident, $CDim: ident) $(for $Storage: ident: $StoragesBound: ident $(<$($BoundParam: ty),*>)*),*;
+     $($Storage: ident: $StoragesBound: ident $(<$($BoundParam: ty),*>)*),*;
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Result: ty;
      [val val] => $action_val_val: expr;
      [ref val] => $action_ref_val: expr;
@@ -168,22 +165,22 @@ macro_rules! complex_op_impl_all(
      [ref ref] => $action_ref_ref: expr;) => {
 
     complex_op_impl!($Op, $op;
-                     ($RDim, $CDim) $(for $Storage: $StoragesBound $(<$($BoundParam),*>)*),*;
+                     $($Storage: $StoragesBound $(<$($BoundParam),*>)*),*;
                      $lhs: $Lhs, $rhs: $Rhs, Output = $Result;
                      $action_val_val; );
 
     complex_op_impl!($Op, $op;
-                     ($RDim, $CDim) $(for $Storage: $StoragesBound $(<$($BoundParam),*>)*),*;
+                     $($Storage: $StoragesBound $(<$($BoundParam),*>)*),*;
                      $lhs: &'a $Lhs, $rhs: $Rhs, Output = $Result;
                      $action_ref_val; 'a);
 
     complex_op_impl!($Op, $op;
-                     ($RDim, $CDim) $(for $Storage: $StoragesBound $(<$($BoundParam),*>)*),*;
+                     $($Storage: $StoragesBound $(<$($BoundParam),*>)*),*;
                      $lhs: $Lhs, $rhs: &'b $Rhs, Output = $Result;
                      $action_val_ref; 'b);
 
     complex_op_impl!($Op, $op;
-                     ($RDim, $CDim) $(for $Storage: $StoragesBound $(<$($BoundParam),*>)*),*;
+                     $($Storage: $StoragesBound $(<$($BoundParam),*>)*),*;
                      $lhs: &'a $Lhs, $rhs: &'b $Rhs, Output = $Result;
                      $action_ref_ref; 'a, 'b);
 
@@ -194,8 +191,8 @@ macro_rules! complex_op_impl_all(
 // UnitComplex × Rotation
 complex_op_impl_all!(
     Mul, mul;
-    (U2, U2);
-    self: UnitComplex<N>, rhs: Rotation<N, U2>, Output = UnitComplex<N>;
+    ;
+    self: UnitComplex<N>, rhs: Rotation<N, 2>, Output = UnitComplex<N>;
     [val val] => &self * &rhs;
     [ref val] =>  self * &rhs;
     [val ref] => &self *  rhs;
@@ -205,8 +202,8 @@ complex_op_impl_all!(
 // UnitComplex ÷ Rotation
 complex_op_impl_all!(
     Div, div;
-    (U2, U2);
-    self: UnitComplex<N>, rhs: Rotation<N, U2>, Output = UnitComplex<N>;
+    ;
+    self: UnitComplex<N>, rhs: Rotation<N, 2>, Output = UnitComplex<N>;
     [val val] => &self / &rhs;
     [ref val] =>  self / &rhs;
     [val ref] => &self /  rhs;
@@ -216,8 +213,8 @@ complex_op_impl_all!(
 // Rotation × UnitComplex
 complex_op_impl_all!(
     Mul, mul;
-    (U2, U2);
-    self: Rotation<N, U2>, rhs: UnitComplex<N>, Output = UnitComplex<N>;
+    ;
+    self: Rotation<N, 2>, rhs: UnitComplex<N>, Output = UnitComplex<N>;
     [val val] => &self * &rhs;
     [ref val] =>  self * &rhs;
     [val ref] => &self *  rhs;
@@ -227,8 +224,8 @@ complex_op_impl_all!(
 // Rotation ÷ UnitComplex
 complex_op_impl_all!(
     Div, div;
-    (U2, U2);
-    self: Rotation<N, U2>, rhs: UnitComplex<N>, Output = UnitComplex<N>;
+    ;
+    self: Rotation<N, 2>, rhs: UnitComplex<N>, Output = UnitComplex<N>;
     [val val] => &self / &rhs;
     [ref val] =>  self / &rhs;
     [val ref] => &self /  rhs;
@@ -238,7 +235,7 @@ complex_op_impl_all!(
 // UnitComplex × Point
 complex_op_impl_all!(
     Mul, mul;
-    (U2, U1);
+    ;
     self: UnitComplex<N>, rhs: Point2<N>, Output = Point2<N>;
     [val val] => &self * &rhs;
     [ref val] =>  self * &rhs;
@@ -249,8 +246,8 @@ complex_op_impl_all!(
 // UnitComplex × Vector
 complex_op_impl_all!(
     Mul, mul;
-    (U2, U1) for S: Storage<N, U2>;
-    self: UnitComplex<N>, rhs: Vector<N, U2, S>, Output = Vector2<N>;
+    S: Storage<N, Const<2>>;
+    self: UnitComplex<N>, rhs: Vector<N, Const<2>, S>, Output = Vector2<N>;
     [val val] => &self * &rhs;
     [ref val] =>  self * &rhs;
     [val ref] => &self *  rhs;
@@ -264,8 +261,8 @@ complex_op_impl_all!(
 // UnitComplex × Unit<Vector>
 complex_op_impl_all!(
     Mul, mul;
-    (U2, U1) for S: Storage<N, U2>;
-    self: UnitComplex<N>, rhs: Unit<Vector<N, U2, S>>, Output = Unit<Vector2<N>>;
+    S: Storage<N, Const<2>>;
+    self: UnitComplex<N>, rhs: Unit<Vector<N, Const<2>, S>>, Output = Unit<Vector2<N>>;
     [val val] => &self * &rhs;
     [ref val] =>  self * &rhs;
     [val ref] => &self *  rhs;
@@ -275,9 +272,9 @@ complex_op_impl_all!(
 // UnitComplex × Isometry<UnitComplex>
 complex_op_impl_all!(
     Mul, mul;
-    (U2, U1);
-    self: UnitComplex<N>, rhs: Isometry<N, U2, UnitComplex<N>>,
-    Output = Isometry<N, U2, UnitComplex<N>>;
+    ;
+    self: UnitComplex<N>, rhs: Isometry<N, UnitComplex<N>, 2>,
+    Output = Isometry<N, UnitComplex<N>, 2>;
     [val val] => &self * &rhs;
     [ref val] =>  self * &rhs;
     [val ref] => &self *  rhs;
@@ -290,9 +287,9 @@ complex_op_impl_all!(
 // UnitComplex × Similarity<UnitComplex>
 complex_op_impl_all!(
     Mul, mul;
-    (U2, U1);
-    self: UnitComplex<N>, rhs: Similarity<N, U2, UnitComplex<N>>,
-    Output = Similarity<N, U2, UnitComplex<N>>;
+    ;
+    self: UnitComplex<N>, rhs: Similarity<N, UnitComplex<N>, 2>,
+    Output = Similarity<N, UnitComplex<N>, 2>;
     [val val] => &self * &rhs;
     [ref val] =>  self * &rhs;
     [val ref] => &self *  rhs;
@@ -302,9 +299,9 @@ complex_op_impl_all!(
 // UnitComplex × Translation
 complex_op_impl_all!(
     Mul, mul;
-    (U2, U1);
-    self: UnitComplex<N>, rhs: Translation<N, U2>,
-    Output = Isometry<N, U2, UnitComplex<N>>;
+    ;
+    self: UnitComplex<N>, rhs: Translation<N, 2>,
+    Output = Isometry<N, UnitComplex<N>, 2>;
     [val val] => Isometry::from_parts(Translation::from(&self *  rhs.vector), self);
     [ref val] => Isometry::from_parts(Translation::from( self *  rhs.vector), *self);
     [val ref] => Isometry::from_parts(Translation::from(&self * &rhs.vector), self);
@@ -314,9 +311,9 @@ complex_op_impl_all!(
 // Translation × UnitComplex
 complex_op_impl_all!(
     Mul, mul;
-    (U2, U1);
-    self: Translation<N, U2>, right: UnitComplex<N>,
-    Output = Isometry<N, U2, UnitComplex<N>>;
+    ;
+    self: Translation<N, 2>, right: UnitComplex<N>,
+    Output = Isometry<N, UnitComplex<N>, 2>;
     [val val] => Isometry::from_parts(self, right);
     [ref val] => Isometry::from_parts(self.clone(), right);
     [val ref] => Isometry::from_parts(self, *right);
@@ -366,56 +363,51 @@ where
 }
 
 // UnitComplex ×= Rotation
-impl<N: SimdRealField> MulAssign<Rotation<N, U2>> for UnitComplex<N>
+impl<N: SimdRealField> MulAssign<Rotation<N, 2>> for UnitComplex<N>
 where
     N::Element: SimdRealField,
-    DefaultAllocator: Allocator<N, U2, U2>,
 {
     #[inline]
-    fn mul_assign(&mut self, rhs: Rotation<N, U2>) {
+    fn mul_assign(&mut self, rhs: Rotation<N, 2>) {
         *self = &*self * rhs
     }
 }
 
-impl<'b, N: SimdRealField> MulAssign<&'b Rotation<N, U2>> for UnitComplex<N>
+impl<'b, N: SimdRealField> MulAssign<&'b Rotation<N, 2>> for UnitComplex<N>
 where
     N::Element: SimdRealField,
-    DefaultAllocator: Allocator<N, U2, U2>,
 {
     #[inline]
-    fn mul_assign(&mut self, rhs: &'b Rotation<N, U2>) {
+    fn mul_assign(&mut self, rhs: &'b Rotation<N, 2>) {
         *self = &*self * rhs
     }
 }
 
 // UnitComplex ÷= Rotation
-impl<N: SimdRealField> DivAssign<Rotation<N, U2>> for UnitComplex<N>
+impl<N: SimdRealField> DivAssign<Rotation<N, 2>> for UnitComplex<N>
 where
     N::Element: SimdRealField,
-    DefaultAllocator: Allocator<N, U2, U2>,
 {
     #[inline]
-    fn div_assign(&mut self, rhs: Rotation<N, U2>) {
+    fn div_assign(&mut self, rhs: Rotation<N, 2>) {
         *self = &*self / rhs
     }
 }
 
-impl<'b, N: SimdRealField> DivAssign<&'b Rotation<N, U2>> for UnitComplex<N>
+impl<'b, N: SimdRealField> DivAssign<&'b Rotation<N, 2>> for UnitComplex<N>
 where
     N::Element: SimdRealField,
-    DefaultAllocator: Allocator<N, U2, U2>,
 {
     #[inline]
-    fn div_assign(&mut self, rhs: &'b Rotation<N, U2>) {
+    fn div_assign(&mut self, rhs: &'b Rotation<N, 2>) {
         *self = &*self / rhs
     }
 }
 
 // Rotation ×= UnitComplex
-impl<N: SimdRealField> MulAssign<UnitComplex<N>> for Rotation<N, U2>
+impl<N: SimdRealField> MulAssign<UnitComplex<N>> for Rotation<N, 2>
 where
     N::Element: SimdRealField,
-    DefaultAllocator: Allocator<N, U2, U2>,
 {
     #[inline]
     fn mul_assign(&mut self, rhs: UnitComplex<N>) {
@@ -423,10 +415,9 @@ where
     }
 }
 
-impl<'b, N: SimdRealField> MulAssign<&'b UnitComplex<N>> for Rotation<N, U2>
+impl<'b, N: SimdRealField> MulAssign<&'b UnitComplex<N>> for Rotation<N, 2>
 where
     N::Element: SimdRealField,
-    DefaultAllocator: Allocator<N, U2, U2>,
 {
     #[inline]
     fn mul_assign(&mut self, rhs: &'b UnitComplex<N>) {
@@ -435,10 +426,9 @@ where
 }
 
 // Rotation ÷= UnitComplex
-impl<N: SimdRealField> DivAssign<UnitComplex<N>> for Rotation<N, U2>
+impl<N: SimdRealField> DivAssign<UnitComplex<N>> for Rotation<N, 2>
 where
     N::Element: SimdRealField,
-    DefaultAllocator: Allocator<N, U2, U2>,
 {
     #[inline]
     fn div_assign(&mut self, rhs: UnitComplex<N>) {
@@ -446,10 +436,9 @@ where
     }
 }
 
-impl<'b, N: SimdRealField> DivAssign<&'b UnitComplex<N>> for Rotation<N, U2>
+impl<'b, N: SimdRealField> DivAssign<&'b UnitComplex<N>> for Rotation<N, 2>
 where
     N::Element: SimdRealField,
-    DefaultAllocator: Allocator<N, U2, U2>,
 {
     #[inline]
     fn div_assign(&mut self, rhs: &'b UnitComplex<N>) {
diff --git a/src/proptest/mod.rs b/src/proptest/mod.rs
index ae263956..2551aa3d 100644
--- a/src/proptest/mod.rs
+++ b/src/proptest/mod.rs
@@ -53,20 +53,20 @@
 //! with [matrix](fn.matrix.html) as follows:
 //!
 //! ```rust
-//! use nalgebra::{Dynamic, MatrixMN, U3};
+//! use nalgebra::{Dynamic, MatrixMN, Const};
 //! use nalgebra::proptest::matrix;
 //! use proptest::prelude::*;
 //!
-//! type MyMatrix = MatrixMN<i32, U3, Dynamic>;
+//! type MyMatrix = MatrixMN<i32, Const::<3>, Dynamic>;
 //!
 //! /// Returns a strategy for pairs of matrices with `U3` rows and the same number of
 //! /// columns.
 //! fn matrix_pairs() -> impl Strategy<Value=(MyMatrix, MyMatrix)> {
-//!     matrix(-5 ..= 5, U3, 0 ..= 10)
+//!     matrix(-5 ..= 5, Const::<3>, 0 ..= 10)
 //!         // We first generate the initial matrix `a`, and then depending on the concrete
 //!         // instances of `a`, we pick a second matrix with the same number of columns
 //!         .prop_flat_map(|a| {
-//!             let b = matrix(-5 .. 5, U3, a.ncols());
+//!             let b = matrix(-5 .. 5, Const::<3>, a.ncols());
 //!             // This returns a new tuple strategy where we keep `a` fixed while
 //!             // the second item is a strategy that generates instances with the same
 //!             // dimensions as `a`
@@ -141,7 +141,7 @@
 //! PROPTEST_MAX_SHRINK_ITERS=100000 cargo test my_failing_test
 //! ```
 use crate::allocator::Allocator;
-use crate::{DefaultAllocator, Dim, DimName, Dynamic, MatrixMN, Scalar, U1};
+use crate::{Const, DefaultAllocator, Dim, DimName, Dynamic, MatrixMN, Scalar, U1};
 use proptest::arbitrary::Arbitrary;
 use proptest::collection::vec;
 use proptest::strategy::{BoxedStrategy, Just, NewTree, Strategy, ValueTree};
@@ -225,16 +225,16 @@ fn dynamic_dim_range() -> DimRange<Dynamic> {
 /// ## Examples
 /// ```
 /// use nalgebra::proptest::matrix;
-/// use nalgebra::{MatrixMN, U3, Dynamic};
+/// use nalgebra::{MatrixMN, Const, Dynamic};
 /// use proptest::prelude::*;
 ///
 /// proptest! {
 ///     # /*
 ///     #[test]
 ///     # */
-///     fn my_test(a in matrix(0 .. 5i32, U3, 0 ..= 5)) {
+///     fn my_test(a in matrix(0 .. 5i32, Const::<3>, 0 ..= 5)) {
 ///         // Let's make sure we've got the correct type first
-///         let a: MatrixMN<_, U3, Dynamic> = a;
+///         let a: MatrixMN<_, Const::<3>, Dynamic> = a;
 ///         prop_assert!(a.nrows() == 3);
 ///         prop_assert!(a.ncols() <= 5);
 ///         prop_assert!(a.iter().all(|x_ij| *x_ij >= 0 && *x_ij < 5));
@@ -329,7 +329,7 @@ where
     D: Dim,
     DefaultAllocator: Allocator<ScalarStrategy::Value, D>,
 {
-    matrix_(value_strategy, length.into(), U1.into())
+    matrix_(value_strategy, length.into(), Const::<1>.into())
 }
 
 impl<NParameters, R, C> Default for MatrixParameters<NParameters, R, C>
diff --git a/src/third_party/alga/alga_isometry.rs b/src/third_party/alga/alga_isometry.rs
index 3cb965a8..68788494 100755
--- a/src/third_party/alga/alga_isometry.rs
+++ b/src/third_party/alga/alga_isometry.rs
@@ -8,9 +8,7 @@ use alga::linear::{
     Transformation,
 };
 
-use crate::base::allocator::Allocator;
-use crate::base::dimension::DimName;
-use crate::base::{DefaultAllocator, VectorN};
+use crate::base::CVectorN;
 
 use crate::geometry::{AbstractRotation, Isometry, Point, Translation};
 
@@ -19,11 +17,10 @@ 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>
+impl<N: RealField + simba::scalar::RealField, R, const D: usize> Identity<Multiplicative>
+    for Isometry<N, R, D>
 where
     R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
-    DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     fn identity() -> Self {
@@ -31,11 +28,10 @@ where
     }
 }
 
-impl<N: RealField + simba::scalar::RealField, D: DimName, R> TwoSidedInverse<Multiplicative>
-    for Isometry<N, D, R>
+impl<N: RealField + simba::scalar::RealField, R, const D: usize> TwoSidedInverse<Multiplicative>
+    for Isometry<N, R, D>
 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()?"]
@@ -49,11 +45,10 @@ where
     }
 }
 
-impl<N: RealField + simba::scalar::RealField, D: DimName, R> AbstractMagma<Multiplicative>
-    for Isometry<N, D, R>
+impl<N: RealField + simba::scalar::RealField, R, const D: usize> AbstractMagma<Multiplicative>
+    for Isometry<N, R, D>
 where
     R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
-    DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     fn operate(&self, rhs: &Self) -> Self {
@@ -63,9 +58,8 @@ where
 
 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<N: RealField + simba::scalar::RealField, R, const D: usize> $marker<$operator> for Isometry<N, R, D>
+            where R: Rotation<Point<N, D>> + AbstractRotation<N, D> { }
     )*}
 );
 
@@ -82,11 +76,10 @@ impl_multiplicative_structures!(
  * Transformation groups.
  *
  */
-impl<N: RealField + simba::scalar::RealField, D: DimName, R> Transformation<Point<N, D>>
-    for Isometry<N, D, R>
+impl<N: RealField + simba::scalar::RealField, R, const D: usize> Transformation<Point<N, D>>
+    for Isometry<N, R, D>
 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> {
@@ -94,16 +87,15 @@ where
     }
 
     #[inline]
-    fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+    fn transform_vector(&self, v: &CVectorN<N, D>) -> CVectorN<N, D> {
         self.transform_vector(v)
     }
 }
 
-impl<N: RealField + simba::scalar::RealField, D: DimName, R> ProjectiveTransformation<Point<N, D>>
-    for Isometry<N, D, R>
+impl<N: RealField + simba::scalar::RealField, R, const D: usize>
+    ProjectiveTransformation<Point<N, D>> for Isometry<N, R, D>
 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> {
@@ -111,16 +103,15 @@ where
     }
 
     #[inline]
-    fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+    fn inverse_transform_vector(&self, v: &CVectorN<N, D>) -> CVectorN<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>
+impl<N: RealField + simba::scalar::RealField, R, const D: usize> AffineTransformation<Point<N, D>>
+    for Isometry<N, R, D>
 where
     R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
-    DefaultAllocator: Allocator<N, D>,
 {
     type Rotation = R;
     type NonUniformScaling = Id;
@@ -175,11 +166,10 @@ where
     }
 }
 
-impl<N: RealField + simba::scalar::RealField, D: DimName, R> Similarity<Point<N, D>>
-    for Isometry<N, D, R>
+impl<N: RealField + simba::scalar::RealField, R, const D: usize> Similarity<Point<N, D>>
+    for Isometry<N, R, D>
 where
     R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
-    DefaultAllocator: Allocator<N, D>,
 {
     type Scaling = Id;
 
@@ -201,9 +191,8 @@ where
 
 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> { }
+        impl<N: RealField + simba::scalar::RealField, R, const D: usize> $Trait<Point<N, D>> for Isometry<N, R, D>
+        where R: Rotation<Point<N, D>> + AbstractRotation<N, D> { }
     )*}
 );
 
diff --git a/src/third_party/alga/alga_point.rs b/src/third_party/alga/alga_point.rs
index 5a7cace5..2e8064f9 100644
--- a/src/third_party/alga/alga_point.rs
+++ b/src/third_party/alga/alga_point.rs
@@ -1,25 +1,19 @@
 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::base::{CVectorN, Scalar};
 
 use crate::geometry::Point;
 
-impl<N: Scalar + Field, D: DimName> AffineSpace for Point<N, D>
+impl<N: Scalar + Field, const D: usize> AffineSpace for Point<N, D>
 where
     N: Scalar + Field,
-    DefaultAllocator: Allocator<N, D>,
 {
-    type Translation = VectorN<N, D>;
+    type Translation = CVectorN<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>;
+impl<N: RealField + simba::scalar::RealField, const D: usize> EuclideanSpace for Point<N, D> {
+    type Coordinates = CVectorN<N, D>;
     type RealField = N;
 
     #[inline]
@@ -48,10 +42,9 @@ where
  * Ordering
  *
  */
-impl<N, D: DimName> MeetSemilattice for Point<N, D>
+impl<N, const D: usize> MeetSemilattice for Point<N, D>
 where
     N: Scalar + MeetSemilattice,
-    DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     fn meet(&self, other: &Self) -> Self {
@@ -59,10 +52,9 @@ where
     }
 }
 
-impl<N, D: DimName> JoinSemilattice for Point<N, D>
+impl<N, const D: usize> JoinSemilattice for Point<N, D>
 where
     N: Scalar + JoinSemilattice,
-    DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     fn join(&self, other: &Self) -> Self {
@@ -70,10 +62,9 @@ where
     }
 }
 
-impl<N, D: DimName> Lattice for Point<N, D>
+impl<N, const D: usize> Lattice for Point<N, D>
 where
     N: Scalar + Lattice,
-    DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     fn meet_join(&self, other: &Self) -> (Self, Self) {
diff --git a/src/third_party/alga/alga_rotation.rs b/src/third_party/alga/alga_rotation.rs
index f37ebbd1..100d3b30 100755
--- a/src/third_party/alga/alga_rotation.rs
+++ b/src/third_party/alga/alga_rotation.rs
@@ -7,10 +7,7 @@ use alga::linear::{
     ProjectiveTransformation, Similarity, Transformation,
 };
 
-use crate::base::allocator::Allocator;
-use crate::base::dimension::DimName;
-use crate::base::{DefaultAllocator, VectorN};
-
+use crate::base::CVectorN;
 use crate::geometry::{Point, Rotation};
 
 /*
@@ -18,10 +15,8 @@ use crate::geometry::{Point, Rotation};
  * Algebraic structures.
  *
  */
-impl<N: RealField + simba::scalar::RealField, D: DimName> Identity<Multiplicative>
+impl<N: RealField + simba::scalar::RealField, const D: usize> Identity<Multiplicative>
     for Rotation<N, D>
-where
-    DefaultAllocator: Allocator<N, D, D>,
 {
     #[inline]
     fn identity() -> Self {
@@ -29,10 +24,8 @@ where
     }
 }
 
-impl<N: RealField + simba::scalar::RealField, D: DimName> TwoSidedInverse<Multiplicative>
+impl<N: RealField + simba::scalar::RealField, const D: usize> TwoSidedInverse<Multiplicative>
     for Rotation<N, D>
-where
-    DefaultAllocator: Allocator<N, D, D>,
 {
     #[inline]
     #[must_use = "Did you mean to use two_sided_inverse_mut()?"]
@@ -46,10 +39,8 @@ where
     }
 }
 
-impl<N: RealField + simba::scalar::RealField, D: DimName> AbstractMagma<Multiplicative>
+impl<N: RealField + simba::scalar::RealField, const D: usize> AbstractMagma<Multiplicative>
     for Rotation<N, D>
-where
-    DefaultAllocator: Allocator<N, D, D>,
 {
     #[inline]
     fn operate(&self, rhs: &Self) -> Self {
@@ -59,8 +50,8 @@ where
 
 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<N: RealField + simba::scalar::RealField, const D: usize> $marker<$operator> for Rotation<N, D>
+            { }
     )*}
 );
 
@@ -77,10 +68,8 @@ impl_multiplicative_structures!(
  * Transformation groups.
  *
  */
-impl<N: RealField + simba::scalar::RealField, D: DimName> Transformation<Point<N, D>>
+impl<N: RealField + simba::scalar::RealField, const D: usize> 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> {
@@ -88,15 +77,13 @@ where
     }
 
     #[inline]
-    fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+    fn transform_vector(&self, v: &CVectorN<N, D>) -> CVectorN<N, D> {
         self.transform_vector(v)
     }
 }
 
-impl<N: RealField + simba::scalar::RealField, D: DimName> ProjectiveTransformation<Point<N, D>>
+impl<N: RealField + simba::scalar::RealField, const D: usize> 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> {
@@ -104,15 +91,13 @@ where
     }
 
     #[inline]
-    fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+    fn inverse_transform_vector(&self, v: &CVectorN<N, D>) -> CVectorN<N, D> {
         self.inverse_transform_vector(v)
     }
 }
 
-impl<N: RealField + simba::scalar::RealField, D: DimName> AffineTransformation<Point<N, D>>
+impl<N: RealField + simba::scalar::RealField, const D: usize> AffineTransformation<Point<N, D>>
     for Rotation<N, D>
-where
-    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
 {
     type Rotation = Self;
     type NonUniformScaling = Id;
@@ -154,9 +139,8 @@ where
     }
 }
 
-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>,
+impl<N: RealField + simba::scalar::RealField, const D: usize> Similarity<Point<N, D>>
+    for Rotation<N, D>
 {
     type Scaling = Id;
 
@@ -178,19 +162,16 @@ where
 
 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> { }
+        impl<N: RealField + simba::scalar::RealField, const D: usize> $Trait<Point<N, D>> for Rotation<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>>
+impl<N: RealField + simba::scalar::RealField, const D: usize> 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> {
@@ -200,14 +181,14 @@ where
     }
 
     #[inline]
-    fn rotation_between(_: &VectorN<N, D>, _: &VectorN<N, D>) -> Option<Self> {
+    fn rotation_between(_: &CVectorN<N, D>, _: &CVectorN<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> {
+    fn scaled_rotation_between(_: &CVectorN<N, D>, _: &CVectorN<N, D>, _: N) -> Option<Self> {
         // XXX: Add the general case.
         // XXX: Use specialization for 2D and 3D.
         unimplemented!()
diff --git a/src/third_party/alga/alga_similarity.rs b/src/third_party/alga/alga_similarity.rs
index 58dd4563..8f3bb126 100755
--- a/src/third_party/alga/alga_similarity.rs
+++ b/src/third_party/alga/alga_similarity.rs
@@ -5,10 +5,7 @@ use alga::general::{
 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::base::CVectorN;
 use crate::geometry::{AbstractRotation, Point, Similarity, Translation};
 
 /*
@@ -16,11 +13,10 @@ 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>
+impl<N: RealField + simba::scalar::RealField, R, const D: usize> Identity<Multiplicative>
+    for Similarity<N, R, D>
 where
     R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
-    DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     fn identity() -> Self {
@@ -28,11 +24,10 @@ where
     }
 }
 
-impl<N: RealField + simba::scalar::RealField, D: DimName, R> TwoSidedInverse<Multiplicative>
-    for Similarity<N, D, R>
+impl<N: RealField + simba::scalar::RealField, R, const D: usize> TwoSidedInverse<Multiplicative>
+    for Similarity<N, R, D>
 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()?"]
@@ -46,11 +41,10 @@ where
     }
 }
 
-impl<N: RealField + simba::scalar::RealField, D: DimName, R> AbstractMagma<Multiplicative>
-    for Similarity<N, D, R>
+impl<N: RealField + simba::scalar::RealField, R, const D: usize> AbstractMagma<Multiplicative>
+    for Similarity<N, R, D>
 where
     R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
-    DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     fn operate(&self, rhs: &Self) -> Self {
@@ -60,9 +54,9 @@ where
 
 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>
+        impl<N: RealField + simba::scalar::RealField, R, const D: usize> $marker<$operator> for Similarity<N, R, D>
             where R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
-                  DefaultAllocator: Allocator<N, D> { }
+                  { }
     )*}
 );
 
@@ -79,11 +73,10 @@ impl_multiplicative_structures!(
  * Transformation groups.
  *
  */
-impl<N: RealField + simba::scalar::RealField, D: DimName, R> Transformation<Point<N, D>>
-    for Similarity<N, D, R>
+impl<N: RealField + simba::scalar::RealField, R, const D: usize> Transformation<Point<N, D>>
+    for Similarity<N, R, D>
 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> {
@@ -91,16 +84,15 @@ where
     }
 
     #[inline]
-    fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+    fn transform_vector(&self, v: &CVectorN<N, D>) -> CVectorN<N, D> {
         self.transform_vector(v)
     }
 }
 
-impl<N: RealField + simba::scalar::RealField, D: DimName, R> ProjectiveTransformation<Point<N, D>>
-    for Similarity<N, D, R>
+impl<N: RealField + simba::scalar::RealField, R, const D: usize>
+    ProjectiveTransformation<Point<N, D>> for Similarity<N, R, D>
 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> {
@@ -108,16 +100,15 @@ where
     }
 
     #[inline]
-    fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+    fn inverse_transform_vector(&self, v: &CVectorN<N, D>) -> CVectorN<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>
+impl<N: RealField + simba::scalar::RealField, R, const D: usize> AffineTransformation<Point<N, D>>
+    for Similarity<N, R, D>
 where
     R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
-    DefaultAllocator: Allocator<N, D>,
 {
     type NonUniformScaling = N;
     type Rotation = R;
@@ -171,11 +162,10 @@ where
     }
 }
 
-impl<N: RealField + simba::scalar::RealField, D: DimName, R> AlgaSimilarity<Point<N, D>>
-    for Similarity<N, D, R>
+impl<N: RealField + simba::scalar::RealField, R, const D: usize> AlgaSimilarity<Point<N, D>>
+    for Similarity<N, R, D>
 where
     R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
-    DefaultAllocator: Allocator<N, D>,
 {
     type Scaling = N;
 
diff --git a/src/third_party/alga/alga_transform.rs b/src/third_party/alga/alga_transform.rs
index f83a0f8c..a4c23e4f 100755
--- a/src/third_party/alga/alga_transform.rs
+++ b/src/third_party/alga/alga_transform.rs
@@ -6,7 +6,7 @@ use alga::linear::{ProjectiveTransformation, Transformation};
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimNameAdd, DimNameSum, U1};
-use crate::base::{DefaultAllocator, VectorN};
+use crate::base::{CVectorN, Const, DefaultAllocator};
 
 use crate::geometry::{Point, SubTCategoryOf, TCategory, TProjective, Transform};
 
@@ -15,11 +15,12 @@ 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>
+impl<N: RealField + simba::scalar::RealField, C, const D: usize> Identity<Multiplicative>
+    for Transform<N, C, D>
 where
+    Const<D>: DimNameAdd<U1>,
     C: TCategory,
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+    DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
 {
     #[inline]
     fn identity() -> Self {
@@ -27,11 +28,12 @@ where
     }
 }
 
-impl<N: RealField + simba::scalar::RealField, D: DimNameAdd<U1>, C> TwoSidedInverse<Multiplicative>
-    for Transform<N, D, C>
+impl<N: RealField + simba::scalar::RealField, C, const D: usize> TwoSidedInverse<Multiplicative>
+    for Transform<N, C, D>
 where
+    Const<D>: DimNameAdd<U1>,
     C: SubTCategoryOf<TProjective>,
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+    DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
 {
     #[inline]
     #[must_use = "Did you mean to use two_sided_inverse_mut()?"]
@@ -45,11 +47,12 @@ where
     }
 }
 
-impl<N: RealField + simba::scalar::RealField, D: DimNameAdd<U1>, C> AbstractMagma<Multiplicative>
-    for Transform<N, D, C>
+impl<N: RealField + simba::scalar::RealField, C, const D: usize> AbstractMagma<Multiplicative>
+    for Transform<N, C, D>
 where
+    Const<D>: DimNameAdd<U1>,
     C: TCategory,
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+    DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
 {
     #[inline]
     fn operate(&self, rhs: &Self) -> Self {
@@ -59,17 +62,21 @@ where
 
 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>> { }
+        impl<N: RealField + simba::scalar::RealField, C, const D: usize> $marker<$operator> for Transform<N, C, D>
+            where
+                  Const<D>: DimNameAdd<U1>,
+                  C: TCategory,
+                  DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<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<N: RealField + simba::scalar::RealField, C, const D: usize> $marker<$operator> for Transform<N, C, D>
+            where
+                  Const<D>: DimNameAdd<U1>,
+                  C: SubTCategoryOf<TProjective>,
+                  DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> { }
     )*}
 );
 
@@ -89,14 +96,13 @@ impl_inversible_multiplicative_structures!(
  * Transformation groups.
  *
  */
-impl<N, D: DimNameAdd<U1>, C> Transformation<Point<N, D>> for Transform<N, D, C>
+impl<N, C, const D: usize> Transformation<Point<N, D>> for Transform<N, C, D>
 where
+    Const<D>: DimNameAdd<U1>,
     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>,
+    DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
+        + Allocator<N, DimNameSum<Const<D>, U1>>,
 {
     #[inline]
     fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
@@ -104,19 +110,18 @@ where
     }
 
     #[inline]
-    fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+    fn transform_vector(&self, v: &CVectorN<N, D>) -> CVectorN<N, D> {
         self.transform_vector(v)
     }
 }
 
-impl<N, D: DimNameAdd<U1>, C> ProjectiveTransformation<Point<N, D>> for Transform<N, D, C>
+impl<N, C, const D: usize> ProjectiveTransformation<Point<N, D>> for Transform<N, C, D>
 where
+    Const<D>: DimNameAdd<U1>,
     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>,
+    DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
+        + Allocator<N, DimNameSum<Const<D>, U1>>,
 {
     #[inline]
     fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
@@ -124,17 +129,17 @@ where
     }
 
     #[inline]
-    fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+    fn inverse_transform_vector(&self, v: &CVectorN<N, D>) -> CVectorN<N, D> {
         self.inverse_transform_vector(v)
     }
 }
 
 // TODO: we need to implement an SVD for this.
 //
-// impl<N, D: DimNameAdd<U1>, C> AffineTransformation<Point<N, D>> for Transform<N, D, C>
+// impl<N, C, const D: usize> AffineTransformation<Point<N, D>> for Transform<N, C, D>
 //     where N:  RealField,
 //           C: SubTCategoryOf<TAffine>,
-//           DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> +
+//           DefaultAllocator: Allocator<N, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> +
 //                             Allocator<N, D, D> +
 //                             Allocator<N, D> {
 //     type PreRotation       = Rotation<N, D>;
diff --git a/src/third_party/alga/alga_translation.rs b/src/third_party/alga/alga_translation.rs
index aba6f1f4..542fde0b 100755
--- a/src/third_party/alga/alga_translation.rs
+++ b/src/third_party/alga/alga_translation.rs
@@ -8,10 +8,7 @@ use alga::linear::{
     Transformation,
 };
 
-use crate::base::allocator::Allocator;
-use crate::base::dimension::DimName;
-use crate::base::{DefaultAllocator, VectorN};
-
+use crate::base::CVectorN;
 use crate::geometry::{Point, Translation};
 
 /*
@@ -19,10 +16,8 @@ use crate::geometry::{Point, Translation};
  * Algebraic structures.
  *
  */
-impl<N: RealField + simba::scalar::RealField, D: DimName> Identity<Multiplicative>
+impl<N: RealField + simba::scalar::RealField, const D: usize> Identity<Multiplicative>
     for Translation<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     fn identity() -> Self {
@@ -30,10 +25,8 @@ where
     }
 }
 
-impl<N: RealField + simba::scalar::RealField, D: DimName> TwoSidedInverse<Multiplicative>
+impl<N: RealField + simba::scalar::RealField, const D: usize> TwoSidedInverse<Multiplicative>
     for Translation<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     #[must_use = "Did you mean to use two_sided_inverse_mut()?"]
@@ -47,10 +40,8 @@ where
     }
 }
 
-impl<N: RealField + simba::scalar::RealField, D: DimName> AbstractMagma<Multiplicative>
+impl<N: RealField + simba::scalar::RealField, const D: usize> AbstractMagma<Multiplicative>
     for Translation<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     fn operate(&self, rhs: &Self) -> Self {
@@ -60,8 +51,8 @@ where
 
 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<N: RealField + simba::scalar::RealField, const D: usize> $marker<$operator> for Translation<N, D>
+            { }
     )*}
 );
 
@@ -78,10 +69,8 @@ impl_multiplicative_structures!(
  * Transformation groups.
  *
  */
-impl<N: RealField + simba::scalar::RealField, D: DimName> Transformation<Point<N, D>>
+impl<N: RealField + simba::scalar::RealField, const D: usize> 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> {
@@ -89,15 +78,13 @@ where
     }
 
     #[inline]
-    fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+    fn transform_vector(&self, v: &CVectorN<N, D>) -> CVectorN<N, D> {
         v.clone()
     }
 }
 
-impl<N: RealField + simba::scalar::RealField, D: DimName> ProjectiveTransformation<Point<N, D>>
+impl<N: RealField + simba::scalar::RealField, const D: usize> 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> {
@@ -105,15 +92,13 @@ where
     }
 
     #[inline]
-    fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+    fn inverse_transform_vector(&self, v: &CVectorN<N, D>) -> CVectorN<N, D> {
         v.clone()
     }
 }
 
-impl<N: RealField + simba::scalar::RealField, D: DimName> AffineTransformation<Point<N, D>>
+impl<N: RealField + simba::scalar::RealField, const D: usize> AffineTransformation<Point<N, D>>
     for Translation<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
 {
     type Rotation = Id;
     type NonUniformScaling = Id;
@@ -155,10 +140,8 @@ where
     }
 }
 
-impl<N: RealField + simba::scalar::RealField, D: DimName> Similarity<Point<N, D>>
+impl<N: RealField + simba::scalar::RealField, const D: usize> Similarity<Point<N, D>>
     for Translation<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
 {
     type Scaling = Id;
 
@@ -180,26 +163,24 @@ where
 
 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> { }
+        impl<N: RealField + simba::scalar::RealField, const D: usize> $Trait<Point<N, D>> for Translation<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>>
+impl<N: RealField + simba::scalar::RealField, const D: usize> AlgaTranslation<Point<N, D>>
     for Translation<N, D>
-where
-    DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
-    fn to_vector(&self) -> VectorN<N, D> {
+    fn to_vector(&self) -> CVectorN<N, D> {
         self.vector.clone()
     }
 
     #[inline]
-    fn from_vector(v: VectorN<N, D>) -> Option<Self> {
+    fn from_vector(v: CVectorN<N, D>) -> Option<Self> {
         Some(Self::from(v))
     }
 
diff --git a/tests/core/conversion.rs b/tests/core/conversion.rs
index 93545004..58ac179a 100644
--- a/tests/core/conversion.rs
+++ b/tests/core/conversion.rs
@@ -287,12 +287,12 @@ fn matrix_slice_from_matrix_ref() {
         ($mref:expr) => {
             MatrixSlice::<_, U3, U4, U1, U3>::from($mref)
         };
-    };
+    }
     macro_rules! fixed_slice_mut {
         ($mref:expr) => {
             MatrixSliceMut::<_, U3, U4, U1, U3>::from($mref)
         };
-    };
+    }
 
     // TODO: The `into_owned()` is a result of `PartialEq` not being implemented for different
     // Self and RHS. See issue #674. Once this is implemented, we can remove `into_owned`
diff --git a/tests/core/matrix.rs b/tests/core/matrix.rs
index 1430aedf..a88f2c1f 100644
--- a/tests/core/matrix.rs
+++ b/tests/core/matrix.rs
@@ -838,17 +838,16 @@ fn swizzle() {
 mod transposition_tests {
     use super::*;
     use crate::proptest::{dmatrix, matrix, vector4, PROPTEST_F64};
-    use na::{U2, U3, U4, U6};
     use proptest::{prop_assert, prop_assert_eq, proptest};
 
     proptest! {
         #[test]
-        fn transpose_transpose_is_self(m in matrix(PROPTEST_F64, U2, U3)) {
+        fn transpose_transpose_is_self(m in matrix(PROPTEST_F64, Const::<2>, Const::<3>)) {
             prop_assert_eq!(m.transpose().transpose(), m)
         }
 
         #[test]
-        fn transpose_mut_transpose_mut_is_self(m in matrix(PROPTEST_F64, U3, U3)) {
+        fn transpose_mut_transpose_mut_is_self(m in matrix(PROPTEST_F64, Const::<3>, Const::<3>)) {
             let mut mm = m;
             mm.transpose_mut();
             mm.transpose_mut();
@@ -875,7 +874,7 @@ mod transposition_tests {
         }
 
         #[test]
-        fn tr_mul_is_transpose_then_mul(m in matrix(PROPTEST_F64, U4, U6), v in vector4()) {
+        fn tr_mul_is_transpose_then_mul(m in matrix(PROPTEST_F64, Const::<4>, Const::<6>), v in vector4()) {
             prop_assert!(relative_eq!(m.transpose() * v, m.tr_mul(&v), epsilon = 1.0e-7))
         }
     }
diff --git a/tests/linalg/cholesky.rs b/tests/linalg/cholesky.rs
index 0e4a3817..bb578d49 100644
--- a/tests/linalg/cholesky.rs
+++ b/tests/linalg/cholesky.rs
@@ -4,7 +4,7 @@ macro_rules! gen_tests(
     ($module: ident, $scalar: ty) => {
         mod $module {
             use na::debug::RandomSDP;
-            use na::dimension::{U4, Const, Dynamic};
+            use na::dimension::{Const, Dynamic};
             use na::{DMatrix, DVector, Matrix4x3, Vector4};
             use rand::random;
             use simba::scalar::ComplexField;
diff --git a/tests/proptest/mod.rs b/tests/proptest/mod.rs
index 174c0fdd..be77f501 100644
--- a/tests/proptest/mod.rs
+++ b/tests/proptest/mod.rs
@@ -8,7 +8,7 @@ use nalgebra::proptest::{DimRange, MatrixStrategy};
 use nalgebra::{
     DMatrix, DVector, DefaultAllocator, Dim, DualQuaternion, Isometry2, Isometry3, Matrix3,
     MatrixMN, Point2, Point3, Quaternion, Rotation2, Rotation3, Scalar, Similarity3, Translation2,
-    Translation3, UnitComplex, UnitDualQuaternion, UnitQuaternion, Vector3, U2, U3, U4, U7, U8,
+    Translation3, UnitComplex, UnitDualQuaternion, UnitQuaternion, Vector3, U3, U4,
 };
 use num_complex::Complex;
 use proptest::prelude::*;
@@ -62,7 +62,7 @@ pub fn isometry3() -> impl Strategy<Value = Isometry3<f64>> {
 // }
 
 pub fn similarity3() -> impl Strategy<Value = Similarity3<f64>> {
-    vector(PROPTEST_F64, U7)
+    vector(PROPTEST_F64, Const::<7>)
         .prop_map(|v| Similarity3::new(v.xyz(), Vector3::new(v[3], v[4], v[5]), v[6]))
 }
 
@@ -71,7 +71,7 @@ pub fn unit_dual_quaternion() -> impl Strategy<Value = UnitDualQuaternion<f64>>
 }
 
 pub fn dual_quaternion() -> impl Strategy<Value = DualQuaternion<f64>> {
-    vector(PROPTEST_F64, U8).prop_map(|v| {
+    vector(PROPTEST_F64, Const::<8>).prop_map(|v| {
         DualQuaternion::from_real_and_dual(
             Quaternion::new(v[0], v[1], v[2], v[3]),
             Quaternion::new(v[4], v[5], v[6], v[7]),
@@ -88,7 +88,7 @@ pub fn unit_quaternion() -> impl Strategy<Value = UnitQuaternion<f64>> {
 }
 
 pub fn complex_f64() -> impl Strategy<Value = Complex<f64>> + Clone {
-    vector(PROPTEST_F64, U2).prop_map(|v| Complex::new(v.x, v.y))
+    vector(PROPTEST_F64, Const::<2>).prop_map(|v| Complex::new(v.x, v.y))
 }
 
 pub fn dmatrix() -> impl Strategy<Value = DMatrix<f64>> {
@@ -120,42 +120,41 @@ where
 // }
 
 macro_rules! define_strategies(
-    ($($strategy_: ident $strategy: ident<$nrows: ident, $ncols: ident>),*) => {$(
-        pub fn $strategy() -> impl Strategy<Value = MatrixMN<f64, $nrows, $ncols>> {
-            matrix(PROPTEST_F64, $nrows, $ncols)
+    ($($strategy_: ident $strategy: ident<$nrows: literal, $ncols: literal>),*) => {$(
+        pub fn $strategy() -> impl Strategy<Value = MatrixMN<f64, Const<$nrows>, Const<$ncols>>> {
+            matrix(PROPTEST_F64, Const::<$nrows>, Const::<$ncols>)
         }
 
-        pub fn $strategy_<ScalarStrategy>(scalar_strategy: ScalarStrategy) -> impl Strategy<Value = MatrixMN<ScalarStrategy::Value, $nrows, $ncols>>
+        pub fn $strategy_<ScalarStrategy>(scalar_strategy: ScalarStrategy) -> impl Strategy<Value = MatrixMN<ScalarStrategy::Value, Const<$nrows>, Const<$ncols>>>
             where
                 ScalarStrategy: Strategy + Clone + 'static,
-                ScalarStrategy::Value: Scalar,
-                DefaultAllocator: Allocator<ScalarStrategy::Value, $nrows, $ncols> {
-            matrix(scalar_strategy, $nrows, $ncols)
+                ScalarStrategy::Value: Scalar, {
+            matrix(scalar_strategy, Const::<$nrows>, Const::<$ncols>)
         }
     )*}
 );
 
 define_strategies!(
-    matrix1_ matrix1<U1, U1>,
-    matrix2_ matrix2<U2, U2>,
-    matrix3_ matrix3<U3, U3>,
-    matrix4_ matrix4<U4, U4>,
-    matrix5_ matrix5<U5, U5>,
-    matrix6_ matrix6<U6, U6>,
+    matrix1_ matrix1<1, 1>,
+    matrix2_ matrix2<2, 2>,
+    matrix3_ matrix3<3, 3>,
+    matrix4_ matrix4<4, 4>,
+    matrix5_ matrix5<5, 5>,
+    matrix6_ matrix6<6, 6>,
 
-    matrix5x2_ matrix5x2<U5, U2>,
-    matrix2x5_ matrix2x5<U2, U5>,
-    matrix5x3_ matrix5x3<U5, U3>,
-    matrix3x5_ matrix3x5<U3, U5>,
-    matrix5x4_ matrix5x4<U5, U4>,
-    matrix4x5_ matrix4x5<U4, U5>,
+    matrix5x2_ matrix5x2<5, 2>,
+    matrix2x5_ matrix2x5<2, 5>,
+    matrix5x3_ matrix5x3<5, 3>,
+    matrix3x5_ matrix3x5<3, 5>,
+    matrix5x4_ matrix5x4<5, 4>,
+    matrix4x5_ matrix4x5<4, 5>,
 
-    vector1_ vector1<U1, U1>,
-    vector2_ vector2<U2, U1>,
-    vector3_ vector3<U3, U1>,
-    vector4_ vector4<U4, U1>,
-    vector5_ vector5<U5, U1>,
-    vector6_ vector6<U6, U1>
+    vector1_ vector1<1, 1>,
+    vector2_ vector2<2, 1>,
+    vector3_ vector3<3, 1>,
+    vector4_ vector4<4, 1>,
+    vector5_ vector5<5, 1>,
+    vector6_ vector6<6, 1>
 );
 
 /// Generate a proptest that tests that all matrices generated with the
@@ -180,16 +179,16 @@ macro_rules! generate_matrix_sanity_test {
 }
 
 // Test all fixed-size matrices with row/col dimensions up to 3
-generate_matrix_sanity_test!(test_matrix_u0_u0, U0, U0);
-generate_matrix_sanity_test!(test_matrix_u1_u0, U1, U0);
-generate_matrix_sanity_test!(test_matrix_u0_u1, U0, U1);
-generate_matrix_sanity_test!(test_matrix_u1_u1, U1, U1);
-generate_matrix_sanity_test!(test_matrix_u2_u1, U2, U1);
-generate_matrix_sanity_test!(test_matrix_u1_u2, U1, U2);
-generate_matrix_sanity_test!(test_matrix_u2_u2, U2, U2);
-generate_matrix_sanity_test!(test_matrix_u3_u2, U3, U2);
-generate_matrix_sanity_test!(test_matrix_u2_u3, U2, U3);
-generate_matrix_sanity_test!(test_matrix_u3_u3, U3, U3);
+generate_matrix_sanity_test!(test_matrix_u0_u0, Const::<0>, Const::<0>);
+generate_matrix_sanity_test!(test_matrix_u1_u0, Const::<1>, Const::<0>);
+generate_matrix_sanity_test!(test_matrix_u0_u1, Const::<0>, Const::<1>);
+generate_matrix_sanity_test!(test_matrix_u1_u1, Const::<1>, Const::<1>);
+generate_matrix_sanity_test!(test_matrix_u2_u1, Const::<2>, Const::<1>);
+generate_matrix_sanity_test!(test_matrix_u1_u2, Const::<1>, Const::<2>);
+generate_matrix_sanity_test!(test_matrix_u2_u2, Const::<2>, Const::<2>);
+generate_matrix_sanity_test!(test_matrix_u3_u2, Const::<3>, Const::<2>);
+generate_matrix_sanity_test!(test_matrix_u2_u3, Const::<2>, Const::<3>);
+generate_matrix_sanity_test!(test_matrix_u3_u3, Const::<3>, Const::<3>);
 
 // Similarly test all heap-allocated but fixed dim ranges
 generate_matrix_sanity_test!(test_matrix_0_0, 0, 0);
@@ -204,18 +203,18 @@ generate_matrix_sanity_test!(test_matrix_2_3, 2, 3);
 generate_matrix_sanity_test!(test_matrix_3_3, 3, 3);
 
 // Test arbitrary inputs
-generate_matrix_sanity_test!(test_matrix_input_1, U5, 1..=5);
+generate_matrix_sanity_test!(test_matrix_input_1, Const::<5>, 1..=5);
 generate_matrix_sanity_test!(test_matrix_input_2, 3..=4, 1..=5);
-generate_matrix_sanity_test!(test_matrix_input_3, 1..=2, U3);
-generate_matrix_sanity_test!(test_matrix_input_4, 3, U4);
+generate_matrix_sanity_test!(test_matrix_input_3, 1..=2, Const::<3>);
+generate_matrix_sanity_test!(test_matrix_input_4, 3, Const::<4>);
 
 #[test]
 fn test_matrix_output_types() {
     // Test that the dimension types are correct for the given inputs
-    let _: MatrixStrategy<_, U3, U4> = matrix(-5..5, U3, U4);
-    let _: MatrixStrategy<_, U3, U3> = matrix(-5..5, U3, U3);
-    let _: MatrixStrategy<_, U3, Dynamic> = matrix(-5..5, U3, 1..=5);
-    let _: MatrixStrategy<_, Dynamic, U3> = matrix(-5..5, 1..=5, U3);
+    let _: MatrixStrategy<_, U3, U4> = matrix(-5..5, Const::<3>, Const::<4>);
+    let _: MatrixStrategy<_, U3, U3> = matrix(-5..5, Const::<3>, Const::<3>);
+    let _: MatrixStrategy<_, U3, Dynamic> = matrix(-5..5, Const::<3>, 1..=5);
+    let _: MatrixStrategy<_, Dynamic, U3> = matrix(-5..5, 1..=5, Const::<3>);
     let _: MatrixStrategy<_, Dynamic, Dynamic> = matrix(-5..5, 1..=5, 1..=5);
 }