From 16b8f4812d5d6cfce8d312af1fa81ffe82b1caef Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Crozet=20S=C3=A9bastien?= <developer@crozet.re>
Date: Sat, 26 Jun 2021 18:39:02 +0200
Subject: [PATCH] Define OPoint, a generic point with D: DimName

And define Point<T, const D: usize> as an alias for OPoint.
---
 CHANGELOG.md                       |   5 +
 src/geometry/point.rs              | 115 ++++++++++++------
 src/geometry/point_alias.rs        |   6 +-
 src/geometry/point_construction.rs |  65 ++++++-----
 src/geometry/point_conversion.rs   |  52 +++++----
 src/geometry/point_coordinates.rs  |  22 ++--
 src/geometry/point_ops.rs          | 180 ++++++++++++++++-------------
 7 files changed, 266 insertions(+), 179 deletions(-)

diff --git a/CHANGELOG.md b/CHANGELOG.md
index 78d5c374..23b4a82e 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -4,6 +4,11 @@ documented here.
 
 This project adheres to [Semantic Versioning](https://semver.org/).
 
+## [0.28.0]
+### Modified
+- The `Point::new` constructors are no longer const-fn. This is due to some limitations in const-fn
+  not allowing custom trait-bounds. Use the `point!` macro instead to build points in const environments.
+
 ## [0.27.1]
 ### Fixed
 - Fixed a bug in the conversion from `glam::Vec2` or `glam::DVec2` to `Isometry2`.
diff --git a/src/geometry/point.rs b/src/geometry/point.rs
index d25b4d7c..dfbd2f88 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, OVector, SVector, Scalar};
+use crate::base::{Const, DefaultAllocator, OVector, Scalar};
 
 /// A point in an euclidean space.
 ///
@@ -40,35 +40,52 @@ use crate::base::{Const, DefaultAllocator, OVector, SVector, Scalar};
 /// of said transformations for details.
 #[repr(C)]
 #[derive(Debug, Clone)]
-pub struct Point<T, const D: usize> {
+pub struct OPoint<T: Scalar, D: DimName>
+where
+    DefaultAllocator: Allocator<T, D>,
+{
     /// The coordinates of this point, i.e., the shift from the origin.
-    pub coords: SVector<T, D>,
+    pub coords: OVector<T, D>,
 }
 
-impl<T: Scalar + hash::Hash, const D: usize> hash::Hash for Point<T, D> {
+impl<T: Scalar + hash::Hash, D: DimName> hash::Hash for OPoint<T, D>
+where
+    DefaultAllocator: Allocator<T, D>,
+{
     fn hash<H: hash::Hasher>(&self, state: &mut H) {
         self.coords.hash(state)
     }
 }
 
-impl<T: Scalar + Copy, const D: usize> Copy for Point<T, D> {}
-
-#[cfg(feature = "bytemuck")]
-unsafe impl<T: Scalar, const D: usize> bytemuck::Zeroable for Point<T, D> where
-    SVector<T, D>: bytemuck::Zeroable
+impl<T: Scalar + Copy, D: DimName> Copy for OPoint<T, D>
+where
+    DefaultAllocator: Allocator<T, D>,
+    OVector<T, D>: Copy,
 {
 }
 
 #[cfg(feature = "bytemuck")]
-unsafe impl<T: Scalar, const D: usize> bytemuck::Pod for Point<T, D>
+unsafe impl<T: Scalar, D: DimName> bytemuck::Zeroable for OPoint<T, D>
+where
+    SVector<T, D>: bytemuck::Zeroable,
+    DefaultAllocator: Allocator<T, D>,
+{
+}
+
+#[cfg(feature = "bytemuck")]
+unsafe impl<T: Scalar, D: DimName> bytemuck::Pod for OPoint<T, D>
 where
     T: Copy,
     SVector<T, D>: bytemuck::Pod,
+    DefaultAllocator: Allocator<T, D>,
 {
 }
 
 #[cfg(feature = "serde-serialize-no-std")]
-impl<T: Scalar + Serialize, const D: usize> Serialize for Point<T, D> {
+impl<T: Scalar + Serialize, D: DimName> Serialize for OPoint<T, D>
+where
+    DefaultAllocator: Allocator<T, D>,
+{
     fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
     where
         S: Serializer,
@@ -78,7 +95,10 @@ impl<T: Scalar + Serialize, const D: usize> Serialize for Point<T, D> {
 }
 
 #[cfg(feature = "serde-serialize-no-std")]
-impl<'a, T: Scalar + Deserialize<'a>, const D: usize> Deserialize<'a> for Point<T, D> {
+impl<'a, T: Scalar + Deserialize<'a>, D: DimName> Deserialize<'a> for OPoint<T, D>
+where
+    DefaultAllocator: Allocator<T, D>,
+{
     fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
     where
         Des: Deserializer<'a>,
@@ -90,10 +110,11 @@ impl<'a, T: Scalar + Deserialize<'a>, const D: usize> Deserialize<'a> for Point<
 }
 
 #[cfg(feature = "abomonation-serialize")]
-impl<T, const D: usize> Abomonation for Point<T, D>
+impl<T, D: DimName> Abomonation for OPoint<T, D>
 where
     T: Scalar,
     SVector<T, D>: Abomonation,
+    DefaultAllocator: Allocator<T, D>,
 {
     unsafe fn entomb<W: Write>(&self, writer: &mut W) -> IOResult<()> {
         self.coords.entomb(writer)
@@ -108,7 +129,10 @@ where
     }
 }
 
-impl<T: Scalar, const D: usize> Point<T, D> {
+impl<T: Scalar, D: DimName> OPoint<T, D>
+where
+    DefaultAllocator: Allocator<T, D>,
+{
     /// Returns a point containing the result of `f` applied to each of its entries.
     ///
     /// # Example
@@ -123,7 +147,10 @@ impl<T: Scalar, const D: usize> Point<T, D> {
     /// ```
     #[inline]
     #[must_use]
-    pub fn map<T2: Scalar, F: FnMut(T) -> T2>(&self, f: F) -> Point<T2, D> {
+    pub fn map<T2: Scalar, F: FnMut(T) -> T2>(&self, f: F) -> OPoint<T2, D>
+    where
+        DefaultAllocator: Allocator<T2, D>,
+    {
         self.coords.map(f).into()
     }
 
@@ -163,20 +190,21 @@ impl<T: Scalar, const D: usize> Point<T, D> {
     /// ```
     #[inline]
     #[must_use]
-    pub fn to_homogeneous(&self) -> OVector<T, DimNameSum<Const<D>, U1>>
+    pub fn to_homogeneous(&self) -> OVector<T, DimNameSum<D, U1>>
     where
         T: One,
-        Const<D>: DimNameAdd<U1>,
-        DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>>,
+        D: DimNameAdd<U1>,
+        DefaultAllocator: Allocator<T, DimNameSum<D, U1>>,
     {
         let mut res = unsafe {
             crate::unimplemented_or_uninitialized_generic!(
-                <DimNameSum<Const<D>, U1> as DimName>::name(),
+                <DimNameSum<D, U1> as DimName>::name(),
                 Const::<1>
             )
         };
-        res.fixed_slice_mut::<D, 1>(0, 0).copy_from(&self.coords);
-        res[(D, 0)] = T::one();
+        res.generic_slice_mut((0, 0), (D::name(), Const::<1>))
+            .copy_from(&self.coords);
+        res[(D::dim(), 0)] = T::one();
 
         res
     }
@@ -184,7 +212,7 @@ impl<T: Scalar, const D: usize> Point<T, D> {
     /// Creates a new point with the given coordinates.
     #[deprecated(note = "Use Point::from(vector) instead.")]
     #[inline]
-    pub fn from_coordinates(coords: SVector<T, D>) -> Self {
+    pub fn from_coordinates(coords: OVector<T, D>) -> Self {
         Self { coords }
     }
 
@@ -243,8 +271,7 @@ impl<T: Scalar, const D: usize> Point<T, D> {
     #[inline]
     pub fn iter(
         &self,
-    ) -> MatrixIter<T, Const<D>, Const<1>, <DefaultAllocator as Allocator<T, Const<D>>>::Buffer>
-    {
+    ) -> MatrixIter<T, D, Const<1>, <DefaultAllocator as Allocator<T, D>>::Buffer> {
         self.coords.iter()
     }
 
@@ -270,8 +297,7 @@ impl<T: Scalar, const D: usize> Point<T, D> {
     #[inline]
     pub fn iter_mut(
         &mut self,
-    ) -> MatrixIterMut<T, Const<D>, Const<1>, <DefaultAllocator as Allocator<T, Const<D>>>::Buffer>
-    {
+    ) -> MatrixIterMut<T, D, Const<1>, <DefaultAllocator as Allocator<T, D>>::Buffer> {
         self.coords.iter_mut()
     }
 
@@ -289,9 +315,10 @@ impl<T: Scalar, const D: usize> Point<T, D> {
     }
 }
 
-impl<T: Scalar + AbsDiffEq, const D: usize> AbsDiffEq for Point<T, D>
+impl<T: Scalar + AbsDiffEq, D: DimName> AbsDiffEq for OPoint<T, D>
 where
     T::Epsilon: Copy,
+    DefaultAllocator: Allocator<T, D>,
 {
     type Epsilon = T::Epsilon;
 
@@ -306,9 +333,10 @@ where
     }
 }
 
-impl<T: Scalar + RelativeEq, const D: usize> RelativeEq for Point<T, D>
+impl<T: Scalar + RelativeEq, D: DimName> RelativeEq for OPoint<T, D>
 where
     T::Epsilon: Copy,
+    DefaultAllocator: Allocator<T, D>,
 {
     #[inline]
     fn default_max_relative() -> Self::Epsilon {
@@ -327,9 +355,10 @@ where
     }
 }
 
-impl<T: Scalar + UlpsEq, const D: usize> UlpsEq for Point<T, D>
+impl<T: Scalar + UlpsEq, D: DimName> UlpsEq for OPoint<T, D>
 where
     T::Epsilon: Copy,
+    DefaultAllocator: Allocator<T, D>,
 {
     #[inline]
     fn default_max_ulps() -> u32 {
@@ -342,16 +371,22 @@ where
     }
 }
 
-impl<T: Scalar + Eq, const D: usize> Eq for Point<T, D> {}
+impl<T: Scalar + Eq, D: DimName> Eq for OPoint<T, D> where DefaultAllocator: Allocator<T, D> {}
 
-impl<T: Scalar, const D: usize> PartialEq for Point<T, D> {
+impl<T: Scalar, D: DimName> PartialEq for OPoint<T, D>
+where
+    DefaultAllocator: Allocator<T, D>,
+{
     #[inline]
     fn eq(&self, right: &Self) -> bool {
         self.coords == right.coords
     }
 }
 
-impl<T: Scalar + PartialOrd, const D: usize> PartialOrd for Point<T, D> {
+impl<T: Scalar + PartialOrd, D: DimName> PartialOrd for OPoint<T, D>
+where
+    DefaultAllocator: Allocator<T, D>,
+{
     #[inline]
     fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
         self.coords.partial_cmp(&other.coords)
@@ -381,25 +416,28 @@ impl<T: Scalar + PartialOrd, const D: usize> PartialOrd for Point<T, D> {
 /*
  * inf/sup
  */
-impl<T: Scalar + SimdPartialOrd, const D: usize> Point<T, D> {
+impl<T: Scalar + SimdPartialOrd, D: DimName> OPoint<T, D>
+where
+    DefaultAllocator: Allocator<T, D>,
+{
     /// Computes the infimum (aka. componentwise min) of two points.
     #[inline]
     #[must_use]
-    pub fn inf(&self, other: &Self) -> Point<T, D> {
+    pub fn inf(&self, other: &Self) -> OPoint<T, D> {
         self.coords.inf(&other.coords).into()
     }
 
     /// Computes the supremum (aka. componentwise max) of two points.
     #[inline]
     #[must_use]
-    pub fn sup(&self, other: &Self) -> Point<T, D> {
+    pub fn sup(&self, other: &Self) -> OPoint<T, D> {
         self.coords.sup(&other.coords).into()
     }
 
     /// Computes the (infimum, supremum) of two points.
     #[inline]
     #[must_use]
-    pub fn inf_sup(&self, other: &Self) -> (Point<T, D>, Point<T, D>) {
+    pub fn inf_sup(&self, other: &Self) -> (OPoint<T, D>, OPoint<T, D>) {
         let (inf, sup) = self.coords.inf_sup(&other.coords);
         (inf.into(), sup.into())
     }
@@ -410,7 +448,10 @@ impl<T: Scalar + SimdPartialOrd, const D: usize> Point<T, D> {
  * Display
  *
  */
-impl<T: Scalar + fmt::Display, const D: usize> fmt::Display for Point<T, D> {
+impl<T: Scalar + fmt::Display, D: DimName> fmt::Display for OPoint<T, D>
+where
+    DefaultAllocator: Allocator<T, D>,
+{
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         write!(f, "{{")?;
 
diff --git a/src/geometry/point_alias.rs b/src/geometry/point_alias.rs
index 54441b09..f5f855c9 100644
--- a/src/geometry/point_alias.rs
+++ b/src/geometry/point_alias.rs
@@ -1,4 +1,8 @@
-use crate::geometry::Point;
+use crate::geometry::OPoint;
+use crate::Const;
+
+/// A point with `D` elements.
+pub type Point<T, const D: usize> = OPoint<T, Const<D>>;
 
 /// A statically sized 1-dimensional column point.
 ///
diff --git a/src/geometry/point_construction.rs b/src/geometry/point_construction.rs
index 7e34137c..03f24cdb 100644
--- a/src/geometry/point_construction.rs
+++ b/src/geometry/point_construction.rs
@@ -10,22 +10,26 @@ use rand::{
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimNameAdd, DimNameSum, U1};
-use crate::base::{DefaultAllocator, SVector, Scalar};
+use crate::base::{DefaultAllocator, Scalar};
 use crate::{
-    Const, OVector, Point1, Point2, Point3, Point4, Point5, Point6, Vector1, Vector2, Vector3,
-    Vector4, Vector5, Vector6,
+    Const, DimName, OPoint, OVector, Point1, Point2, Point3, Point4, Point5, Point6, Vector1,
+    Vector2, Vector3, Vector4, Vector5, Vector6,
 };
 use simba::scalar::{ClosedDiv, SupersetOf};
 
 use crate::geometry::Point;
 
 /// # Other construction methods
-impl<T: Scalar, const D: usize> Point<T, D> {
+impl<T: Scalar, D: DimName> OPoint<T, D>
+where
+    DefaultAllocator: Allocator<T, D>,
+{
     /// Creates a new point with uninitialized coordinates.
     #[inline]
     pub unsafe fn new_uninitialized() -> Self {
         Self::from(crate::unimplemented_or_uninitialized_generic!(
-            Const::<D>, Const::<1>
+            D::name(),
+            Const::<1>
         ))
     }
 
@@ -49,7 +53,7 @@ impl<T: Scalar, const D: usize> Point<T, D> {
     where
         T: Zero,
     {
-        Self::from(SVector::from_element(T::zero()))
+        Self::from(OVector::from_element(T::zero()))
     }
 
     /// Creates a new point from a slice.
@@ -68,7 +72,7 @@ impl<T: Scalar, const D: usize> Point<T, D> {
     /// ```
     #[inline]
     pub fn from_slice(components: &[T]) -> Self {
-        Self::from(SVector::from_row_slice(components))
+        Self::from(OVector::from_row_slice(components))
     }
 
     /// Creates a new point from its homogeneous vector representation.
@@ -102,14 +106,15 @@ impl<T: Scalar, const D: usize> Point<T, D> {
     /// assert_eq!(pt, Some(Point2::new(1.0, 2.0)));
     /// ```
     #[inline]
-    pub fn from_homogeneous(v: OVector<T, DimNameSum<Const<D>, U1>>) -> Option<Self>
+    pub fn from_homogeneous(v: OVector<T, DimNameSum<D, U1>>) -> Option<Self>
     where
         T: Scalar + Zero + One + ClosedDiv,
-        Const<D>: DimNameAdd<U1>,
-        DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>>,
+        D: DimNameAdd<U1>,
+        DefaultAllocator: Allocator<T, DimNameSum<D, U1>>,
     {
-        if !v[D].is_zero() {
-            let coords = v.fixed_slice::<D, 1>(0, 0) / v[D].inlined_clone();
+        if !v[D::dim()].is_zero() {
+            let coords =
+                v.generic_slice((0, 0), (D::name(), Const::<1>)) / v[D::dim()].inlined_clone();
             Some(Self::from(coords))
         } else {
             None
@@ -125,9 +130,10 @@ impl<T: Scalar, const D: usize> Point<T, D> {
     /// let pt2 = pt.cast::<f32>();
     /// assert_eq!(pt2, Point2::new(1.0f32, 2.0));
     /// ```
-    pub fn cast<To: Scalar>(self) -> Point<To, D>
+    pub fn cast<To: Scalar>(self) -> OPoint<To, D>
     where
-        Point<To, D>: SupersetOf<Self>,
+        OPoint<To, D>: SupersetOf<Self>,
+        DefaultAllocator: Allocator<To, D>,
     {
         crate::convert(self)
     }
@@ -138,38 +144,43 @@ impl<T: Scalar, const D: usize> Point<T, D> {
  * Traits that build points.
  *
  */
-impl<T: Scalar + Bounded, const D: usize> Bounded for Point<T, D> {
+impl<T: Scalar + Bounded, D: DimName> Bounded for OPoint<T, D>
+where
+    DefaultAllocator: Allocator<T, D>,
+{
     #[inline]
     fn max_value() -> Self {
-        Self::from(SVector::max_value())
+        Self::from(OVector::max_value())
     }
 
     #[inline]
     fn min_value() -> Self {
-        Self::from(SVector::min_value())
+        Self::from(OVector::min_value())
     }
 }
 
 #[cfg(feature = "rand-no-std")]
-impl<T: Scalar, const D: usize> Distribution<Point<T, D>> for Standard
+impl<T: Scalar, D: DimName> Distribution<OPoint<T, D>> for Standard
 where
     Standard: Distribution<T>,
+    DefaultAllocator: Allocator<T, D>,
 {
     /// 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<T, D> {
-        Point::from(rng.gen::<SVector<T, D>>())
+    fn sample<'a, G: Rng + ?Sized>(&self, rng: &mut G) -> OPoint<T, D> {
+        Point::from(rng.gen::<OVector<T, D>>())
     }
 }
 
 #[cfg(feature = "arbitrary")]
-impl<T: Scalar + Arbitrary + Send, const D: usize> Arbitrary for Point<T, D>
+impl<T: Scalar + Arbitrary + Send, D: DimName> Arbitrary for OPoint<T, D>
 where
-    <DefaultAllocator as Allocator<T, Const<D>>>::Buffer: Send,
+    <DefaultAllocator as Allocator<T, D>>::Buffer: Send,
+    DefaultAllocator: Allocator<T, D>,
 {
     #[inline]
     fn arbitrary(g: &mut Gen) -> Self {
-        Self::from(SVector::arbitrary(g))
+        Self::from(OVector::arbitrary(g))
     }
 }
 
@@ -181,7 +192,7 @@ where
 // NOTE: the impl for Point1 is not with the others so that we
 // can add a section with the impl block comment.
 /// # Construction from individual components
-impl<T> Point1<T> {
+impl<T: Scalar> Point1<T> {
     /// Initializes this point from its components.
     ///
     /// # Example
@@ -192,7 +203,7 @@ impl<T> Point1<T> {
     /// assert_eq!(p.x, 1.0);
     /// ```
     #[inline]
-    pub const fn new(x: T) -> Self {
+    pub fn new(x: T) -> Self {
         Point {
             coords: Vector1::new(x),
         }
@@ -200,13 +211,13 @@ impl<T> Point1<T> {
 }
 macro_rules! componentwise_constructors_impl(
     ($($doc: expr; $Point: ident, $Vector: ident, $($args: ident:$irow: expr),*);* $(;)*) => {$(
-        impl<T> $Point<T> {
+        impl<T: Scalar> $Point<T> {
             #[doc = "Initializes this point from its components."]
             #[doc = "# Example\n```"]
             #[doc = $doc]
             #[doc = "```"]
             #[inline]
-            pub const fn new($($args: T),*) -> Self {
+            pub fn new($($args: T),*) -> Self {
                 Point { coords: $Vector::new($($args),*) }
             }
         }
diff --git a/src/geometry/point_conversion.rs b/src/geometry/point_conversion.rs
index e5ab8272..f35a9fc6 100644
--- a/src/geometry/point_conversion.rs
+++ b/src/geometry/point_conversion.rs
@@ -7,6 +7,7 @@ use crate::base::dimension::{DimNameAdd, DimNameSum, U1};
 use crate::base::{Const, DefaultAllocator, Matrix, OVector, Scalar};
 
 use crate::geometry::Point;
+use crate::{DimName, OPoint};
 
 /*
  * This file provides the following conversions:
@@ -16,67 +17,69 @@ use crate::geometry::Point;
  * Point -> Vector (homogeneous)
  */
 
-impl<T1, T2, const D: usize> SubsetOf<Point<T2, D>> for Point<T1, D>
+impl<T1, T2, D: DimName> SubsetOf<OPoint<T2, D>> for OPoint<T1, D>
 where
     T1: Scalar,
     T2: Scalar + SupersetOf<T1>,
+    DefaultAllocator: Allocator<T1, D> + Allocator<T2, D>,
 {
     #[inline]
-    fn to_superset(&self) -> Point<T2, D> {
-        Point::from(self.coords.to_superset())
+    fn to_superset(&self) -> OPoint<T2, D> {
+        OPoint::from(self.coords.to_superset())
     }
 
     #[inline]
-    fn is_in_subset(m: &Point<T2, D>) -> bool {
+    fn is_in_subset(m: &OPoint<T2, D>) -> bool {
         // TODO: is there a way to reuse the `.is_in_subset` from the matrix implementation of
         // SubsetOf?
         m.iter().all(|e| e.is_in_subset())
     }
 
     #[inline]
-    fn from_superset_unchecked(m: &Point<T2, D>) -> Self {
+    fn from_superset_unchecked(m: &OPoint<T2, D>) -> Self {
         Self::from(Matrix::from_superset_unchecked(&m.coords))
     }
 }
 
-impl<T1, T2, const D: usize> SubsetOf<OVector<T2, DimNameSum<Const<D>, U1>>> for Point<T1, D>
+impl<T1, T2, D> SubsetOf<OVector<T2, DimNameSum<D, U1>>> for OPoint<T1, D>
 where
-    Const<D>: DimNameAdd<U1>,
+    D: DimNameAdd<U1>,
     T1: Scalar,
     T2: Scalar + Zero + One + ClosedDiv + SupersetOf<T1>,
-    DefaultAllocator:
-        Allocator<T1, DimNameSum<Const<D>, U1>> + Allocator<T2, DimNameSum<Const<D>, U1>>,
+    DefaultAllocator: Allocator<T1, D>
+        + Allocator<T2, D>
+        + Allocator<T1, DimNameSum<D, U1>>
+        + Allocator<T2, DimNameSum<D, U1>>,
     // + Allocator<T1, D>
     // + Allocator<T2, D>,
 {
     #[inline]
-    fn to_superset(&self) -> OVector<T2, DimNameSum<Const<D>, U1>> {
-        let p: Point<T2, D> = self.to_superset();
+    fn to_superset(&self) -> OVector<T2, DimNameSum<D, U1>> {
+        let p: OPoint<T2, D> = self.to_superset();
         p.to_homogeneous()
     }
 
     #[inline]
-    fn is_in_subset(v: &OVector<T2, DimNameSum<Const<D>, U1>>) -> bool {
-        crate::is_convertible::<_, OVector<T1, DimNameSum<Const<D>, U1>>>(v) && !v[D].is_zero()
+    fn is_in_subset(v: &OVector<T2, DimNameSum<D, U1>>) -> bool {
+        crate::is_convertible::<_, OVector<T1, DimNameSum<D, U1>>>(v) && !v[D::dim()].is_zero()
     }
 
     #[inline]
-    fn from_superset_unchecked(v: &OVector<T2, DimNameSum<Const<D>, U1>>) -> Self {
-        let coords = v.fixed_slice::<D, 1>(0, 0) / v[D].inlined_clone();
+    fn from_superset_unchecked(v: &OVector<T2, DimNameSum<D, U1>>) -> Self {
+        let coords = v.generic_slice((0, 0), (D::name(), Const::<1>)) / v[D::dim()].inlined_clone();
         Self {
             coords: crate::convert_unchecked(coords),
         }
     }
 }
 
-impl<T: Scalar + Zero + One, const D: usize> From<Point<T, D>>
-    for OVector<T, DimNameSum<Const<D>, U1>>
+impl<T: Scalar + Zero + One, D: DimName> From<OPoint<T, D>> for OVector<T, DimNameSum<D, U1>>
 where
-    Const<D>: DimNameAdd<U1>,
-    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>>,
+    D: DimNameAdd<U1>,
+    DefaultAllocator: Allocator<T, DimNameSum<D, U1>> + Allocator<T, D>,
 {
     #[inline]
-    fn from(t: Point<T, D>) -> Self {
+    fn from(t: OPoint<T, D>) -> Self {
         t.to_homogeneous()
     }
 }
@@ -97,10 +100,13 @@ impl<T: Scalar, const D: usize> From<Point<T, D>> for [T; D] {
     }
 }
 
-impl<T: Scalar, const D: usize> From<OVector<T, Const<D>>> for Point<T, D> {
+impl<T: Scalar, D: DimName> From<OVector<T, D>> for OPoint<T, D>
+where
+    DefaultAllocator: Allocator<T, D>,
+{
     #[inline]
-    fn from(coords: OVector<T, Const<D>>) -> Self {
-        Point { coords }
+    fn from(coords: OVector<T, D>) -> Self {
+        OPoint { coords }
     }
 }
 
diff --git a/src/geometry/point_coordinates.rs b/src/geometry/point_coordinates.rs
index 8d9e9ccc..984a2fae 100644
--- a/src/geometry/point_coordinates.rs
+++ b/src/geometry/point_coordinates.rs
@@ -1,9 +1,9 @@
 use std::ops::{Deref, DerefMut};
 
 use crate::base::coordinates::{X, XY, XYZ, XYZW, XYZWA, XYZWAB};
-use crate::base::Scalar;
+use crate::base::{Scalar, U1, U2, U3, U4, U5, U6};
 
-use crate::geometry::Point;
+use crate::geometry::OPoint;
 
 /*
  *
@@ -12,8 +12,8 @@ use crate::geometry::Point;
  */
 
 macro_rules! deref_impl(
-    ($D: expr, $Target: ident $(, $comps: ident)*) => {
-        impl<T: Scalar> Deref for Point<T, $D>
+    ($D: ty, $Target: ident $(, $comps: ident)*) => {
+        impl<T: Scalar> Deref for OPoint<T, $D>
         {
             type Target = $Target<T>;
 
@@ -23,7 +23,7 @@ macro_rules! deref_impl(
             }
         }
 
-        impl<T: Scalar> DerefMut for Point<T, $D>
+        impl<T: Scalar> DerefMut for OPoint<T, $D>
         {
             #[inline]
             fn deref_mut(&mut self) -> &mut Self::Target {
@@ -33,9 +33,9 @@ macro_rules! deref_impl(
     }
 );
 
-deref_impl!(1, X, x);
-deref_impl!(2, XY, x, y);
-deref_impl!(3, XYZ, x, y, z);
-deref_impl!(4, XYZW, x, y, z, w);
-deref_impl!(5, XYZWA, x, y, z, w, a);
-deref_impl!(6, XYZWAB, x, y, z, w, a, b);
+deref_impl!(U1, X, x);
+deref_impl!(U2, XY, x, y);
+deref_impl!(U3, XYZ, x, y, z);
+deref_impl!(U4, XYZW, x, y, z, w);
+deref_impl!(U5, XYZWA, x, y, z, w, a);
+deref_impl!(U6, XYZWAB, x, y, z, w, a, b);
diff --git a/src/geometry/point_ops.rs b/src/geometry/point_ops.rs
index 576028cc..5b019a9d 100644
--- a/src/geometry/point_ops.rs
+++ b/src/geometry/point_ops.rs
@@ -8,18 +8,23 @@ use simba::scalar::{ClosedAdd, ClosedDiv, ClosedMul, ClosedNeg, ClosedSub};
 use crate::base::constraint::{
     AreMultipliable, SameNumberOfColumns, SameNumberOfRows, ShapeConstraint,
 };
-use crate::base::dimension::{Dim, U1};
+use crate::base::dimension::{Dim, DimName, U1};
 use crate::base::storage::Storage;
-use crate::base::{Const, Matrix, SVector, Scalar, Vector};
+use crate::base::{Const, Matrix, OVector, Scalar, Vector};
 
-use crate::geometry::Point;
+use crate::allocator::Allocator;
+use crate::geometry::{OPoint, Point};
+use crate::DefaultAllocator;
 
 /*
  *
  * Indexing.
  *
  */
-impl<T: Scalar, const D: usize> Index<usize> for Point<T, D> {
+impl<T: Scalar, D: DimName> Index<usize> for OPoint<T, D>
+where
+    DefaultAllocator: Allocator<T, D>,
+{
     type Output = T;
 
     #[inline]
@@ -28,7 +33,10 @@ impl<T: Scalar, const D: usize> Index<usize> for Point<T, D> {
     }
 }
 
-impl<T: Scalar, const D: usize> IndexMut<usize> for Point<T, D> {
+impl<T: Scalar, D: DimName> IndexMut<usize> for OPoint<T, D>
+where
+    DefaultAllocator: Allocator<T, D>,
+{
     #[inline]
     fn index_mut(&mut self, i: usize) -> &mut Self::Output {
         &mut self.coords[i]
@@ -40,7 +48,10 @@ impl<T: Scalar, const D: usize> IndexMut<usize> for Point<T, D> {
  * Neg.
  *
  */
-impl<T: Scalar + ClosedNeg, const D: usize> Neg for Point<T, D> {
+impl<T: Scalar + ClosedNeg, D: DimName> Neg for OPoint<T, D>
+where
+    DefaultAllocator: Allocator<T, D>,
+{
     type Output = Self;
 
     #[inline]
@@ -49,8 +60,11 @@ impl<T: Scalar + ClosedNeg, const D: usize> Neg for Point<T, D> {
     }
 }
 
-impl<'a, T: Scalar + ClosedNeg, const D: usize> Neg for &'a Point<T, D> {
-    type Output = Point<T, D>;
+impl<'a, T: Scalar + ClosedNeg, D: DimName> Neg for &'a OPoint<T, D>
+where
+    DefaultAllocator: Allocator<T, D>,
+{
+    type Output = OPoint<T, D>;
 
     #[inline]
     fn neg(self) -> Self::Output {
@@ -66,102 +80,103 @@ impl<'a, T: Scalar + ClosedNeg, const D: usize> Neg for &'a Point<T, D> {
 
 // Point - Point
 add_sub_impl!(Sub, sub, ClosedSub;
-    (Const<D>, U1), (Const<D>, U1) -> (Const<D>, U1)
-    const D; for; where;
-    self: &'a Point<T, D>, right: &'b Point<T, D>, Output = SVector<T, D>;
+    (D, U1), (D, U1) -> (D, U1)
+    const; for D; where D: DimName, DefaultAllocator: Allocator<T, D>;
+    self: &'a OPoint<T, D>, right: &'b OPoint<T, D>, Output = OVector<T, D>;
     &self.coords - &right.coords; 'a, 'b);
 
 add_sub_impl!(Sub, sub, ClosedSub;
-    (Const<D>, U1), (Const<D>, U1) -> (Const<D>, U1)
-    const D; for; where;
-    self: &'a Point<T, D>, right: Point<T, D>, Output = SVector<T, D>;
+    (D, U1), (D, U1) -> (D, U1)
+    const; for D; where D: DimName, DefaultAllocator: Allocator<T, D>;
+    self: &'a OPoint<T, D>, right: OPoint<T, D>, Output = OVector<T, D>;
     &self.coords - right.coords; 'a);
 
 add_sub_impl!(Sub, sub, ClosedSub;
-    (Const<D>, U1), (Const<D>, U1) -> (Const<D>, U1)
-    const D; for; where;
-    self: Point<T, D>, right: &'b Point<T, D>, Output = SVector<T, D>;
+    (D, U1), (D, U1) -> (D, U1)
+    const; for D; where D: DimName, DefaultAllocator: Allocator<T, D>;
+    self: OPoint<T, D>, right: &'b OPoint<T, D>, Output = OVector<T, D>;
     self.coords - &right.coords; 'b);
 
 add_sub_impl!(Sub, sub, ClosedSub;
-    (Const<D>, U1), (Const<D>, U1) -> (Const<D>, U1)
-    const D; for; where;
-    self: Point<T, D>, right: Point<T, D>, Output = SVector<T, D>;
+    (D, U1), (D, U1) -> (D, U1)
+    const; for D; where D: DimName, DefaultAllocator: Allocator<T, D>;
+    self: OPoint<T, D>, right: OPoint<T, D>, Output = OVector<T, D>;
     self.coords - right.coords; );
 
 // Point - Vector
 add_sub_impl!(Sub, sub, ClosedSub;
-    (Const<D1>, U1), (D2, U1) -> (Const<D1>, U1)
-    const D1;
-    for D2, SB;
-    where D2: Dim, SB: Storage<T, D2>;
-    self: &'a Point<T, D1>, right: &'b Vector<T, D2, SB>, Output = Point<T, D1>;
+    (D1, U1), (D2, U1) -> (D1, U1)
+    const;
+    for D1, D2, SB;
+    where D1: DimName, D2: Dim, SB: Storage<T, D2>, DefaultAllocator: Allocator<T, D1>;
+    self: &'a OPoint<T, D1>, right: &'b Vector<T, D2, SB>, Output = OPoint<T, D1>;
     Self::Output::from(&self.coords - right); 'a, 'b);
 
 add_sub_impl!(Sub, sub, ClosedSub;
-    (Const<D1>, U1), (D2, U1) -> (Const<D1>, U1)
-    const D1;
-    for D2, SB;
-    where D2: Dim, SB: Storage<T, D2>;
-    self: &'a Point<T, D1>, right: Vector<T, D2, SB>, Output = Point<T, D1>;
+    (D1, U1), (D2, U1) -> (D1, U1)
+    const;
+    for D1, D2, SB;
+    where D1: DimName, D2: Dim, SB: Storage<T, D2>, DefaultAllocator: Allocator<T, D1>;
+    self: &'a OPoint<T, D1>, right: Vector<T, D2, SB>, Output = OPoint<T, D1>;
     Self::Output::from(&self.coords - &right); 'a); // TODO: should not be a ref to `right`.
 
 add_sub_impl!(Sub, sub, ClosedSub;
-    (Const<D1>, U1), (D2, U1) -> (Const<D1>, U1)
-    const D1;
-    for D2, SB;
-    where D2: Dim, SB: Storage<T, D2>;
-    self: Point<T, D1>, right: &'b Vector<T, D2, SB>, Output = Point<T, D1>;
+    (D1, U1), (D2, U1) -> (D1, U1)
+    const;
+    for D1, D2, SB;
+    where D1: DimName, D2: Dim, SB: Storage<T, D2>, DefaultAllocator: Allocator<T, D1>;
+    self: OPoint<T, D1>, right: &'b Vector<T, D2, SB>, Output = OPoint<T, D1>;
     Self::Output::from(self.coords - right); 'b);
 
 add_sub_impl!(Sub, sub, ClosedSub;
-    (Const<D1>, U1), (D2, U1) -> (Const<D1>, U1)
-    const D1;
-    for D2, SB;
-    where D2: Dim, SB: Storage<T, D2>;
-    self: Point<T, D1>, right: Vector<T, D2, SB>, Output = Point<T, D1>;
+    (D1, U1), (D2, U1) -> (D1, U1)
+    const;
+    for D1, D2, SB;
+    where D1: DimName, D2: Dim, SB: Storage<T, D2>, DefaultAllocator: Allocator<T, D1>;
+    self: OPoint<T, D1>, right: Vector<T, D2, SB>, Output = OPoint<T, D1>;
     Self::Output::from(self.coords - right); );
 
 // Point + Vector
 add_sub_impl!(Add, add, ClosedAdd;
-    (Const<D1>, U1), (D2, U1) -> (Const<D1>, U1)
-    const D1;
-    for D2, SB;
-    where D2: Dim, SB: Storage<T, D2>;
-    self: &'a Point<T, D1>, right: &'b Vector<T, D2, SB>, Output = Point<T, D1>;
+    (D1, U1), (D2, U1) -> (D1, U1)
+    const;
+    for D1, D2, SB;
+    where D1: DimName, D2: Dim, SB: Storage<T, D2>, DefaultAllocator: Allocator<T, D1>;
+    self: &'a OPoint<T, D1>, right: &'b Vector<T, D2, SB>, Output = OPoint<T, D1>;
     Self::Output::from(&self.coords + right); 'a, 'b);
 
 add_sub_impl!(Add, add, ClosedAdd;
-    (Const<D1>, U1), (D2, U1) -> (Const<D1>, U1)
-    const D1;
-    for D2, SB;
-    where D2: Dim, SB: Storage<T, D2>;
-    self: &'a Point<T, D1>, right: Vector<T, D2, SB>, Output = Point<T, D1>;
+    (D1, U1), (D2, U1) -> (D1, U1)
+    const;
+    for D1, D2, SB;
+    where D1: DimName, D2: Dim, SB: Storage<T, D2>, DefaultAllocator: Allocator<T, D1>;
+    self: &'a OPoint<T, D1>, right: Vector<T, D2, SB>, Output = OPoint<T, D1>;
     Self::Output::from(&self.coords + &right); 'a); // TODO: should not be a ref to `right`.
 
 add_sub_impl!(Add, add, ClosedAdd;
-    (Const<D1>, U1), (D2, U1) -> (Const<D1>, U1)
-    const D1;
-    for D2, SB;
-    where D2: Dim, SB: Storage<T, D2>;
-    self: Point<T, D1>, right: &'b Vector<T, D2, SB>, Output = Point<T, D1>;
+    (D1, U1), (D2, U1) -> (D1, U1)
+    const;
+    for D1, D2, SB;
+    where D1: DimName, D2: Dim, SB: Storage<T, D2>, DefaultAllocator: Allocator<T, D1>;
+    self: OPoint<T, D1>, right: &'b Vector<T, D2, SB>, Output = OPoint<T, D1>;
     Self::Output::from(self.coords + right); 'b);
 
 add_sub_impl!(Add, add, ClosedAdd;
-    (Const<D1>, U1), (D2, U1) -> (Const<D1>, U1)
-    const D1;
-    for D2, SB;
-    where D2: Dim, SB: Storage<T, D2>;
-    self: Point<T, D1>, right: Vector<T, D2, SB>, Output = Point<T, D1>;
+    (D1, U1), (D2, U1) -> (D1, U1)
+    const;
+    for D1, D2, SB;
+    where D1: DimName, D2: Dim, SB: Storage<T, D2>, DefaultAllocator: Allocator<T, D1>;
+    self: OPoint<T, D1>, right: Vector<T, D2, SB>, Output = OPoint<T, D1>;
     Self::Output::from(self.coords + right); );
 
 // TODO: replace by the shared macro: add_sub_assign_impl?
 macro_rules! op_assign_impl(
     ($($TraitAssign: ident, $method_assign: ident, $bound: ident);* $(;)*) => {$(
-        impl<'b, T, D2: Dim, SB, const D1: usize> $TraitAssign<&'b Vector<T, D2, SB>> for Point<T, D1>
+        impl<'b, T, D1: DimName, D2: Dim, SB> $TraitAssign<&'b Vector<T, D2, SB>> for OPoint<T, D1>
             where T: Scalar + $bound,
                   SB: Storage<T, D2>,
-                  ShapeConstraint: SameNumberOfRows<Const<D1>, D2> {
+                  ShapeConstraint: SameNumberOfRows<D1, D2>,
+                  DefaultAllocator: Allocator<T, D1> {
 
             #[inline]
             fn $method_assign(&mut self, right: &'b Vector<T, D2, SB>) {
@@ -169,10 +184,11 @@ macro_rules! op_assign_impl(
             }
         }
 
-        impl<T, D2: Dim, SB, const D1: usize> $TraitAssign<Vector<T, D2, SB>> for Point<T, D1>
+        impl<T, D1: DimName, D2: Dim, SB> $TraitAssign<Vector<T, D2, SB>> for OPoint<T, D1>
             where T: Scalar + $bound,
                   SB: Storage<T, D2>,
-                  ShapeConstraint: SameNumberOfRows<Const<D1>, D2> {
+                  ShapeConstraint: SameNumberOfRows<D1, D2>,
+                  DefaultAllocator: Allocator<T, D1> {
 
             #[inline]
             fn $method_assign(&mut self, right: Vector<T, D2, SB>) {
@@ -214,28 +230,30 @@ md_impl_all!(
 macro_rules! componentwise_scalarop_impl(
     ($Trait: ident, $method: ident, $bound: ident;
      $TraitAssign: ident, $method_assign: ident) => {
-        impl<T: Scalar + $bound, const D: usize> $Trait<T> for Point<T, D>
+        impl<T: Scalar + $bound, D: DimName> $Trait<T> for OPoint<T, D>
+        where DefaultAllocator: Allocator<T, D>
         {
-            type Output = Point<T, D>;
+            type Output = OPoint<T, D>;
 
             #[inline]
             fn $method(self, right: T) -> Self::Output {
-                Point::from(self.coords.$method(right))
+                OPoint::from(self.coords.$method(right))
             }
         }
 
-        impl<'a, T: Scalar + $bound, const D: usize> $Trait<T> for &'a Point<T, D>
+        impl<'a, T: Scalar + $bound, D: DimName> $Trait<T> for &'a OPoint<T, D>
+        where DefaultAllocator: Allocator<T, D>
         {
-            type Output = Point<T, D>;
+            type Output = OPoint<T, D>;
 
             #[inline]
             fn $method(self, right: T) -> Self::Output {
-                Point::from((&self.coords).$method(right))
+                OPoint::from((&self.coords).$method(right))
             }
         }
 
-        impl<T: Scalar + $bound, const D: usize> $TraitAssign<T> for Point<T, D>
-            /* where DefaultAllocator: Allocator<T, D> */
+        impl<T: Scalar + $bound, D: DimName> $TraitAssign<T> for OPoint<T, D>
+            where DefaultAllocator: Allocator<T, D>
         {
             #[inline]
             fn $method_assign(&mut self, right: T) {
@@ -250,23 +268,25 @@ componentwise_scalarop_impl!(Div, div, ClosedDiv; DivAssign, div_assign);
 
 macro_rules! left_scalar_mul_impl(
     ($($T: ty),* $(,)*) => {$(
-        impl<const D: usize> Mul<Point<$T, D>> for $T
+        impl<D: DimName> Mul<OPoint<$T, D>> for $T
+        where DefaultAllocator: Allocator<$T, D>
         {
-            type Output = Point<$T, D>;
+            type Output = OPoint<$T, D>;
 
             #[inline]
-            fn mul(self, right: Point<$T, D>) -> Self::Output {
-                Point::from(self * right.coords)
+            fn mul(self, right: OPoint<$T, D>) -> Self::Output {
+                OPoint::from(self * right.coords)
             }
         }
 
-        impl<'b, const D: usize> Mul<&'b Point<$T, D>> for $T
+        impl<'b, D: DimName> Mul<&'b OPoint<$T, D>> for $T
+        where DefaultAllocator: Allocator<$T, D>
         {
-            type Output = Point<$T, D>;
+            type Output = OPoint<$T, D>;
 
             #[inline]
-            fn mul(self, right: &'b Point<$T, D>) -> Self::Output {
-                Point::from(self * &right.coords)
+            fn mul(self, right: &'b OPoint<$T, D>) -> Self::Output {
+                OPoint::from(self * &right.coords)
             }
         }
     )*}