Merge pull request #846 from dimforge/dev

Release v0.25.2

CHANGELOG.md

@@ -4,6 +4,17 @@ documented here.
 
 This project adheres to [Semantic Versioning](https://semver.org/).
 
+## [0.25.2]
+### Added
+- A `convert-glam` cargo feature to enable implementations of `From` traits to convert
+  between `glam` types and `nalgebra` types.
+- A `convert-glam-unchecked` cargo feature to enable some extra `glam`/`nalgebra` conversions that may
+  lead to unexpected results if used improperly. For example, this enables the conversion from a
+  `glam::Mat4` to a `na::Isometry3`. This conversion will be cheap (without any check) but willlead to
+  unexpected results if the glam matrix contains non-isometric components (like scaling for example).
+- A `cast` method has been added to most types. This can be used to change the
+  type of the components of a given entity. Example: `vector.cast::<f32>()`.
+
 ## [0.25.1]
 This release replaces the version 0.25.0 which has been yanked. The 0.25.0 version
 added significant complication to build `nalgebra` targeting a `#[no-std]` platform

Cargo.toml

@@ -1,6 +1,6 @@
 [package]
 name    = "nalgebra"
-version = "0.25.1"
+version = "0.25.2"
 authors = [ "Sébastien Crozet <developer@crozet.re>" ]
 
 description = "General-purpose linear algebra library with transformations and statically-sized or dynamically-sized matrices."
@@ -24,11 +24,6 @@ path = "src/lib.rs"
 [features]
 default         = [ "std" ]
 std             = [ "matrixmultiply", "simba/std" ]
-rand-no-std     = [ "rand-package" ]
-rand            = [ "rand-no-std", "rand-package/std", "rand-package/std_rng", "rand_distr" ]
-arbitrary       = [ "quickcheck" ]
-serde-serialize = [ "serde", "num-complex/serde" ]
-abomonation-serialize = [ "abomonation" ]
 sparse = [ ]
 debug = [ "approx/num-complex", "rand" ]
 alloc = [ ]
@@ -36,10 +31,25 @@ io = [ "pest", "pest_derive" ]
 compare = [ "matrixcompare-core" ]
 libm = [ "simba/libm" ]
 libm-force = [ "simba/libm_force" ]
-proptest-support = [ "proptest" ]
 no_unsound_assume_init = [ ]
 
-# This feature is only used for tests, and enables tests that require more time to run
+# Conversion
+convert-mint = [ "mint" ]
+convert-glam = [ "glam" ]
+convert-glam-unchecked = [ "convert-glam" ] # Unable edgy conversions like Mat4 -> Isometry3
+convert-bytemuck = [ "bytemuck" ]
+
+# Serialization
+serde-serialize = [ "serde", "num-complex/serde" ]
+abomonation-serialize = [ "abomonation" ]
+
+# Randomness
+rand-no-std = [ "rand-package" ]
+rand        = [ "rand-no-std", "rand-package/std", "rand-package/std_rng", "rand_distr" ]
+
+# Tests
+arbitrary        = [ "quickcheck" ]
+proptest-support = [ "proptest" ]
 slow-tests       = []
 
 [dependencies]
@@ -57,6 +67,7 @@ matrixmultiply = { version = "0.3", optional = true }
 serde          = { version = "1.0", default-features = false, features = [ "derive" ], optional = true }
 abomonation    = { version = "0.7", optional = true }
 mint           = { version = "0.5", optional = true }
+glam           = { version = "0.13", optional = true }
 quickcheck     = { version = "1", optional = true }
 pest           = { version = "2", optional = true }
 pest_derive    = { version = "2", optional = true }

src/base/conversion.rs

@@ -1,7 +1,5 @@
 #[cfg(all(feature = "alloc", not(feature = "std")))]
 use alloc::vec::Vec;
-#[cfg(feature = "mint")]
-use mint;
 use simba::scalar::{SubsetOf, SupersetOf};
 use std::convert::{AsMut, AsRef, From, Into};
 use std::mem;
@@ -235,119 +233,6 @@ impl_from_into_asref_2D!(
     (U6, U2) => (6, 2); (U6, U3) => (6, 3); (U6, U4) => (6, 4); (U6, U5) => (6, 5); (U6, U6) => (6, 6);
 );
 
-#[cfg(feature = "mint")]
-macro_rules! impl_from_into_mint_1D(
-    ($($NRows: ident => $VT:ident [$SZ: expr]);* $(;)*) => {$(
-        impl<N> From<mint::$VT<N>> for MatrixMN<N, $NRows, U1>
-        where N: Scalar,
-              DefaultAllocator: Allocator<N, $NRows, U1> {
-            #[inline]
-            fn from(v: mint::$VT<N>) -> Self {
-                unsafe {
-                    let mut res = Self::new_uninitialized();
-                    ptr::copy_nonoverlapping(&v.x, (*res.as_mut_ptr()).data.ptr_mut(), $SZ);
-
-                    res.assume_init()
-                }
-            }
-        }
-
-        impl<N, S> Into<mint::$VT<N>> for Matrix<N, $NRows, U1, S>
-        where N: Scalar,
-              S: ContiguousStorage<N, $NRows, U1> {
-            #[inline]
-            fn into(self) -> mint::$VT<N> {
-                unsafe {
-                    let mut res: mint::$VT<N> = mem::MaybeUninit::uninit().assume_init();
-                    ptr::copy_nonoverlapping(self.data.ptr(), &mut res.x, $SZ);
-                    res
-                }
-            }
-        }
-
-        impl<N, S> AsRef<mint::$VT<N>> for Matrix<N, $NRows, U1, S>
-        where N: Scalar,
-              S: ContiguousStorage<N, $NRows, U1> {
-            #[inline]
-            fn as_ref(&self) -> &mint::$VT<N> {
-                unsafe {
-                    mem::transmute(self.data.ptr())
-                }
-            }
-        }
-
-        impl<N, S> AsMut<mint::$VT<N>> for Matrix<N, $NRows, U1, S>
-        where N: Scalar,
-              S: ContiguousStorageMut<N, $NRows, U1> {
-            #[inline]
-            fn as_mut(&mut self) -> &mut mint::$VT<N> {
-                unsafe {
-                    mem::transmute(self.data.ptr_mut())
-                }
-            }
-        }
-    )*}
-);
-
-// Implement for vectors of dimension 2 .. 4.
-#[cfg(feature = "mint")]
-impl_from_into_mint_1D!(
-    U2 => Vector2[2];
-    U3 => Vector3[3];
-    U4 => Vector4[4];
-);
-
-#[cfg(feature = "mint")]
-macro_rules! impl_from_into_mint_2D(
-    ($(($NRows: ty, $NCols: ty) => $MV:ident{ $($component:ident),* }[$SZRows: expr]);* $(;)*) => {$(
-        impl<N> From<mint::$MV<N>> for MatrixMN<N, $NRows, $NCols>
-        where N: Scalar,
-              DefaultAllocator: Allocator<N, $NRows, $NCols> {
-            #[inline]
-            fn from(m: mint::$MV<N>) -> Self {
-                unsafe {
-                    let mut res = Self::new_uninitialized();
-                    let mut ptr = (*res.as_mut_ptr()).data.ptr_mut();
-                    $(
-                        ptr::copy_nonoverlapping(&m.$component.x, ptr, $SZRows);
-                        ptr = ptr.offset($SZRows);
-                    )*
-                    let _ = ptr;
-                    res.assume_init()
-                }
-            }
-        }
-
-        impl<N> Into<mint::$MV<N>> for MatrixMN<N, $NRows, $NCols>
-        where N: Scalar,
-              DefaultAllocator: Allocator<N, $NRows, $NCols> {
-            #[inline]
-            fn into(self) -> mint::$MV<N> {
-                unsafe {
-                    let mut res: mint::$MV<N> = mem::MaybeUninit::uninit().assume_init();
-                    let mut ptr = self.data.ptr();
-                    $(
-                        ptr::copy_nonoverlapping(ptr, &mut res.$component.x, $SZRows);
-                        ptr = ptr.offset($SZRows);
-                    )*
-                    let _ = ptr;
-                    res
-                }
-            }
-        }
-    )*}
-);
-
-// Implement for matrices with shape 2x2 .. 4x4.
-#[cfg(feature = "mint")]
-impl_from_into_mint_2D!(
-    (U2, U2) => ColumnMatrix2{x, y}[2];
-    (U2, U3) => ColumnMatrix2x3{x, y, z}[2];
-    (U3, U3) => ColumnMatrix3{x, y, z}[3];
-    (U3, U4) => ColumnMatrix3x4{x, y, z, w}[3];
-    (U4, U4) => ColumnMatrix4{x, y, z, w}[4];
-);
-
 impl<'a, N, R, C, RStride, CStride> From<MatrixSlice<'a, N, R, C, RStride, CStride>>
     for Matrix<N, R, C, ArrayStorage<N, R, C>>
 where

src/base/matrix.rs

@@ -16,7 +16,7 @@ use serde::{Deserialize, Deserializer, Serialize, Serializer};
 #[cfg(feature = "abomonation-serialize")]
 use abomonation::Abomonation;
 
-use simba::scalar::{ClosedAdd, ClosedMul, ClosedSub, Field};
+use simba::scalar::{ClosedAdd, ClosedMul, ClosedSub, Field, SupersetOf};
 use simba::simd::SimdPartialOrd;
 
 use crate::base::allocator::{Allocator, SameShapeAllocator, SameShapeC, SameShapeR};
@@ -610,6 +610,23 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
         res
     }
 
+    /// Cast the components of `self` to another type.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::Vector3;
+    /// let q = Vector3::new(1.0f64, 2.0, 3.0);
+    /// let q2 = q.cast::<f32>();
+    /// assert_eq!(q2, Vector3::new(1.0f32, 2.0, 3.0));
+    /// ```
+    pub fn cast<N2: Scalar>(self) -> MatrixMN<N2, R, C>
+    where
+        MatrixMN<N2, R, C>: SupersetOf<Self>,
+        DefaultAllocator: Allocator<N2, R, C>,
+    {
+        crate::convert(self)
+    }
+
     /// Similar to `self.iter().fold(init, f)` except that `init` is replaced by a closure.
     ///
     /// The initialization closure is given the first component of this matrix:

src/base/mod.rs

@@ -22,8 +22,6 @@ mod conversion;
 mod edition;
 pub mod indexing;
 mod matrix;
-#[cfg(feature = "alga")]
-mod matrix_alga;
 mod matrix_simba;
 mod matrix_slice;
 mod norm;

src/geometry/dual_quaternion_construction.rs

@@ -5,6 +5,7 @@ use crate::{
 use num::{One, Zero};
 #[cfg(feature = "arbitrary")]
 use quickcheck::{Arbitrary, Gen};
+use simba::scalar::SupersetOf;
 
 impl<N: Scalar> DualQuaternion<N> {
     /// Creates a dual quaternion from its rotation and translation components.
@@ -49,6 +50,22 @@ impl<N: Scalar> DualQuaternion<N> {
             Quaternion::from_real(N::zero()),
         )
     }
+
+    /// Cast the components of `self` to another type.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::{Quaternion, DualQuaternion};
+    /// let q = DualQuaternion::from_real(Quaternion::new(1.0f64, 2.0, 3.0, 4.0));
+    /// let q2 = q.cast::<f32>();
+    /// assert_eq!(q2, DualQuaternion::from_real(Quaternion::new(1.0f32, 2.0, 3.0, 4.0)));
+    /// ```
+    pub fn cast<To: Scalar>(self) -> DualQuaternion<To>
+    where
+        DualQuaternion<To>: SupersetOf<Self>,
+    {
+        crate::convert(self)
+    }
 }
 
 impl<N: SimdRealField> DualQuaternion<N>
@@ -129,6 +146,22 @@ impl<N: SimdRealField> UnitDualQuaternion<N> {
     pub fn identity() -> Self {
         Self::new_unchecked(DualQuaternion::identity())
     }
+
+    /// Cast the components of `self` to another type.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::UnitDualQuaternion;
+    /// let q = UnitDualQuaternion::<f64>::identity();
+    /// let q2 = q.cast::<f32>();
+    /// assert_eq!(q2, UnitDualQuaternion::<f32>::identity());
+    /// ```
+    pub fn cast<To: Scalar>(self) -> UnitDualQuaternion<To>
+    where
+        UnitDualQuaternion<To>: SupersetOf<Self>,
+    {
+        crate::convert(self)
+    }
 }
 
 impl<N: SimdRealField> UnitDualQuaternion<N>

src/geometry/isometry_construction.rs

@@ -10,15 +10,16 @@ use rand::{
     Rng,
 };
 
+use simba::scalar::SupersetOf;
 use simba::simd::SimdRealField;
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, U2};
 use crate::base::{DefaultAllocator, Vector2, Vector3};
 
-use crate::geometry::{
+use crate::{
     AbstractRotation, Isometry, Isometry2, Isometry3, IsometryMatrix2, IsometryMatrix3, Point,
-    Point3, Rotation, Rotation3, Translation, Translation2, Translation3, UnitComplex,
+    Point3, Rotation, Rotation3, Scalar, Translation, Translation2, Translation3, UnitComplex,
     UnitQuaternion,
 };
 
@@ -153,6 +154,22 @@ where
     pub fn rotation(angle: N) -> Self {
         Self::new(Vector2::zeros(), angle)
     }
+
+    /// Cast the components of `self` to another type.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::IsometryMatrix2;
+    /// let iso = IsometryMatrix2::<f64>::identity();
+    /// let iso2 = iso.cast::<f32>();
+    /// assert_eq!(iso2, IsometryMatrix2::<f32>::identity());
+    /// ```
+    pub fn cast<To: Scalar>(self) -> IsometryMatrix2<To>
+    where
+        IsometryMatrix2<To>: SupersetOf<Self>,
+    {
+        crate::convert(self)
+    }
 }
 
 impl<N: SimdRealField> Isometry2<N>
@@ -191,6 +208,22 @@ where
     pub fn rotation(angle: N) -> Self {
         Self::new(Vector2::zeros(), angle)
     }
+
+    /// Cast the components of `self` to another type.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::Isometry2;
+    /// let iso = Isometry2::<f64>::identity();
+    /// let iso2 = iso.cast::<f32>();
+    /// assert_eq!(iso2, Isometry2::<f32>::identity());
+    /// ```
+    pub fn cast<To: Scalar>(self) -> Isometry2<To>
+    where
+        Isometry2<To>: SupersetOf<Self>,
+    {
+        crate::convert(self)
+    }
 }
 
 // 3D rotation.
@@ -387,6 +420,22 @@ where
     N::Element: SimdRealField,
 {
     basic_isometry_construction_impl!(UnitQuaternion<N>);
+
+    /// Cast the components of `self` to another type.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::Isometry3;
+    /// let iso = Isometry3::<f64>::identity();
+    /// let iso2 = iso.cast::<f32>();
+    /// assert_eq!(iso2, Isometry3::<f32>::identity());
+    /// ```
+    pub fn cast<To: Scalar>(self) -> Isometry3<To>
+    where
+        Isometry3<To>: SupersetOf<Self>,
+    {
+        crate::convert(self)
+    }
 }
 
 impl<N: SimdRealField> IsometryMatrix3<N>
@@ -394,6 +443,22 @@ where
     N::Element: SimdRealField,
 {
     basic_isometry_construction_impl!(Rotation3<N>);
+
+    /// Cast the components of `self` to another type.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::IsometryMatrix3;
+    /// let iso = IsometryMatrix3::<f64>::identity();
+    /// let iso2 = iso.cast::<f32>();
+    /// assert_eq!(iso2, IsometryMatrix3::<f32>::identity());
+    /// ```
+    pub fn cast<To: Scalar>(self) -> IsometryMatrix3<To>
+    where
+        IsometryMatrix3<To>: SupersetOf<Self>,
+    {
+        crate::convert(self)
+    }
 }
 
 /// # Construction from a 3D eye position and target point

src/geometry/mod.rs

@@ -6,8 +6,6 @@ mod op_macros;
 mod abstract_rotation;
 
 mod point;
-#[cfg(feature = "alga")]
-mod point_alga;
 mod point_alias;
 mod point_construction;
 mod point_conversion;
@@ -16,8 +14,6 @@ mod point_ops;
 mod point_simba;
 
 mod rotation;
-#[cfg(feature = "alga")]
-mod rotation_alga;
 mod rotation_alias;
 mod rotation_construction;
 mod rotation_conversion;
@@ -27,8 +23,6 @@ mod rotation_simba; // TODO: implement Rotation methods.
 mod rotation_specialization;
 
 mod quaternion;
-#[cfg(feature = "alga")]
-mod quaternion_alga;
 mod quaternion_construction;
 mod quaternion_conversion;
 mod quaternion_coordinates;
@@ -36,23 +30,17 @@ mod quaternion_ops;
 mod quaternion_simba;
 
 mod dual_quaternion;
-#[cfg(feature = "alga")]
-mod dual_quaternion_alga;
 mod dual_quaternion_construction;
 mod dual_quaternion_conversion;
 mod dual_quaternion_ops;
 
 mod unit_complex;
-#[cfg(feature = "alga")]
-mod unit_complex_alga;
 mod unit_complex_construction;
 mod unit_complex_conversion;
 mod unit_complex_ops;
 mod unit_complex_simba;
 
 mod translation;
-#[cfg(feature = "alga")]
-mod translation_alga;
 mod translation_alias;
 mod translation_construction;
 mod translation_conversion;
@@ -61,8 +49,6 @@ mod translation_ops;
 mod translation_simba;
 
 mod isometry;
-#[cfg(feature = "alga")]
-mod isometry_alga;
 mod isometry_alias;
 mod isometry_construction;
 mod isometry_conversion;
@@ -71,8 +57,6 @@ mod isometry_ops;
 mod isometry_simba;
 
 mod similarity;
-#[cfg(feature = "alga")]
-mod similarity_alga;
 mod similarity_alias;
 mod similarity_construction;
 mod similarity_conversion;
@@ -82,8 +66,6 @@ mod similarity_simba;
 mod swizzle;
 
 mod transform;
-#[cfg(feature = "alga")]
-mod transform_alga;
 mod transform_alias;
 mod transform_construction;
 mod transform_conversion;

src/geometry/point_construction.rs

@@ -15,7 +15,7 @@ use crate::{
     Point1, Point2, Point3, Point4, Point5, Point6, Vector1, Vector2, Vector3, Vector4, Vector5,
     Vector6,
 };
-use simba::scalar::ClosedDiv;
+use simba::scalar::{ClosedDiv, SupersetOf};
 
 use crate::geometry::Point;
 
@@ -119,6 +119,23 @@ where
             None
         }
     }
+
+    /// Cast the components of `self` to another type.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::Point2;
+    /// let pt = Point2::new(1.0f64, 2.0);
+    /// let pt2 = pt.cast::<f32>();
+    /// assert_eq!(pt2, Point2::new(1.0f32, 2.0));
+    /// ```
+    pub fn cast<To: Scalar>(self) -> Point<To, D>
+    where
+        Point<To, D>: SupersetOf<Self>,
+        DefaultAllocator: Allocator<To, D>,
+    {
+        crate::convert(self)
+    }
 }
 
 /*

src/geometry/point_conversion.rs

@@ -6,23 +6,14 @@ use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
 use crate::base::{DefaultAllocator, Matrix, Scalar, VectorN};
 
-#[cfg(feature = "mint")]
-use crate::base::dimension::{U2, U3};
-#[cfg(feature = "mint")]
-use crate::base::storage::{Storage, StorageMut};
 use crate::geometry::Point;
-#[cfg(feature = "mint")]
+
-use mint;
-#[cfg(feature = "mint")]
-use std::convert::{AsMut, AsRef, From, Into};
 /*
  * This file provides the following conversions:
  * =============================================
  *
  * Point -> Point
  * Point -> Vector (homogeneous)
- *
- * mint::Point <-> Point
  */
 
 impl<N1, N2, D> SubsetOf<Point<N2, D>> for Point<N1, D>
@@ -80,57 +71,6 @@ where
     }
 }
 
-#[cfg(feature = "mint")]
-macro_rules! impl_from_into_mint_1D(
-    ($($NRows: ident => $PT:ident, $VT:ident [$SZ: expr]);* $(;)*) => {$(
-        impl<N> From<mint::$PT<N>> for Point<N, $NRows>
-        where N: Scalar {
-            #[inline]
-            fn from(p: mint::$PT<N>) -> Self {
-                Self {
-                    coords: VectorN::from(mint::$VT::from(p)),
-                }
-            }
-        }
-
-        impl<N> Into<mint::$PT<N>> for Point<N, $NRows>
-        where N: Scalar {
-            #[inline]
-            fn into(self) -> mint::$PT<N> {
-                let mint_vec: mint::$VT<N> = self.coords.into();
-                mint::$PT::from(mint_vec)
-            }
-        }
-
-        impl<N> AsRef<mint::$PT<N>> for Point<N, $NRows>
-        where N: Scalar {
-            #[inline]
-            fn as_ref(&self) -> &mint::$PT<N> {
-                unsafe {
-                    &*(self.coords.data.ptr() as *const mint::$PT<N>)
-                }
-            }
-        }
-
-        impl<N> AsMut<mint::$PT<N>> for Point<N, $NRows>
-        where N: Scalar {
-            #[inline]
-            fn as_mut(&mut self) -> &mut mint::$PT<N> {
-                unsafe {
-                    &mut *(self.coords.data.ptr_mut() as *mut mint::$PT<N>)
-                }
-            }
-        }
-    )*}
-);
-
-// Implement for points of dimension 2, 3.
-#[cfg(feature = "mint")]
-impl_from_into_mint_1D!(
-    U2 => Point2, Vector2[2];
-    U3 => Point3, Vector3[3];
-);
-
 impl<N: Scalar + Zero + One, D: DimName> From<Point<N, D>> for VectorN<N, DimNameSum<D, U1>>
 where
     D: DimNameAdd<U1>,

src/geometry/quaternion_construction.rs

@@ -13,7 +13,7 @@ use rand::{
 
 use num::{One, Zero};
 
-use simba::scalar::RealField;
+use simba::scalar::{RealField, SupersetOf};
 use simba::simd::SimdBool;
 
 use crate::base::dimension::U3;
@@ -49,6 +49,22 @@ impl<N: Scalar> Quaternion<N> {
     pub fn new(w: N, i: N, j: N, k: N) -> Self {
         Self::from(Vector4::new(i, j, k, w))
     }
+
+    /// Cast the components of `self` to another type.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::Quaternion;
+    /// let q = Quaternion::new(1.0f64, 2.0, 3.0, 4.0);
+    /// let q2 = q.cast::<f32>();
+    /// assert_eq!(q2, Quaternion::new(1.0f32, 2.0, 3.0, 4.0));
+    /// ```
+    pub fn cast<To: Scalar>(self) -> Quaternion<To>
+    where
+        To: SupersetOf<N>,
+    {
+        crate::convert(self)
+    }
 }
 
 impl<N: SimdRealField> Quaternion<N> {
@@ -199,6 +215,23 @@ where
         Self::new_unchecked(Quaternion::identity())
     }
 
+    /// Cast the components of `self` to another type.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::UnitQuaternion;
+    /// # use approx::assert_relative_eq;
+    /// let q = UnitQuaternion::from_euler_angles(1.0f64, 2.0, 3.0);
+    /// let q2 = q.cast::<f32>();
+    /// assert_relative_eq!(q2, UnitQuaternion::from_euler_angles(1.0f32, 2.0, 3.0), epsilon = 1.0e-6);
+    /// ```
+    pub fn cast<To: Scalar>(self) -> UnitQuaternion<To>
+    where
+        To: SupersetOf<N>,
+    {
+        crate::convert(self)
+    }
+
     /// Creates a new quaternion from a unit vector (the rotation axis) and an angle
     /// (the rotation angle).
     ///

src/geometry/quaternion_conversion.rs

@@ -3,9 +3,6 @@ use num::Zero;
 use simba::scalar::{RealField, SubsetOf, SupersetOf};
 use simba::simd::{PrimitiveSimdValue, SimdRealField, SimdValue};
 
-#[cfg(feature = "mint")]
-use mint;
-
 use crate::base::dimension::U3;
 use crate::base::{Matrix3, Matrix4, Scalar, Vector4};
 use crate::geometry::{
@@ -26,17 +23,14 @@ use crate::geometry::{
  * UnitQuaternion -> Transform<U3>
  * UnitQuaternion -> Matrix<U4> (homogeneous)
  *
- * mint::Quaternion <-> Quaternion
- * UnitQuaternion -> mint::Quaternion
- *
  * NOTE:
  * UnitQuaternion -> Quaternion is already provided by: Unit<T> -> T
  */
 
 impl<N1, N2> SubsetOf<Quaternion<N2>> for Quaternion<N1>
 where
-    N1: SimdRealField,
+    N1: Scalar,
-    N2: SimdRealField + SupersetOf<N1>,
+    N2: Scalar + SupersetOf<N1>,
 {
     #[inline]
     fn to_superset(&self) -> Quaternion<N2> {
@@ -58,8 +52,8 @@ where
 
 impl<N1, N2> SubsetOf<UnitQuaternion<N2>> for UnitQuaternion<N1>
 where
-    N1: SimdRealField,
+    N1: Scalar,
-    N2: SimdRealField + SupersetOf<N1>,
+    N2: Scalar + SupersetOf<N1>,
 {
     #[inline]
     fn to_superset(&self) -> UnitQuaternion<N2> {
@@ -206,41 +200,6 @@ impl<N1: RealField, N2: RealField + SupersetOf<N1>> SubsetOf<Matrix4<N2>> for Un
     }
 }
 
-#[cfg(feature = "mint")]
-impl<N: Scalar> From<mint::Quaternion<N>> for Quaternion<N> {
-    fn from(q: mint::Quaternion<N>) -> Self {
-        Self::new(q.s, q.v.x, q.v.y, q.v.z)
-    }
-}
-
-#[cfg(feature = "mint")]
-impl<N: Scalar> Into<mint::Quaternion<N>> for Quaternion<N> {
-    fn into(self) -> mint::Quaternion<N> {
-        mint::Quaternion {
-            v: mint::Vector3 {
-                x: self[0].inlined_clone(),
-                y: self[1].inlined_clone(),
-                z: self[2].inlined_clone(),
-            },
-            s: self[3].inlined_clone(),
-        }
-    }
-}
-
-#[cfg(feature = "mint")]
-impl<N: Scalar + SimdValue> Into<mint::Quaternion<N>> for UnitQuaternion<N> {
-    fn into(self) -> mint::Quaternion<N> {
-        mint::Quaternion {
-            v: mint::Vector3 {
-                x: self[0].inlined_clone(),
-                y: self[1].inlined_clone(),
-                z: self[2].inlined_clone(),
-            },
-            s: self[3].inlined_clone(),
-        }
-    }
-}
-
 impl<N: SimdRealField> From<UnitQuaternion<N>> for Matrix4<N>
 where
     N::Element: SimdRealField,

src/geometry/rotation_construction.rs

@@ -1,6 +1,6 @@
 use num::{One, Zero};
 
-use simba::scalar::{ClosedAdd, ClosedMul};
+use simba::scalar::{ClosedAdd, ClosedMul, SupersetOf};
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::DimName;
@@ -31,6 +31,28 @@ where
     }
 }
 
+impl<N: Scalar, D: DimName> Rotation<N, D>
+where
+    DefaultAllocator: Allocator<N, D, D>,
+{
+    /// Cast the components of `self` to another type.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::Rotation2;
+    /// let rot = Rotation2::<f64>::identity();
+    /// let rot2 = rot.cast::<f32>();
+    /// assert_eq!(rot2, Rotation2::<f32>::identity());
+    /// ```
+    pub fn cast<To: Scalar>(self) -> Rotation<To, D>
+    where
+        Rotation<To, D>: SupersetOf<Self>,
+        DefaultAllocator: Allocator<To, D, D>,
+    {
+        crate::convert(self)
+    }
+}
+
 impl<N, D: DimName> One for Rotation<N, D>
 where
     N: Scalar + Zero + One + ClosedAdd + ClosedMul,

src/geometry/rotation_conversion.rs

@@ -3,9 +3,6 @@ use num::Zero;
 use simba::scalar::{RealField, SubsetOf, SupersetOf};
 use simba::simd::{PrimitiveSimdValue, SimdValue};
 
-#[cfg(feature = "mint")]
-use mint;
-
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimMin, DimName, DimNameAdd, DimNameSum, U1};
 use crate::base::{DefaultAllocator, Matrix2, Matrix3, Matrix4, MatrixN, Scalar};
@@ -27,7 +24,6 @@ use crate::geometry::{
  * Rotation  -> Similarity
  * Rotation  -> Transform
  * Rotation  -> Matrix (homogeneous)
- * mint::EulerAngles -> Rotation
 
 */
 
@@ -236,13 +232,6 @@ where
     }
 }
 
-#[cfg(feature = "mint")]
-impl<N: RealField> From<mint::EulerAngles<N, mint::IntraXYZ>> for Rotation3<N> {
-    fn from(euler: mint::EulerAngles<N, mint::IntraXYZ>) -> Self {
-        Self::from_euler_angles(euler.a, euler.b, euler.c)
-    }
-}
-
 impl<N: RealField> From<Rotation2<N>> for Matrix3<N> {
     #[inline]
     fn from(q: Rotation2<N>) -> Self {

src/geometry/similarity_construction.rs

@@ -10,15 +10,16 @@ use rand::{
     Rng,
 };
 
+use simba::scalar::SupersetOf;
 use simba::simd::SimdRealField;
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, U2, U3};
 use crate::base::{DefaultAllocator, Vector2, Vector3};
 
-use crate::geometry::{
+use crate::{
-    AbstractRotation, Isometry, Point, Point3, Rotation2, Rotation3, Similarity, Translation,
+    AbstractRotation, Isometry, Point, Point3, Rotation2, Rotation3, Scalar, Similarity,
-    UnitComplex, UnitQuaternion,
+    Translation, UnitComplex, UnitQuaternion,
 };
 
 impl<N: SimdRealField, D: DimName, R> Similarity<N, D, R>
@@ -158,6 +159,22 @@ where
             scaling,
         )
     }
+
+    /// Cast the components of `self` to another type.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::SimilarityMatrix2;
+    /// let sim = SimilarityMatrix2::<f64>::identity();
+    /// let sim2 = sim.cast::<f32>();
+    /// assert_eq!(sim2, SimilarityMatrix2::<f32>::identity());
+    /// ```
+    pub fn cast<To: Scalar>(self) -> Similarity<To, U2, Rotation2<To>>
+    where
+        Similarity<To, U2, Rotation2<To>>: SupersetOf<Self>,
+    {
+        crate::convert(self)
+    }
 }
 
 impl<N: SimdRealField> Similarity<N, U2, UnitComplex<N>>
@@ -184,12 +201,28 @@ where
             scaling,
         )
     }
+
+    /// Cast the components of `self` to another type.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::Similarity2;
+    /// let sim = Similarity2::<f64>::identity();
+    /// let sim2 = sim.cast::<f32>();
+    /// assert_eq!(sim2, Similarity2::<f32>::identity());
+    /// ```
+    pub fn cast<To: Scalar>(self) -> Similarity<To, U2, UnitComplex<To>>
+    where
+        Similarity<To, U2, UnitComplex<To>>: SupersetOf<Self>,
+    {
+        crate::convert(self)
+    }
 }
 
 // 3D rotation.
 macro_rules! similarity_construction_impl(
-    ($Rot: ty) => {
+    ($Rot: ident) => {
-        impl<N: SimdRealField> Similarity<N, U3, $Rot>
+        impl<N: SimdRealField> Similarity<N, U3, $Rot<N>>
         where N::Element: SimdRealField {
             /// Creates a new similarity from a translation, rotation axis-angle, and scaling
             /// factor.
@@ -219,7 +252,23 @@ macro_rules! similarity_construction_impl(
             #[inline]
             pub fn new(translation: Vector3<N>, axisangle: Vector3<N>, scaling: N) -> Self
             {
-                Self::from_isometry(Isometry::<_, U3, $Rot>::new(translation, axisangle), scaling)
+                Self::from_isometry(Isometry::<_, U3, $Rot<N>>::new(translation, axisangle), scaling)
+            }
+
+            /// Cast the components of `self` to another type.
+            ///
+            /// # Example
+            /// ```
+            /// # use nalgebra::Similarity3;
+            /// let sim = Similarity3::<f64>::identity();
+            /// let sim2 = sim.cast::<f32>();
+            /// assert_eq!(sim2, Similarity3::<f32>::identity());
+            /// ```
+            pub fn cast<To: Scalar>(self) -> Similarity<To, U3, $Rot<To>>
+            where
+                Similarity<To, U3, $Rot<To>>: SupersetOf<Self>,
+            {
+                crate::convert(self)
             }
 
             /// Creates an similarity that corresponds to a scaling factor and a local frame of
@@ -260,7 +309,7 @@ macro_rules! similarity_construction_impl(
                                       up:     &Vector3<N>,
                                       scaling: N)
                                       -> Self {
-                Self::from_isometry(Isometry::<_, U3, $Rot>::face_towards(eye, target, up), scaling)
+                Self::from_isometry(Isometry::<_, U3, $Rot<N>>::face_towards(eye, target, up), scaling)
             }
 
             /// Deprecated: Use [SimilarityMatrix3::face_towards] instead.
@@ -308,7 +357,7 @@ macro_rules! similarity_construction_impl(
                               up:      &Vector3<N>,
                               scaling: N)
                               -> Self {
-                Self::from_isometry(Isometry::<_, U3, $Rot>::look_at_rh(eye, target, up), scaling)
+                Self::from_isometry(Isometry::<_, U3, $Rot<N>>::look_at_rh(eye, target, up), scaling)
             }
 
             /// Builds a left-handed look-at view matrix including a scaling factor.
@@ -346,11 +395,11 @@ macro_rules! similarity_construction_impl(
                               up:      &Vector3<N>,
                               scaling: N)
                               -> Self {
-                Self::from_isometry(Isometry::<_, _, $Rot>::look_at_lh(eye, target, up), scaling)
+                Self::from_isometry(Isometry::<_, _, $Rot<N>>::look_at_lh(eye, target, up), scaling)
             }
         }
     }
 );
 
-similarity_construction_impl!(Rotation3<N>);
+similarity_construction_impl!(Rotation3);
-similarity_construction_impl!(UnitQuaternion<N>);
+similarity_construction_impl!(UnitQuaternion);

src/geometry/translation_construction.rs

@@ -10,7 +10,7 @@ use rand::{
     Rng,
 };
 
-use simba::scalar::ClosedAdd;
+use simba::scalar::{ClosedAdd, SupersetOf};
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, U1, U2, U3, U4, U5, U6};
@@ -18,7 +18,7 @@ use crate::base::{DefaultAllocator, Scalar, VectorN};
 
 use crate::geometry::Translation;
 
-impl<N: Scalar + Zero, D: DimName> Translation<N, D>
+impl<N: Scalar, D: DimName> Translation<N, D>
 where
     DefaultAllocator: Allocator<N, D>,
 {
@@ -37,9 +37,29 @@ where
     /// assert_eq!(t * p, p);
     /// ```
     #[inline]
-    pub fn identity() -> Translation<N, D> {
+    pub fn identity() -> Translation<N, D>
+    where
+        N: Zero,
+    {
         Self::from(VectorN::<N, D>::from_element(N::zero()))
     }
+
+    /// Cast the components of `self` to another type.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::Translation2;
+    /// let tra = Translation2::new(1.0f64, 2.0);
+    /// let tra2 = tra.cast::<f32>();
+    /// assert_eq!(tra2, Translation2::new(1.0f32, 2.0));
+    /// ```
+    pub fn cast<To: Scalar>(self) -> Translation<To, D>
+    where
+        Translation<To, D>: SupersetOf<Self>,
+        DefaultAllocator: Allocator<To, D>,
+    {
+        crate::convert(self)
+    }
 }
 
 impl<N: Scalar + Zero + ClosedAdd, D: DimName> One for Translation<N, D>

src/geometry/unit_complex_construction.rs

@@ -12,9 +12,9 @@ use num_complex::Complex;
 
 use crate::base::dimension::{U1, U2};
 use crate::base::storage::Storage;
-use crate::base::{Matrix2, Unit, Vector, Vector2};
+use crate::base::{Matrix2, Scalar, Unit, Vector, Vector2};
 use crate::geometry::{Rotation2, UnitComplex};
-use simba::scalar::RealField;
+use simba::scalar::{RealField, SupersetOf};
 use simba::simd::SimdRealField;
 
 /// # Identity
@@ -118,6 +118,22 @@ impl<N: SimdRealField> UnitComplex<N>
 where
     N::Element: SimdRealField,
 {
+    /// Cast the components of `self` to another type.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::UnitComplex;
+    /// let c = UnitComplex::new(1.0f64);
+    /// let c2 = c.cast::<f32>();
+    /// assert_eq!(c2, UnitComplex::new(1.0f32));
+    /// ```
+    pub fn cast<To: Scalar>(self) -> UnitComplex<To>
+    where
+        UnitComplex<To>: SupersetOf<Self>,
+    {
+        crate::convert(self)
+    }
+
     /// The underlying complex number.
     ///
     /// Same as `self.as_ref()`.

src/lib.rs

@@ -123,6 +123,7 @@ pub mod linalg;
 pub mod proptest;
 #[cfg(feature = "sparse")]
 pub mod sparse;
+mod third_party;
 
 pub use crate::base::*;
 pub use crate::geometry::*;

src/third_party/alga/mod.rs

@@ -0,0 +1,10 @@
+mod alga_dual_quaternion;
+mod alga_isometry;
+mod alga_matrix;
+mod alga_point;
+mod alga_quaternion;
+mod alga_rotation;
+mod alga_similarity;
+mod alga_transform;
+mod alga_translation;
+mod alga_unit_complex;

src/third_party/glam/glam_isometry.rs

@@ -0,0 +1,54 @@
+use crate::{Isometry2, Isometry3};
+use glam::{DMat3, DMat4, Mat3, Mat4};
+
+impl From<Isometry2<f32>> for Mat3 {
+    fn from(iso: Isometry2<f32>) -> Mat3 {
+        iso.to_homogeneous().into()
+    }
+}
+impl From<Isometry3<f32>> for Mat4 {
+    fn from(iso: Isometry3<f32>) -> Mat4 {
+        iso.to_homogeneous().into()
+    }
+}
+
+impl From<Isometry2<f64>> for DMat3 {
+    fn from(iso: Isometry2<f64>) -> DMat3 {
+        iso.to_homogeneous().into()
+    }
+}
+impl From<Isometry3<f64>> for DMat4 {
+    fn from(iso: Isometry3<f64>) -> DMat4 {
+        iso.to_homogeneous().into()
+    }
+}
+
+#[cfg(feature = "convert-glam-unchecked")]
+mod unchecked {
+    use crate::{Isometry2, Isometry3, Matrix3, Matrix4};
+    use glam::{DMat3, DMat4, Mat3, Mat4};
+
+    impl From<Mat3> for Isometry2<f32> {
+        fn from(mat3: Mat3) -> Isometry2<f32> {
+            crate::convert_unchecked(Matrix3::from(mat3))
+        }
+    }
+
+    impl From<Mat4> for Isometry3<f32> {
+        fn from(mat4: Mat4) -> Isometry3<f32> {
+            crate::convert_unchecked(Matrix4::from(mat4))
+        }
+    }
+
+    impl From<DMat3> for Isometry2<f64> {
+        fn from(mat3: DMat3) -> Isometry2<f64> {
+            crate::convert_unchecked(Matrix3::from(mat3))
+        }
+    }
+
+    impl From<DMat4> for Isometry3<f64> {
+        fn from(mat4: DMat4) -> Isometry3<f64> {
+            crate::convert_unchecked(Matrix4::from(mat4))
+        }
+    }
+}

src/third_party/glam/glam_matrix.rs

@@ -0,0 +1,210 @@
+use crate::storage::Storage;
+use crate::{Matrix, Matrix2, Matrix3, Matrix4, Vector, Vector2, Vector3, Vector4, U2, U3, U4};
+use glam::{
+    BVec2, BVec3, BVec4, DMat2, DMat3, DMat4, DVec2, DVec3, DVec4, IVec2, IVec3, IVec4, Mat2, Mat3,
+    Mat4, UVec2, UVec3, UVec4, Vec2, Vec3, Vec3A, Vec4,
+};
+
+macro_rules! impl_vec_conversion(
+    ($N: ty, $Vec2: ty, $Vec3: ty, $Vec4: ty) => {
+        impl From<$Vec2> for Vector2<$N> {
+            #[inline]
+            fn from(e: $Vec2) -> Vector2<$N> {
+                (*e.as_ref()).into()
+            }
+        }
+
+        impl<S> From<Vector<$N, U2, S>> for $Vec2
+        where
+            S: Storage<$N, U2>,
+        {
+            #[inline]
+            fn from(e: Vector<$N, U2, S>) -> $Vec2 {
+                <$Vec2>::new(e[0], e[1])
+            }
+        }
+
+        impl From<$Vec3> for Vector3<$N> {
+            #[inline]
+            fn from(e: $Vec3) -> Vector3<$N> {
+                (*e.as_ref()).into()
+            }
+        }
+
+        impl<S> From<Vector<$N, U3, S>> for $Vec3
+        where
+            S: Storage<$N, U3>,
+        {
+            #[inline]
+            fn from(e: Vector<$N, U3, S>) -> $Vec3 {
+                <$Vec3>::new(e[0], e[1], e[2])
+            }
+        }
+
+        impl From<$Vec4> for Vector4<$N> {
+            #[inline]
+            fn from(e: $Vec4) -> Vector4<$N> {
+                (*e.as_ref()).into()
+            }
+        }
+
+        impl<S> From<Vector<$N, U4, S>> for $Vec4
+        where
+            S: Storage<$N, U4>,
+        {
+            #[inline]
+            fn from(e: Vector<$N, U4, S>) -> $Vec4 {
+                <$Vec4>::new(e[0], e[1], e[2], e[3])
+            }
+        }
+    }
+);
+
+impl_vec_conversion!(f32, Vec2, Vec3, Vec4);
+impl_vec_conversion!(f64, DVec2, DVec3, DVec4);
+impl_vec_conversion!(i32, IVec2, IVec3, IVec4);
+impl_vec_conversion!(u32, UVec2, UVec3, UVec4);
+impl_vec_conversion!(bool, BVec2, BVec3, BVec4);
+
+impl From<Vec3A> for Vector3<f32> {
+    #[inline]
+    fn from(e: Vec3A) -> Vector3<f32> {
+        (*e.as_ref()).into()
+    }
+}
+
+impl<S> From<Vector<f32, U3, S>> for Vec3A
+where
+    S: Storage<f32, U3>,
+{
+    #[inline]
+    fn from(e: Vector<f32, U3, S>) -> Vec3A {
+        Vec3A::new(e[0], e[1], e[2])
+    }
+}
+
+impl From<Mat2> for Matrix2<f32> {
+    #[inline]
+    fn from(e: Mat2) -> Matrix2<f32> {
+        e.to_cols_array_2d().into()
+    }
+}
+
+impl<S> From<Matrix<f32, U2, U2, S>> for Mat2
+where
+    S: Storage<f32, U2, U2>,
+{
+    #[inline]
+    fn from(e: Matrix<f32, U2, U2, S>) -> Mat2 {
+        Mat2::from_cols(
+            Vec2::new(e[(0, 0)], e[(1, 0)]),
+            Vec2::new(e[(0, 1)], e[(1, 1)]),
+        )
+    }
+}
+
+impl From<Mat3> for Matrix3<f32> {
+    #[inline]
+    fn from(e: Mat3) -> Matrix3<f32> {
+        e.to_cols_array_2d().into()
+    }
+}
+
+impl<S> From<Matrix<f32, U3, U3, S>> for Mat3
+where
+    S: Storage<f32, U3, U3>,
+{
+    #[inline]
+    fn from(e: Matrix<f32, U3, U3, S>) -> Mat3 {
+        Mat3::from_cols(
+            Vec3::new(e[(0, 0)], e[(1, 0)], e[(2, 0)]),
+            Vec3::new(e[(0, 1)], e[(1, 1)], e[(2, 1)]),
+            Vec3::new(e[(0, 2)], e[(1, 2)], e[(2, 2)]),
+        )
+    }
+}
+
+impl From<Mat4> for Matrix4<f32> {
+    #[inline]
+    fn from(e: Mat4) -> Matrix4<f32> {
+        e.to_cols_array_2d().into()
+    }
+}
+
+impl<S> From<Matrix<f32, U4, U4, S>> for Mat4
+where
+    S: Storage<f32, U4, U4>,
+{
+    #[inline]
+    fn from(e: Matrix<f32, U4, U4, S>) -> Mat4 {
+        Mat4::from_cols(
+            Vec4::new(e[(0, 0)], e[(1, 0)], e[(2, 0)], e[(3, 0)]),
+            Vec4::new(e[(0, 1)], e[(1, 1)], e[(2, 1)], e[(3, 1)]),
+            Vec4::new(e[(0, 2)], e[(1, 2)], e[(2, 2)], e[(3, 2)]),
+            Vec4::new(e[(0, 3)], e[(1, 3)], e[(2, 3)], e[(3, 3)]),
+        )
+    }
+}
+
+impl From<DMat2> for Matrix2<f64> {
+    #[inline]
+    fn from(e: DMat2) -> Matrix2<f64> {
+        e.to_cols_array_2d().into()
+    }
+}
+
+impl<S> From<Matrix<f64, U2, U2, S>> for DMat2
+where
+    S: Storage<f64, U2, U2>,
+{
+    #[inline]
+    fn from(e: Matrix<f64, U2, U2, S>) -> DMat2 {
+        DMat2::from_cols(
+            DVec2::new(e[(0, 0)], e[(1, 0)]),
+            DVec2::new(e[(0, 1)], e[(1, 1)]),
+        )
+    }
+}
+
+impl From<DMat3> for Matrix3<f64> {
+    #[inline]
+    fn from(e: DMat3) -> Matrix3<f64> {
+        e.to_cols_array_2d().into()
+    }
+}
+
+impl<S> From<Matrix<f64, U3, U3, S>> for DMat3
+where
+    S: Storage<f64, U3, U3>,
+{
+    #[inline]
+    fn from(e: Matrix<f64, U3, U3, S>) -> DMat3 {
+        DMat3::from_cols(
+            DVec3::new(e[(0, 0)], e[(1, 0)], e[(2, 0)]),
+            DVec3::new(e[(0, 1)], e[(1, 1)], e[(2, 1)]),
+            DVec3::new(e[(0, 2)], e[(1, 2)], e[(2, 2)]),
+        )
+    }
+}
+
+impl From<DMat4> for Matrix4<f64> {
+    #[inline]
+    fn from(e: DMat4) -> Matrix4<f64> {
+        e.to_cols_array_2d().into()
+    }
+}
+
+impl<S> From<Matrix<f64, U4, U4, S>> for DMat4
+where
+    S: Storage<f64, U4, U4>,
+{
+    #[inline]
+    fn from(e: Matrix<f64, U4, U4, S>) -> DMat4 {
+        DMat4::from_cols(
+            DVec4::new(e[(0, 0)], e[(1, 0)], e[(2, 0)], e[(3, 0)]),
+            DVec4::new(e[(0, 1)], e[(1, 1)], e[(2, 1)], e[(3, 1)]),
+            DVec4::new(e[(0, 2)], e[(1, 2)], e[(2, 2)], e[(3, 2)]),
+            DVec4::new(e[(0, 3)], e[(1, 3)], e[(2, 3)], e[(3, 3)]),
+        )
+    }
+}

src/third_party/glam/glam_point.rs

@@ -0,0 +1,71 @@
+use crate::{Point2, Point3, Point4};
+use glam::{
+    BVec2, BVec3, BVec4, DVec2, DVec3, DVec4, IVec2, IVec3, IVec4, UVec2, UVec3, UVec4, Vec2, Vec3,
+    Vec3A, Vec4,
+};
+
+macro_rules! impl_point_conversion(
+    ($N: ty, $Vec2: ty, $Vec3: ty, $Vec4: ty) => {
+        impl From<$Vec2> for Point2<$N> {
+            #[inline]
+            fn from(e: $Vec2) -> Point2<$N> {
+                (*e.as_ref()).into()
+            }
+        }
+
+        impl From<Point2<$N>> for $Vec2 {
+            #[inline]
+            fn from(e: Point2<$N>) -> $Vec2 {
+                <$Vec2>::new(e[0], e[1])
+            }
+        }
+
+        impl From<$Vec3> for Point3<$N> {
+            #[inline]
+            fn from(e: $Vec3) -> Point3<$N> {
+                (*e.as_ref()).into()
+            }
+        }
+
+        impl From<Point3<$N>> for $Vec3 {
+            #[inline]
+            fn from(e: Point3<$N>) -> $Vec3 {
+                <$Vec3>::new(e[0], e[1], e[2])
+            }
+        }
+
+        impl From<$Vec4> for Point4<$N> {
+            #[inline]
+            fn from(e: $Vec4) -> Point4<$N> {
+                (*e.as_ref()).into()
+            }
+        }
+
+        impl From<Point4<$N>> for $Vec4 {
+            #[inline]
+            fn from(e: Point4<$N>) -> $Vec4 {
+                <$Vec4>::new(e[0], e[1], e[2], e[3])
+            }
+        }
+    }
+);
+
+impl_point_conversion!(f32, Vec2, Vec3, Vec4);
+impl_point_conversion!(f64, DVec2, DVec3, DVec4);
+impl_point_conversion!(i32, IVec2, IVec3, IVec4);
+impl_point_conversion!(u32, UVec2, UVec3, UVec4);
+impl_point_conversion!(bool, BVec2, BVec3, BVec4);
+
+impl From<Vec3A> for Point3<f32> {
+    #[inline]
+    fn from(e: Vec3A) -> Point3<f32> {
+        (*e.as_ref()).into()
+    }
+}
+
+impl From<Point3<f32>> for Vec3A {
+    #[inline]
+    fn from(e: Point3<f32>) -> Vec3A {
+        Vec3A::new(e[0], e[1], e[2])
+    }
+}

src/third_party/glam/glam_quaternion.rs

@@ -0,0 +1,64 @@
+use crate::{Quaternion, UnitQuaternion};
+use glam::{DQuat, Quat};
+
+impl From<Quat> for Quaternion<f32> {
+    #[inline]
+    fn from(e: Quat) -> Quaternion<f32> {
+        Quaternion::new(e.w, e.x, e.y, e.z)
+    }
+}
+
+impl From<Quaternion<f32>> for Quat {
+    #[inline]
+    fn from(e: Quaternion<f32>) -> Quat {
+        Quat::from_xyzw(e.i, e.j, e.k, e.w)
+    }
+}
+
+impl From<UnitQuaternion<f32>> for Quat {
+    #[inline]
+    fn from(e: UnitQuaternion<f32>) -> Quat {
+        Quat::from_xyzw(e.i, e.j, e.k, e.w)
+    }
+}
+
+impl From<DQuat> for Quaternion<f64> {
+    #[inline]
+    fn from(e: DQuat) -> Quaternion<f64> {
+        Quaternion::new(e.w, e.x, e.y, e.z)
+    }
+}
+
+impl From<Quaternion<f64>> for DQuat {
+    #[inline]
+    fn from(e: Quaternion<f64>) -> DQuat {
+        DQuat::from_xyzw(e.i, e.j, e.k, e.w)
+    }
+}
+
+impl From<UnitQuaternion<f64>> for DQuat {
+    #[inline]
+    fn from(e: UnitQuaternion<f64>) -> DQuat {
+        DQuat::from_xyzw(e.i, e.j, e.k, e.w)
+    }
+}
+
+#[cfg(feature = "convert-glam-unchecked")]
+mod unchecked {
+    use crate::{Quaternion, UnitQuaternion};
+    use glam::{DQuat, Quat};
+
+    impl From<Quat> for UnitQuaternion<f32> {
+        #[inline]
+        fn from(e: Quat) -> UnitQuaternion<f32> {
+            UnitQuaternion::new_unchecked(Quaternion::from(e))
+        }
+    }
+
+    impl From<DQuat> for UnitQuaternion<f64> {
+        #[inline]
+        fn from(e: DQuat) -> UnitQuaternion<f64> {
+            UnitQuaternion::new_unchecked(Quaternion::from(e))
+        }
+    }
+}

src/third_party/glam/glam_rotation.rs

@@ -0,0 +1,64 @@
+use crate::{Rotation2, Rotation3, UnitQuaternion};
+use glam::{DMat2, DQuat, Mat2, Quat};
+
+impl From<Rotation2<f32>> for Mat2 {
+    #[inline]
+    fn from(e: Rotation2<f32>) -> Mat2 {
+        e.into_inner().into()
+    }
+}
+
+impl From<Rotation2<f64>> for DMat2 {
+    #[inline]
+    fn from(e: Rotation2<f64>) -> DMat2 {
+        e.into_inner().into()
+    }
+}
+
+impl From<Rotation3<f32>> for Quat {
+    #[inline]
+    fn from(e: Rotation3<f32>) -> Quat {
+        UnitQuaternion::from(e).into()
+    }
+}
+
+impl From<Rotation3<f64>> for DQuat {
+    #[inline]
+    fn from(e: Rotation3<f64>) -> DQuat {
+        UnitQuaternion::from(e).into()
+    }
+}
+
+#[cfg(feature = "convert-glam-unchecked")]
+mod unchecked {
+    use crate::{Rotation2, Rotation3, UnitQuaternion};
+    use glam::{DMat2, DQuat, Mat2, Quat};
+
+    impl From<Mat2> for Rotation2<f32> {
+        #[inline]
+        fn from(e: Mat2) -> Rotation2<f32> {
+            Rotation2::from_matrix_unchecked(e.into())
+        }
+    }
+
+    impl From<DMat2> for Rotation2<f64> {
+        #[inline]
+        fn from(e: DMat2) -> Rotation2<f64> {
+            Rotation2::from_matrix_unchecked(e.into())
+        }
+    }
+
+    impl From<Quat> for Rotation3<f32> {
+        #[inline]
+        fn from(e: Quat) -> Rotation3<f32> {
+            Rotation3::from(UnitQuaternion::from(e))
+        }
+    }
+
+    impl From<DQuat> for Rotation3<f64> {
+        #[inline]
+        fn from(e: DQuat) -> Rotation3<f64> {
+            Rotation3::from(UnitQuaternion::from(e))
+        }
+    }
+}

src/third_party/glam/glam_similarity.rs

@@ -0,0 +1,54 @@
+use crate::{Similarity2, Similarity3};
+use glam::{DMat3, DMat4, Mat3, Mat4};
+
+impl From<Similarity2<f32>> for Mat3 {
+    fn from(iso: Similarity2<f32>) -> Mat3 {
+        iso.to_homogeneous().into()
+    }
+}
+impl From<Similarity3<f32>> for Mat4 {
+    fn from(iso: Similarity3<f32>) -> Mat4 {
+        iso.to_homogeneous().into()
+    }
+}
+
+impl From<Similarity2<f64>> for DMat3 {
+    fn from(iso: Similarity2<f64>) -> DMat3 {
+        iso.to_homogeneous().into()
+    }
+}
+impl From<Similarity3<f64>> for DMat4 {
+    fn from(iso: Similarity3<f64>) -> DMat4 {
+        iso.to_homogeneous().into()
+    }
+}
+
+#[cfg(feature = "convert-glam-unchecked")]
+mod unchecked {
+    use crate::{Matrix3, Matrix4, Similarity2, Similarity3};
+    use glam::{DMat3, DMat4, Mat3, Mat4};
+
+    impl From<Mat3> for Similarity2<f32> {
+        fn from(mat3: Mat3) -> Similarity2<f32> {
+            crate::convert_unchecked(Matrix3::from(mat3))
+        }
+    }
+
+    impl From<Mat4> for Similarity3<f32> {
+        fn from(mat4: Mat4) -> Similarity3<f32> {
+            crate::convert_unchecked(Matrix4::from(mat4))
+        }
+    }
+
+    impl From<DMat3> for Similarity2<f64> {
+        fn from(mat3: DMat3) -> Similarity2<f64> {
+            crate::convert_unchecked(Matrix3::from(mat3))
+        }
+    }
+
+    impl From<DMat4> for Similarity3<f64> {
+        fn from(mat4: DMat4) -> Similarity3<f64> {
+            crate::convert_unchecked(Matrix4::from(mat4))
+        }
+    }
+}

src/third_party/glam/glam_unit_complex.rs

@@ -0,0 +1,36 @@
+use crate::UnitComplex;
+use glam::{DMat2, Mat2};
+
+impl From<UnitComplex<f32>> for Mat2 {
+    #[inline]
+    fn from(e: UnitComplex<f32>) -> Mat2 {
+        e.to_rotation_matrix().into_inner().into()
+    }
+}
+
+impl From<UnitComplex<f64>> for DMat2 {
+    #[inline]
+    fn from(e: UnitComplex<f64>) -> DMat2 {
+        e.to_rotation_matrix().into_inner().into()
+    }
+}
+
+#[cfg(feature = "convert-glam-unchecked")]
+mod unchecked {
+    use crate::{Rotation2, UnitComplex};
+    use glam::{DMat2, Mat2};
+
+    impl From<Mat2> for UnitComplex<f32> {
+        #[inline]
+        fn from(e: Mat2) -> UnitComplex<f32> {
+            Rotation2::from_matrix_unchecked(e.into()).into()
+        }
+    }
+
+    impl From<DMat2> for UnitComplex<f64> {
+        #[inline]
+        fn from(e: DMat2) -> UnitComplex<f64> {
+            Rotation2::from_matrix_unchecked(e.into()).into()
+        }
+    }
+}

src/third_party/glam/mod.rs

@@ -0,0 +1,7 @@
+mod glam_isometry;
+mod glam_matrix;
+mod glam_point;
+mod glam_quaternion;
+mod glam_rotation;
+mod glam_similarity;
+mod glam_unit_complex;

src/third_party/mint/mint_matrix.rs

@@ -0,0 +1,117 @@
+use std::convert::{AsMut, AsRef, From, Into};
+use std::mem;
+use std::ptr;
+
+use crate::base::allocator::Allocator;
+use crate::base::dimension::{U1, U2, U3, U4};
+use crate::base::storage::{ContiguousStorage, ContiguousStorageMut, Storage, StorageMut};
+use crate::base::{DefaultAllocator, Matrix, MatrixMN, Scalar};
+
+macro_rules! impl_from_into_mint_1D(
+    ($($NRows: ident => $VT:ident [$SZ: expr]);* $(;)*) => {$(
+        impl<N> From<mint::$VT<N>> for MatrixMN<N, $NRows, U1>
+        where N: Scalar,
+              DefaultAllocator: Allocator<N, $NRows, U1> {
+            #[inline]
+            fn from(v: mint::$VT<N>) -> Self {
+                unsafe {
+                    let mut res = Self::new_uninitialized();
+                    ptr::copy_nonoverlapping(&v.x, (*res.as_mut_ptr()).data.ptr_mut(), $SZ);
+
+                    res.assume_init()
+                }
+            }
+        }
+
+        impl<N, S> Into<mint::$VT<N>> for Matrix<N, $NRows, U1, S>
+        where N: Scalar,
+              S: ContiguousStorage<N, $NRows, U1> {
+            #[inline]
+            fn into(self) -> mint::$VT<N> {
+                unsafe {
+                    let mut res: mint::$VT<N> = mem::MaybeUninit::uninit().assume_init();
+                    ptr::copy_nonoverlapping(self.data.ptr(), &mut res.x, $SZ);
+                    res
+                }
+            }
+        }
+
+        impl<N, S> AsRef<mint::$VT<N>> for Matrix<N, $NRows, U1, S>
+        where N: Scalar,
+              S: ContiguousStorage<N, $NRows, U1> {
+            #[inline]
+            fn as_ref(&self) -> &mint::$VT<N> {
+                unsafe {
+                    mem::transmute(self.data.ptr())
+                }
+            }
+        }
+
+        impl<N, S> AsMut<mint::$VT<N>> for Matrix<N, $NRows, U1, S>
+        where N: Scalar,
+              S: ContiguousStorageMut<N, $NRows, U1> {
+            #[inline]
+            fn as_mut(&mut self) -> &mut mint::$VT<N> {
+                unsafe {
+                    mem::transmute(self.data.ptr_mut())
+                }
+            }
+        }
+    )*}
+);
+
+// Implement for vectors of dimension 2 .. 4.
+impl_from_into_mint_1D!(
+    U2 => Vector2[2];
+    U3 => Vector3[3];
+    U4 => Vector4[4];
+);
+
+macro_rules! impl_from_into_mint_2D(
+    ($(($NRows: ty, $NCols: ty) => $MV:ident{ $($component:ident),* }[$SZRows: expr]);* $(;)*) => {$(
+        impl<N> From<mint::$MV<N>> for MatrixMN<N, $NRows, $NCols>
+        where N: Scalar,
+              DefaultAllocator: Allocator<N, $NRows, $NCols> {
+            #[inline]
+            fn from(m: mint::$MV<N>) -> Self {
+                unsafe {
+                    let mut res = Self::new_uninitialized();
+                    let mut ptr = (*res.as_mut_ptr()).data.ptr_mut();
+                    $(
+                        ptr::copy_nonoverlapping(&m.$component.x, ptr, $SZRows);
+                        ptr = ptr.offset($SZRows);
+                    )*
+                    let _ = ptr;
+                    res.assume_init()
+                }
+            }
+        }
+
+        impl<N> Into<mint::$MV<N>> for MatrixMN<N, $NRows, $NCols>
+        where N: Scalar,
+              DefaultAllocator: Allocator<N, $NRows, $NCols> {
+            #[inline]
+            fn into(self) -> mint::$MV<N> {
+                unsafe {
+                    let mut res: mint::$MV<N> = mem::MaybeUninit::uninit().assume_init();
+                    let mut ptr = self.data.ptr();
+                    $(
+                        ptr::copy_nonoverlapping(ptr, &mut res.$component.x, $SZRows);
+                        ptr = ptr.offset($SZRows);
+                    )*
+                    let _ = ptr;
+                    res
+                }
+            }
+        }
+    )*}
+);
+
+// Implement for matrices with shape 2x2 .. 4x4.
+impl_from_into_mint_2D!(
+    (U2, U2) => ColumnMatrix2{x, y}[2];
+    (U2, U3) => ColumnMatrix2x3{x, y, z}[2];
+    (U3, U3) => ColumnMatrix3{x, y, z}[3];
+    (U3, U4) => ColumnMatrix3x4{x, y, z, w}[3];
+    (U4, U4) => ColumnMatrix4{x, y, z, w}[4];
+);

src/third_party/mint/mint_point.rs

@@ -0,0 +1,52 @@
+use crate::base::storage::{Storage, StorageMut};
+use crate::{Point, Scalar, VectorN, U2, U3};
+use std::convert::{AsMut, AsRef};
+
+macro_rules! impl_from_into_mint_1D(
+    ($($NRows: ident => $PT:ident, $VT:ident [$SZ: expr]);* $(;)*) => {$(
+        impl<N> From<mint::$PT<N>> for Point<N, $NRows>
+        where N: Scalar {
+            #[inline]
+            fn from(p: mint::$PT<N>) -> Self {
+                Self {
+                    coords: VectorN::from(mint::$VT::from(p)),
+                }
+            }
+        }
+
+        impl<N> Into<mint::$PT<N>> for Point<N, $NRows>
+        where N: Scalar {
+            #[inline]
+            fn into(self) -> mint::$PT<N> {
+                let mint_vec: mint::$VT<N> = self.coords.into();
+                mint::$PT::from(mint_vec)
+            }
+        }
+
+        impl<N> AsRef<mint::$PT<N>> for Point<N, $NRows>
+        where N: Scalar {
+            #[inline]
+            fn as_ref(&self) -> &mint::$PT<N> {
+                unsafe {
+                    &*(self.coords.data.ptr() as *const mint::$PT<N>)
+                }
+            }
+        }
+
+        impl<N> AsMut<mint::$PT<N>> for Point<N, $NRows>
+        where N: Scalar {
+            #[inline]
+            fn as_mut(&mut self) -> &mut mint::$PT<N> {
+                unsafe {
+                    &mut *(self.coords.data.ptr_mut() as *mut mint::$PT<N>)
+                }
+            }
+        }
+    )*}
+);
+
+// Implement for points of dimension 2, 3.
+impl_from_into_mint_1D!(
+    U2 => Point2, Vector2[2];
+    U3 => Point3, Vector3[3];
+);

src/third_party/mint/mint_quaternion.rs

@@ -0,0 +1,33 @@
+use crate::{Quaternion, Scalar, SimdValue, UnitQuaternion};
+
+impl<N: Scalar> From<mint::Quaternion<N>> for Quaternion<N> {
+    fn from(q: mint::Quaternion<N>) -> Self {
+        Self::new(q.s, q.v.x, q.v.y, q.v.z)
+    }
+}
+
+impl<N: Scalar> Into<mint::Quaternion<N>> for Quaternion<N> {
+    fn into(self) -> mint::Quaternion<N> {
+        mint::Quaternion {
+            v: mint::Vector3 {
+                x: self[0].inlined_clone(),
+                y: self[1].inlined_clone(),
+                z: self[2].inlined_clone(),
+            },
+            s: self[3].inlined_clone(),
+        }
+    }
+}
+
+impl<N: Scalar + SimdValue> Into<mint::Quaternion<N>> for UnitQuaternion<N> {
+    fn into(self) -> mint::Quaternion<N> {
+        mint::Quaternion {
+            v: mint::Vector3 {
+                x: self[0].inlined_clone(),
+                y: self[1].inlined_clone(),
+                z: self[2].inlined_clone(),
+            },
+            s: self[3].inlined_clone(),
+        }
+    }
+}

src/third_party/mint/mint_rotation.rs

@@ -0,0 +1,7 @@
+use crate::{RealField, Rotation3};
+
+impl<N: RealField> From<mint::EulerAngles<N, mint::IntraXYZ>> for Rotation3<N> {
+    fn from(euler: mint::EulerAngles<N, mint::IntraXYZ>) -> Self {
+        Self::from_euler_angles(euler.a, euler.b, euler.c)
+    }
+}

src/third_party/mint/mod.rs

@@ -0,0 +1,4 @@
+mod mint_matrix;
+mod mint_point;
+mod mint_quaternion;
+mod mint_rotation;

src/third_party/mod.rs

@@ -0,0 +1,6 @@
+#[cfg(feature = "alga")]
+mod alga;
+#[cfg(feature = "glam")]
+mod glam;
+#[cfg(feature = "mint")]
+mod mint;