Add "cast" methods to cast the type of the components of most nalgebra types.

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/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/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/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

@@ -35,8 +35,8 @@ use crate::geometry::{
 
 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 +58,8 @@ 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> {

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/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()`.