Merge pull request #780 from dimforge/misc

Add various utility functions

CHANGELOG.md

@@ -4,6 +4,22 @@ documented here.
 
 This project adheres to [Semantic Versioning](https://semver.org/).
 
+## [0.23.0] - WIP
+
+### Added
+ * The `.inverse_transform_unit_vector(v)` was added to `Rotation2/3`, `Isometry2/3`, `UnitQuaternion`, and `UnitComplex`.
+   It applies the corresponding rotation to a unit vector `Unit<Vector2/3>`.
+ * The `Point.map(f)` and `Point.apply(f)` to apply a function to each component of the point, similarly to `Vector.map(f)`
+   and `Vector.apply(f)`.
+ * The `Quaternion::from([N; 4])` conversion to build a quaternion from an array of four elements.
+ * The `Isometry::from(Translation)` conversion to build an isometry from a translation.
+ * The `Vector::ith_axis(i)` which build a unit vector, e.g., `Unit<Vector3<f32>>` with its i-th component set to 1.0 and the
+   others set to zero.
+ * The `Isometry.lerp_slerp` and `Isometry.try_lerp_slerp` methods to interpolate between two isometries using linear
+   interpolation for the translational part, and spherical interpolation for the rotational part.
+ * The `Rotation2.slerp`, `Rotation3.slerp`, and `UnitQuaternion.slerp` method for 
+   spherical interpolation.
+   
 ## [0.22.0]
 In this release, we are using the new version 0.2 of simba. One major change of that version is that the
 use of `libm` is now opt-in when building targetting `no-std` environment. If you are using floating-point

Cargo.toml

@@ -36,23 +36,23 @@ libm-force = [ "simba/libm_force" ]
 
 
 [dependencies]
-typenum        = "1.11"
+typenum        = "1.12"
-generic-array  = "0.13"
+generic-array  = "0.14"
 rand           = { version = "0.7", default-features = false }
 num-traits     = { version = "0.2", default-features = false }
-num-complex    = { version = "0.2", default-features = false }
+num-complex    = { version = "0.3", default-features = false }
-num-rational   = { version = "0.2", default-features = false }
+num-rational   = { version = "0.3", default-features = false }
-approx         = { version = "0.3", default-features = false }
+approx         = { version = "0.4", default-features = false }
-simba          = { version = "0.2", default-features = false }
+simba          = { version = "0.3", default-features = false }
 alga           = { version = "0.9", default-features = false, optional = true }
-rand_distr     = { version = "0.2", optional = true }
+rand_distr     = { version = "0.3", optional = true }
 matrixmultiply = { version = "0.2", optional = true }
 serde          = { version = "1.0", features = [ "derive" ], optional = true }
 abomonation    = { version = "0.7", optional = true }
 mint           = { version = "0.5", optional = true }
 quickcheck     = { version = "0.9", optional = true }
-pest           = { version = "2.0", optional = true }
+pest           = { version = "2", optional = true }
-pest_derive    = { version = "2.0", optional = true }
+pest_derive    = { version = "2", optional = true }
 matrixcompare-core = { version = "0.1", optional = true }
 
 [dev-dependencies]

nalgebra-glm/Cargo.toml

@@ -23,6 +23,6 @@ abomonation-serialize = [ "nalgebra/abomonation-serialize" ]
 
 [dependencies]
 num-traits = { version = "0.2", default-features = false }
-approx = { version = "0.3", default-features = false }
+approx = { version = "0.4", default-features = false }
-simba = { version = "0.2", default-features = false }
+simba = { version = "0.3", default-features = false }
 nalgebra = { path =  "..", version = "0.22", default-features = false }

nalgebra-lapack/Cargo.toml

@@ -23,7 +23,7 @@ accelerate = ["lapack-src/accelerate"]
 intel-mkl  = ["lapack-src/intel-mkl"]
 
 [dependencies]
-nalgebra      = { version = "0.22", path = ".." }
+nalgebra      = { version = "0.22" } # , path = ".." }
 num-traits    = "0.2"
 num-complex   = { version = "0.2", default-features = false }
 simba         = "0.2"
@@ -34,7 +34,7 @@ lapack-src    = { version = "0.5", default-features = false }
 # clippy = "*"
 
 [dev-dependencies]
-nalgebra   = { version = "0.22", path = "..", features = [ "arbitrary" ] }
+nalgebra   = { version = "0.22", features = [ "arbitrary" ] } # path = ".." }
 quickcheck = "0.9"
 approx     = "0.3"
 rand       = "0.7"

src/base/construction.rs

@@ -1019,6 +1019,12 @@ where
         res
     }
 
+    /// The column unit vector with `N::one()` as its i-th component.
+    #[inline]
+    pub fn ith_axis(i: usize) -> Unit<Self> {
+        Unit::new_unchecked(Self::ith(i, N::one()))
+    }
+
     /// The column vector with a 1 as its first component, and zero elsewhere.
     #[inline]
     pub fn x() -> Self

src/geometry/abstract_rotation.rs

@@ -1,6 +1,6 @@
 use crate::allocator::Allocator;
 use crate::geometry::{Rotation, UnitComplex, UnitQuaternion};
-use crate::{DefaultAllocator, DimName, Point, Scalar, SimdRealField, VectorN, U2, U3};
+use crate::{DefaultAllocator, DimName, Point, Scalar, SimdRealField, Unit, VectorN, U2, U3};
 
 use simba::scalar::ClosedMul;
 
@@ -24,6 +24,13 @@ pub trait AbstractRotation<N: Scalar, D: DimName>: PartialEq + ClosedMul + Clone
     fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D>
     where
         DefaultAllocator: Allocator<N, D>;
+    /// Apply the inverse rotation to the given unit vector.
+    fn inverse_transform_unit_vector(&self, v: &Unit<VectorN<N, D>>) -> Unit<VectorN<N, D>>
+    where
+        DefaultAllocator: Allocator<N, D>,
+    {
+        Unit::new_unchecked(self.inverse_transform_vector(&**v))
+    }
     /// Apply the inverse rotation to the given point.
     fn inverse_transform_point(&self, p: &Point<N, D>) -> Point<N, D>
     where
@@ -74,6 +81,14 @@ where
         self.inverse_transform_vector(v)
     }
 
+    #[inline]
+    fn inverse_transform_unit_vector(&self, v: &Unit<VectorN<N, D>>) -> Unit<VectorN<N, D>>
+    where
+        DefaultAllocator: Allocator<N, D>,
+    {
+        self.inverse_transform_unit_vector(v)
+    }
+
     #[inline]
     fn inverse_transform_point(&self, p: &Point<N, D>) -> Point<N, D>
     where

src/geometry/isometry.rs

@@ -14,10 +14,12 @@ use simba::scalar::{RealField, SubsetOf};
 use simba::simd::SimdRealField;
 
 use crate::base::allocator::Allocator;
-use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
+use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1, U2, U3};
 use crate::base::storage::Owned;
-use crate::base::{DefaultAllocator, MatrixN, Scalar, VectorN};
+use crate::base::{DefaultAllocator, MatrixN, Scalar, Unit, VectorN};
-use crate::geometry::{AbstractRotation, Point, Translation};
+use crate::geometry::{
+    AbstractRotation, Point, Rotation2, Rotation3, Translation, UnitComplex, UnitQuaternion,
+};
 
 /// A direct isometry, i.e., a rotation followed by a translation, aka. a rigid-body motion, aka. an element of a Special Euclidean (SE) group.
 #[repr(C)]
@@ -350,6 +352,237 @@ where
     pub fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
         self.rotation.inverse_transform_vector(v)
     }
+
+    /// Transform the given unit vector by the inverse of this isometry, ignoring the
+    /// translation component of the isometry. This may be
+    /// less expensive than computing the entire isometry inverse and then
+    /// transforming the point.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # use std::f32;
+    /// # use nalgebra::{Isometry3, Translation3, UnitQuaternion, Vector3};
+    /// let tra = Translation3::new(0.0, 0.0, 3.0);
+    /// let rot = UnitQuaternion::from_scaled_axis(Vector3::z() * f32::consts::FRAC_PI_2);
+    /// let iso = Isometry3::from_parts(tra, rot);
+    ///
+    /// let transformed_point = iso.inverse_transform_unit_vector(&Vector3::x_axis());
+    /// assert_relative_eq!(transformed_point, -Vector3::y_axis(), epsilon = 1.0e-6);
+    /// ```
+    #[inline]
+    pub fn inverse_transform_unit_vector(&self, v: &Unit<VectorN<N, D>>) -> Unit<VectorN<N, D>> {
+        self.rotation.inverse_transform_unit_vector(v)
+    }
+}
+
+impl<N: SimdRealField> Isometry<N, U3, UnitQuaternion<N>> {
+    /// Interpolates between two isometries using a linear interpolation for the translation part,
+    /// and a spherical interpolation for the rotation part.
+    ///
+    /// Panics if the angle between both rotations is 180 degrees (in which case the interpolation
+    /// is not well-defined). Use `.try_lerp_slerp` instead to avoid the panic.
+    ///
+    /// # Examples:
+    ///
+    /// ```
+    /// # use nalgebra::{Vector3, Translation3, Isometry3, UnitQuaternion};
+    ///
+    /// let t1 = Translation3::new(1.0, 2.0, 3.0);
+    /// let t2 = Translation3::new(4.0, 8.0, 12.0);
+    /// let q1 = UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
+    /// let q2 = UnitQuaternion::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);
+    /// let iso1 = Isometry3::from_parts(t1, q1);
+    /// let iso2 = Isometry3::from_parts(t2, q2);
+    ///
+    /// let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);
+    ///
+    /// assert_eq!(iso3.translation.vector, Vector3::new(2.0, 4.0, 6.0));
+    /// assert_eq!(iso3.rotation.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));
+    /// ```
+    #[inline]
+    pub fn lerp_slerp(&self, other: &Self, t: N) -> Self
+    where
+        N: RealField,
+    {
+        let tr = self.translation.vector.lerp(&other.translation.vector, t);
+        let rot = self.rotation.slerp(&other.rotation, t);
+        Self::from_parts(tr.into(), rot)
+    }
+
+    /// Attempts to interpolate between two isometries using a linear interpolation for the translation part,
+    /// and a spherical interpolation for the rotation part.
+    ///
+    /// Retuns `None` if the angle between both rotations is 180 degrees (in which case the interpolation
+    /// is not well-defined).
+    ///
+    /// # Examples:
+    ///
+    /// ```
+    /// # use nalgebra::{Vector3, Translation3, Isometry3, UnitQuaternion};
+    ///
+    /// let t1 = Translation3::new(1.0, 2.0, 3.0);
+    /// let t2 = Translation3::new(4.0, 8.0, 12.0);
+    /// let q1 = UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
+    /// let q2 = UnitQuaternion::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);
+    /// let iso1 = Isometry3::from_parts(t1, q1);
+    /// let iso2 = Isometry3::from_parts(t2, q2);
+    ///
+    /// let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);
+    ///
+    /// assert_eq!(iso3.translation.vector, Vector3::new(2.0, 4.0, 6.0));
+    /// assert_eq!(iso3.rotation.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));
+    /// ```
+    #[inline]
+    pub fn try_lerp_slerp(&self, other: &Self, t: N, epsilon: N) -> Option<Self>
+    where
+        N: RealField,
+    {
+        let tr = self.translation.vector.lerp(&other.translation.vector, t);
+        let rot = self.rotation.try_slerp(&other.rotation, t, epsilon)?;
+        Some(Self::from_parts(tr.into(), rot))
+    }
+}
+
+impl<N: SimdRealField> Isometry<N, U3, Rotation3<N>> {
+    /// Interpolates between two isometries using a linear interpolation for the translation part,
+    /// and a spherical interpolation for the rotation part.
+    ///
+    /// Panics if the angle between both rotations is 180 degrees (in which case the interpolation
+    /// is not well-defined). Use `.try_lerp_slerp` instead to avoid the panic.
+    ///
+    /// # Examples:
+    ///
+    /// ```
+    /// # use nalgebra::{Vector3, Translation3, Rotation3, IsometryMatrix3};
+    ///
+    /// let t1 = Translation3::new(1.0, 2.0, 3.0);
+    /// let t2 = Translation3::new(4.0, 8.0, 12.0);
+    /// let q1 = Rotation3::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
+    /// let q2 = Rotation3::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);
+    /// let iso1 = IsometryMatrix3::from_parts(t1, q1);
+    /// let iso2 = IsometryMatrix3::from_parts(t2, q2);
+    ///
+    /// let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);
+    ///
+    /// assert_eq!(iso3.translation.vector, Vector3::new(2.0, 4.0, 6.0));
+    /// assert_eq!(iso3.rotation.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));
+    /// ```
+    #[inline]
+    pub fn lerp_slerp(&self, other: &Self, t: N) -> Self
+    where
+        N: RealField,
+    {
+        let tr = self.translation.vector.lerp(&other.translation.vector, t);
+        let rot = self.rotation.slerp(&other.rotation, t);
+        Self::from_parts(tr.into(), rot)
+    }
+
+    /// Attempts to interpolate between two isometries using a linear interpolation for the translation part,
+    /// and a spherical interpolation for the rotation part.
+    ///
+    /// Retuns `None` if the angle between both rotations is 180 degrees (in which case the interpolation
+    /// is not well-defined).
+    ///
+    /// # Examples:
+    ///
+    /// ```
+    /// # use nalgebra::{Vector3, Translation3, Rotation3, IsometryMatrix3};
+    ///
+    /// let t1 = Translation3::new(1.0, 2.0, 3.0);
+    /// let t2 = Translation3::new(4.0, 8.0, 12.0);
+    /// let q1 = Rotation3::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
+    /// let q2 = Rotation3::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);
+    /// let iso1 = IsometryMatrix3::from_parts(t1, q1);
+    /// let iso2 = IsometryMatrix3::from_parts(t2, q2);
+    ///
+    /// let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);
+    ///
+    /// assert_eq!(iso3.translation.vector, Vector3::new(2.0, 4.0, 6.0));
+    /// assert_eq!(iso3.rotation.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));
+    /// ```
+    #[inline]
+    pub fn try_lerp_slerp(&self, other: &Self, t: N, epsilon: N) -> Option<Self>
+    where
+        N: RealField,
+    {
+        let tr = self.translation.vector.lerp(&other.translation.vector, t);
+        let rot = self.rotation.try_slerp(&other.rotation, t, epsilon)?;
+        Some(Self::from_parts(tr.into(), rot))
+    }
+}
+
+impl<N: SimdRealField> Isometry<N, U2, UnitComplex<N>> {
+    /// Interpolates between two isometries using a linear interpolation for the translation part,
+    /// and a spherical interpolation for the rotation part.
+    ///
+    /// Panics if the angle between both rotations is 180 degrees (in which case the interpolation
+    /// is not well-defined). Use `.try_lerp_slerp` instead to avoid the panic.
+    ///
+    /// # Examples:
+    ///
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # use nalgebra::{Vector2, Translation2, UnitComplex, Isometry2};
+    ///
+    /// let t1 = Translation2::new(1.0, 2.0);
+    /// let t2 = Translation2::new(4.0, 8.0);
+    /// let q1 = UnitComplex::new(std::f32::consts::FRAC_PI_4);
+    /// let q2 = UnitComplex::new(-std::f32::consts::PI);
+    /// let iso1 = Isometry2::from_parts(t1, q1);
+    /// let iso2 = Isometry2::from_parts(t2, q2);
+    ///
+    /// let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);
+    ///
+    /// assert_eq!(iso3.translation.vector, Vector2::new(2.0, 4.0));
+    /// assert_relative_eq!(iso3.rotation.angle(), std::f32::consts::FRAC_PI_2);
+    /// ```
+    #[inline]
+    pub fn lerp_slerp(&self, other: &Self, t: N) -> Self
+    where
+        N: RealField,
+    {
+        let tr = self.translation.vector.lerp(&other.translation.vector, t);
+        let rot = self.rotation.slerp(&other.rotation, t);
+        Self::from_parts(tr.into(), rot)
+    }
+}
+
+impl<N: SimdRealField> Isometry<N, U2, Rotation2<N>> {
+    /// Interpolates between two isometries using a linear interpolation for the translation part,
+    /// and a spherical interpolation for the rotation part.
+    ///
+    /// Panics if the angle between both rotations is 180 degrees (in which case the interpolation
+    /// is not well-defined). Use `.try_lerp_slerp` instead to avoid the panic.
+    ///
+    /// # Examples:
+    ///
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # use nalgebra::{Vector2, Translation2, Rotation2, IsometryMatrix2};
+    ///
+    /// let t1 = Translation2::new(1.0, 2.0);
+    /// let t2 = Translation2::new(4.0, 8.0);
+    /// let q1 = Rotation2::new(std::f32::consts::FRAC_PI_4);
+    /// let q2 = Rotation2::new(-std::f32::consts::PI);
+    /// let iso1 = IsometryMatrix2::from_parts(t1, q1);
+    /// let iso2 = IsometryMatrix2::from_parts(t2, q2);
+    ///
+    /// let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);
+    ///
+    /// assert_eq!(iso3.translation.vector, Vector2::new(2.0, 4.0));
+    /// assert_relative_eq!(iso3.rotation.angle(), std::f32::consts::FRAC_PI_2);
+    /// ```
+    #[inline]
+    pub fn lerp_slerp(&self, other: &Self, t: N) -> Self
+    where
+        N: RealField,
+    {
+        let tr = self.translation.vector.lerp(&other.translation.vector, t);
+        let rot = self.rotation.slerp(&other.rotation, t);
+        Self::from_parts(tr.into(), rot)
+    }
 }
 
 // NOTE: we don't require `R: Rotation<...>` here because this is not useful for the implementation

src/geometry/isometry_conversion.rs

@@ -151,6 +151,17 @@ where
     }
 }
 
+impl<N: SimdRealField, D: DimName, R: AbstractRotation<N, D>> From<Translation<N, D>>
+    for Isometry<N, D, R>
+where
+    DefaultAllocator: Allocator<N, D>,
+{
+    #[inline]
+    fn from(tra: Translation<N, D>) -> Self {
+        Self::from_parts(tra, R::identity())
+    }
+}
+
 impl<N: SimdRealField, D: DimName, R> From<Isometry<N, D, R>> for MatrixN<N, DimNameSum<D, U1>>
 where
     D: DimNameAdd<U1>,

src/geometry/point.rs

@@ -102,6 +102,45 @@ impl<N: Scalar, D: DimName> Point<N, D>
 where
     DefaultAllocator: Allocator<N, D>,
 {
+    /// Returns a point containing the result of `f` applied to each of its entries.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::{Point2, Point3};
+    /// let p = Point2::new(1.0, 2.0);
+    /// assert_eq!(p.map(|e| e * 10.0), Point2::new(10.0, 20.0));
+    ///
+    /// // This works in any dimension.
+    /// let p = Point3::new(1.1, 2.1, 3.1);
+    /// assert_eq!(p.map(|e| e as u32), Point3::new(1, 2, 3));
+    /// ```
+    #[inline]
+    pub fn map<N2: Scalar, F: FnMut(N) -> N2>(&self, f: F) -> Point<N2, D>
+    where
+        DefaultAllocator: Allocator<N2, D>,
+    {
+        self.coords.map(f).into()
+    }
+
+    /// Replaces each component of `self` by the result of a closure `f` applied on it.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::{Point2, Point3};
+    /// let mut p = Point2::new(1.0, 2.0);
+    /// p.apply(|e| e * 10.0);
+    /// assert_eq!(p, Point2::new(10.0, 20.0));
+    ///
+    /// // This works in any dimension.
+    /// let mut p = Point3::new(1.0, 2.0, 3.0);
+    /// p.apply(|e| e * 10.0);
+    /// assert_eq!(p, Point3::new(10.0, 20.0, 30.0));
+    /// ```
+    #[inline]
+    pub fn apply<F: FnMut(N) -> N>(&mut self, f: F) {
+        self.coords.apply(f)
+    }
+
     /// Converts this point into a vector in homogeneous coordinates, i.e., appends a `1` at the
     /// end of it.
     ///

src/geometry/quaternion.rs

@@ -1542,6 +1542,26 @@ where
     pub fn inverse_transform_vector(&self, v: &Vector3<N>) -> Vector3<N> {
         self.inverse() * v
     }
+
+    /// Rotate a vector by the inverse of this unit quaternion. This may be
+    /// cheaper than inverting the unit quaternion and transforming the
+    /// vector.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # use std::f32;
+    /// # use nalgebra::{UnitQuaternion, Vector3};
+    /// let rot = UnitQuaternion::from_axis_angle(&Vector3::z_axis(), f32::consts::FRAC_PI_2);
+    /// let transformed_vector = rot.inverse_transform_unit_vector(&Vector3::x_axis());
+    ///
+    /// assert_relative_eq!(transformed_vector, -Vector3::y_axis(), epsilon = 1.0e-6);
+    /// ```
+    #[inline]
+    pub fn inverse_transform_unit_vector(&self, v: &Unit<Vector3<N>>) -> Unit<Vector3<N>> {
+        self.inverse() * v
+    }
 }
 
 impl<N: RealField> Default for UnitQuaternion<N> {

src/geometry/quaternion_conversion.rs

@@ -265,6 +265,15 @@ impl<N: Scalar + SimdValue> From<Vector4<N>> for Quaternion<N> {
     }
 }
 
+impl<N: Scalar + SimdValue> From<[N; 4]> for Quaternion<N> {
+    #[inline]
+    fn from(coords: [N; 4]) -> Self {
+        Self {
+            coords: coords.into(),
+        }
+    }
+}
+
 impl<N: Scalar + PrimitiveSimdValue> From<[Quaternion<N::Element>; 2]> for Quaternion<N>
 where
     N: From<[<N as SimdValue>::Element; 2]>,

src/geometry/rotation.rs

@@ -19,7 +19,7 @@ use simba::simd::SimdRealField;
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
-use crate::base::{DefaultAllocator, MatrixN, Scalar, VectorN};
+use crate::base::{DefaultAllocator, MatrixN, Scalar, Unit, VectorN};
 use crate::geometry::Point;
 
 /// A rotation matrix.
@@ -441,6 +441,25 @@ where
     pub fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
         self.matrix().tr_mul(v)
     }
+
+    /// Rotate the given vector by the inverse of this rotation. This may be
+    /// cheaper than inverting the rotation and then transforming the given
+    /// vector.
+    ///
+    /// # Example
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # use std::f32;
+    /// # use nalgebra::{Rotation2, Rotation3, UnitQuaternion, Vector3};
+    /// let rot = Rotation3::new(Vector3::z() * f32::consts::FRAC_PI_2);
+    /// let transformed_vector = rot.inverse_transform_unit_vector(&Vector3::x_axis());
+    ///
+    /// assert_relative_eq!(transformed_vector, -Vector3::y_axis(), epsilon = 1.0e-6);
+    /// ```
+    #[inline]
+    pub fn inverse_transform_unit_vector(&self, v: &Unit<VectorN<N, D>>) -> Unit<VectorN<N, D>> {
+        Unit::new_unchecked(self.inverse_transform_vector(&**v))
+    }
 }
 
 impl<N: Scalar + Eq, D: DimName> Eq for Rotation<N, D> where DefaultAllocator: Allocator<N, D, D> {}

src/geometry/rotation_specialization.rs

@@ -236,6 +236,31 @@ impl<N: SimdRealField> Rotation2<N> {
     pub fn scaled_axis(&self) -> VectorN<N, U1> {
         Vector1::new(self.angle())
     }
+
+    /// Spherical linear interpolation between two rotation matrices.
+    ///
+    /// # Examples:
+    ///
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # use nalgebra::geometry::Rotation2;
+    ///
+    /// let rot1 = Rotation2::new(std::f32::consts::FRAC_PI_4);
+    /// let rot2 = Rotation2::new(-std::f32::consts::PI);
+    ///
+    /// let rot = rot1.slerp(&rot2, 1.0 / 3.0);
+    ///
+    /// assert_relative_eq!(rot.angle(), std::f32::consts::FRAC_PI_2);
+    /// ```
+    #[inline]
+    pub fn slerp(&self, other: &Self, t: N) -> Self
+    where
+        N::Element: SimdRealField,
+    {
+        let c1 = UnitComplex::from(*self);
+        let c2 = UnitComplex::from(*other);
+        c1.slerp(&c2, t).into()
+    }
 }
 
 impl<N: SimdRealField> Distribution<Rotation2<N>> for Standard
@@ -862,6 +887,53 @@ where
             Self::identity()
         }
     }
+
+    /// Spherical linear interpolation between two rotation matrices.
+    ///
+    /// Panics if the angle between both rotations is 180 degrees (in which case the interpolation
+    /// is not well-defined). Use `.try_slerp` instead to avoid the panic.
+    ///
+    /// # Examples:
+    ///
+    /// ```
+    /// # use nalgebra::geometry::Rotation3;
+    ///
+    /// let q1 = Rotation3::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
+    /// let q2 = Rotation3::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);
+    ///
+    /// let q = q1.slerp(&q2, 1.0 / 3.0);
+    ///
+    /// assert_eq!(q.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));
+    /// ```
+    #[inline]
+    pub fn slerp(&self, other: &Self, t: N) -> Self
+    where
+        N: RealField,
+    {
+        let q1 = UnitQuaternion::from(*self);
+        let q2 = UnitQuaternion::from(*other);
+        q1.slerp(&q2, t).into()
+    }
+
+    /// Computes the spherical linear interpolation between two rotation matrices or returns `None`
+    /// if both rotations are approximately 180 degrees apart (in which case the interpolation is
+    /// not well-defined).
+    ///
+    /// # Arguments
+    /// * `self`: the first rotation to interpolate from.
+    /// * `other`: the second rotation to interpolate toward.
+    /// * `t`: the interpolation parameter. Should be between 0 and 1.
+    /// * `epsilon`: the value below which the sinus of the angle separating both rotations
+    /// must be to return `None`.
+    #[inline]
+    pub fn try_slerp(&self, other: &Self, t: N, epsilon: N) -> Option<Self>
+    where
+        N: RealField,
+    {
+        let q1 = Rotation3::from(*self);
+        let q2 = Rotation3::from(*other);
+        q1.try_slerp(&q2, t, epsilon).map(|q| q.into())
+    }
 }
 
 impl<N: SimdRealField> Distribution<Rotation3<N>> for Standard

src/geometry/unit_complex.rs

@@ -360,6 +360,43 @@ where
     pub fn inverse_transform_vector(&self, v: &Vector2<N>) -> Vector2<N> {
         self.inverse() * v
     }
+
+    /// Rotate the given vector by the inverse of this unit complex number.
+    ///
+    /// # Example
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # use nalgebra::{UnitComplex, Vector2};
+    /// # use std::f32;
+    /// let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
+    /// let transformed_vector = rot.inverse_transform_unit_vector(&Vector2::x_axis());
+    /// assert_relative_eq!(transformed_vector, -Vector2::y_axis(), epsilon = 1.0e-6);
+    /// ```
+    #[inline]
+    pub fn inverse_transform_unit_vector(&self, v: &Unit<Vector2<N>>) -> Unit<Vector2<N>> {
+        self.inverse() * v
+    }
+
+    /// Spherical linear interpolation between two rotations represented as unit complex numbers.
+    ///
+    /// # Examples:
+    ///
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # use nalgebra::geometry::UnitComplex;
+    ///
+    /// let rot1 = UnitComplex::new(std::f32::consts::FRAC_PI_4);
+    /// let rot2 = UnitComplex::new(-std::f32::consts::PI);
+    ///
+    /// let rot = rot1.slerp(&rot2, 1.0 / 3.0);
+    ///
+    /// assert_relative_eq!(rot.angle(), std::f32::consts::FRAC_PI_2);
+    /// ```
+
+    #[inline]
+    pub fn slerp(&self, other: &Self, t: N) -> Self {
+        Self::new(self.angle() * (N::one() - t) + other.angle() * t)
+    }
 }
 
 impl<N: RealField + fmt::Display> fmt::Display for UnitComplex<N> {