Add inverse_transform_unit_vector to rotations and isometries.

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

@@ -16,7 +16,7 @@ use simba::simd::SimdRealField;
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
 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};
 
 /// 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.
@@ -350,6 +350,29 @@ 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)
+    }
 }
 
 // NOTE: we don't require `R: Rotation<...>` here because this is not useful for the implementation

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/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/unit_complex.rs

@@ -360,6 +360,22 @@ 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
+    }
 }
 
 impl<N: RealField + fmt::Display> fmt::Display for UnitComplex<N> {