nalgebra/src/geometry/rotation.rs

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use approx::{AbsDiffEq, RelativeEq, UlpsEq};
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use num::{One, Zero};
use std::fmt;
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use std::hash;
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#[cfg(feature = "abomonation-serialize")]
use std::io::{Result as IOResult, Write};
#[cfg(feature = "serde-serialize-no-std")]
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use serde::{Deserialize, Deserializer, Serialize, Serializer};
#[cfg(feature = "serde-serialize-no-std")]
use crate::base::storage::Owned;
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#[cfg(feature = "abomonation-serialize")]
use abomonation::Abomonation;
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use simba::scalar::RealField;
use simba::simd::SimdRealField;
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use crate::base::allocator::Allocator;
use crate::base::dimension::{DimNameAdd, DimNameSum, U1};
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use crate::base::{Const, DefaultAllocator, OMatrix, SMatrix, SVector, Scalar, Unit};
use crate::geometry::Point;
/// A rotation matrix.
///
/// This is also known as an element of a Special Orthogonal (SO) group.
/// The `Rotation` type can either represent a 2D or 3D rotation, represented as a matrix.
/// For a rotation based on quaternions, see [`UnitQuaternion`](crate::UnitQuaternion) instead.
///
/// Note that instead of using the [`Rotation`](crate::Rotation) type in your code directly, you should use one
/// of its aliases: [`Rotation2`](crate::Rotation2), or [`Rotation3`](crate::Rotation3). Though
/// keep in mind that all the documentation of all the methods of these aliases will also appears on
/// this page.
///
/// # Construction
/// * [Identity <span style="float:right;">`identity`</span>](#identity)
/// * [From a 2D rotation angle <span style="float:right;">`new`…</span>](#construction-from-a-2d-rotation-angle)
/// * [From an existing 2D matrix or rotations <span style="float:right;">`from_matrix`, `rotation_between`, `powf`…</span>](#construction-from-an-existing-2d-matrix-or-rotations)
/// * [From a 3D axis and/or angles <span style="float:right;">`new`, `from_euler_angles`, `from_axis_angle`…</span>](#construction-from-a-3d-axis-andor-angles)
/// * [From a 3D eye position and target point <span style="float:right;">`look_at`, `look_at_lh`, `rotation_between`…</span>](#construction-from-a-3d-eye-position-and-target-point)
/// * [From an existing 3D matrix or rotations <span style="float:right;">`from_matrix`, `rotation_between`, `powf`…</span>](#construction-from-an-existing-3d-matrix-or-rotations)
///
/// # Transformation and composition
/// Note that transforming vectors and points can be done by multiplication, e.g., `rotation * point`.
/// Composing an rotation with another transformation can also be done by multiplication or division.
/// * [3D axis and angle extraction <span style="float:right;">`angle`, `euler_angles`, `scaled_axis`, `angle_to`…</span>](#3d-axis-and-angle-extraction)
/// * [2D angle extraction <span style="float:right;">`angle`, `angle_to`…</span>](#2d-angle-extraction)
/// * [Transformation of a vector or a point <span style="float:right;">`transform_vector`, `inverse_transform_point`…</span>](#transformation-of-a-vector-or-a-point)
/// * [Transposition and inversion <span style="float:right;">`transpose`, `inverse`…</span>](#transposition-and-inversion)
/// * [Interpolation <span style="float:right;">`slerp`…</span>](#interpolation)
///
/// # Conversion
/// * [Conversion to a matrix <span style="float:right;">`matrix`, `to_homogeneous`…</span>](#conversion-to-a-matrix)
///
#[repr(C)]
#[derive(Debug)]
pub struct Rotation<T, const D: usize> {
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matrix: SMatrix<T, D, D>,
}
impl<T: Scalar + hash::Hash, const D: usize> hash::Hash for Rotation<T, D>
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where
<DefaultAllocator as Allocator<T, Const<D>, Const<D>>>::Buffer: hash::Hash,
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{
fn hash<H: hash::Hasher>(&self, state: &mut H) {
self.matrix.hash(state)
}
}
impl<T: Scalar + Copy, const D: usize> Copy for Rotation<T, D> where
<DefaultAllocator as Allocator<T, Const<D>, Const<D>>>::Buffer: Copy
{
}
impl<T: Scalar, const D: usize> Clone for Rotation<T, D>
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where
<DefaultAllocator as Allocator<T, Const<D>, Const<D>>>::Buffer: Clone,
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{
#[inline]
fn clone(&self) -> Self {
Self::from_matrix_unchecked(self.matrix.clone())
}
}
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#[cfg(feature = "bytemuck")]
unsafe impl<T, const D: usize> bytemuck::Zeroable for Rotation<T, D>
where
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T: Scalar + bytemuck::Zeroable,
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SMatrix<T, D, D>: bytemuck::Zeroable,
{
}
#[cfg(feature = "bytemuck")]
unsafe impl<T, const D: usize> bytemuck::Pod for Rotation<T, D>
where
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T: Scalar + bytemuck::Pod,
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SMatrix<T, D, D>: bytemuck::Pod,
{
}
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#[cfg(feature = "abomonation-serialize")]
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impl<T, const D: usize> Abomonation for Rotation<T, D>
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where
T: Scalar,
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SMatrix<T, D, D>: Abomonation,
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{
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unsafe fn entomb<W: Write>(&self, writer: &mut W) -> IOResult<()> {
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self.matrix.entomb(writer)
}
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fn extent(&self) -> usize {
self.matrix.extent()
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}
unsafe fn exhume<'a, 'b>(&'a mut self, bytes: &'b mut [u8]) -> Option<&'b mut [u8]> {
self.matrix.exhume(bytes)
}
}
#[cfg(feature = "serde-serialize-no-std")]
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impl<T: Scalar, const D: usize> Serialize for Rotation<T, D>
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where
Owned<T, Const<D>, Const<D>>: Serialize,
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{
fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
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where
S: Serializer,
{
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self.matrix.serialize(serializer)
}
}
#[cfg(feature = "serde-serialize-no-std")]
impl<'a, T: Scalar, const D: usize> Deserialize<'a> for Rotation<T, D>
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where
Owned<T, Const<D>, Const<D>>: Deserialize<'a>,
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{
fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
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where
Des: Deserializer<'a>,
{
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let matrix = SMatrix::<T, D, D>::deserialize(deserializer)?;
Ok(Self::from_matrix_unchecked(matrix))
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}
}
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impl<T, const D: usize> Rotation<T, D> {
/// Creates a new rotation from the given square matrix.
///
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/// The matrix orthonormality is not checked.
///
/// # Example
/// ```
/// # use nalgebra::{Rotation2, Rotation3, Matrix2, Matrix3};
/// # use std::f32;
/// let mat = Matrix3::new(0.8660254, -0.5, 0.0,
/// 0.5, 0.8660254, 0.0,
/// 0.0, 0.0, 1.0);
/// let rot = Rotation3::from_matrix_unchecked(mat);
///
/// assert_eq!(*rot.matrix(), mat);
///
///
/// let mat = Matrix2::new(0.8660254, -0.5,
/// 0.5, 0.8660254);
/// let rot = Rotation2::from_matrix_unchecked(mat);
///
/// assert_eq!(*rot.matrix(), mat);
/// ```
#[inline]
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pub const fn from_matrix_unchecked(matrix: SMatrix<T, D, D>) -> Self {
Self { matrix }
}
}
/// # Conversion to a matrix
impl<T: Scalar, const D: usize> Rotation<T, D> {
/// A reference to the underlying matrix representation of this rotation.
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///
/// # Example
/// ```
/// # use nalgebra::{Rotation2, Rotation3, Vector3, Matrix2, Matrix3};
/// # use std::f32;
/// let rot = Rotation3::from_axis_angle(&Vector3::z_axis(), f32::consts::FRAC_PI_6);
/// let expected = Matrix3::new(0.8660254, -0.5, 0.0,
/// 0.5, 0.8660254, 0.0,
/// 0.0, 0.0, 1.0);
/// assert_eq!(*rot.matrix(), expected);
///
///
/// let rot = Rotation2::new(f32::consts::FRAC_PI_6);
/// let expected = Matrix2::new(0.8660254, -0.5,
/// 0.5, 0.8660254);
/// assert_eq!(*rot.matrix(), expected);
/// ```
#[inline]
#[must_use]
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pub fn matrix(&self) -> &SMatrix<T, D, D> {
&self.matrix
}
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/// A mutable reference to the underlying matrix representation of this rotation.
#[inline]
#[deprecated(note = "Use `.matrix_mut_unchecked()` instead.")]
pub unsafe fn matrix_mut(&mut self) -> &mut SMatrix<T, D, D> {
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&mut self.matrix
}
/// A mutable reference to the underlying matrix representation of this rotation.
///
/// This is suffixed by "_unchecked" because this allows the user to replace the
/// matrix by another one that is non-inversible or non-orthonormal. If one of
/// those properties is broken, subsequent method calls may return bogus results.
#[inline]
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pub fn matrix_mut_unchecked(&mut self) -> &mut SMatrix<T, D, D> {
&mut self.matrix
}
/// Unwraps the underlying matrix.
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///
/// # Example
/// ```
/// # use nalgebra::{Rotation2, Rotation3, Vector3, Matrix2, Matrix3};
/// # use std::f32;
/// let rot = Rotation3::from_axis_angle(&Vector3::z_axis(), f32::consts::FRAC_PI_6);
/// let mat = rot.into_inner();
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/// let expected = Matrix3::new(0.8660254, -0.5, 0.0,
/// 0.5, 0.8660254, 0.0,
/// 0.0, 0.0, 1.0);
/// assert_eq!(mat, expected);
///
///
/// let rot = Rotation2::new(f32::consts::FRAC_PI_6);
/// let mat = rot.into_inner();
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/// let expected = Matrix2::new(0.8660254, -0.5,
/// 0.5, 0.8660254);
/// assert_eq!(mat, expected);
/// ```
#[inline]
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pub fn into_inner(self) -> SMatrix<T, D, D> {
self.matrix
}
/// Unwraps the underlying matrix.
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/// Deprecated: Use [`Rotation::into_inner`] instead.
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#[deprecated(note = "use `.into_inner()` instead")]
#[inline]
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pub fn unwrap(self) -> SMatrix<T, D, D> {
self.matrix
}
/// Converts this rotation into its equivalent homogeneous transformation matrix.
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///
/// This is the same as `self.into()`.
///
/// # Example
/// ```
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/// # use nalgebra::{Rotation2, Rotation3, Vector3, Matrix3, Matrix4};
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/// # use std::f32;
/// let rot = Rotation3::from_axis_angle(&Vector3::z_axis(), f32::consts::FRAC_PI_6);
/// let expected = Matrix4::new(0.8660254, -0.5, 0.0, 0.0,
/// 0.5, 0.8660254, 0.0, 0.0,
/// 0.0, 0.0, 1.0, 0.0,
/// 0.0, 0.0, 0.0, 1.0);
/// assert_eq!(rot.to_homogeneous(), expected);
///
///
/// let rot = Rotation2::new(f32::consts::FRAC_PI_6);
/// let expected = Matrix3::new(0.8660254, -0.5, 0.0,
/// 0.5, 0.8660254, 0.0,
/// 0.0, 0.0, 1.0);
/// assert_eq!(rot.to_homogeneous(), expected);
/// ```
#[inline]
#[must_use]
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pub fn to_homogeneous(&self) -> OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
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where
T: Zero + One,
Const<D>: DimNameAdd<U1>,
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DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
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{
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// We could use `SMatrix::to_homogeneous()` here, but that would imply
// adding the additional traits `DimAdd` and `IsNotStaticOne`. Maybe
// these things will get nicer once specialization lands in Rust.
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let mut res = OMatrix::<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>::identity();
res.fixed_slice_mut::<D, D>(0, 0).copy_from(&self.matrix);
res
}
}
/// # Transposition and inversion
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impl<T: Scalar, const D: usize> Rotation<T, D> {
/// Transposes `self`.
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///
/// Same as `.inverse()` because the inverse of a rotation matrix is its transform.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use nalgebra::{Rotation2, Rotation3, Vector3};
/// let rot = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
/// let tr_rot = rot.transpose();
/// assert_relative_eq!(rot * tr_rot, Rotation3::identity(), epsilon = 1.0e-6);
/// assert_relative_eq!(tr_rot * rot, Rotation3::identity(), epsilon = 1.0e-6);
///
/// let rot = Rotation2::new(1.2);
/// let tr_rot = rot.transpose();
/// assert_relative_eq!(rot * tr_rot, Rotation2::identity(), epsilon = 1.0e-6);
/// assert_relative_eq!(tr_rot * rot, Rotation2::identity(), epsilon = 1.0e-6);
/// ```
#[inline]
#[must_use = "Did you mean to use transpose_mut()?"]
pub fn transpose(&self) -> Self {
Self::from_matrix_unchecked(self.matrix.transpose())
}
/// Inverts `self`.
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///
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/// Same as `.transpose()` because the inverse of a rotation matrix is its transform.
///
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/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use nalgebra::{Rotation2, Rotation3, Vector3};
/// let rot = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
/// let inv = rot.inverse();
/// assert_relative_eq!(rot * inv, Rotation3::identity(), epsilon = 1.0e-6);
/// assert_relative_eq!(inv * rot, Rotation3::identity(), epsilon = 1.0e-6);
///
/// let rot = Rotation2::new(1.2);
/// let inv = rot.inverse();
/// assert_relative_eq!(rot * inv, Rotation2::identity(), epsilon = 1.0e-6);
/// assert_relative_eq!(inv * rot, Rotation2::identity(), epsilon = 1.0e-6);
/// ```
#[inline]
#[must_use = "Did you mean to use inverse_mut()?"]
pub fn inverse(&self) -> Self {
self.transpose()
}
/// Transposes `self` in-place.
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///
/// Same as `.inverse_mut()` because the inverse of a rotation matrix is its transform.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use nalgebra::{Rotation2, Rotation3, Vector3};
/// let rot = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
/// let mut tr_rot = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
/// tr_rot.transpose_mut();
///
/// assert_relative_eq!(rot * tr_rot, Rotation3::identity(), epsilon = 1.0e-6);
/// assert_relative_eq!(tr_rot * rot, Rotation3::identity(), epsilon = 1.0e-6);
///
/// let rot = Rotation2::new(1.2);
/// let mut tr_rot = Rotation2::new(1.2);
/// tr_rot.transpose_mut();
///
/// assert_relative_eq!(rot * tr_rot, Rotation2::identity(), epsilon = 1.0e-6);
/// assert_relative_eq!(tr_rot * rot, Rotation2::identity(), epsilon = 1.0e-6);
/// ```
#[inline]
pub fn transpose_mut(&mut self) {
self.matrix.transpose_mut()
}
/// Inverts `self` in-place.
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///
/// Same as `.transpose_mut()` because the inverse of a rotation matrix is its transform.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use nalgebra::{Rotation2, Rotation3, Vector3};
/// let rot = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
/// let mut inv = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
/// inv.inverse_mut();
///
/// assert_relative_eq!(rot * inv, Rotation3::identity(), epsilon = 1.0e-6);
/// assert_relative_eq!(inv * rot, Rotation3::identity(), epsilon = 1.0e-6);
///
/// let rot = Rotation2::new(1.2);
/// let mut inv = Rotation2::new(1.2);
/// inv.inverse_mut();
///
/// assert_relative_eq!(rot * inv, Rotation2::identity(), epsilon = 1.0e-6);
/// assert_relative_eq!(inv * rot, Rotation2::identity(), epsilon = 1.0e-6);
/// ```
#[inline]
pub fn inverse_mut(&mut self) {
self.transpose_mut()
}
}
/// # Transformation of a vector or a point
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impl<T: SimdRealField, const D: usize> Rotation<T, D>
where
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T::Element: SimdRealField,
{
/// Rotate the given point.
///
/// This is the same as the multiplication `self * pt`.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{Point3, Rotation2, Rotation3, UnitQuaternion, Vector3};
/// let rot = Rotation3::new(Vector3::y() * f32::consts::FRAC_PI_2);
/// let transformed_point = rot.transform_point(&Point3::new(1.0, 2.0, 3.0));
///
/// assert_relative_eq!(transformed_point, Point3::new(3.0, 2.0, -1.0), epsilon = 1.0e-6);
/// ```
#[inline]
#[must_use]
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pub fn transform_point(&self, pt: &Point<T, D>) -> Point<T, D> {
self * pt
}
/// Rotate the given vector.
///
/// This is the same as the multiplication `self * v`.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{Rotation2, Rotation3, UnitQuaternion, Vector3};
/// let rot = Rotation3::new(Vector3::y() * f32::consts::FRAC_PI_2);
/// let transformed_vector = rot.transform_vector(&Vector3::new(1.0, 2.0, 3.0));
///
/// assert_relative_eq!(transformed_vector, Vector3::new(3.0, 2.0, -1.0), epsilon = 1.0e-6);
/// ```
#[inline]
#[must_use]
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pub fn transform_vector(&self, v: &SVector<T, D>) -> SVector<T, D> {
self * v
}
/// Rotate the given point by the inverse of this rotation. This may be
/// cheaper than inverting the rotation and then transforming the given
/// point.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{Point3, Rotation2, Rotation3, UnitQuaternion, Vector3};
/// let rot = Rotation3::new(Vector3::y() * f32::consts::FRAC_PI_2);
/// let transformed_point = rot.inverse_transform_point(&Point3::new(1.0, 2.0, 3.0));
///
/// assert_relative_eq!(transformed_point, Point3::new(-3.0, 2.0, 1.0), epsilon = 1.0e-6);
/// ```
#[inline]
#[must_use]
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pub fn inverse_transform_point(&self, pt: &Point<T, D>) -> Point<T, D> {
Point::from(self.inverse_transform_vector(&pt.coords))
}
/// 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::y() * f32::consts::FRAC_PI_2);
/// let transformed_vector = rot.inverse_transform_vector(&Vector3::new(1.0, 2.0, 3.0));
///
/// assert_relative_eq!(transformed_vector, Vector3::new(-3.0, 2.0, 1.0), epsilon = 1.0e-6);
/// ```
#[inline]
#[must_use]
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pub fn inverse_transform_vector(&self, v: &SVector<T, D>) -> SVector<T, 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]
#[must_use]
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pub fn inverse_transform_unit_vector(&self, v: &Unit<SVector<T, D>>) -> Unit<SVector<T, D>> {
Unit::new_unchecked(self.inverse_transform_vector(&**v))
}
}
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impl<T: Scalar + Eq, const D: usize> Eq for Rotation<T, D> {}
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impl<T: Scalar + PartialEq, const D: usize> PartialEq for Rotation<T, D> {
#[inline]
fn eq(&self, right: &Self) -> bool {
self.matrix == right.matrix
}
}
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impl<T, const D: usize> AbsDiffEq for Rotation<T, D>
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where
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T: Scalar + AbsDiffEq,
T::Epsilon: Copy,
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{
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type Epsilon = T::Epsilon;
#[inline]
fn default_epsilon() -> Self::Epsilon {
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T::default_epsilon()
}
#[inline]
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fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool {
self.matrix.abs_diff_eq(&other.matrix, epsilon)
}
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}
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impl<T, const D: usize> RelativeEq for Rotation<T, D>
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where
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T: Scalar + RelativeEq,
T::Epsilon: Copy,
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{
#[inline]
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fn default_max_relative() -> Self::Epsilon {
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T::default_max_relative()
}
#[inline]
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fn relative_eq(
&self,
other: &Self,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon,
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) -> bool {
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self.matrix
.relative_eq(&other.matrix, epsilon, max_relative)
}
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}
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impl<T, const D: usize> UlpsEq for Rotation<T, D>
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where
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T: Scalar + UlpsEq,
T::Epsilon: Copy,
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{
#[inline]
fn default_max_ulps() -> u32 {
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T::default_max_ulps()
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}
#[inline]
fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool {
self.matrix.ulps_eq(&other.matrix, epsilon, max_ulps)
}
}
/*
*
* Display
*
*/
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impl<T, const D: usize> fmt::Display for Rotation<T, D>
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where
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T: RealField + fmt::Display,
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{
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fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
let precision = f.precision().unwrap_or(3);
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writeln!(f, "Rotation matrix {{")?;
write!(f, "{:.*}", precision, self.matrix)?;
writeln!(f, "}}")
}
}
// // /*
// // *
// // * Absolute
// // *
// // */
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// // impl<T: Absolute> Absolute for $t<T> {
// // type AbsoluteValue = $submatrix<T::AbsoluteValue>;
// //
// // #[inline]
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// // fn abs(m: &$t<T>) -> $submatrix<T::AbsoluteValue> {
// // Absolute::abs(&m.submatrix)
// // }
// // }