568 lines
18 KiB
Rust
Executable File
568 lines
18 KiB
Rust
Executable File
use approx::{AbsDiffEq, RelativeEq, UlpsEq};
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use num::{One, Zero};
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use std::fmt;
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use std::hash;
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#[cfg(feature = "abomonation-serialize")]
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use std::io::{Result as IOResult, Write};
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#[cfg(feature = "serde-serialize")]
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use serde::{Deserialize, Deserializer, Serialize, Serializer};
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#[cfg(feature = "serde-serialize")]
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use crate::base::storage::Owned;
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#[cfg(feature = "abomonation-serialize")]
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use abomonation::Abomonation;
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use simba::scalar::RealField;
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use simba::simd::SimdRealField;
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use crate::base::allocator::Allocator;
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use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
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use crate::base::{DefaultAllocator, MatrixN, Scalar, Unit, VectorN};
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use crate::geometry::Point;
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/// A rotation matrix.
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#[repr(C)]
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#[derive(Debug)]
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pub struct Rotation<N: Scalar, D: DimName>
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where
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DefaultAllocator: Allocator<N, D, D>,
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{
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matrix: MatrixN<N, D>,
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}
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impl<N: Scalar + hash::Hash, D: DimName + hash::Hash> hash::Hash for Rotation<N, D>
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where
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DefaultAllocator: Allocator<N, D, D>,
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<DefaultAllocator as Allocator<N, D, D>>::Buffer: hash::Hash,
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{
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fn hash<H: hash::Hasher>(&self, state: &mut H) {
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self.matrix.hash(state)
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}
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}
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impl<N: Scalar + Copy, D: DimName> Copy for Rotation<N, D>
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where
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DefaultAllocator: Allocator<N, D, D>,
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<DefaultAllocator as Allocator<N, D, D>>::Buffer: Copy,
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{
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}
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impl<N: Scalar, D: DimName> Clone for Rotation<N, D>
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where
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DefaultAllocator: Allocator<N, D, D>,
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<DefaultAllocator as Allocator<N, D, D>>::Buffer: Clone,
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{
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#[inline]
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fn clone(&self) -> Self {
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Self::from_matrix_unchecked(self.matrix.clone())
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}
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}
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#[cfg(feature = "abomonation-serialize")]
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impl<N, D> Abomonation for Rotation<N, D>
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where
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N: Scalar,
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D: DimName,
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MatrixN<N, D>: Abomonation,
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DefaultAllocator: Allocator<N, D, D>,
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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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}
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fn extent(&self) -> usize {
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self.matrix.extent()
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}
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unsafe fn exhume<'a, 'b>(&'a mut self, bytes: &'b mut [u8]) -> Option<&'b mut [u8]> {
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self.matrix.exhume(bytes)
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}
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}
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#[cfg(feature = "serde-serialize")]
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impl<N: Scalar, D: DimName> Serialize for Rotation<N, D>
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where
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DefaultAllocator: Allocator<N, D, D>,
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Owned<N, D, D>: Serialize,
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{
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fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
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where
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S: Serializer,
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{
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self.matrix.serialize(serializer)
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}
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}
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#[cfg(feature = "serde-serialize")]
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impl<'a, N: Scalar, D: DimName> Deserialize<'a> for Rotation<N, D>
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where
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DefaultAllocator: Allocator<N, D, D>,
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Owned<N, D, D>: Deserialize<'a>,
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{
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fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
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where
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Des: Deserializer<'a>,
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{
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let matrix = MatrixN::<N, D>::deserialize(deserializer)?;
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Ok(Self::from_matrix_unchecked(matrix))
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}
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}
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impl<N: Scalar, D: DimName> Rotation<N, D>
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where
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DefaultAllocator: Allocator<N, D, D>,
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{
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/// A reference to the underlying matrix representation of this rotation.
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///
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/// # Example
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/// ```
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/// # use nalgebra::{Rotation2, Rotation3, Vector3, Matrix2, Matrix3};
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/// # use std::f32;
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/// let rot = Rotation3::from_axis_angle(&Vector3::z_axis(), f32::consts::FRAC_PI_6);
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/// let expected = Matrix3::new(0.8660254, -0.5, 0.0,
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/// 0.5, 0.8660254, 0.0,
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/// 0.0, 0.0, 1.0);
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/// assert_eq!(*rot.matrix(), expected);
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///
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///
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/// let rot = Rotation2::new(f32::consts::FRAC_PI_6);
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/// let expected = Matrix2::new(0.8660254, -0.5,
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/// 0.5, 0.8660254);
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/// assert_eq!(*rot.matrix(), expected);
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/// ```
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#[inline]
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pub fn matrix(&self) -> &MatrixN<N, D> {
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&self.matrix
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}
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/// A mutable reference to the underlying matrix representation of this rotation.
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#[inline]
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#[deprecated(note = "Use `.matrix_mut_unchecked()` instead.")]
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pub unsafe fn matrix_mut(&mut self) -> &mut MatrixN<N, D> {
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&mut self.matrix
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}
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/// A mutable reference to the underlying matrix representation of this rotation.
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///
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/// This is suffixed by "_unchecked" because this allows the user to replace the matrix by another one that is
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/// non-square, non-inversible, or non-orthonormal. If one of those properties is broken,
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/// subsequent method calls may be UB.
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#[inline]
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pub fn matrix_mut_unchecked(&mut self) -> &mut MatrixN<N, D> {
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&mut self.matrix
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}
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/// Unwraps the underlying matrix.
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///
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/// # Example
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/// ```
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/// # use nalgebra::{Rotation2, Rotation3, Vector3, Matrix2, Matrix3};
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/// # use std::f32;
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/// let rot = Rotation3::from_axis_angle(&Vector3::z_axis(), f32::consts::FRAC_PI_6);
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/// let mat = rot.into_inner();
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/// let expected = Matrix3::new(0.8660254, -0.5, 0.0,
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/// 0.5, 0.8660254, 0.0,
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/// 0.0, 0.0, 1.0);
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/// assert_eq!(mat, expected);
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///
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///
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/// let rot = Rotation2::new(f32::consts::FRAC_PI_6);
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/// let mat = rot.into_inner();
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/// let expected = Matrix2::new(0.8660254, -0.5,
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/// 0.5, 0.8660254);
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/// assert_eq!(mat, expected);
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/// ```
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#[inline]
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pub fn into_inner(self) -> MatrixN<N, D> {
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self.matrix
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}
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/// Unwraps the underlying matrix.
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/// Deprecated: Use [Rotation::into_inner] instead.
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#[deprecated(note = "use `.into_inner()` instead")]
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#[inline]
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pub fn unwrap(self) -> MatrixN<N, D> {
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self.matrix
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}
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/// Converts this rotation into its equivalent homogeneous transformation matrix.
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///
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/// This is the same as `self.into()`.
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///
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/// # Example
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/// ```
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/// # use nalgebra::{Rotation2, Rotation3, Vector3, Matrix3, Matrix4};
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/// # use std::f32;
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/// let rot = Rotation3::from_axis_angle(&Vector3::z_axis(), f32::consts::FRAC_PI_6);
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/// let expected = Matrix4::new(0.8660254, -0.5, 0.0, 0.0,
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/// 0.5, 0.8660254, 0.0, 0.0,
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/// 0.0, 0.0, 1.0, 0.0,
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/// 0.0, 0.0, 0.0, 1.0);
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/// assert_eq!(rot.to_homogeneous(), expected);
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///
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///
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/// let rot = Rotation2::new(f32::consts::FRAC_PI_6);
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/// let expected = Matrix3::new(0.8660254, -0.5, 0.0,
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/// 0.5, 0.8660254, 0.0,
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/// 0.0, 0.0, 1.0);
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/// assert_eq!(rot.to_homogeneous(), expected);
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/// ```
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#[inline]
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pub fn to_homogeneous(&self) -> MatrixN<N, DimNameSum<D, U1>>
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where
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N: Zero + One,
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D: DimNameAdd<U1>,
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DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
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{
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// We could use `MatrixN::to_homogeneous()` here, but that would imply
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// adding the additional traits `DimAdd` and `IsNotStaticOne`. Maybe
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// these things will get nicer once specialization lands in Rust.
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let mut res = MatrixN::<N, DimNameSum<D, U1>>::identity();
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res.fixed_slice_mut::<D, D>(0, 0).copy_from(&self.matrix);
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res
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}
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/// Creates a new rotation from the given square matrix.
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///
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/// The matrix squareness is checked but not its orthonormality.
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///
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/// # Example
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/// ```
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/// # use nalgebra::{Rotation2, Rotation3, Matrix2, Matrix3};
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/// # use std::f32;
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/// let mat = Matrix3::new(0.8660254, -0.5, 0.0,
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/// 0.5, 0.8660254, 0.0,
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/// 0.0, 0.0, 1.0);
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/// let rot = Rotation3::from_matrix_unchecked(mat);
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///
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/// assert_eq!(*rot.matrix(), mat);
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///
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///
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/// let mat = Matrix2::new(0.8660254, -0.5,
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/// 0.5, 0.8660254);
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/// let rot = Rotation2::from_matrix_unchecked(mat);
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///
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/// assert_eq!(*rot.matrix(), mat);
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/// ```
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#[inline]
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pub fn from_matrix_unchecked(matrix: MatrixN<N, D>) -> Self {
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assert!(
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matrix.is_square(),
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"Unable to create a rotation from a non-square matrix."
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);
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Self { matrix }
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}
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/// Transposes `self`.
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///
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/// Same as `.inverse()` because the inverse of a rotation matrix is its transform.
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///
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/// # Example
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/// ```
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/// # #[macro_use] extern crate approx;
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/// # use nalgebra::{Rotation2, Rotation3, Vector3};
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/// let rot = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
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/// let tr_rot = rot.transpose();
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/// assert_relative_eq!(rot * tr_rot, Rotation3::identity(), epsilon = 1.0e-6);
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/// assert_relative_eq!(tr_rot * rot, Rotation3::identity(), epsilon = 1.0e-6);
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///
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/// let rot = Rotation2::new(1.2);
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/// let tr_rot = rot.transpose();
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/// assert_relative_eq!(rot * tr_rot, Rotation2::identity(), epsilon = 1.0e-6);
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/// assert_relative_eq!(tr_rot * rot, Rotation2::identity(), epsilon = 1.0e-6);
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/// ```
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#[inline]
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#[must_use = "Did you mean to use transpose_mut()?"]
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pub fn transpose(&self) -> Self {
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Self::from_matrix_unchecked(self.matrix.transpose())
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}
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/// 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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///
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/// # Example
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/// ```
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/// # #[macro_use] extern crate approx;
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/// # use nalgebra::{Rotation2, Rotation3, Vector3};
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/// let rot = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
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/// let inv = rot.inverse();
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/// assert_relative_eq!(rot * inv, Rotation3::identity(), epsilon = 1.0e-6);
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/// assert_relative_eq!(inv * rot, Rotation3::identity(), epsilon = 1.0e-6);
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///
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/// let rot = Rotation2::new(1.2);
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/// let inv = rot.inverse();
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/// assert_relative_eq!(rot * inv, Rotation2::identity(), epsilon = 1.0e-6);
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/// assert_relative_eq!(inv * rot, Rotation2::identity(), epsilon = 1.0e-6);
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/// ```
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#[inline]
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#[must_use = "Did you mean to use inverse_mut()?"]
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pub fn inverse(&self) -> Self {
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self.transpose()
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}
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/// Transposes `self` in-place.
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///
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/// Same as `.inverse_mut()` because the inverse of a rotation matrix is its transform.
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///
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/// # Example
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/// ```
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/// # #[macro_use] extern crate approx;
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/// # use nalgebra::{Rotation2, Rotation3, Vector3};
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/// let rot = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
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/// let mut tr_rot = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
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/// tr_rot.transpose_mut();
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///
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/// assert_relative_eq!(rot * tr_rot, Rotation3::identity(), epsilon = 1.0e-6);
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/// assert_relative_eq!(tr_rot * rot, Rotation3::identity(), epsilon = 1.0e-6);
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///
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/// let rot = Rotation2::new(1.2);
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/// let mut tr_rot = Rotation2::new(1.2);
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/// tr_rot.transpose_mut();
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///
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/// assert_relative_eq!(rot * tr_rot, Rotation2::identity(), epsilon = 1.0e-6);
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/// assert_relative_eq!(tr_rot * rot, Rotation2::identity(), epsilon = 1.0e-6);
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/// ```
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#[inline]
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pub fn transpose_mut(&mut self) {
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self.matrix.transpose_mut()
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}
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/// Inverts `self` in-place.
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///
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/// Same as `.transpose_mut()` because the inverse of a rotation matrix is its transform.
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///
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/// # Example
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/// ```
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/// # #[macro_use] extern crate approx;
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/// # use nalgebra::{Rotation2, Rotation3, Vector3};
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/// let rot = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
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/// let mut inv = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
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/// inv.inverse_mut();
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///
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/// assert_relative_eq!(rot * inv, Rotation3::identity(), epsilon = 1.0e-6);
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/// assert_relative_eq!(inv * rot, Rotation3::identity(), epsilon = 1.0e-6);
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///
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/// let rot = Rotation2::new(1.2);
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/// let mut inv = Rotation2::new(1.2);
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/// inv.inverse_mut();
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///
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/// assert_relative_eq!(rot * inv, Rotation2::identity(), epsilon = 1.0e-6);
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/// assert_relative_eq!(inv * rot, Rotation2::identity(), epsilon = 1.0e-6);
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/// ```
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#[inline]
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pub fn inverse_mut(&mut self) {
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self.transpose_mut()
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}
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}
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impl<N: SimdRealField, D: DimName> Rotation<N, D>
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where
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N::Element: SimdRealField,
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DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
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{
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/// Rotate the given point.
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///
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/// This is the same as the multiplication `self * pt`.
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///
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/// # Example
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/// ```
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/// # #[macro_use] extern crate approx;
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/// # use std::f32;
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/// # use nalgebra::{Point3, Rotation2, Rotation3, UnitQuaternion, Vector3};
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/// let rot = Rotation3::new(Vector3::y() * f32::consts::FRAC_PI_2);
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/// let transformed_point = rot.transform_point(&Point3::new(1.0, 2.0, 3.0));
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///
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/// assert_relative_eq!(transformed_point, Point3::new(3.0, 2.0, -1.0), epsilon = 1.0e-6);
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/// ```
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#[inline]
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pub fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
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self * pt
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}
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/// Rotate the given vector.
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///
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/// This is the same as the multiplication `self * v`.
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///
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/// # Example
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/// ```
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/// # #[macro_use] extern crate approx;
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/// # use std::f32;
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/// # use nalgebra::{Rotation2, Rotation3, UnitQuaternion, Vector3};
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/// let rot = Rotation3::new(Vector3::y() * f32::consts::FRAC_PI_2);
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/// let transformed_vector = rot.transform_vector(&Vector3::new(1.0, 2.0, 3.0));
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///
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/// assert_relative_eq!(transformed_vector, Vector3::new(3.0, 2.0, -1.0), epsilon = 1.0e-6);
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/// ```
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#[inline]
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pub fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
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self * v
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}
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/// Rotate the given point by the inverse of this rotation. This may be
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/// cheaper than inverting the rotation and then transforming the given
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/// point.
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///
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/// # Example
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/// ```
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/// # #[macro_use] extern crate approx;
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/// # use std::f32;
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/// # use nalgebra::{Point3, Rotation2, Rotation3, UnitQuaternion, Vector3};
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/// let rot = Rotation3::new(Vector3::y() * f32::consts::FRAC_PI_2);
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/// let transformed_point = rot.inverse_transform_point(&Point3::new(1.0, 2.0, 3.0));
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///
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/// assert_relative_eq!(transformed_point, Point3::new(-3.0, 2.0, 1.0), epsilon = 1.0e-6);
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/// ```
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#[inline]
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pub fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
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Point::from(self.inverse_transform_vector(&pt.coords))
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}
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/// Rotate the given vector by the inverse of this rotation. This may be
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/// cheaper than inverting the rotation and then transforming the given
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/// vector.
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///
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/// # Example
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/// ```
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/// # #[macro_use] extern crate approx;
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/// # use std::f32;
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/// # use nalgebra::{Rotation2, Rotation3, UnitQuaternion, Vector3};
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/// let rot = Rotation3::new(Vector3::y() * f32::consts::FRAC_PI_2);
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/// let transformed_vector = rot.inverse_transform_vector(&Vector3::new(1.0, 2.0, 3.0));
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///
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/// assert_relative_eq!(transformed_vector, Vector3::new(-3.0, 2.0, 1.0), epsilon = 1.0e-6);
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/// ```
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#[inline]
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pub fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
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self.matrix().tr_mul(v)
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}
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/// Rotate the given vector by the inverse of this rotation. This may be
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/// cheaper than inverting the rotation and then transforming the given
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/// vector.
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///
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/// # Example
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/// ```
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/// # #[macro_use] extern crate approx;
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/// # use std::f32;
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/// # use nalgebra::{Rotation2, Rotation3, UnitQuaternion, Vector3};
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/// let rot = Rotation3::new(Vector3::z() * f32::consts::FRAC_PI_2);
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/// let transformed_vector = rot.inverse_transform_unit_vector(&Vector3::x_axis());
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|
///
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|
/// assert_relative_eq!(transformed_vector, -Vector3::y_axis(), epsilon = 1.0e-6);
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|
/// ```
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|
#[inline]
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|
pub fn inverse_transform_unit_vector(&self, v: &Unit<VectorN<N, D>>) -> Unit<VectorN<N, D>> {
|
|
Unit::new_unchecked(self.inverse_transform_vector(&**v))
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|
}
|
|
}
|
|
|
|
impl<N: Scalar + Eq, D: DimName> Eq for Rotation<N, D> where DefaultAllocator: Allocator<N, D, D> {}
|
|
|
|
impl<N: Scalar + PartialEq, D: DimName> PartialEq for Rotation<N, D>
|
|
where
|
|
DefaultAllocator: Allocator<N, D, D>,
|
|
{
|
|
#[inline]
|
|
fn eq(&self, right: &Self) -> bool {
|
|
self.matrix == right.matrix
|
|
}
|
|
}
|
|
|
|
impl<N, D: DimName> AbsDiffEq for Rotation<N, D>
|
|
where
|
|
N: Scalar + AbsDiffEq,
|
|
DefaultAllocator: Allocator<N, D, D>,
|
|
N::Epsilon: Copy,
|
|
{
|
|
type Epsilon = N::Epsilon;
|
|
|
|
#[inline]
|
|
fn default_epsilon() -> Self::Epsilon {
|
|
N::default_epsilon()
|
|
}
|
|
|
|
#[inline]
|
|
fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool {
|
|
self.matrix.abs_diff_eq(&other.matrix, epsilon)
|
|
}
|
|
}
|
|
|
|
impl<N, D: DimName> RelativeEq for Rotation<N, D>
|
|
where
|
|
N: Scalar + RelativeEq,
|
|
DefaultAllocator: Allocator<N, D, D>,
|
|
N::Epsilon: Copy,
|
|
{
|
|
#[inline]
|
|
fn default_max_relative() -> Self::Epsilon {
|
|
N::default_max_relative()
|
|
}
|
|
|
|
#[inline]
|
|
fn relative_eq(
|
|
&self,
|
|
other: &Self,
|
|
epsilon: Self::Epsilon,
|
|
max_relative: Self::Epsilon,
|
|
) -> bool {
|
|
self.matrix
|
|
.relative_eq(&other.matrix, epsilon, max_relative)
|
|
}
|
|
}
|
|
|
|
impl<N, D: DimName> UlpsEq for Rotation<N, D>
|
|
where
|
|
N: Scalar + UlpsEq,
|
|
DefaultAllocator: Allocator<N, D, D>,
|
|
N::Epsilon: Copy,
|
|
{
|
|
#[inline]
|
|
fn default_max_ulps() -> u32 {
|
|
N::default_max_ulps()
|
|
}
|
|
|
|
#[inline]
|
|
fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool {
|
|
self.matrix.ulps_eq(&other.matrix, epsilon, max_ulps)
|
|
}
|
|
}
|
|
|
|
/*
|
|
*
|
|
* Display
|
|
*
|
|
*/
|
|
impl<N, D: DimName> fmt::Display for Rotation<N, D>
|
|
where
|
|
N: RealField + fmt::Display,
|
|
DefaultAllocator: Allocator<N, D, D> + Allocator<usize, D, D>,
|
|
{
|
|
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
|
|
let precision = f.precision().unwrap_or(3);
|
|
|
|
writeln!(f, "Rotation matrix {{")?;
|
|
write!(f, "{:.*}", precision, self.matrix)?;
|
|
writeln!(f, "}}")
|
|
}
|
|
}
|
|
|
|
// // /*
|
|
// // *
|
|
// // * Absolute
|
|
// // *
|
|
// // */
|
|
// // impl<N: Absolute> Absolute for $t<N> {
|
|
// // type AbsoluteValue = $submatrix<N::AbsoluteValue>;
|
|
// //
|
|
// // #[inline]
|
|
// // fn abs(m: &$t<N>) -> $submatrix<N::AbsoluteValue> {
|
|
// // Absolute::abs(&m.submatrix)
|
|
// // }
|
|
// // }
|