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")]
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use serde::{Deserialize, Deserializer, Serialize, Serializer};
#[cfg(feature = "serde-serialize")]
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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::{DimName, DimNameAdd, DimNameSum, U1};
use crate::base::{DefaultAllocator, MatrixN, Scalar, Unit, VectorN};
use crate::geometry::Point;
/// A rotation matrix.
#[repr(C)]
#[derive(Debug)]
pub struct Rotation<N: Scalar, D: DimName>
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where
DefaultAllocator: Allocator<N, D, D>,
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{
matrix: MatrixN<N, D>,
}
impl<N: Scalar + hash::Hash, D: DimName + hash::Hash> hash::Hash for Rotation<N, D>
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where
DefaultAllocator: Allocator<N, D, D>,
<DefaultAllocator as Allocator<N, D, D>>::Buffer: hash::Hash,
{
fn hash<H: hash::Hasher>(&self, state: &mut H) {
self.matrix.hash(state)
}
}
Move `Copy` constraint from the definition of `Scalar` to all its use-sites. This should semantically be a no-op, but enables refactorings to use non-Copy scalars on a case-by-case basis. Also, the only instance of a `One + Zero` trait bound was changed into a `Zero + One` bound to match the others. The following sed scripts were used in the refactoring (with each clause added to reduce the error count of `cargo check`): ```bash export RELEVANT_SOURCEFILES="$(find src -name '*.rs') $(find examples -name '*.rs')" for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar,/N: Scalar+Copy,/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + Field/N: Scalar + Copy + Field/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + Zero/N: Scalar + Copy + Zero/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + Closed/N: Scalar + Copy + Closed/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + Eq/N: Scalar + Copy + Eq/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + PartialOrd/N: Scalar + Copy + PartialOrd/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: *Scalar + Zero/N: Scalar + Copy + Zero/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + PartialEq/N: Scalar + Copy + PartialEq/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar>/N: Scalar+Copy>/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + $bound/N: Scalar + Copy + $bound/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: *Scalar + $bound/N: Scalar + Copy + $bound/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\): *Scalar,/N\1: Scalar+Copy,/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: *Scalar + $trait/N: Scalar + Copy + $trait/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\): *Scalar + Superset/N\1: Scalar + Copy + Superset/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\): *Scalar + \([a-zA-Z]*Eq\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \([a-zA-Z]*Eq\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(hash::\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar {/N\1: Scalar + Copy {/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Zero\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Bounded\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Lattice\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Meet\|Join\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(fmt::\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Ring\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Hash\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Send\|Sync\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/One + Zero/Zero + One/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Zero\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \($marker\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar>/N\1: Scalar + Copy>/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/Scalar+Copy/Scalar + Copy/' $f; done ```
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impl<N: Scalar + Copy, D: DimName> Copy for Rotation<N, D>
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where
DefaultAllocator: Allocator<N, D, D>,
<DefaultAllocator as Allocator<N, D, D>>::Buffer: Copy,
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{
}
impl<N: Scalar, D: DimName> Clone for Rotation<N, D>
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where
DefaultAllocator: Allocator<N, D, D>,
<DefaultAllocator as Allocator<N, D, D>>::Buffer: Clone,
{
#[inline]
fn clone(&self) -> Self {
Self::from_matrix_unchecked(self.matrix.clone())
}
}
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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
N: Scalar,
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D: DimName,
MatrixN<N, D>: Abomonation,
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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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")]
impl<N: Scalar, D: DimName> Serialize for Rotation<N, D>
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where
DefaultAllocator: Allocator<N, D, D>,
Owned<N, D, 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")]
impl<'a, N: Scalar, D: DimName> Deserialize<'a> for Rotation<N, D>
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where
DefaultAllocator: Allocator<N, D, D>,
Owned<N, D, 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 = MatrixN::<N, D>::deserialize(deserializer)?;
Ok(Self::from_matrix_unchecked(matrix))
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}
}
impl<N: Scalar, D: DimName> Rotation<N, D>
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where
DefaultAllocator: Allocator<N, D, D>,
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{
/// 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]
pub fn matrix(&self) -> &MatrixN<N, 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 MatrixN<N, D> {
&mut self.matrix
}
/// A mutable reference to the underlying matrix representation of this rotation.
///
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/// This is suffixed by "_unchecked" because this allows the user to replace the matrix by another one that is
/// non-square, non-inversible, or non-orthonormal. If one of those properties is broken,
/// subsequent method calls may be UB.
#[inline]
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pub fn matrix_mut_unchecked(&mut self) -> &mut MatrixN<N, 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]
pub fn into_inner(self) -> MatrixN<N, D> {
self.matrix
}
/// Unwraps the underlying matrix.
/// Deprecated: Use [Rotation::into_inner] instead.
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#[deprecated(note = "use `.into_inner()` instead")]
#[inline]
pub fn unwrap(self) -> MatrixN<N, 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]
pub fn to_homogeneous(&self) -> MatrixN<N, DimNameSum<D, U1>>
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where
N: Zero + One,
D: DimNameAdd<U1>,
DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
{
// We could use `MatrixN::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.
let mut res = MatrixN::<N, DimNameSum<D, U1>>::identity();
res.fixed_slice_mut::<D, D>(0, 0).copy_from(&self.matrix);
res
}
/// Creates a new rotation from the given square matrix.
///
/// The matrix squareness is checked but not its orthonormality.
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///
/// # 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]
pub fn from_matrix_unchecked(matrix: MatrixN<N, D>) -> Self {
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assert!(
matrix.is_square(),
"Unable to create a rotation from a non-square matrix."
);
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Self { matrix }
}
/// 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()
}
}
impl<N: SimdRealField, D: DimName> Rotation<N, D>
where
N::Element: SimdRealField,
DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
{
/// 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]
pub fn transform_point(&self, pt: &Point<N, D>) -> Point<N, 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]
pub fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, 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]
pub fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, 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]
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> {}
impl<N: Scalar + PartialEq, D: DimName> PartialEq for Rotation<N, D>
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where
DefaultAllocator: Allocator<N, D, D>,
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{
#[inline]
fn eq(&self, right: &Self) -> bool {
self.matrix == right.matrix
}
}
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impl<N, D: DimName> AbsDiffEq for Rotation<N, D>
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where
N: Scalar + AbsDiffEq,
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DefaultAllocator: Allocator<N, D, D>,
N::Epsilon: Copy,
{
type Epsilon = N::Epsilon;
#[inline]
fn default_epsilon() -> Self::Epsilon {
N::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<N, D: DimName> RelativeEq for Rotation<N, D>
where
N: Scalar + RelativeEq,
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DefaultAllocator: Allocator<N, D, D>,
N::Epsilon: Copy,
{
#[inline]
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fn default_max_relative() -> Self::Epsilon {
N::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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}
impl<N, D: DimName> UlpsEq for Rotation<N, D>
where
N: Scalar + UlpsEq,
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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>
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where
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N: RealField + fmt::Display,
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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);
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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)
// // }
// // }