forked from M-Labs/nalgebra
679 lines
20 KiB
Rust
679 lines
20 KiB
Rust
use approx::{AbsDiffEq, RelativeEq, UlpsEq};
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use num::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 base::storage::Owned;
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#[cfg(feature = "serde-serialize")]
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use serde::{Serialize, Deserialize, Serializer, Deserializer};
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#[cfg(feature = "abomonation-serialize")]
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use abomonation::Abomonation;
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use alga::general::Real;
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use base::dimension::{U1, U3, U4};
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use base::storage::{CStride, RStride};
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use base::{Matrix3, MatrixN, MatrixSlice, MatrixSliceMut, Unit, Vector3, Vector4};
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use geometry::Rotation;
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/// A quaternion. See the type alias `UnitQuaternion = Unit<Quaternion>` for a quaternion
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/// that may be used as a rotation.
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#[repr(C)]
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#[derive(Debug)]
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pub struct Quaternion<N: Real> {
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/// This quaternion as a 4D vector of coordinates in the `[ x, y, z, w ]` storage order.
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pub coords: Vector4<N>,
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}
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#[cfg(feature = "abomonation-serialize")]
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impl<N: Real> Abomonation for Quaternion<N>
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where
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Vector4<N>: Abomonation,
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{
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unsafe fn entomb<W: Write>(&self, writer: &mut W) -> IOResult<()> {
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self.coords.entomb(writer)
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}
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fn extent(&self) -> usize {
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self.coords.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.coords.exhume(bytes)
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}
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}
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impl<N: Real + Eq> Eq for Quaternion<N> {}
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impl<N: Real> PartialEq for Quaternion<N> {
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fn eq(&self, rhs: &Self) -> bool {
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self.coords == rhs.coords ||
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// Account for the double-covering of S², i.e. q = -q
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self.as_vector().iter().zip(rhs.as_vector().iter()).all(|(a, b)| *a == -*b)
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}
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}
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impl<N: Real + hash::Hash> hash::Hash for Quaternion<N> {
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fn hash<H: hash::Hasher>(&self, state: &mut H) {
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self.coords.hash(state)
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}
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}
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impl<N: Real> Copy for Quaternion<N> {}
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impl<N: Real> Clone for Quaternion<N> {
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#[inline]
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fn clone(&self) -> Self {
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Quaternion::from_vector(self.coords.clone())
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}
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}
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#[cfg(feature = "serde-serialize")]
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impl<N: Real> Serialize for Quaternion<N>
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where
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Owned<N, U4>: 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.coords.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: Real> Deserialize<'a> for Quaternion<N>
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where
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Owned<N, U4>: 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 coords = Vector4::<N>::deserialize(deserializer)?;
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Ok(Quaternion::from_vector(coords))
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}
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}
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impl<N: Real> Quaternion<N> {
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/// Moves this unit quaternion into one that owns its data.
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#[inline]
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#[deprecated(note = "This method is a no-op and will be removed in a future release.")]
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pub fn into_owned(self) -> Quaternion<N> {
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self
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}
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/// Clones this unit quaternion into one that owns its data.
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#[inline]
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#[deprecated(note = "This method is a no-op and will be removed in a future release.")]
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pub fn clone_owned(&self) -> Quaternion<N> {
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Quaternion::from_vector(self.coords.clone_owned())
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}
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/// Normalizes this quaternion.
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#[inline]
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pub fn normalize(&self) -> Quaternion<N> {
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Quaternion::from_vector(self.coords.normalize())
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}
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/// Compute the conjugate of this quaternion.
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#[inline]
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pub fn conjugate(&self) -> Quaternion<N> {
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let v = Vector4::new(
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-self.coords[0],
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-self.coords[1],
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-self.coords[2],
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self.coords[3],
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);
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Quaternion::from_vector(v)
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}
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/// Inverts this quaternion if it is not zero.
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#[inline]
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pub fn try_inverse(&self) -> Option<Quaternion<N>> {
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let mut res = Quaternion::from_vector(self.coords.clone_owned());
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if res.try_inverse_mut() {
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Some(res)
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} else {
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None
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}
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}
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/// Linear interpolation between two quaternion.
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#[inline]
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pub fn lerp(&self, other: &Quaternion<N>, t: N) -> Quaternion<N> {
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self * (N::one() - t) + other * t
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}
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/// The vector part `(i, j, k)` of this quaternion.
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#[inline]
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pub fn vector(&self) -> MatrixSlice<N, U3, U1, RStride<N, U4, U1>, CStride<N, U4, U1>> {
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self.coords.fixed_rows::<U3>(0)
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}
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/// The scalar part `w` of this quaternion.
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#[inline]
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pub fn scalar(&self) -> N {
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self.coords[3]
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}
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/// Reinterprets this quaternion as a 4D vector.
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#[inline]
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pub fn as_vector(&self) -> &Vector4<N> {
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&self.coords
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}
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/// The norm of this quaternion.
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#[inline]
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pub fn norm(&self) -> N {
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self.coords.norm()
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}
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/// A synonym for the norm of this quaternion.
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///
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/// Aka the length.
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///
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/// This function is simply implemented as a call to `norm()`
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#[inline]
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pub fn magnitude(&self) -> N {
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self.norm()
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}
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/// A synonym for the squared norm of this quaternion.
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///
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/// Aka the squared length.
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///
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/// This function is simply implemented as a call to `norm_squared()`
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#[inline]
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pub fn magnitude_squared(&self) -> N {
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self.norm_squared()
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}
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/// The squared norm of this quaternion.
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#[inline]
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pub fn norm_squared(&self) -> N {
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self.coords.norm_squared()
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}
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/// The dot product of two quaternions.
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#[inline]
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pub fn dot(&self, rhs: &Self) -> N {
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self.coords.dot(&rhs.coords)
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}
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/// The polar decomposition of this quaternion.
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///
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/// Returns, from left to right: the quaternion norm, the half rotation angle, the rotation
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/// axis. If the rotation angle is zero, the rotation axis is set to `None`.
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pub fn polar_decomposition(&self) -> (N, N, Option<Unit<Vector3<N>>>) {
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if let Some((q, n)) = Unit::try_new_and_get(*self, N::zero()) {
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if let Some(axis) = Unit::try_new(self.vector().clone_owned(), N::zero()) {
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let angle = q.angle() / ::convert(2.0f64);
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(n, angle, Some(axis))
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} else {
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(n, N::zero(), None)
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}
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} else {
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(N::zero(), N::zero(), None)
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}
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}
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/// Compute the exponential of a quaternion.
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#[inline]
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pub fn exp(&self) -> Quaternion<N> {
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self.exp_eps(N::default_epsilon())
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}
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/// Compute the exponential of a quaternion.
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#[inline]
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pub fn exp_eps(&self, eps: N) -> Quaternion<N> {
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let v = self.vector();
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let nn = v.norm_squared();
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if nn <= eps * eps {
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Quaternion::identity()
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} else {
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let w_exp = self.scalar().exp();
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let n = nn.sqrt();
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let nv = v * (w_exp * n.sin() / n);
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Quaternion::from_parts(n.cos(), nv)
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}
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}
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/// Compute the natural logarithm of a quaternion.
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#[inline]
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pub fn ln(&self) -> Quaternion<N> {
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let n = self.norm();
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let v = self.vector();
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let s = self.scalar();
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Quaternion::from_parts(n.ln(), v.normalize() * (s / n).acos())
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}
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/// Raise the quaternion to a given floating power.
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#[inline]
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pub fn powf(&self, n: N) -> Quaternion<N> {
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(self.ln() * n).exp()
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}
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/// Transforms this quaternion into its 4D vector form (Vector part, Scalar part).
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#[inline]
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pub fn as_vector_mut(&mut self) -> &mut Vector4<N> {
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&mut self.coords
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}
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/// The mutable vector part `(i, j, k)` of this quaternion.
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#[inline]
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pub fn vector_mut(
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&mut self,
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) -> MatrixSliceMut<N, U3, U1, RStride<N, U4, U1>, CStride<N, U4, U1>> {
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self.coords.fixed_rows_mut::<U3>(0)
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}
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/// Replaces this quaternion by its conjugate.
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#[inline]
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pub fn conjugate_mut(&mut self) {
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self.coords[0] = -self.coords[0];
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self.coords[1] = -self.coords[1];
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self.coords[2] = -self.coords[2];
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}
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/// Inverts this quaternion in-place if it is not zero.
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#[inline]
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pub fn try_inverse_mut(&mut self) -> bool {
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let norm_squared = self.norm_squared();
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if relative_eq!(&norm_squared, &N::zero()) {
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false
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} else {
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self.conjugate_mut();
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self.coords /= norm_squared;
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true
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}
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}
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/// Normalizes this quaternion.
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#[inline]
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pub fn normalize_mut(&mut self) -> N {
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self.coords.normalize_mut()
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}
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}
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impl<N: Real + AbsDiffEq<Epsilon = N>> AbsDiffEq for Quaternion<N> {
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type Epsilon = N;
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#[inline]
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fn default_epsilon() -> Self::Epsilon {
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N::default_epsilon()
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}
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#[inline]
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fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool {
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self.as_vector().abs_diff_eq(other.as_vector(), epsilon) ||
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// Account for the double-covering of S², i.e. q = -q
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self.as_vector().iter().zip(other.as_vector().iter()).all(|(a, b)| a.abs_diff_eq(&-*b, epsilon))
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}
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}
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impl<N: Real + RelativeEq<Epsilon = N>> RelativeEq for Quaternion<N> {
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#[inline]
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fn default_max_relative() -> Self::Epsilon {
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N::default_max_relative()
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}
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#[inline]
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fn relative_eq(
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&self,
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other: &Self,
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epsilon: Self::Epsilon,
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max_relative: Self::Epsilon,
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) -> bool {
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self.as_vector().relative_eq(other.as_vector(), epsilon, max_relative) ||
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// Account for the double-covering of S², i.e. q = -q
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self.as_vector().iter().zip(other.as_vector().iter()).all(|(a, b)| a.relative_eq(&-*b, epsilon, max_relative))
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}
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}
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impl<N: Real + UlpsEq<Epsilon = N>> UlpsEq for Quaternion<N> {
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#[inline]
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fn default_max_ulps() -> u32 {
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N::default_max_ulps()
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}
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#[inline]
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fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool {
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self.as_vector().ulps_eq(other.as_vector(), epsilon, max_ulps) ||
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// Account for the double-covering of S², i.e. q = -q.
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self.as_vector().iter().zip(other.as_vector().iter()).all(|(a, b)| a.ulps_eq(&-*b, epsilon, max_ulps))
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}
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}
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impl<N: Real + fmt::Display> fmt::Display for Quaternion<N> {
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fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
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write!(
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f,
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"Quaternion {} − ({}, {}, {})",
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self[3], self[0], self[1], self[2]
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)
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}
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}
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/// A unit quaternions. May be used to represent a rotation.
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pub type UnitQuaternion<N> = Unit<Quaternion<N>>;
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impl<N: Real> UnitQuaternion<N> {
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/// Moves this unit quaternion into one that owns its data.
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#[inline]
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#[deprecated(note = "This method is a no-op and will be removed in a future release.")]
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pub fn into_owned(self) -> UnitQuaternion<N> {
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self
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}
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/// Clones this unit quaternion into one that owns its data.
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#[inline]
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#[deprecated(note = "This method is a no-op and will be removed in a future release.")]
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pub fn clone_owned(&self) -> UnitQuaternion<N> {
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*self
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}
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/// The rotation angle in [0; pi] of this unit quaternion.
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#[inline]
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pub fn angle(&self) -> N {
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let w = self.quaternion().scalar().abs();
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// Handle inaccuracies that make break `.acos`.
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if w >= N::one() {
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N::zero()
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} else {
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w.acos() * ::convert(2.0f64)
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}
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}
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/// The underlying quaternion.
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///
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/// Same as `self.as_ref()`.
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#[inline]
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pub fn quaternion(&self) -> &Quaternion<N> {
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self.as_ref()
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}
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/// Compute the conjugate of this unit quaternion.
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#[inline]
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pub fn conjugate(&self) -> UnitQuaternion<N> {
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UnitQuaternion::new_unchecked(self.as_ref().conjugate())
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}
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/// Inverts this quaternion if it is not zero.
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#[inline]
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pub fn inverse(&self) -> UnitQuaternion<N> {
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self.conjugate()
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}
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/// The rotation angle needed to make `self` and `other` coincide.
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#[inline]
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pub fn angle_to(&self, other: &UnitQuaternion<N>) -> N {
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let delta = self.rotation_to(other);
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delta.angle()
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}
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/// The unit quaternion needed to make `self` and `other` coincide.
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///
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/// The result is such that: `self.rotation_to(other) * self == other`.
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#[inline]
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pub fn rotation_to(&self, other: &UnitQuaternion<N>) -> UnitQuaternion<N> {
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other / self
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}
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/// Linear interpolation between two unit quaternions.
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///
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/// The result is not normalized.
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#[inline]
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pub fn lerp(&self, other: &UnitQuaternion<N>, t: N) -> Quaternion<N> {
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self.as_ref().lerp(other.as_ref(), t)
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}
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/// Normalized linear interpolation between two unit quaternions.
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#[inline]
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pub fn nlerp(&self, other: &UnitQuaternion<N>, t: N) -> UnitQuaternion<N> {
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let mut res = self.lerp(other, t);
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let _ = res.normalize_mut();
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UnitQuaternion::new_unchecked(res)
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}
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/// Spherical linear interpolation between two unit quaternions.
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///
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/// Panics if the angle between both quaternion is 180 degrees (in which case the interpolation
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/// is not well-defined).
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#[inline]
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pub fn slerp(&self, other: &UnitQuaternion<N>, t: N) -> UnitQuaternion<N> {
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Unit::new_unchecked(
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Quaternion::from_vector(Unit::new_unchecked(self.coords).slerp(&Unit::new_unchecked(other.coords), t).unwrap())
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)
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}
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/// Computes the spherical linear interpolation between two unit quaternions or returns `None`
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/// if both quaternions are approximately 180 degrees apart (in which case the interpolation is
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/// not well-defined).
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///
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/// # Arguments
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/// * `self`: the first quaternion to interpolate from.
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/// * `other`: the second quaternion to interpolate toward.
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/// * `t`: the interpolation parameter. Should be between 0 and 1.
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/// * `epsilon`: the value below which the sinus of the angle separating both quaternion
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/// must be to return `None`.
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#[inline]
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pub fn try_slerp(
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&self,
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other: &UnitQuaternion<N>,
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t: N,
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epsilon: N,
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) -> Option<UnitQuaternion<N>> {
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Unit::new_unchecked(self.coords).try_slerp(&Unit::new_unchecked(other.coords), t, epsilon)
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.map(|q| Unit::new_unchecked(Quaternion::from_vector(q.unwrap())))
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}
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/// Compute the conjugate of this unit quaternion in-place.
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#[inline]
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pub fn conjugate_mut(&mut self) {
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self.as_mut_unchecked().conjugate_mut()
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}
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/// Inverts this quaternion if it is not zero.
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#[inline]
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pub fn inverse_mut(&mut self) {
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self.as_mut_unchecked().conjugate_mut()
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}
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/// The rotation axis of this unit quaternion or `None` if the rotation is zero.
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#[inline]
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pub fn axis(&self) -> Option<Unit<Vector3<N>>> {
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let v = if self.quaternion().scalar() >= N::zero() {
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self.as_ref().vector().clone_owned()
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} else {
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-self.as_ref().vector()
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};
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Unit::try_new(v, N::zero())
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}
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/// The rotation axis of this unit quaternion multiplied by the rotation angle.
|
||
#[inline]
|
||
pub fn scaled_axis(&self) -> Vector3<N> {
|
||
if let Some(axis) = self.axis() {
|
||
axis.unwrap() * self.angle()
|
||
} else {
|
||
Vector3::zero()
|
||
}
|
||
}
|
||
|
||
/// The rotation axis and angle in ]0, pi] of this unit quaternion.
|
||
///
|
||
/// Returns `None` if the angle is zero.
|
||
#[inline]
|
||
pub fn axis_angle(&self) -> Option<(Unit<Vector3<N>>, N)> {
|
||
if let Some(axis) = self.axis() {
|
||
Some((axis, self.angle()))
|
||
} else {
|
||
None
|
||
}
|
||
}
|
||
|
||
/// Compute the exponential of a quaternion.
|
||
///
|
||
/// Note that this function yields a `Quaternion<N>` because it looses the unit property.
|
||
#[inline]
|
||
pub fn exp(&self) -> Quaternion<N> {
|
||
self.as_ref().exp()
|
||
}
|
||
|
||
/// Compute the natural logarithm of a quaternion.
|
||
///
|
||
/// Note that this function yields a `Quaternion<N>` because it looses the unit property.
|
||
/// The vector part of the return value corresponds to the axis-angle representation (divided
|
||
/// by 2.0) of this unit quaternion.
|
||
#[inline]
|
||
pub fn ln(&self) -> Quaternion<N> {
|
||
if let Some(v) = self.axis() {
|
||
Quaternion::from_parts(N::zero(), v.unwrap() * self.angle())
|
||
} else {
|
||
Quaternion::zero()
|
||
}
|
||
}
|
||
|
||
/// Raise the quaternion to a given floating power.
|
||
///
|
||
/// This returns the unit quaternion that identifies a rotation with axis `self.axis()` and
|
||
/// angle `self.angle() × n`.
|
||
#[inline]
|
||
pub fn powf(&self, n: N) -> UnitQuaternion<N> {
|
||
if let Some(v) = self.axis() {
|
||
UnitQuaternion::from_axis_angle(&v, self.angle() * n)
|
||
} else {
|
||
UnitQuaternion::identity()
|
||
}
|
||
}
|
||
|
||
/// Builds a rotation matrix from this unit quaternion.
|
||
#[inline]
|
||
pub fn to_rotation_matrix(&self) -> Rotation<N, U3> {
|
||
let i = self.as_ref()[0];
|
||
let j = self.as_ref()[1];
|
||
let k = self.as_ref()[2];
|
||
let w = self.as_ref()[3];
|
||
|
||
let ww = w * w;
|
||
let ii = i * i;
|
||
let jj = j * j;
|
||
let kk = k * k;
|
||
let ij = i * j * ::convert(2.0f64);
|
||
let wk = w * k * ::convert(2.0f64);
|
||
let wj = w * j * ::convert(2.0f64);
|
||
let ik = i * k * ::convert(2.0f64);
|
||
let jk = j * k * ::convert(2.0f64);
|
||
let wi = w * i * ::convert(2.0f64);
|
||
|
||
Rotation::from_matrix_unchecked(Matrix3::new(
|
||
ww + ii - jj - kk,
|
||
ij - wk,
|
||
wj + ik,
|
||
wk + ij,
|
||
ww - ii + jj - kk,
|
||
jk - wi,
|
||
ik - wj,
|
||
wi + jk,
|
||
ww - ii - jj + kk,
|
||
))
|
||
}
|
||
|
||
/// Converts this unit quaternion into its equivalent Euler angles.
|
||
///
|
||
/// The angles are produced in the form (roll, yaw, pitch).
|
||
#[inline]
|
||
pub fn to_euler_angles(&self) -> (N, N, N) {
|
||
self.to_rotation_matrix().to_euler_angles()
|
||
}
|
||
|
||
/// Converts this unit quaternion into its equivalent homogeneous transformation matrix.
|
||
#[inline]
|
||
pub fn to_homogeneous(&self) -> MatrixN<N, U4> {
|
||
self.to_rotation_matrix().to_homogeneous()
|
||
}
|
||
}
|
||
|
||
impl<N: Real + fmt::Display> fmt::Display for UnitQuaternion<N> {
|
||
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
|
||
if let Some(axis) = self.axis() {
|
||
let axis = axis.unwrap();
|
||
write!(
|
||
f,
|
||
"UnitQuaternion angle: {} − axis: ({}, {}, {})",
|
||
self.angle(),
|
||
axis[0],
|
||
axis[1],
|
||
axis[2]
|
||
)
|
||
} else {
|
||
write!(
|
||
f,
|
||
"UnitQuaternion angle: {} − axis: (undefined)",
|
||
self.angle()
|
||
)
|
||
}
|
||
}
|
||
}
|
||
|
||
impl<N: Real + AbsDiffEq<Epsilon = N>> AbsDiffEq for UnitQuaternion<N> {
|
||
type Epsilon = N;
|
||
|
||
#[inline]
|
||
fn default_epsilon() -> Self::Epsilon {
|
||
N::default_epsilon()
|
||
}
|
||
|
||
#[inline]
|
||
fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool {
|
||
self.as_ref().abs_diff_eq(other.as_ref(), epsilon)
|
||
}
|
||
}
|
||
|
||
impl<N: Real + RelativeEq<Epsilon = N>> RelativeEq for UnitQuaternion<N> {
|
||
#[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.as_ref()
|
||
.relative_eq(other.as_ref(), epsilon, max_relative)
|
||
}
|
||
}
|
||
|
||
impl<N: Real + UlpsEq<Epsilon = N>> UlpsEq for UnitQuaternion<N> {
|
||
#[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.as_ref().ulps_eq(other.as_ref(), epsilon, max_ulps)
|
||
}
|
||
}
|