forked from M-Labs/nalgebra
c97dfaf381
* Add From impls to convert between UnitQuaterion/UnitComplex and Rotation2/3 * Add rotation extraction from a Matrix2 or Matrix3. * Add fast Taylor renormalization for Unit. Fix 376. * Add renormalization for Rotation3. Renormalization for Rotation2 requires Complex to implement VectorSpace which will be fixed only on alga v0.9 * Update Changelog.
731 lines
26 KiB
Rust
731 lines
26 KiB
Rust
#[cfg(feature = "arbitrary")]
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use base::dimension::U4;
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#[cfg(feature = "arbitrary")]
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use base::storage::Owned;
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#[cfg(feature = "arbitrary")]
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use quickcheck::{Arbitrary, Gen};
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use num::{One, Zero};
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use rand::distributions::{Distribution, OpenClosed01, Standard};
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use rand::Rng;
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use alga::general::Real;
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use base::dimension::U3;
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use base::storage::Storage;
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#[cfg(feature = "arbitrary")]
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use base::Vector3;
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use base::{Unit, Vector, Vector4, Matrix3};
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use geometry::{Quaternion, Rotation3, UnitQuaternion};
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impl<N: Real> Quaternion<N> {
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/// Creates a quaternion from a 4D vector. The quaternion scalar part corresponds to the `w`
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/// vector component.
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#[inline]
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#[deprecated(note = "Use `::from` instead.")]
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pub fn from_vector(vector: Vector4<N>) -> Self {
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Self { coords: vector }
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}
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/// Creates a new quaternion from its individual components. Note that the arguments order does
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/// **not** follow the storage order.
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///
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/// The storage order is `[ i, j, k, w ]` while the arguments for this functions are in the
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/// order `(w, i, j, k)`.
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///
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/// # Example
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/// ```
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/// # use nalgebra::{Quaternion, Vector4};
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/// let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
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/// assert!(q.i == 2.0 && q.j == 3.0 && q.k == 4.0 && q.w == 1.0);
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/// assert_eq!(*q.as_vector(), Vector4::new(2.0, 3.0, 4.0, 1.0));
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/// ```
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#[inline]
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pub fn new(w: N, i: N, j: N, k: N) -> Self {
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let v = Vector4::<N>::new(i, j, k, w);
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Self::from(v)
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}
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/// Creates a new quaternion from its scalar and vector parts. Note that the arguments order does
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/// **not** follow the storage order.
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///
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/// The storage order is [ vector, scalar ].
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///
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/// # Example
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/// ```
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/// # use nalgebra::{Quaternion, Vector3, Vector4};
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/// let w = 1.0;
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/// let ijk = Vector3::new(2.0, 3.0, 4.0);
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/// let q = Quaternion::from_parts(w, ijk);
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/// assert!(q.i == 2.0 && q.j == 3.0 && q.k == 4.0 && q.w == 1.0);
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/// assert_eq!(*q.as_vector(), Vector4::new(2.0, 3.0, 4.0, 1.0));
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/// ```
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#[inline]
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// FIXME: take a reference to `vector`?
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pub fn from_parts<SB>(scalar: N, vector: Vector<N, U3, SB>) -> Self
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where SB: Storage<N, U3> {
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Self::new(scalar, vector[0], vector[1], vector[2])
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}
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/// Creates a new quaternion from its polar decomposition.
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///
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/// Note that `axis` is assumed to be a unit vector.
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// FIXME: take a reference to `axis`?
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pub fn from_polar_decomposition<SB>(scale: N, theta: N, axis: Unit<Vector<N, U3, SB>>) -> Self
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where SB: Storage<N, U3> {
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let rot = UnitQuaternion::<N>::from_axis_angle(&axis, theta * ::convert(2.0f64));
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rot.into_inner() * scale
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}
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/// The quaternion multiplicative identity.
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///
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/// # Example
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/// ```
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/// # use nalgebra::Quaternion;
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/// let q = Quaternion::identity();
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/// let q2 = Quaternion::new(1.0, 2.0, 3.0, 4.0);
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///
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/// assert_eq!(q * q2, q2);
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/// assert_eq!(q2 * q, q2);
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/// ```
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#[inline]
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pub fn identity() -> Self {
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Self::new(N::one(), N::zero(), N::zero(), N::zero())
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}
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}
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impl<N: Real> One for Quaternion<N> {
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#[inline]
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fn one() -> Self {
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Self::identity()
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}
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}
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impl<N: Real> Zero for Quaternion<N> {
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#[inline]
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fn zero() -> Self {
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Self::new(N::zero(), N::zero(), N::zero(), N::zero())
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}
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#[inline]
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fn is_zero(&self) -> bool {
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self.coords.is_zero()
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}
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}
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impl<N: Real> Distribution<Quaternion<N>> for Standard
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where Standard: Distribution<N>
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{
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#[inline]
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fn sample<'a, R: Rng + ?Sized>(&self, rng: &'a mut R) -> Quaternion<N> {
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Quaternion::new(rng.gen(), rng.gen(), rng.gen(), rng.gen())
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}
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}
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#[cfg(feature = "arbitrary")]
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impl<N: Real + Arbitrary> Arbitrary for Quaternion<N>
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where Owned<N, U4>: Send
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{
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#[inline]
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fn arbitrary<G: Gen>(g: &mut G) -> Self {
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Self::new(
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N::arbitrary(g),
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N::arbitrary(g),
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N::arbitrary(g),
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N::arbitrary(g),
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)
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}
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}
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impl<N: Real> UnitQuaternion<N> {
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/// The rotation identity.
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///
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/// # Example
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/// ```
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/// # use nalgebra::{UnitQuaternion, Vector3, Point3};
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/// let q = UnitQuaternion::identity();
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/// let q2 = UnitQuaternion::new(Vector3::new(1.0, 2.0, 3.0));
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/// let v = Vector3::new_random();
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/// let p = Point3::from(v);
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///
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/// assert_eq!(q * q2, q2);
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/// assert_eq!(q2 * q, q2);
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/// assert_eq!(q * v, v);
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/// assert_eq!(q * p, p);
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/// ```
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#[inline]
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pub fn identity() -> Self {
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Self::new_unchecked(Quaternion::identity())
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}
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/// Creates a new quaternion from a unit vector (the rotation axis) and an angle
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/// (the rotation angle).
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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::{UnitQuaternion, Point3, Vector3};
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/// let axis = Vector3::y_axis();
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/// let angle = f32::consts::FRAC_PI_2;
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/// // Point and vector being transformed in the tests.
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/// let pt = Point3::new(4.0, 5.0, 6.0);
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/// let vec = Vector3::new(4.0, 5.0, 6.0);
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/// let q = UnitQuaternion::from_axis_angle(&axis, angle);
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///
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/// assert_eq!(q.axis().unwrap(), axis);
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/// assert_eq!(q.angle(), angle);
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/// assert_relative_eq!(q * pt, Point3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
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/// assert_relative_eq!(q * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
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///
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/// // A zero vector yields an identity.
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/// assert_eq!(UnitQuaternion::from_scaled_axis(Vector3::<f32>::zeros()), UnitQuaternion::identity());
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/// ```
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#[inline]
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pub fn from_axis_angle<SB>(axis: &Unit<Vector<N, U3, SB>>, angle: N) -> Self
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where SB: Storage<N, U3> {
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let (sang, cang) = (angle / ::convert(2.0f64)).sin_cos();
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let q = Quaternion::from_parts(cang, axis.as_ref() * sang);
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Self::new_unchecked(q)
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}
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/// Creates a new unit quaternion from a quaternion.
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///
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/// The input quaternion will be normalized.
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#[inline]
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pub fn from_quaternion(q: Quaternion<N>) -> Self {
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Self::new_normalize(q)
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}
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/// Creates a new unit quaternion from Euler angles.
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///
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/// The primitive rotations are applied in order: 1 roll − 2 pitch − 3 yaw.
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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::UnitQuaternion;
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/// let rot = UnitQuaternion::from_euler_angles(0.1, 0.2, 0.3);
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/// let euler = rot.euler_angles();
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/// assert_relative_eq!(euler.0, 0.1, epsilon = 1.0e-6);
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/// assert_relative_eq!(euler.1, 0.2, epsilon = 1.0e-6);
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/// assert_relative_eq!(euler.2, 0.3, epsilon = 1.0e-6);
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/// ```
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#[inline]
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pub fn from_euler_angles(roll: N, pitch: N, yaw: N) -> Self {
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let (sr, cr) = (roll * ::convert(0.5f64)).sin_cos();
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let (sp, cp) = (pitch * ::convert(0.5f64)).sin_cos();
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let (sy, cy) = (yaw * ::convert(0.5f64)).sin_cos();
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let q = Quaternion::new(
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cr * cp * cy + sr * sp * sy,
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sr * cp * cy - cr * sp * sy,
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cr * sp * cy + sr * cp * sy,
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cr * cp * sy - sr * sp * cy,
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);
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Self::new_unchecked(q)
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}
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/// Builds an unit quaternion from a rotation matrix.
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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::{Rotation3, UnitQuaternion, Vector3};
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/// let axis = Vector3::y_axis();
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/// let angle = 0.1;
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/// let rot = Rotation3::from_axis_angle(&axis, angle);
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/// let q = UnitQuaternion::from_rotation_matrix(&rot);
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/// assert_relative_eq!(q.to_rotation_matrix(), rot, epsilon = 1.0e-6);
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/// assert_relative_eq!(q.axis().unwrap(), rot.axis().unwrap(), epsilon = 1.0e-6);
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/// assert_relative_eq!(q.angle(), rot.angle(), epsilon = 1.0e-6);
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/// ```
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#[inline]
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pub fn from_rotation_matrix(rotmat: &Rotation3<N>) -> Self {
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// Robust matrix to quaternion transformation.
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// See http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion
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let tr = rotmat[(0, 0)] + rotmat[(1, 1)] + rotmat[(2, 2)];
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let res;
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let _0_25: N = ::convert(0.25);
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if tr > N::zero() {
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let denom = (tr + N::one()).sqrt() * ::convert(2.0);
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res = Quaternion::new(
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_0_25 * denom,
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(rotmat[(2, 1)] - rotmat[(1, 2)]) / denom,
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(rotmat[(0, 2)] - rotmat[(2, 0)]) / denom,
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(rotmat[(1, 0)] - rotmat[(0, 1)]) / denom,
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);
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} else if rotmat[(0, 0)] > rotmat[(1, 1)] && rotmat[(0, 0)] > rotmat[(2, 2)] {
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let denom = (N::one() + rotmat[(0, 0)] - rotmat[(1, 1)] - rotmat[(2, 2)]).sqrt()
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* ::convert(2.0);
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res = Quaternion::new(
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(rotmat[(2, 1)] - rotmat[(1, 2)]) / denom,
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_0_25 * denom,
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(rotmat[(0, 1)] + rotmat[(1, 0)]) / denom,
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(rotmat[(0, 2)] + rotmat[(2, 0)]) / denom,
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);
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} else if rotmat[(1, 1)] > rotmat[(2, 2)] {
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let denom = (N::one() + rotmat[(1, 1)] - rotmat[(0, 0)] - rotmat[(2, 2)]).sqrt()
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* ::convert(2.0);
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res = Quaternion::new(
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(rotmat[(0, 2)] - rotmat[(2, 0)]) / denom,
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(rotmat[(0, 1)] + rotmat[(1, 0)]) / denom,
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_0_25 * denom,
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(rotmat[(1, 2)] + rotmat[(2, 1)]) / denom,
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);
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} else {
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let denom = (N::one() + rotmat[(2, 2)] - rotmat[(0, 0)] - rotmat[(1, 1)]).sqrt()
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* ::convert(2.0);
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res = Quaternion::new(
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(rotmat[(1, 0)] - rotmat[(0, 1)]) / denom,
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(rotmat[(0, 2)] + rotmat[(2, 0)]) / denom,
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(rotmat[(1, 2)] + rotmat[(2, 1)]) / denom,
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_0_25 * denom,
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);
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}
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Self::new_unchecked(res)
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}
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/// Builds an unit quaternion by extracting the rotation part of the given transformation `m`.
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///
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/// This is an iterative method. See `.from_matrix_eps` to provide mover
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/// convergence parameters and starting solution.
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/// This implements "A Robust Method to Extract the Rotational Part of Deformations" by Müller et al.
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pub fn from_matrix(m: &Matrix3<N>) -> Self {
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Rotation3::from_matrix(m).into()
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}
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/// Builds an unit quaternion by extracting the rotation part of the given transformation `m`.
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///
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/// This implements "A Robust Method to Extract the Rotational Part of Deformations" by Müller et al.
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///
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/// # Parameters
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///
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/// * `m`: the matrix from which the rotational part is to be extracted.
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/// * `eps`: the angular errors tolerated between the current rotation and the optimal one.
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/// * `max_iter`: the maximum number of iterations. Loops indefinitely until convergence if set to `0`.
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/// * `guess`: an estimate of the solution. Convergence will be significantly faster if an initial solution close
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/// to the actual solution is provided. Can be set to `UnitQuaternion::identity()` if no other
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/// guesses come to mind.
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pub fn from_matrix_eps(m: &Matrix3<N>, eps: N, max_iter: usize, guess: Self) -> Self {
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let guess = Rotation3::from(guess);
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Rotation3::from_matrix_eps(m, eps, max_iter, guess).into()
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}
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/// The unit quaternion needed to make `a` and `b` be collinear and point toward the same
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/// direction.
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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::{Vector3, UnitQuaternion};
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/// let a = Vector3::new(1.0, 2.0, 3.0);
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/// let b = Vector3::new(3.0, 1.0, 2.0);
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/// let q = UnitQuaternion::rotation_between(&a, &b).unwrap();
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/// assert_relative_eq!(q * a, b);
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/// assert_relative_eq!(q.inverse() * b, a);
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/// ```
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#[inline]
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pub fn rotation_between<SB, SC>(a: &Vector<N, U3, SB>, b: &Vector<N, U3, SC>) -> Option<Self>
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where
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SB: Storage<N, U3>,
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SC: Storage<N, U3>,
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{
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Self::scaled_rotation_between(a, b, N::one())
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}
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|
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/// The smallest rotation needed to make `a` and `b` collinear and point toward the same
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/// direction, raised to the power `s`.
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///
|
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/// # Example
|
||
/// ```
|
||
/// # #[macro_use] extern crate approx;
|
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/// # use nalgebra::{Vector3, UnitQuaternion};
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/// let a = Vector3::new(1.0, 2.0, 3.0);
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/// let b = Vector3::new(3.0, 1.0, 2.0);
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/// let q2 = UnitQuaternion::scaled_rotation_between(&a, &b, 0.2).unwrap();
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/// let q5 = UnitQuaternion::scaled_rotation_between(&a, &b, 0.5).unwrap();
|
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/// assert_relative_eq!(q2 * q2 * q2 * q2 * q2 * a, b, epsilon = 1.0e-6);
|
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/// assert_relative_eq!(q5 * q5 * a, b, epsilon = 1.0e-6);
|
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/// ```
|
||
#[inline]
|
||
pub fn scaled_rotation_between<SB, SC>(
|
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a: &Vector<N, U3, SB>,
|
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b: &Vector<N, U3, SC>,
|
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s: N,
|
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) -> Option<Self>
|
||
where
|
||
SB: Storage<N, U3>,
|
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SC: Storage<N, U3>,
|
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{
|
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// FIXME: code duplication with Rotation.
|
||
if let (Some(na), Some(nb)) = (
|
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Unit::try_new(a.clone_owned(), N::zero()),
|
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Unit::try_new(b.clone_owned(), N::zero()),
|
||
) {
|
||
Self::scaled_rotation_between_axis(&na, &nb, s)
|
||
} else {
|
||
Some(Self::identity())
|
||
}
|
||
}
|
||
|
||
/// The unit quaternion needed to make `a` and `b` be collinear and point toward the same
|
||
/// direction.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # #[macro_use] extern crate approx;
|
||
/// # use nalgebra::{Unit, Vector3, UnitQuaternion};
|
||
/// let a = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
|
||
/// let b = Unit::new_normalize(Vector3::new(3.0, 1.0, 2.0));
|
||
/// let q = UnitQuaternion::rotation_between(&a, &b).unwrap();
|
||
/// assert_relative_eq!(q * a, b);
|
||
/// assert_relative_eq!(q.inverse() * b, a);
|
||
/// ```
|
||
#[inline]
|
||
pub fn rotation_between_axis<SB, SC>(
|
||
a: &Unit<Vector<N, U3, SB>>,
|
||
b: &Unit<Vector<N, U3, SC>>,
|
||
) -> Option<Self>
|
||
where
|
||
SB: Storage<N, U3>,
|
||
SC: Storage<N, U3>,
|
||
{
|
||
Self::scaled_rotation_between_axis(a, b, N::one())
|
||
}
|
||
|
||
/// The smallest rotation needed to make `a` and `b` collinear and point toward the same
|
||
/// direction, raised to the power `s`.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # #[macro_use] extern crate approx;
|
||
/// # use nalgebra::{Unit, Vector3, UnitQuaternion};
|
||
/// let a = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
|
||
/// let b = Unit::new_normalize(Vector3::new(3.0, 1.0, 2.0));
|
||
/// let q2 = UnitQuaternion::scaled_rotation_between(&a, &b, 0.2).unwrap();
|
||
/// let q5 = UnitQuaternion::scaled_rotation_between(&a, &b, 0.5).unwrap();
|
||
/// assert_relative_eq!(q2 * q2 * q2 * q2 * q2 * a, b, epsilon = 1.0e-6);
|
||
/// assert_relative_eq!(q5 * q5 * a, b, epsilon = 1.0e-6);
|
||
/// ```
|
||
#[inline]
|
||
pub fn scaled_rotation_between_axis<SB, SC>(
|
||
na: &Unit<Vector<N, U3, SB>>,
|
||
nb: &Unit<Vector<N, U3, SC>>,
|
||
s: N,
|
||
) -> Option<Self>
|
||
where
|
||
SB: Storage<N, U3>,
|
||
SC: Storage<N, U3>,
|
||
{
|
||
// FIXME: code duplication with Rotation.
|
||
let c = na.cross(&nb);
|
||
|
||
if let Some(axis) = Unit::try_new(c, N::default_epsilon()) {
|
||
let cos = na.dot(&nb);
|
||
|
||
// The cosinus may be out of [-1, 1] because of inaccuracies.
|
||
if cos <= -N::one() {
|
||
return None;
|
||
} else if cos >= N::one() {
|
||
return Some(Self::identity());
|
||
} else {
|
||
return Some(Self::from_axis_angle(&axis, cos.acos() * s));
|
||
}
|
||
} else if na.dot(&nb) < N::zero() {
|
||
// PI
|
||
//
|
||
// The rotation axis is undefined but the angle not zero. This is not a
|
||
// simple rotation.
|
||
return None;
|
||
} else {
|
||
// Zero
|
||
Some(Self::identity())
|
||
}
|
||
}
|
||
|
||
/// Creates an unit quaternion that corresponds to the local frame of an observer standing at the
|
||
/// origin and looking toward `dir`.
|
||
///
|
||
/// It maps the `z` axis to the direction `dir`.
|
||
///
|
||
/// # Arguments
|
||
/// * dir - The look direction. It does not need to be normalized.
|
||
/// * up - The vertical direction. It does not need to be normalized.
|
||
/// The only requirement of this parameter is to not be collinear to `dir`. Non-collinearity
|
||
/// is not checked.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # #[macro_use] extern crate approx;
|
||
/// # use std::f32;
|
||
/// # use nalgebra::{UnitQuaternion, Vector3};
|
||
/// let dir = Vector3::new(1.0, 2.0, 3.0);
|
||
/// let up = Vector3::y();
|
||
///
|
||
/// let q = UnitQuaternion::face_towards(&dir, &up);
|
||
/// assert_relative_eq!(q * Vector3::z(), dir.normalize());
|
||
/// ```
|
||
#[inline]
|
||
pub fn face_towards<SB, SC>(dir: &Vector<N, U3, SB>, up: &Vector<N, U3, SC>) -> Self
|
||
where
|
||
SB: Storage<N, U3>,
|
||
SC: Storage<N, U3>,
|
||
{
|
||
Self::from_rotation_matrix(&Rotation3::face_towards(dir, up))
|
||
}
|
||
|
||
/// Deprecated: Use [UnitQuaternion::face_towards] instead.
|
||
#[deprecated(note="renamed to `face_towards`")]
|
||
pub fn new_observer_frames<SB, SC>(dir: &Vector<N, U3, SB>, up: &Vector<N, U3, SC>) -> Self
|
||
where
|
||
SB: Storage<N, U3>,
|
||
SC: Storage<N, U3>,
|
||
{
|
||
Self::face_towards(dir, up)
|
||
}
|
||
|
||
/// Builds a right-handed look-at view matrix without translation.
|
||
///
|
||
/// It maps the view direction `dir` to the **negative** `z` axis.
|
||
/// This conforms to the common notion of right handed look-at matrix from the computer
|
||
/// graphics community.
|
||
///
|
||
/// # Arguments
|
||
/// * dir − The view direction. It does not need to be normalized.
|
||
/// * up - A vector approximately aligned with required the vertical axis. It does not need
|
||
/// to be normalized. The only requirement of this parameter is to not be collinear to `dir`.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # #[macro_use] extern crate approx;
|
||
/// # use std::f32;
|
||
/// # use nalgebra::{UnitQuaternion, Vector3};
|
||
/// let dir = Vector3::new(1.0, 2.0, 3.0);
|
||
/// let up = Vector3::y();
|
||
///
|
||
/// let q = UnitQuaternion::look_at_rh(&dir, &up);
|
||
/// assert_relative_eq!(q * dir.normalize(), -Vector3::z());
|
||
/// ```
|
||
#[inline]
|
||
pub fn look_at_rh<SB, SC>(dir: &Vector<N, U3, SB>, up: &Vector<N, U3, SC>) -> Self
|
||
where
|
||
SB: Storage<N, U3>,
|
||
SC: Storage<N, U3>,
|
||
{
|
||
Self::face_towards(&-dir, up).inverse()
|
||
}
|
||
|
||
/// Builds a left-handed look-at view matrix without translation.
|
||
///
|
||
/// It maps the view direction `dir` to the **positive** `z` axis.
|
||
/// This conforms to the common notion of left handed look-at matrix from the computer
|
||
/// graphics community.
|
||
///
|
||
/// # Arguments
|
||
/// * dir − The view direction. It does not need to be normalized.
|
||
/// * up - A vector approximately aligned with required the vertical axis. The only
|
||
/// requirement of this parameter is to not be collinear to `dir`.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # #[macro_use] extern crate approx;
|
||
/// # use std::f32;
|
||
/// # use nalgebra::{UnitQuaternion, Vector3};
|
||
/// let dir = Vector3::new(1.0, 2.0, 3.0);
|
||
/// let up = Vector3::y();
|
||
///
|
||
/// let q = UnitQuaternion::look_at_lh(&dir, &up);
|
||
/// assert_relative_eq!(q * dir.normalize(), Vector3::z());
|
||
/// ```
|
||
#[inline]
|
||
pub fn look_at_lh<SB, SC>(dir: &Vector<N, U3, SB>, up: &Vector<N, U3, SC>) -> Self
|
||
where
|
||
SB: Storage<N, U3>,
|
||
SC: Storage<N, U3>,
|
||
{
|
||
Self::face_towards(dir, up).inverse()
|
||
}
|
||
|
||
/// Creates a new unit quaternion rotation from a rotation axis scaled by the rotation angle.
|
||
///
|
||
/// If `axisangle` has a magnitude smaller than `N::default_epsilon()`, this returns the identity rotation.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # #[macro_use] extern crate approx;
|
||
/// # use std::f32;
|
||
/// # use nalgebra::{UnitQuaternion, Point3, Vector3};
|
||
/// let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
|
||
/// // Point and vector being transformed in the tests.
|
||
/// let pt = Point3::new(4.0, 5.0, 6.0);
|
||
/// let vec = Vector3::new(4.0, 5.0, 6.0);
|
||
/// let q = UnitQuaternion::new(axisangle);
|
||
///
|
||
/// assert_relative_eq!(q * pt, Point3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
|
||
/// assert_relative_eq!(q * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
|
||
///
|
||
/// // A zero vector yields an identity.
|
||
/// assert_eq!(UnitQuaternion::new(Vector3::<f32>::zeros()), UnitQuaternion::identity());
|
||
/// ```
|
||
#[inline]
|
||
pub fn new<SB>(axisangle: Vector<N, U3, SB>) -> Self
|
||
where SB: Storage<N, U3> {
|
||
let two: N = ::convert(2.0f64);
|
||
let q = Quaternion::<N>::from_parts(N::zero(), axisangle / two).exp();
|
||
Self::new_unchecked(q)
|
||
}
|
||
|
||
/// Creates a new unit quaternion rotation from a rotation axis scaled by the rotation angle.
|
||
///
|
||
/// If `axisangle` has a magnitude smaller than `eps`, this returns the identity rotation.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # #[macro_use] extern crate approx;
|
||
/// # use std::f32;
|
||
/// # use nalgebra::{UnitQuaternion, Point3, Vector3};
|
||
/// let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
|
||
/// // Point and vector being transformed in the tests.
|
||
/// let pt = Point3::new(4.0, 5.0, 6.0);
|
||
/// let vec = Vector3::new(4.0, 5.0, 6.0);
|
||
/// let q = UnitQuaternion::new_eps(axisangle, 1.0e-6);
|
||
///
|
||
/// assert_relative_eq!(q * pt, Point3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
|
||
/// assert_relative_eq!(q * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
|
||
///
|
||
/// // An almost zero vector yields an identity.
|
||
/// assert_eq!(UnitQuaternion::new_eps(Vector3::new(1.0e-8, 1.0e-9, 1.0e-7), 1.0e-6), UnitQuaternion::identity());
|
||
/// ```
|
||
#[inline]
|
||
pub fn new_eps<SB>(axisangle: Vector<N, U3, SB>, eps: N) -> Self
|
||
where SB: Storage<N, U3> {
|
||
let two: N = ::convert(2.0f64);
|
||
let q = Quaternion::<N>::from_parts(N::zero(), axisangle / two).exp_eps(eps);
|
||
Self::new_unchecked(q)
|
||
}
|
||
|
||
/// Creates a new unit quaternion rotation from a rotation axis scaled by the rotation angle.
|
||
///
|
||
/// If `axisangle` has a magnitude smaller than `N::default_epsilon()`, this returns the identity rotation.
|
||
/// Same as `Self::new(axisangle)`.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # #[macro_use] extern crate approx;
|
||
/// # use std::f32;
|
||
/// # use nalgebra::{UnitQuaternion, Point3, Vector3};
|
||
/// let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
|
||
/// // Point and vector being transformed in the tests.
|
||
/// let pt = Point3::new(4.0, 5.0, 6.0);
|
||
/// let vec = Vector3::new(4.0, 5.0, 6.0);
|
||
/// let q = UnitQuaternion::from_scaled_axis(axisangle);
|
||
///
|
||
/// assert_relative_eq!(q * pt, Point3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
|
||
/// assert_relative_eq!(q * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
|
||
///
|
||
/// // A zero vector yields an identity.
|
||
/// assert_eq!(UnitQuaternion::from_scaled_axis(Vector3::<f32>::zeros()), UnitQuaternion::identity());
|
||
/// ```
|
||
#[inline]
|
||
pub fn from_scaled_axis<SB>(axisangle: Vector<N, U3, SB>) -> Self
|
||
where SB: Storage<N, U3> {
|
||
Self::new(axisangle)
|
||
}
|
||
|
||
/// Creates a new unit quaternion rotation from a rotation axis scaled by the rotation angle.
|
||
///
|
||
/// If `axisangle` has a magnitude smaller than `eps`, this returns the identity rotation.
|
||
/// Same as `Self::new_eps(axisangle, eps)`.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # #[macro_use] extern crate approx;
|
||
/// # use std::f32;
|
||
/// # use nalgebra::{UnitQuaternion, Point3, Vector3};
|
||
/// let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
|
||
/// // Point and vector being transformed in the tests.
|
||
/// let pt = Point3::new(4.0, 5.0, 6.0);
|
||
/// let vec = Vector3::new(4.0, 5.0, 6.0);
|
||
/// let q = UnitQuaternion::from_scaled_axis_eps(axisangle, 1.0e-6);
|
||
///
|
||
/// assert_relative_eq!(q * pt, Point3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
|
||
/// assert_relative_eq!(q * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
|
||
///
|
||
/// // An almost zero vector yields an identity.
|
||
/// assert_eq!(UnitQuaternion::from_scaled_axis_eps(Vector3::new(1.0e-8, 1.0e-9, 1.0e-7), 1.0e-6), UnitQuaternion::identity());
|
||
/// ```
|
||
#[inline]
|
||
pub fn from_scaled_axis_eps<SB>(axisangle: Vector<N, U3, SB>, eps: N) -> Self
|
||
where SB: Storage<N, U3> {
|
||
Self::new_eps(axisangle, eps)
|
||
}
|
||
}
|
||
|
||
impl<N: Real> One for UnitQuaternion<N> {
|
||
#[inline]
|
||
fn one() -> Self {
|
||
Self::identity()
|
||
}
|
||
}
|
||
|
||
impl<N: Real> Distribution<UnitQuaternion<N>> for Standard
|
||
where OpenClosed01: Distribution<N>
|
||
{
|
||
/// Generate a uniformly distributed random rotation quaternion.
|
||
#[inline]
|
||
fn sample<'a, R: Rng + ?Sized>(&self, rng: &'a mut R) -> UnitQuaternion<N> {
|
||
// Ken Shoemake's Subgroup Algorithm
|
||
// Uniform random rotations.
|
||
// In D. Kirk, editor, Graphics Gems III, pages 124-132. Academic, New York, 1992.
|
||
let x0 = rng.sample(OpenClosed01);
|
||
let x1 = rng.sample(OpenClosed01);
|
||
let x2 = rng.sample(OpenClosed01);
|
||
let theta1 = N::two_pi() * x1;
|
||
let theta2 = N::two_pi() * x2;
|
||
let s1 = theta1.sin();
|
||
let c1 = theta1.cos();
|
||
let s2 = theta2.sin();
|
||
let c2 = theta2.cos();
|
||
let r1 = (N::one() - x0).sqrt();
|
||
let r2 = x0.sqrt();
|
||
Unit::new_unchecked(Quaternion::new(s1 * r1, c1 * r1, s2 * r2, c2 * r2))
|
||
}
|
||
}
|
||
|
||
#[cfg(feature = "arbitrary")]
|
||
impl<N: Real + Arbitrary> Arbitrary for UnitQuaternion<N>
|
||
where
|
||
Owned<N, U4>: Send,
|
||
Owned<N, U3>: Send,
|
||
{
|
||
#[inline]
|
||
fn arbitrary<G: Gen>(g: &mut G) -> Self {
|
||
let axisangle = Vector3::arbitrary(g);
|
||
Self::from_scaled_axis(axisangle)
|
||
}
|
||
}
|
||
|
||
#[cfg(test)]
|
||
mod tests {
|
||
extern crate rand_xorshift;
|
||
use super::*;
|
||
use rand::SeedableRng;
|
||
|
||
#[test]
|
||
fn random_unit_quats_are_unit() {
|
||
let mut rng = rand_xorshift::XorShiftRng::from_seed([0xAB; 16]);
|
||
for _ in 0..1000 {
|
||
let x = rng.gen::<UnitQuaternion<f32>>();
|
||
assert!(relative_eq!(x.into_inner().norm(), 1.0))
|
||
}
|
||
}
|
||
}
|