108 lines
3.2 KiB
Rust
108 lines
3.2 KiB
Rust
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#[cfg(feature = "arbitrary")]
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use quickcheck::{Arbitrary, Gen};
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use num::One;
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use num_complex::Complex;
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use rand::{Rand, Rng};
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use alga::general::Real;
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use core::ColumnVector;
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use core::dimension::{U1, U2};
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use core::storage::Storage;
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use geometry::{UnitComplex, RotationBase};
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impl<N: Real> UnitComplex<N> {
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/// The unit complex number multiplicative identity.
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#[inline]
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pub fn identity() -> Self {
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Self::new_unchecked(Complex::new(N::one(), N::zero()))
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}
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/// Builds the unit complex number corresponding to the rotation with the angle.
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#[inline]
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pub fn new(angle: N) -> Self {
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let (s, c) = angle.sin_cos();
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UnitComplex::new_unchecked(Complex::new(c, s))
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}
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/// Builds the unit complex number corresponding to the rotation with the angle.
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///
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/// Same as `Self::new(angle)`.
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#[inline]
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pub fn from_angle(angle: N) -> Self {
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Self::new(angle)
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}
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/// Builds a unit complex rotation from an angle in radian wrapped in a 1-dimensional vector.
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///
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/// Equivalent to `Self::new(axisangle[0])`.
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#[inline]
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pub fn from_scaled_axis<SB: Storage<N, U1, U1>>(axisangle: ColumnVector<N, U1, SB>) -> Self {
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Self::from_angle(axisangle[0])
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}
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/// Creates a new unit complex number from a complex number.
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///
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/// The input complex number will be normalized.
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#[inline]
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pub fn from_complex(q: Complex<N>) -> Self {
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Self::new_unchecked(q / (q.im * q.im + q.re * q.re).sqrt())
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}
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/// Builds the unit complex number from the corresponding 2D rotation matrix.
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#[inline]
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pub fn from_rotation_matrix<S: Storage<N, U2, U2>>(rotmat: &RotationBase<N, U2, S>) -> Self {
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Self::new_unchecked(Complex::new(rotmat[(0, 0)], rotmat[(1, 0)]))
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}
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/// The unit complex needed to make `a` and `b` be collinear and point toward the same
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/// direction.
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#[inline]
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pub fn rotation_between<SB, SC>(a: &ColumnVector<N, U2, SB>, b: &ColumnVector<N, U2, SC>) -> Self
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where SB: Storage<N, U2, U1>,
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SC: Storage<N, U2, U1> {
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Self::scaled_rotation_between(a, b, N::one())
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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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#[inline]
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pub fn scaled_rotation_between<SB, SC>(a: &ColumnVector<N, U2, SB>, b: &ColumnVector<N, U2, SC>, s: N) -> Self
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where SB: Storage<N, U2, U1>,
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SC: Storage<N, U2, U1> {
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if let (Some(na), Some(nb)) = (a.try_normalize(N::zero()), b.try_normalize(N::zero())) {
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let sang = na.perp(&nb);
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let cang = na.dot(&nb);
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Self::from_angle(sang.atan2(cang) * s)
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}
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else {
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Self::identity()
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}
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}
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}
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impl<N: Real> One for UnitComplex<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 + Rand> Rand for UnitComplex<N> {
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#[inline]
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fn rand<R: Rng>(rng: &mut R) -> Self {
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UnitComplex::from_angle(N::rand(rng))
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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 UnitComplex<N> {
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#[inline]
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fn arbitrary<G: Gen>(g: &mut G) -> Self {
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UnitComplex::from_angle(N::arbitrary(g))
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}
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}
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