nalgebra/src/geometry/unit_complex_construction.rs

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#[cfg(feature = "arbitrary")]
use quickcheck::{Arbitrary, Gen};
use num::One;
use num_complex::Complex;
use rand::{Rand, Rng};
use alga::general::Real;
use core::{DefaultAllocator, Unit, Vector};
use core::dimension::{U1, U2};
use core::storage::Storage;
use core::allocator::Allocator;
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use geometry::{Rotation, UnitComplex};
impl<N: Real> UnitComplex<N> {
/// The unit complex number multiplicative identity.
#[inline]
pub fn identity() -> Self {
Self::new_unchecked(Complex::new(N::one(), N::zero()))
}
/// Builds the unit complex number corresponding to the rotation with the angle.
#[inline]
pub fn new(angle: N) -> Self {
let (sin, cos) = angle.sin_cos();
Self::from_cos_sin_unchecked(cos, sin)
}
/// Builds the unit complex number corresponding to the rotation with the angle.
///
/// Same as `Self::new(angle)`.
#[inline]
pub fn from_angle(angle: N) -> Self {
Self::new(angle)
}
/// Builds the unit complex number frow the sinus and cosinus of the rotation angle.
///
/// The input values are not checked.
#[inline]
pub fn from_cos_sin_unchecked(cos: N, sin: N) -> Self {
UnitComplex::new_unchecked(Complex::new(cos, sin))
}
/// Builds a unit complex rotation from an angle in radian wrapped in a 1-dimensional vector.
///
/// Equivalent to `Self::new(axisangle[0])`.
#[inline]
pub fn from_scaled_axis<SB: Storage<N, U1, U1>>(axisangle: Vector<N, U1, SB>) -> Self {
Self::from_angle(axisangle[0])
}
/// Creates a new unit complex number from a complex number.
///
/// The input complex number will be normalized.
#[inline]
pub fn from_complex(q: Complex<N>) -> Self {
Self::from_complex_and_get(q).0
}
/// Creates a new unit complex number from a complex number.
///
/// The input complex number will be normalized. Returns the complex number norm as well.
#[inline]
pub fn from_complex_and_get(q: Complex<N>) -> (Self, N) {
let norm = (q.im * q.im + q.re * q.re).sqrt();
(Self::new_unchecked(q / norm), norm)
}
/// Builds the unit complex number from the corresponding 2D rotation matrix.
#[inline]
pub fn from_rotation_matrix(rotmat: &Rotation<N, U2>) -> Self
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where
DefaultAllocator: Allocator<N, U2, U2>,
{
Self::new_unchecked(Complex::new(rotmat[(0, 0)], rotmat[(1, 0)]))
}
/// The unit complex needed to make `a` and `b` be collinear and point toward the same
/// direction.
#[inline]
pub fn rotation_between<SB, SC>(a: &Vector<N, U2, SB>, b: &Vector<N, U2, SC>) -> Self
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where
SB: Storage<N, U2, U1>,
SC: Storage<N, U2, U1>,
{
Self::scaled_rotation_between(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`.
#[inline]
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pub fn scaled_rotation_between<SB, SC>(
a: &Vector<N, U2, SB>,
b: &Vector<N, U2, SC>,
s: N,
) -> Self
where
SB: Storage<N, U2, U1>,
SC: Storage<N, U2, U1>,
{
// FIXME: code duplication with Rotation.
if let (Some(na), Some(nb)) = (
Unit::try_new(a.clone_owned(), N::zero()),
Unit::try_new(b.clone_owned(), N::zero()),
) {
Self::scaled_rotation_between_axis(&na, &nb, s)
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} else {
Self::identity()
}
}
/// The unit complex needed to make `a` and `b` be collinear and point toward the same
/// direction.
#[inline]
pub fn rotation_between_axis<SB, SC>(
a: &Unit<Vector<N, U2, SB>>,
b: &Unit<Vector<N, U2, SC>>,
) -> Self
where
SB: Storage<N, U2>,
SC: Storage<N, U2>,
{
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`.
#[inline]
pub fn scaled_rotation_between_axis<SB, SC>(
na: &Unit<Vector<N, U2, SB>>,
nb: &Unit<Vector<N, U2, SC>>,
s: N,
) -> Self
where
SB: Storage<N, U2>,
SC: Storage<N, U2>,
{
let sang = na.perp(&nb);
let cang = na.dot(&nb);
Self::from_angle(sang.atan2(cang) * s)
}
}
impl<N: Real> One for UnitComplex<N> {
#[inline]
fn one() -> Self {
Self::identity()
}
}
impl<N: Real + Rand> Rand for UnitComplex<N> {
#[inline]
fn rand<R: Rng>(rng: &mut R) -> Self {
UnitComplex::from_angle(N::rand(rng))
}
}
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#[cfg(feature = "arbitrary")]
impl<N: Real + Arbitrary> Arbitrary for UnitComplex<N> {
#[inline]
fn arbitrary<G: Gen>(g: &mut G) -> Self {
UnitComplex::from_angle(N::arbitrary(g))
}
}