295 lines
10 KiB
Rust
295 lines
10 KiB
Rust
#[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::distributions::{Distribution, OpenClosed01, Standard};
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use rand::Rng;
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use alga::general::Real;
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use crate::base::dimension::{U1, U2};
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use crate::base::storage::Storage;
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use crate::base::{Unit, Vector, Matrix2};
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use crate::geometry::{Rotation2, UnitComplex};
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impl<N: Real> UnitComplex<N> {
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/// The unit complex number multiplicative identity.
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///
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/// # Example
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/// ```
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/// # use nalgebra::UnitComplex;
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/// let rot1 = UnitComplex::identity();
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/// let rot2 = UnitComplex::new(1.7);
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///
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/// assert_eq!(rot1 * rot2, rot2);
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/// assert_eq!(rot2 * rot1, rot2);
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/// ```
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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 given angle.
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///
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/// # Example
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///
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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::{UnitComplex, Point2};
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/// let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
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///
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/// assert_relative_eq!(rot * Point2::new(3.0, 4.0), Point2::new(-4.0, 3.0));
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/// ```
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#[inline]
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pub fn new(angle: N) -> Self {
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let (sin, cos) = angle.sin_cos();
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Self::from_cos_sin_unchecked(cos, sin)
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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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///
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/// # Example
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///
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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::{UnitComplex, Point2};
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/// let rot = UnitComplex::from_angle(f32::consts::FRAC_PI_2);
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///
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/// assert_relative_eq!(rot * Point2::new(3.0, 4.0), Point2::new(-4.0, 3.0));
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/// ```
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// FIXME: deprecate this.
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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 the unit complex number from the sinus and cosinus of the rotation angle.
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///
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/// The input values are not checked to actually be cosines and sine of the same value.
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/// Is is generally preferable to use the `::new(angle)` constructor instead.
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///
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/// # Example
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///
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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::{UnitComplex, Vector2, Point2};
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/// let angle = f32::consts::FRAC_PI_2;
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/// let rot = UnitComplex::from_cos_sin_unchecked(angle.cos(), angle.sin());
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///
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/// assert_relative_eq!(rot * Point2::new(3.0, 4.0), Point2::new(-4.0, 3.0));
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/// ```
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#[inline]
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pub fn from_cos_sin_unchecked(cos: N, sin: N) -> Self {
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Self::new_unchecked(Complex::new(cos, sin))
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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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/// This is generally used in the context of generic programming. Using
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/// the `::new(angle)` method instead is more common.
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#[inline]
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pub fn from_scaled_axis<SB: Storage<N, U1>>(axisangle: Vector<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::from_complex_and_get(q).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. Returns the norm of the complex number as well.
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#[inline]
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pub fn from_complex_and_get(q: Complex<N>) -> (Self, N) {
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let norm = (q.im * q.im + q.re * q.re).sqrt();
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(Self::new_unchecked(q / norm), norm)
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}
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/// Builds the unit complex number from the corresponding 2D rotation matrix.
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///
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/// # Example
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/// ```
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/// # use nalgebra::{Rotation2, UnitComplex};
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/// let rot = Rotation2::new(1.7);
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/// let complex = UnitComplex::from_rotation_matrix(&rot);
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/// assert_eq!(complex, UnitComplex::new(1.7));
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/// ```
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// FIXME: add UnitComplex::from(...) instead?
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#[inline]
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pub fn from_rotation_matrix(rotmat: &Rotation2<N>) -> Self {
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Self::new_unchecked(Complex::new(rotmat[(0, 0)], rotmat[(1, 0)]))
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}
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/// Builds an unit complex 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: &Matrix2<N>) -> Self {
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Rotation2::from_matrix(m).into()
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}
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/// Builds an unit complex 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: &Matrix2<N>, eps: N, max_iter: usize, guess: Self) -> Self {
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let guess = Rotation2::from(guess);
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Rotation2::from_matrix_eps(m, eps, max_iter, guess).into()
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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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///
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/// # Example
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/// ```
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/// # #[macro_use] extern crate approx;
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/// # use nalgebra::{Vector2, UnitComplex};
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/// let a = Vector2::new(1.0, 2.0);
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/// let b = Vector2::new(2.0, 1.0);
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/// let rot = UnitComplex::rotation_between(&a, &b);
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/// assert_relative_eq!(rot * a, b);
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/// assert_relative_eq!(rot.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, U2, SB>, b: &Vector<N, U2, SC>) -> Self
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where
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SB: Storage<N, U2>,
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SC: Storage<N, U2>,
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{
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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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///
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/// # Example
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/// ```
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/// # #[macro_use] extern crate approx;
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/// # use nalgebra::{Vector2, UnitComplex};
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/// let a = Vector2::new(1.0, 2.0);
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/// let b = Vector2::new(2.0, 1.0);
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/// let rot2 = UnitComplex::scaled_rotation_between(&a, &b, 0.2);
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/// let rot5 = UnitComplex::scaled_rotation_between(&a, &b, 0.5);
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/// assert_relative_eq!(rot2 * rot2 * rot2 * rot2 * rot2 * a, b, epsilon = 1.0e-6);
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/// assert_relative_eq!(rot5 * rot5 * a, b, epsilon = 1.0e-6);
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/// ```
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#[inline]
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pub fn scaled_rotation_between<SB, SC>(
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a: &Vector<N, U2, SB>,
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b: &Vector<N, U2, SC>,
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s: N,
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) -> Self
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where
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SB: Storage<N, U2>,
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SC: Storage<N, U2>,
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{
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// FIXME: code duplication with Rotation.
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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()),
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) {
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Self::scaled_rotation_between_axis(&na, &nb, s)
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} else {
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Self::identity()
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}
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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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///
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/// # Example
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/// ```
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/// # #[macro_use] extern crate approx;
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/// # use nalgebra::{Unit, Vector2, UnitComplex};
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/// let a = Unit::new_normalize(Vector2::new(1.0, 2.0));
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/// let b = Unit::new_normalize(Vector2::new(2.0, 1.0));
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/// let rot = UnitComplex::rotation_between_axis(&a, &b);
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/// assert_relative_eq!(rot * a, b);
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/// assert_relative_eq!(rot.inverse() * b, a);
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/// ```
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#[inline]
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pub fn rotation_between_axis<SB, SC>(
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a: &Unit<Vector<N, U2, SB>>,
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b: &Unit<Vector<N, U2, SC>>,
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) -> Self
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where
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SB: Storage<N, U2>,
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SC: Storage<N, U2>,
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{
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Self::scaled_rotation_between_axis(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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///
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/// # Example
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/// ```
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/// # #[macro_use] extern crate approx;
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/// # use nalgebra::{Unit, Vector2, UnitComplex};
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/// let a = Unit::new_normalize(Vector2::new(1.0, 2.0));
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/// let b = Unit::new_normalize(Vector2::new(2.0, 1.0));
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/// let rot2 = UnitComplex::scaled_rotation_between_axis(&a, &b, 0.2);
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/// let rot5 = UnitComplex::scaled_rotation_between_axis(&a, &b, 0.5);
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/// assert_relative_eq!(rot2 * rot2 * rot2 * rot2 * rot2 * a, b, epsilon = 1.0e-6);
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/// assert_relative_eq!(rot5 * rot5 * a, b, epsilon = 1.0e-6);
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/// ```
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#[inline]
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pub fn scaled_rotation_between_axis<SB, SC>(
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na: &Unit<Vector<N, U2, SB>>,
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nb: &Unit<Vector<N, U2, SC>>,
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s: N,
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) -> Self
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where
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SB: Storage<N, U2>,
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SC: Storage<N, U2>,
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{
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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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}
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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> Distribution<UnitComplex<N>> for Standard
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where OpenClosed01: Distribution<N>
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{
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/// Generate a uniformly distributed random `UnitComplex`.
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#[inline]
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fn sample<'a, R: Rng + ?Sized>(&self, rng: &mut R) -> UnitComplex<N> {
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UnitComplex::from_angle(rng.sample(OpenClosed01) * N::two_pi())
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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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