nalgebra/src/geometry/unit_complex_construction.rs
2020-04-05 18:49:48 +02:00

315 lines
10 KiB
Rust

#[cfg(feature = "arbitrary")]
use quickcheck::{Arbitrary, Gen};
use num::One;
use num_complex::Complex;
use rand::distributions::{Distribution, OpenClosed01, Standard};
use rand::Rng;
use crate::base::dimension::{U1, U2};
use crate::base::storage::Storage;
use crate::base::{Matrix2, Unit, Vector};
use crate::geometry::{Rotation2, UnitComplex};
use simba::scalar::RealField;
use simba::simd::SimdRealField;
impl<N: SimdRealField> UnitComplex<N>
where
N::Element: SimdRealField,
{
/// The unit complex number multiplicative identity.
///
/// # Example
/// ```
/// # use nalgebra::UnitComplex;
/// let rot1 = UnitComplex::identity();
/// let rot2 = UnitComplex::new(1.7);
///
/// assert_eq!(rot1 * rot2, rot2);
/// assert_eq!(rot2 * rot1, rot2);
/// ```
#[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 given angle.
///
/// # Example
///
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{UnitComplex, Point2};
/// let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
///
/// assert_relative_eq!(rot * Point2::new(3.0, 4.0), Point2::new(-4.0, 3.0));
/// ```
#[inline]
pub fn new(angle: N) -> Self {
let (sin, cos) = angle.simd_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)`.
///
/// # Example
///
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{UnitComplex, Point2};
/// let rot = UnitComplex::from_angle(f32::consts::FRAC_PI_2);
///
/// assert_relative_eq!(rot * Point2::new(3.0, 4.0), Point2::new(-4.0, 3.0));
/// ```
// FIXME: deprecate this.
#[inline]
pub fn from_angle(angle: N) -> Self {
Self::new(angle)
}
/// Builds the unit complex number from the sinus and cosinus of the rotation angle.
///
/// The input values are not checked to actually be cosines and sine of the same value.
/// Is is generally preferable to use the `::new(angle)` constructor instead.
///
/// # Example
///
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{UnitComplex, Vector2, Point2};
/// let angle = f32::consts::FRAC_PI_2;
/// let rot = UnitComplex::from_cos_sin_unchecked(angle.cos(), angle.sin());
///
/// assert_relative_eq!(rot * Point2::new(3.0, 4.0), Point2::new(-4.0, 3.0));
/// ```
#[inline]
pub fn from_cos_sin_unchecked(cos: N, sin: N) -> Self {
Self::new_unchecked(Complex::new(cos, sin))
}
/// Builds a unit complex rotation from an angle in radian wrapped in a 1-dimensional vector.
///
/// This is generally used in the context of generic programming. Using
/// the `::new(angle)` method instead is more common.
#[inline]
pub fn from_scaled_axis<SB: Storage<N, 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 norm of the complex number as well.
#[inline]
pub fn from_complex_and_get(q: Complex<N>) -> (Self, N) {
let norm = (q.im * q.im + q.re * q.re).simd_sqrt();
(Self::new_unchecked(q / norm), norm)
}
/// Builds the unit complex number from the corresponding 2D rotation matrix.
///
/// # Example
/// ```
/// # use nalgebra::{Rotation2, UnitComplex};
/// let rot = Rotation2::new(1.7);
/// let complex = UnitComplex::from_rotation_matrix(&rot);
/// assert_eq!(complex, UnitComplex::new(1.7));
/// ```
// FIXME: add UnitComplex::from(...) instead?
#[inline]
pub fn from_rotation_matrix(rotmat: &Rotation2<N>) -> Self {
Self::new_unchecked(Complex::new(rotmat[(0, 0)], rotmat[(1, 0)]))
}
/// Builds an unit complex by extracting the rotation part of the given transformation `m`.
///
/// This is an iterative method. See `.from_matrix_eps` to provide mover
/// convergence parameters and starting solution.
/// This implements "A Robust Method to Extract the Rotational Part of Deformations" by Müller et al.
pub fn from_matrix(m: &Matrix2<N>) -> Self
where
N: RealField,
{
Rotation2::from_matrix(m).into()
}
/// Builds an unit complex by extracting the rotation part of the given transformation `m`.
///
/// This implements "A Robust Method to Extract the Rotational Part of Deformations" by Müller et al.
///
/// # Parameters
///
/// * `m`: the matrix from which the rotational part is to be extracted.
/// * `eps`: the angular errors tolerated between the current rotation and the optimal one.
/// * `max_iter`: the maximum number of iterations. Loops indefinitely until convergence if set to `0`.
/// * `guess`: an estimate of the solution. Convergence will be significantly faster if an initial solution close
/// to the actual solution is provided. Can be set to `UnitQuaternion::identity()` if no other
/// guesses come to mind.
pub fn from_matrix_eps(m: &Matrix2<N>, eps: N, max_iter: usize, guess: Self) -> Self
where
N: RealField,
{
let guess = Rotation2::from(guess);
Rotation2::from_matrix_eps(m, eps, max_iter, guess).into()
}
/// The unit complex needed to make `a` and `b` be collinear and point toward the same
/// direction.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use nalgebra::{Vector2, UnitComplex};
/// let a = Vector2::new(1.0, 2.0);
/// let b = Vector2::new(2.0, 1.0);
/// let rot = UnitComplex::rotation_between(&a, &b);
/// assert_relative_eq!(rot * a, b);
/// assert_relative_eq!(rot.inverse() * b, a);
/// ```
#[inline]
pub fn rotation_between<SB, SC>(a: &Vector<N, U2, SB>, b: &Vector<N, U2, SC>) -> Self
where
N: RealField,
SB: Storage<N, U2>,
SC: Storage<N, U2>,
{
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`.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use nalgebra::{Vector2, UnitComplex};
/// let a = Vector2::new(1.0, 2.0);
/// let b = Vector2::new(2.0, 1.0);
/// let rot2 = UnitComplex::scaled_rotation_between(&a, &b, 0.2);
/// let rot5 = UnitComplex::scaled_rotation_between(&a, &b, 0.5);
/// assert_relative_eq!(rot2 * rot2 * rot2 * rot2 * rot2 * a, b, epsilon = 1.0e-6);
/// assert_relative_eq!(rot5 * rot5 * a, b, epsilon = 1.0e-6);
/// ```
#[inline]
pub fn scaled_rotation_between<SB, SC>(
a: &Vector<N, U2, SB>,
b: &Vector<N, U2, SC>,
s: N,
) -> Self
where
N: RealField,
SB: Storage<N, U2>,
SC: Storage<N, U2>,
{
// 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)
} else {
Self::identity()
}
}
/// The unit complex needed to make `a` and `b` be collinear and point toward the same
/// direction.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use nalgebra::{Unit, Vector2, UnitComplex};
/// let a = Unit::new_normalize(Vector2::new(1.0, 2.0));
/// let b = Unit::new_normalize(Vector2::new(2.0, 1.0));
/// let rot = UnitComplex::rotation_between_axis(&a, &b);
/// assert_relative_eq!(rot * a, b);
/// assert_relative_eq!(rot.inverse() * b, a);
/// ```
#[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`.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use nalgebra::{Unit, Vector2, UnitComplex};
/// let a = Unit::new_normalize(Vector2::new(1.0, 2.0));
/// let b = Unit::new_normalize(Vector2::new(2.0, 1.0));
/// let rot2 = UnitComplex::scaled_rotation_between_axis(&a, &b, 0.2);
/// let rot5 = UnitComplex::scaled_rotation_between_axis(&a, &b, 0.5);
/// assert_relative_eq!(rot2 * rot2 * rot2 * rot2 * rot2 * a, b, epsilon = 1.0e-6);
/// assert_relative_eq!(rot5 * rot5 * a, b, epsilon = 1.0e-6);
/// ```
#[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.simd_atan2(cang) * s)
}
}
impl<N: SimdRealField> One for UnitComplex<N>
where
N::Element: SimdRealField,
{
#[inline]
fn one() -> Self {
Self::identity()
}
}
impl<N: SimdRealField> Distribution<UnitComplex<N>> for Standard
where
N::Element: SimdRealField,
OpenClosed01: Distribution<N>,
{
/// Generate a uniformly distributed random `UnitComplex`.
#[inline]
fn sample<'a, R: Rng + ?Sized>(&self, rng: &mut R) -> UnitComplex<N> {
UnitComplex::from_angle(rng.sample(OpenClosed01) * N::simd_two_pi())
}
}
#[cfg(feature = "arbitrary")]
impl<N: SimdRealField + Arbitrary> Arbitrary for UnitComplex<N>
where
N::Element: SimdRealField,
{
#[inline]
fn arbitrary<G: Gen>(g: &mut G) -> Self {
UnitComplex::from_angle(N::arbitrary(g))
}
}