<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="Source of the Rust file `/Users/erlendbasso/.cargo/registry/src/github.com-1ecc6299db9ec823/nalgebra-0.32.1/src/geometry/unit_complex_construction.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>unit_complex_construction.rs - source</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceSerif4-Regular-1f7d512b176f0f72.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/FiraSans-Regular-018c141bf0843ffd.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/FiraSans-Medium-8f9a781e4970d388.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceCodePro-Regular-562dcc5011b6de7d.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceSerif4-Bold-124a1ca42af929b6.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceCodePro-Semibold-d899c5a5c4aeb14a.ttf.woff2"><link rel="stylesheet" href="../../../static.files/normalize-76eba96aa4d2e634.css"><link rel="stylesheet" href="../../../static.files/rustdoc-6827029ac823cab7.css" id="mainThemeStyle"><link rel="stylesheet" id="themeStyle" href="../../../static.files/light-ebce58d0a40c3431.css"><link rel="stylesheet" disabled href="../../../static.files/dark-f23faae4a2daf9a6.css"><link rel="stylesheet" disabled href="../../../static.files/ayu-8af5e100b21cd173.css"><script id="default-settings" ></script><script src="../../../static.files/storage-d43fa987303ecbbb.js"></script><script defer src="../../../static.files/source-script-5cf2e01a42cc9858.js"></script><script defer src="../../../source-files.js"></script><script defer src="../../../static.files/main-c55e1eb52e1886b4.js"></script><noscript><link rel="stylesheet" href="../../../static.files/noscript-13285aec31fa243e.css"></noscript><link rel="icon" href="https://nalgebra.org/img/favicon.ico"></head><body class="rustdoc source"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"></nav><main><div class="width-limiter"><nav class="sub"><a class="sub-logo-container" href="../../../nalgebra/index.html"><img class="rust-logo" src="../../../static.files/rust-logo-151179464ae7ed46.svg" alt="logo"></a><form class="search-form"><span></span><input class="search-input" name="search" aria-label="Run search in the documentation" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" title="help" tabindex="-1"><a href="../../../help.html">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../../static.files/wheel-5ec35bf9ca753509.svg"></a></div></form></nav><section id="main-content" class="content"><div class="example-wrap"><pre class="src-line-numbers"><a href="#1" id="1">1</a>
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</pre><pre class="rust"><code><span class="attr">#[cfg(feature = <span class="string">"arbitrary"</span>)]
</span><span class="kw">use </span>quickcheck::{Arbitrary, Gen};
<span class="attr">#[cfg(feature = <span class="string">"rand-no-std"</span>)]
</span><span class="kw">use </span>rand::{
distributions::{Distribution, Standard},
Rng,
};
<span class="kw">use </span>num::One;
<span class="kw">use </span>num_complex::Complex;
<span class="kw">use </span><span class="kw">crate</span>::base::dimension::{U1, U2};
<span class="kw">use </span><span class="kw">crate</span>::base::storage::Storage;
<span class="kw">use </span><span class="kw">crate</span>::base::{Matrix2, Scalar, Unit, Vector, Vector2};
<span class="kw">use </span><span class="kw">crate</span>::geometry::{Rotation2, UnitComplex};
<span class="kw">use </span>simba::scalar::{RealField, SupersetOf};
<span class="kw">use </span>simba::simd::SimdRealField;
<span class="kw">impl</span><T: SimdRealField> Default <span class="kw">for </span>UnitComplex<T>
<span class="kw">where
</span>T::Element: SimdRealField,
{
<span class="kw">fn </span>default() -> <span class="self">Self </span>{
<span class="self">Self</span>::identity()
}
}
<span class="doccomment">/// # Identity
</span><span class="kw">impl</span><T: SimdRealField> UnitComplex<T>
<span class="kw">where
</span>T::Element: SimdRealField,
{
<span class="doccomment">/// 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);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>identity() -> <span class="self">Self </span>{
<span class="self">Self</span>::new_unchecked(Complex::new(T::one(), T::zero()))
}
}
<span class="doccomment">/// # Construction from a 2D rotation angle
</span><span class="kw">impl</span><T: SimdRealField> UnitComplex<T>
<span class="kw">where
</span>T::Element: SimdRealField,
{
<span class="doccomment">/// 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));
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>new(angle: T) -> <span class="self">Self </span>{
<span class="kw">let </span>(sin, cos) = angle.simd_sin_cos();
<span class="self">Self</span>::from_cos_sin_unchecked(cos, sin)
}
<span class="doccomment">/// 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));
/// ```
</span><span class="comment">// TODO: deprecate this.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>from_angle(angle: T) -> <span class="self">Self </span>{
<span class="self">Self</span>::new(angle)
}
<span class="doccomment">/// 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));
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>from_cos_sin_unchecked(cos: T, sin: T) -> <span class="self">Self </span>{
<span class="self">Self</span>::new_unchecked(Complex::new(cos, sin))
}
<span class="doccomment">/// 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.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>from_scaled_axis<SB: Storage<T, U1>>(axisangle: Vector<T, U1, SB>) -> <span class="self">Self </span>{
<span class="self">Self</span>::from_angle(axisangle[<span class="number">0</span>].clone())
}
}
<span class="doccomment">/// # Construction from an existing 2D matrix or complex number
</span><span class="kw">impl</span><T: SimdRealField> UnitComplex<T>
<span class="kw">where
</span>T::Element: SimdRealField,
{
<span class="doccomment">/// Cast the components of `self` to another type.
///
/// # Example
/// ```
/// #[macro_use] extern crate approx;
/// # use nalgebra::UnitComplex;
/// let c = UnitComplex::new(1.0f64);
/// let c2 = c.cast::<f32>();
/// assert_relative_eq!(c2, UnitComplex::new(1.0f32));
/// ```
</span><span class="kw">pub fn </span>cast<To: Scalar>(<span class="self">self</span>) -> UnitComplex<To>
<span class="kw">where
</span>UnitComplex<To>: SupersetOf<<span class="self">Self</span>>,
{
<span class="kw">crate</span>::convert(<span class="self">self</span>)
}
<span class="doccomment">/// The underlying complex number.
///
/// Same as `self.as_ref()`.
///
/// # Example
/// ```
/// # extern crate num_complex;
/// # use num_complex::Complex;
/// # use nalgebra::UnitComplex;
/// let angle = 1.78f32;
/// let rot = UnitComplex::new(angle);
/// assert_eq!(*rot.complex(), Complex::new(angle.cos(), angle.sin()));
/// ```
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>complex(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="kw-2">&</span>Complex<T> {
<span class="self">self</span>.as_ref()
}
<span class="doccomment">/// Creates a new unit complex number from a complex number.
///
/// The input complex number will be normalized.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>from_complex(q: Complex<T>) -> <span class="self">Self </span>{
<span class="self">Self</span>::from_complex_and_get(q).<span class="number">0
</span>}
<span class="doccomment">/// 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.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>from_complex_and_get(q: Complex<T>) -> (<span class="self">Self</span>, T) {
<span class="kw">let </span>norm = (q.im.clone() * q.im.clone() + q.re.clone() * q.re.clone()).simd_sqrt();
(<span class="self">Self</span>::new_unchecked(q / norm.clone()), norm)
}
<span class="doccomment">/// 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));
/// ```
</span><span class="comment">// TODO: add UnitComplex::from(...) instead?
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>from_rotation_matrix(rotmat: <span class="kw-2">&</span>Rotation2<T>) -> <span class="self">Self </span>{
<span class="self">Self</span>::new_unchecked(Complex::new(rotmat[(<span class="number">0</span>, <span class="number">0</span>)].clone(), rotmat[(<span class="number">1</span>, <span class="number">0</span>)].clone()))
}
<span class="doccomment">/// Builds a rotation from a basis assumed to be orthonormal.
///
/// In order to get a valid unit-quaternion, the input must be an
/// orthonormal basis, i.e., all vectors are normalized, and the are
/// all orthogonal to each other. These invariants are not checked
/// by this method.
</span><span class="kw">pub fn </span>from_basis_unchecked(basis: <span class="kw-2">&</span>[Vector2<T>; <span class="number">2</span>]) -> <span class="self">Self </span>{
<span class="kw">let </span>mat = Matrix2::from_columns(<span class="kw-2">&</span>basis[..]);
<span class="kw">let </span>rot = Rotation2::from_matrix_unchecked(mat);
<span class="self">Self</span>::from_rotation_matrix(<span class="kw-2">&</span>rot)
}
<span class="doccomment">/// 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.
</span><span class="kw">pub fn </span>from_matrix(m: <span class="kw-2">&</span>Matrix2<T>) -> <span class="self">Self
</span><span class="kw">where
</span>T: RealField,
{
Rotation2::from_matrix(m).into()
}
<span class="doccomment">/// 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.
</span><span class="kw">pub fn </span>from_matrix_eps(m: <span class="kw-2">&</span>Matrix2<T>, eps: T, max_iter: usize, guess: <span class="self">Self</span>) -> <span class="self">Self
</span><span class="kw">where
</span>T: RealField,
{
<span class="kw">let </span>guess = Rotation2::from(guess);
Rotation2::from_matrix_eps(m, eps, max_iter, guess).into()
}
<span class="doccomment">/// The unit complex number needed to make `self` and `other` coincide.
///
/// The result is such that: `self.rotation_to(other) * self == other`.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use nalgebra::UnitComplex;
/// let rot1 = UnitComplex::new(0.1);
/// let rot2 = UnitComplex::new(1.7);
/// let rot_to = rot1.rotation_to(&rot2);
///
/// assert_relative_eq!(rot_to * rot1, rot2);
/// assert_relative_eq!(rot_to.inverse() * rot2, rot1);
/// ```
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>rotation_to(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>) -> <span class="self">Self </span>{
other / <span class="self">self
</span>}
<span class="doccomment">/// Raise this unit complex number to a given floating power.
///
/// This returns the unit complex number that identifies a rotation angle equal to
/// `self.angle() × n`.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use nalgebra::UnitComplex;
/// let rot = UnitComplex::new(0.78);
/// let pow = rot.powf(2.0);
/// assert_relative_eq!(pow.angle(), 2.0 * 0.78);
/// ```
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>powf(<span class="kw-2">&</span><span class="self">self</span>, n: T) -> <span class="self">Self </span>{
<span class="self">Self</span>::from_angle(<span class="self">self</span>.angle() * n)
}
}
<span class="doccomment">/// # Construction from two vectors
</span><span class="kw">impl</span><T: SimdRealField> UnitComplex<T>
<span class="kw">where
</span>T::Element: SimdRealField,
{
<span class="doccomment">/// 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);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>rotation_between<SB, SC>(a: <span class="kw-2">&</span>Vector<T, U2, SB>, b: <span class="kw-2">&</span>Vector<T, U2, SC>) -> <span class="self">Self
</span><span class="kw">where
</span>T: RealField,
SB: Storage<T, U2>,
SC: Storage<T, U2>,
{
<span class="self">Self</span>::scaled_rotation_between(a, b, T::one())
}
<span class="doccomment">/// 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);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>scaled_rotation_between<SB, SC>(
a: <span class="kw-2">&</span>Vector<T, U2, SB>,
b: <span class="kw-2">&</span>Vector<T, U2, SC>,
s: T,
) -> <span class="self">Self
</span><span class="kw">where
</span>T: RealField,
SB: Storage<T, U2>,
SC: Storage<T, U2>,
{
<span class="comment">// TODO: code duplication with Rotation.
</span><span class="kw">if let </span>(<span class="prelude-val">Some</span>(na), <span class="prelude-val">Some</span>(nb)) = (
Unit::try_new(a.clone_owned(), T::zero()),
Unit::try_new(b.clone_owned(), T::zero()),
) {
<span class="self">Self</span>::scaled_rotation_between_axis(<span class="kw-2">&</span>na, <span class="kw-2">&</span>nb, s)
} <span class="kw">else </span>{
<span class="self">Self</span>::identity()
}
}
<span class="doccomment">/// 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);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>rotation_between_axis<SB, SC>(
a: <span class="kw-2">&</span>Unit<Vector<T, U2, SB>>,
b: <span class="kw-2">&</span>Unit<Vector<T, U2, SC>>,
) -> <span class="self">Self
</span><span class="kw">where
</span>SB: Storage<T, U2>,
SC: Storage<T, U2>,
{
<span class="self">Self</span>::scaled_rotation_between_axis(a, b, T::one())
}
<span class="doccomment">/// 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);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>scaled_rotation_between_axis<SB, SC>(
na: <span class="kw-2">&</span>Unit<Vector<T, U2, SB>>,
nb: <span class="kw-2">&</span>Unit<Vector<T, U2, SC>>,
s: T,
) -> <span class="self">Self
</span><span class="kw">where
</span>SB: Storage<T, U2>,
SC: Storage<T, U2>,
{
<span class="kw">let </span>sang = na.perp(nb);
<span class="kw">let </span>cang = na.dot(nb);
<span class="self">Self</span>::from_angle(sang.simd_atan2(cang) * s)
}
}
<span class="kw">impl</span><T: SimdRealField> One <span class="kw">for </span>UnitComplex<T>
<span class="kw">where
</span>T::Element: SimdRealField,
{
<span class="attr">#[inline]
</span><span class="kw">fn </span>one() -> <span class="self">Self </span>{
<span class="self">Self</span>::identity()
}
}
<span class="attr">#[cfg(feature = <span class="string">"rand"</span>)]
</span><span class="kw">impl</span><T: SimdRealField> Distribution<UnitComplex<T>> <span class="kw">for </span>Standard
<span class="kw">where
</span>T::Element: SimdRealField,
rand_distr::UnitCircle: Distribution<[T; <span class="number">2</span>]>,
{
<span class="doccomment">/// Generate a uniformly distributed random `UnitComplex`.
</span><span class="attr">#[inline]
</span><span class="kw">fn </span>sample<<span class="lifetime">'a</span>, R: Rng + <span class="question-mark">?</span>Sized>(<span class="kw-2">&</span><span class="self">self</span>, rng: <span class="kw-2">&mut </span>R) -> UnitComplex<T> {
<span class="kw">let </span>x = rng.sample(rand_distr::UnitCircle);
UnitComplex::new_unchecked(Complex::new(x[<span class="number">0</span>].clone(), x[<span class="number">1</span>].clone()))
}
}
<span class="attr">#[cfg(feature = <span class="string">"arbitrary"</span>)]
</span><span class="kw">impl</span><T: SimdRealField + Arbitrary> Arbitrary <span class="kw">for </span>UnitComplex<T>
<span class="kw">where
</span>T::Element: SimdRealField,
{
<span class="attr">#[inline]
</span><span class="kw">fn </span>arbitrary(g: <span class="kw-2">&mut </span>Gen) -> <span class="self">Self </span>{
UnitComplex::from_angle(T::arbitrary(g))
}
}
</code></pre></div>
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