376 lines
11 KiB
Rust
Executable File
376 lines
11 KiB
Rust
Executable File
use approx::{AbsDiffEq, RelativeEq, UlpsEq};
|
||
use num_complex::Complex;
|
||
use std::fmt;
|
||
|
||
use alga::general::RealField;
|
||
use crate::base::{Matrix2, Matrix3, Unit, Vector1, Vector2};
|
||
use crate::geometry::{Rotation2, Point2};
|
||
|
||
/// A complex number with a norm equal to 1.
|
||
pub type UnitComplex<N> = Unit<Complex<N>>;
|
||
|
||
impl<N: RealField> UnitComplex<N> {
|
||
/// The rotation angle in `]-pi; pi]` of this unit complex number.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # use nalgebra::UnitComplex;
|
||
/// let rot = UnitComplex::new(1.78);
|
||
/// assert_eq!(rot.angle(), 1.78);
|
||
/// ```
|
||
#[inline]
|
||
pub fn angle(&self) -> N {
|
||
self.im.atan2(self.re)
|
||
}
|
||
|
||
/// The sine of the rotation angle.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # use nalgebra::UnitComplex;
|
||
/// let angle = 1.78f32;
|
||
/// let rot = UnitComplex::new(angle);
|
||
/// assert_eq!(rot.sin_angle(), angle.sin());
|
||
/// ```
|
||
#[inline]
|
||
pub fn sin_angle(&self) -> N {
|
||
self.im
|
||
}
|
||
|
||
/// The cosine of the rotation angle.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # use nalgebra::UnitComplex;
|
||
/// let angle = 1.78f32;
|
||
/// let rot = UnitComplex::new(angle);
|
||
/// assert_eq!(rot.cos_angle(),angle.cos());
|
||
/// ```
|
||
#[inline]
|
||
pub fn cos_angle(&self) -> N {
|
||
self.re
|
||
}
|
||
|
||
/// The rotation angle returned as a 1-dimensional vector.
|
||
///
|
||
/// This is generally used in the context of generic programming. Using
|
||
/// the `.angle()` method instead is more common.
|
||
#[inline]
|
||
pub fn scaled_axis(&self) -> Vector1<N> {
|
||
Vector1::new(self.angle())
|
||
}
|
||
|
||
/// The rotation axis and angle in ]0, pi] of this complex number.
|
||
///
|
||
/// This is generally used in the context of generic programming. Using
|
||
/// the `.angle()` method instead is more common.
|
||
/// Returns `None` if the angle is zero.
|
||
#[inline]
|
||
pub fn axis_angle(&self) -> Option<(Unit<Vector1<N>>, N)> {
|
||
let ang = self.angle();
|
||
|
||
if ang.is_zero() {
|
||
None
|
||
} else if ang.is_sign_negative() {
|
||
Some((Unit::new_unchecked(Vector1::x()), -ang))
|
||
} else {
|
||
Some((Unit::new_unchecked(-Vector1::<N>::x()), ang))
|
||
}
|
||
}
|
||
|
||
/// 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()));
|
||
/// ```
|
||
#[inline]
|
||
pub fn complex(&self) -> &Complex<N> {
|
||
self.as_ref()
|
||
}
|
||
|
||
/// Compute the conjugate of this unit complex number.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # use nalgebra::UnitComplex;
|
||
/// let rot = UnitComplex::new(1.78);
|
||
/// let conj = rot.conjugate();
|
||
/// assert_eq!(rot.complex().im, -conj.complex().im);
|
||
/// assert_eq!(rot.complex().re, conj.complex().re);
|
||
/// ```
|
||
#[inline]
|
||
pub fn conjugate(&self) -> Self {
|
||
Self::new_unchecked(self.conj())
|
||
}
|
||
|
||
/// Inverts this complex number if it is not zero.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # #[macro_use] extern crate approx;
|
||
/// # use nalgebra::UnitComplex;
|
||
/// let rot = UnitComplex::new(1.2);
|
||
/// let inv = rot.inverse();
|
||
/// assert_relative_eq!(rot * inv, UnitComplex::identity(), epsilon = 1.0e-6);
|
||
/// assert_relative_eq!(inv * rot, UnitComplex::identity(), epsilon = 1.0e-6);
|
||
/// ```
|
||
#[inline]
|
||
pub fn inverse(&self) -> Self {
|
||
self.conjugate()
|
||
}
|
||
|
||
/// The rotation angle needed to make `self` and `other` coincide.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # #[macro_use] extern crate approx;
|
||
/// # use nalgebra::UnitComplex;
|
||
/// let rot1 = UnitComplex::new(0.1);
|
||
/// let rot2 = UnitComplex::new(1.7);
|
||
/// assert_relative_eq!(rot1.angle_to(&rot2), 1.6);
|
||
/// ```
|
||
#[inline]
|
||
pub fn angle_to(&self, other: &Self) -> N {
|
||
let delta = self.rotation_to(other);
|
||
delta.angle()
|
||
}
|
||
|
||
/// 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);
|
||
/// ```
|
||
#[inline]
|
||
pub fn rotation_to(&self, other: &Self) -> Self {
|
||
other / self
|
||
}
|
||
|
||
/// Compute in-place the conjugate of this unit complex number.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # #[macro_use] extern crate approx;
|
||
/// # use nalgebra::UnitComplex;
|
||
/// let angle = 1.7;
|
||
/// let rot = UnitComplex::new(angle);
|
||
/// let mut conj = UnitComplex::new(angle);
|
||
/// conj.conjugate_mut();
|
||
/// assert_eq!(rot.complex().im, -conj.complex().im);
|
||
/// assert_eq!(rot.complex().re, conj.complex().re);
|
||
/// ```
|
||
#[inline]
|
||
pub fn conjugate_mut(&mut self) {
|
||
let me = self.as_mut_unchecked();
|
||
me.im = -me.im;
|
||
}
|
||
|
||
/// Inverts in-place this unit complex number.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # #[macro_use] extern crate approx;
|
||
/// # use nalgebra::UnitComplex;
|
||
/// let angle = 1.7;
|
||
/// let mut rot = UnitComplex::new(angle);
|
||
/// rot.inverse_mut();
|
||
/// assert_relative_eq!(rot * UnitComplex::new(angle), UnitComplex::identity());
|
||
/// assert_relative_eq!(UnitComplex::new(angle) * rot, UnitComplex::identity());
|
||
/// ```
|
||
#[inline]
|
||
pub fn inverse_mut(&mut self) {
|
||
self.conjugate_mut()
|
||
}
|
||
|
||
/// 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);
|
||
/// ```
|
||
#[inline]
|
||
pub fn powf(&self, n: N) -> Self {
|
||
Self::from_angle(self.angle() * n)
|
||
}
|
||
|
||
/// Builds the rotation matrix corresponding to this unit complex number.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # use nalgebra::{UnitComplex, Rotation2};
|
||
/// # use std::f32;
|
||
/// let rot = UnitComplex::new(f32::consts::FRAC_PI_6);
|
||
/// let expected = Rotation2::new(f32::consts::FRAC_PI_6);
|
||
/// assert_eq!(rot.to_rotation_matrix(), expected);
|
||
/// ```
|
||
#[inline]
|
||
pub fn to_rotation_matrix(&self) -> Rotation2<N> {
|
||
let r = self.re;
|
||
let i = self.im;
|
||
|
||
Rotation2::from_matrix_unchecked(Matrix2::new(r, -i, i, r))
|
||
}
|
||
|
||
/// Converts this unit complex number into its equivalent homogeneous transformation matrix.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # use nalgebra::{UnitComplex, Matrix3};
|
||
/// # use std::f32;
|
||
/// let rot = UnitComplex::new(f32::consts::FRAC_PI_6);
|
||
/// let expected = Matrix3::new(0.8660254, -0.5, 0.0,
|
||
/// 0.5, 0.8660254, 0.0,
|
||
/// 0.0, 0.0, 1.0);
|
||
/// assert_eq!(rot.to_homogeneous(), expected);
|
||
/// ```
|
||
#[inline]
|
||
pub fn to_homogeneous(&self) -> Matrix3<N> {
|
||
self.to_rotation_matrix().to_homogeneous()
|
||
}
|
||
|
||
/// Rotate the given point by this unit complex number.
|
||
///
|
||
/// This is the same as the multiplication `self * pt`.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # #[macro_use] extern crate approx;
|
||
/// # use nalgebra::{UnitComplex, Point2};
|
||
/// # use std::f32;
|
||
/// let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
|
||
/// let transformed_point = rot.transform_point(&Point2::new(1.0, 2.0));
|
||
/// assert_relative_eq!(transformed_point, Point2::new(-2.0, 1.0), epsilon = 1.0e-6);
|
||
/// ```
|
||
#[inline]
|
||
pub fn transform_point(&self, pt: &Point2<N>) -> Point2<N> {
|
||
self * pt
|
||
}
|
||
|
||
/// Rotate the given vector by this unit complex number.
|
||
///
|
||
/// This is the same as the multiplication `self * v`.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # #[macro_use] extern crate approx;
|
||
/// # use nalgebra::{UnitComplex, Vector2};
|
||
/// # use std::f32;
|
||
/// let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
|
||
/// let transformed_vector = rot.transform_vector(&Vector2::new(1.0, 2.0));
|
||
/// assert_relative_eq!(transformed_vector, Vector2::new(-2.0, 1.0), epsilon = 1.0e-6);
|
||
/// ```
|
||
#[inline]
|
||
pub fn transform_vector(&self, v: &Vector2<N>) -> Vector2<N> {
|
||
self * v
|
||
}
|
||
|
||
/// Rotate the given point by the inverse of this unit complex number.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # #[macro_use] extern crate approx;
|
||
/// # use nalgebra::{UnitComplex, Point2};
|
||
/// # use std::f32;
|
||
/// let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
|
||
/// let transformed_point = rot.inverse_transform_point(&Point2::new(1.0, 2.0));
|
||
/// assert_relative_eq!(transformed_point, Point2::new(2.0, -1.0), epsilon = 1.0e-6);
|
||
/// ```
|
||
#[inline]
|
||
pub fn inverse_transform_point(&self, pt: &Point2<N>) -> Point2<N> {
|
||
// FIXME: would it be useful performancewise not to call inverse explicitly (i-e. implement
|
||
// the inverse transformation explicitly here) ?
|
||
self.inverse() * pt
|
||
}
|
||
|
||
/// Rotate the given vector by the inverse of this unit complex number.
|
||
///
|
||
/// # Example
|
||
/// ```
|
||
/// # #[macro_use] extern crate approx;
|
||
/// # use nalgebra::{UnitComplex, Vector2};
|
||
/// # use std::f32;
|
||
/// let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
|
||
/// let transformed_vector = rot.inverse_transform_vector(&Vector2::new(1.0, 2.0));
|
||
/// assert_relative_eq!(transformed_vector, Vector2::new(2.0, -1.0), epsilon = 1.0e-6);
|
||
/// ```
|
||
#[inline]
|
||
pub fn inverse_transform_vector(&self, v: &Vector2<N>) -> Vector2<N> {
|
||
self.inverse() * v
|
||
}
|
||
}
|
||
|
||
impl<N: RealField + fmt::Display> fmt::Display for UnitComplex<N> {
|
||
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
|
||
write!(f, "UnitComplex angle: {}", self.angle())
|
||
}
|
||
}
|
||
|
||
impl<N: RealField> AbsDiffEq for UnitComplex<N> {
|
||
type Epsilon = N;
|
||
|
||
#[inline]
|
||
fn default_epsilon() -> Self::Epsilon {
|
||
N::default_epsilon()
|
||
}
|
||
|
||
#[inline]
|
||
fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool {
|
||
self.re.abs_diff_eq(&other.re, epsilon) && self.im.abs_diff_eq(&other.im, epsilon)
|
||
}
|
||
}
|
||
|
||
impl<N: RealField> RelativeEq for UnitComplex<N> {
|
||
#[inline]
|
||
fn default_max_relative() -> Self::Epsilon {
|
||
N::default_max_relative()
|
||
}
|
||
|
||
#[inline]
|
||
fn relative_eq(
|
||
&self,
|
||
other: &Self,
|
||
epsilon: Self::Epsilon,
|
||
max_relative: Self::Epsilon,
|
||
) -> bool
|
||
{
|
||
self.re.relative_eq(&other.re, epsilon, max_relative)
|
||
&& self.im.relative_eq(&other.im, epsilon, max_relative)
|
||
}
|
||
}
|
||
|
||
impl<N: RealField> UlpsEq for UnitComplex<N> {
|
||
#[inline]
|
||
fn default_max_ulps() -> u32 {
|
||
N::default_max_ulps()
|
||
}
|
||
|
||
#[inline]
|
||
fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool {
|
||
self.re.ulps_eq(&other.re, epsilon, max_ulps)
|
||
&& self.im.ulps_eq(&other.im, epsilon, max_ulps)
|
||
}
|
||
} |