nalgebra/src/geometry/unit_complex.rs

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use approx::{AbsDiffEq, RelativeEq, UlpsEq};
use num_complex::Complex;
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use std::fmt;
use alga::general::Real;
use base::{Matrix2, Matrix3, Unit, Vector1};
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use geometry::Rotation2;
/// A complex number with a norm equal to 1.
pub type UnitComplex<N> = Unit<Complex<N>>;
impl<N: Real> UnitComplex<N> {
/// The rotation angle in `]-pi; pi]` of this unit complex number.
#[inline]
pub fn angle(&self) -> N {
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self.im.atan2(self.re)
}
/// The sine of the rotation angle.
#[inline]
pub fn sin_angle(&self) -> N {
self.im
}
/// The cosine of the rotation angle.
#[inline]
pub fn cos_angle(&self) -> N {
self.re
}
/// The rotation angle returned as a 1-dimensional vector.
#[inline]
pub fn scaled_axis(&self) -> Vector1<N> {
Vector1::new(self.angle())
}
/// The rotation axis and angle in ]0, pi] of this complex number.
///
/// 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()`.
#[inline]
pub fn complex(&self) -> &Complex<N> {
self.as_ref()
}
/// Compute the conjugate of this unit complex number.
#[inline]
pub fn conjugate(&self) -> Self {
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UnitComplex::new_unchecked(self.conj())
}
/// Inverts this complex number if it is not zero.
#[inline]
pub fn inverse(&self) -> Self {
self.conjugate()
}
/// The rotation angle needed to make `self` and `other` coincide.
#[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`.
#[inline]
pub fn rotation_to(&self, other: &Self) -> Self {
other / self
}
/// Compute in-place the conjugate of this unit complex number.
#[inline]
pub fn conjugate_mut(&mut self) {
let me = self.as_mut_unchecked();
me.im = -me.im;
}
/// Inverts in-place this unit complex number.
#[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`.
#[inline]
pub fn powf(&self, n: N) -> Self {
Self::from_angle(self.angle() * n)
}
/// Builds the rotation matrix corresponding to this unit complex number.
#[inline]
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pub fn to_rotation_matrix(&self) -> Rotation2<N> {
let r = self.re;
let i = self.im;
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Rotation2::from_matrix_unchecked(Matrix2::new(r, -i, i, r))
}
/// Converts this unit complex number into its equivalent homogeneous transformation matrix.
#[inline]
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pub fn to_homogeneous(&self) -> Matrix3<N> {
self.to_rotation_matrix().to_homogeneous()
}
}
impl<N: Real + fmt::Display> fmt::Display for UnitComplex<N> {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
write!(f, "UnitComplex angle: {}", self.angle())
}
}
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impl<N: Real> AbsDiffEq for UnitComplex<N> {
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type Epsilon = N;
#[inline]
fn default_epsilon() -> Self::Epsilon {
N::default_epsilon()
}
#[inline]
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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)
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}
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}
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impl<N: Real> RelativeEq for UnitComplex<N> {
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#[inline]
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fn default_max_relative() -> Self::Epsilon {
N::default_max_relative()
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}
#[inline]
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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)
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}
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}
impl<N: Real> UlpsEq for UnitComplex<N> {
#[inline]
fn default_max_ulps() -> u32 {
N::default_max_ulps()
}
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#[inline]
fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool {
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self.re.ulps_eq(&other.re, epsilon, max_ulps)
&& self.im.ulps_eq(&other.im, epsilon, max_ulps)
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}
}
impl<N: Real> From<UnitComplex<N>> for Matrix3<N> {
#[inline]
fn from(q: UnitComplex<N>) -> Matrix3<N> {
q.to_homogeneous()
}
}
impl<N: Real> From<UnitComplex<N>> for Matrix2<N> {
#[inline]
fn from(q: UnitComplex<N>) -> Matrix2<N> {
q.to_rotation_matrix().unwrap()
}
}