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use glam::FloatExt;
use crate::prelude::{Mat2, Vec2};
#[cfg(feature = "bevy_reflect")]
use bevy_reflect::{std_traits::ReflectDefault, Reflect};
#[cfg(all(feature = "serialize", feature = "bevy_reflect"))]
use bevy_reflect::{ReflectDeserialize, ReflectSerialize};
/// A counterclockwise 2D rotation.
///
/// # Example
///
/// ```
/// # use approx::assert_relative_eq;
/// # use bevy_math::{Rot2, Vec2};
/// use std::f32::consts::PI;
///
/// // Create rotations from radians or degrees
/// let rotation1 = Rot2::radians(PI / 2.0);
/// let rotation2 = Rot2::degrees(45.0);
///
/// // Get the angle back as radians or degrees
/// assert_eq!(rotation1.as_degrees(), 90.0);
/// assert_eq!(rotation2.as_radians(), PI / 4.0);
///
/// // "Add" rotations together using `*`
/// assert_relative_eq!(rotation1 * rotation2, Rot2::degrees(135.0));
///
/// // Rotate vectors
/// assert_relative_eq!(rotation1 * Vec2::X, Vec2::Y);
/// ```
#[derive(Clone, Copy, Debug, PartialEq)]
#[cfg_attr(feature = "serialize", derive(serde::Serialize, serde::Deserialize))]
#[cfg_attr(
feature = "bevy_reflect",
derive(Reflect),
reflect(Debug, PartialEq, Default)
)]
#[cfg_attr(
all(feature = "serialize", feature = "bevy_reflect"),
reflect(Serialize, Deserialize)
)]
#[doc(alias = "rotation", alias = "rotation2d", alias = "rotation_2d")]
pub struct Rot2 {
/// The cosine of the rotation angle in radians.
///
/// This is the real part of the unit complex number representing the rotation.
pub cos: f32,
/// The sine of the rotation angle in radians.
///
/// This is the imaginary part of the unit complex number representing the rotation.
pub sin: f32,
}
impl Default for Rot2 {
fn default() -> Self {
Self::IDENTITY
}
}
impl Rot2 {
/// No rotation.
pub const IDENTITY: Self = Self { cos: 1.0, sin: 0.0 };
/// A rotation of π radians.
pub const PI: Self = Self {
cos: -1.0,
sin: 0.0,
};
/// A counterclockwise rotation of π/2 radians.
pub const FRAC_PI_2: Self = Self { cos: 0.0, sin: 1.0 };
/// A counterclockwise rotation of π/3 radians.
pub const FRAC_PI_3: Self = Self {
cos: 0.5,
sin: 0.866_025_4,
};
/// A counterclockwise rotation of π/4 radians.
pub const FRAC_PI_4: Self = Self {
cos: core::f32::consts::FRAC_1_SQRT_2,
sin: core::f32::consts::FRAC_1_SQRT_2,
};
/// A counterclockwise rotation of π/6 radians.
pub const FRAC_PI_6: Self = Self {
cos: 0.866_025_4,
sin: 0.5,
};
/// A counterclockwise rotation of π/8 radians.
pub const FRAC_PI_8: Self = Self {
cos: 0.923_879_5,
sin: 0.382_683_43,
};
/// Creates a [`Rot2`] from a counterclockwise angle in radians.
#[inline]
pub fn radians(radians: f32) -> Self {
#[cfg(feature = "libm")]
let (sin, cos) = (
libm::sin(radians as f64) as f32,
libm::cos(radians as f64) as f32,
);
#[cfg(not(feature = "libm"))]
let (sin, cos) = radians.sin_cos();
Self::from_sin_cos(sin, cos)
}
/// Creates a [`Rot2`] from a counterclockwise angle in degrees.
#[inline]
pub fn degrees(degrees: f32) -> Self {
Self::radians(degrees.to_radians())
}
/// Creates a [`Rot2`] from the sine and cosine of an angle in radians.
///
/// The rotation is only valid if `sin * sin + cos * cos == 1.0`.
///
/// # Panics
///
/// Panics if `sin * sin + cos * cos != 1.0` when the `glam_assert` feature is enabled.
#[inline]
pub fn from_sin_cos(sin: f32, cos: f32) -> Self {
let rotation = Self { sin, cos };
debug_assert!(
rotation.is_normalized(),
"the given sine and cosine produce an invalid rotation"
);
rotation
}
/// Returns the rotation in radians in the `(-pi, pi]` range.
#[inline]
pub fn as_radians(self) -> f32 {
#[cfg(feature = "libm")]
{
libm::atan2(self.sin as f64, self.cos as f64) as f32
}
#[cfg(not(feature = "libm"))]
{
f32::atan2(self.sin, self.cos)
}
}
/// Returns the rotation in degrees in the `(-180, 180]` range.
#[inline]
pub fn as_degrees(self) -> f32 {
self.as_radians().to_degrees()
}
/// Returns the sine and cosine of the rotation angle in radians.
#[inline]
pub const fn sin_cos(self) -> (f32, f32) {
(self.sin, self.cos)
}
/// Computes the length or norm of the complex number used to represent the rotation.
///
/// The length is typically expected to be `1.0`. Unexpectedly denormalized rotations
/// can be a result of incorrect construction or floating point error caused by
/// successive operations.
#[inline]
#[doc(alias = "norm")]
pub fn length(self) -> f32 {
Vec2::new(self.sin, self.cos).length()
}
/// Computes the squared length or norm of the complex number used to represent the rotation.
///
/// This is generally faster than [`Rot2::length()`], as it avoids a square
/// root operation.
///
/// The length is typically expected to be `1.0`. Unexpectedly denormalized rotations
/// can be a result of incorrect construction or floating point error caused by
/// successive operations.
#[inline]
#[doc(alias = "norm2")]
pub fn length_squared(self) -> f32 {
Vec2::new(self.sin, self.cos).length_squared()
}
/// Computes `1.0 / self.length()`.
///
/// For valid results, `self` must _not_ have a length of zero.
#[inline]
pub fn length_recip(self) -> f32 {
Vec2::new(self.sin, self.cos).length_recip()
}
/// Returns `self` with a length of `1.0` if possible, and `None` otherwise.
///
/// `None` will be returned if the sine and cosine of `self` are both zero (or very close to zero),
/// or if either of them is NaN or infinite.
///
/// Note that [`Rot2`] should typically already be normalized by design.
/// Manual normalization is only needed when successive operations result in
/// accumulated floating point error, or if the rotation was constructed
/// with invalid values.
#[inline]
pub fn try_normalize(self) -> Option<Self> {
let recip = self.length_recip();
if recip.is_finite() && recip > 0.0 {
Some(Self::from_sin_cos(self.sin * recip, self.cos * recip))
} else {
None
}
}
/// Returns `self` with a length of `1.0`.
///
/// Note that [`Rot2`] should typically already be normalized by design.
/// Manual normalization is only needed when successive operations result in
/// accumulated floating point error, or if the rotation was constructed
/// with invalid values.
///
/// # Panics
///
/// Panics if `self` has a length of zero, NaN, or infinity when debug assertions are enabled.
#[inline]
pub fn normalize(self) -> Self {
let length_recip = self.length_recip();
Self::from_sin_cos(self.sin * length_recip, self.cos * length_recip)
}
/// Returns `true` if the rotation is neither infinite nor NaN.
#[inline]
pub fn is_finite(self) -> bool {
self.sin.is_finite() && self.cos.is_finite()
}
/// Returns `true` if the rotation is NaN.
#[inline]
pub fn is_nan(self) -> bool {
self.sin.is_nan() || self.cos.is_nan()
}
/// Returns whether `self` has a length of `1.0` or not.
///
/// Uses a precision threshold of approximately `1e-4`.
#[inline]
pub fn is_normalized(self) -> bool {
// The allowed length is 1 +/- 1e-4, so the largest allowed
// squared length is (1 + 1e-4)^2 = 1.00020001, which makes
// the threshold for the squared length approximately 2e-4.
(self.length_squared() - 1.0).abs() <= 2e-4
}
/// Returns `true` if the rotation is near [`Rot2::IDENTITY`].
#[inline]
pub fn is_near_identity(self) -> bool {
// Same as `Quat::is_near_identity`, but using sine and cosine
let threshold_angle_sin = 0.000_049_692_047; // let threshold_angle = 0.002_847_144_6;
self.cos > 0.0 && self.sin.abs() < threshold_angle_sin
}
/// Returns the angle in radians needed to make `self` and `other` coincide.
#[inline]
pub fn angle_between(self, other: Self) -> f32 {
(other * self.inverse()).as_radians()
}
/// Returns the inverse of the rotation. This is also the conjugate
/// of the unit complex number representing the rotation.
#[inline]
#[must_use]
#[doc(alias = "conjugate")]
pub fn inverse(self) -> Self {
Self {
cos: self.cos,
sin: -self.sin,
}
}
/// Performs a linear interpolation between `self` and `rhs` based on
/// the value `s`, and normalizes the rotation afterwards.
///
/// When `s == 0.0`, the result will be equal to `self`.
/// When `s == 1.0`, the result will be equal to `rhs`.
///
/// This is slightly more efficient than [`slerp`](Self::slerp), and produces a similar result
/// when the difference between the two rotations is small. At larger differences,
/// the result resembles a kind of ease-in-out effect.
///
/// If you would like the angular velocity to remain constant, consider using [`slerp`](Self::slerp) instead.
///
/// # Details
///
/// `nlerp` corresponds to computing an angle for a point at position `s` on a line drawn
/// between the endpoints of the arc formed by `self` and `rhs` on a unit circle,
/// and normalizing the result afterwards.
///
/// Note that if the angles are opposite like 0 and π, the line will pass through the origin,
/// and the resulting angle will always be either `self` or `rhs` depending on `s`.
/// If `s` happens to be `0.5` in this case, a valid rotation cannot be computed, and `self`
/// will be returned as a fallback.
///
/// # Example
///
/// ```
/// # use bevy_math::Rot2;
/// #
/// let rot1 = Rot2::IDENTITY;
/// let rot2 = Rot2::degrees(135.0);
///
/// let result1 = rot1.nlerp(rot2, 1.0 / 3.0);
/// assert_eq!(result1.as_degrees(), 28.675055);
///
/// let result2 = rot1.nlerp(rot2, 0.5);
/// assert_eq!(result2.as_degrees(), 67.5);
/// ```
#[inline]
pub fn nlerp(self, end: Self, s: f32) -> Self {
Self {
sin: self.sin.lerp(end.sin, s),
cos: self.cos.lerp(end.cos, s),
}
.try_normalize()
// Fall back to the start rotation.
// This can happen when `self` and `end` are opposite angles and `s == 0.5`,
// because the resulting rotation would be zero, which cannot be normalized.
.unwrap_or(self)
}
/// Performs a spherical linear interpolation between `self` and `end`
/// based on the value `s`.
///
/// This corresponds to interpolating between the two angles at a constant angular velocity.
///
/// When `s == 0.0`, the result will be equal to `self`.
/// When `s == 1.0`, the result will be equal to `rhs`.
///
/// If you would like the rotation to have a kind of ease-in-out effect, consider
/// using the slightly more efficient [`nlerp`](Self::nlerp) instead.
///
/// # Example
///
/// ```
/// # use bevy_math::Rot2;
/// #
/// let rot1 = Rot2::IDENTITY;
/// let rot2 = Rot2::degrees(135.0);
///
/// let result1 = rot1.slerp(rot2, 1.0 / 3.0);
/// assert_eq!(result1.as_degrees(), 45.0);
///
/// let result2 = rot1.slerp(rot2, 0.5);
/// assert_eq!(result2.as_degrees(), 67.5);
/// ```
#[inline]
pub fn slerp(self, end: Self, s: f32) -> Self {
self * Self::radians(self.angle_between(end) * s)
}
}
impl From<f32> for Rot2 {
/// Creates a [`Rot2`] from a counterclockwise angle in radians.
fn from(rotation: f32) -> Self {
Self::radians(rotation)
}
}
impl From<Rot2> for Mat2 {
/// Creates a [`Mat2`] rotation matrix from a [`Rot2`].
fn from(rot: Rot2) -> Self {
Mat2::from_cols_array(&[rot.cos, -rot.sin, rot.sin, rot.cos])
}
}
impl std::ops::Mul for Rot2 {
type Output = Self;
fn mul(self, rhs: Self) -> Self::Output {
Self {
cos: self.cos * rhs.cos - self.sin * rhs.sin,
sin: self.sin * rhs.cos + self.cos * rhs.sin,
}
}
}
impl std::ops::MulAssign for Rot2 {
fn mul_assign(&mut self, rhs: Self) {
*self = *self * rhs;
}
}
impl std::ops::Mul<Vec2> for Rot2 {
type Output = Vec2;
/// Rotates a [`Vec2`] by a [`Rot2`].
fn mul(self, rhs: Vec2) -> Self::Output {
Vec2::new(
rhs.x * self.cos - rhs.y * self.sin,
rhs.x * self.sin + rhs.y * self.cos,
)
}
}
#[cfg(any(feature = "approx", test))]
impl approx::AbsDiffEq for Rot2 {
type Epsilon = f32;
fn default_epsilon() -> f32 {
f32::EPSILON
}
fn abs_diff_eq(&self, other: &Self, epsilon: f32) -> bool {
self.cos.abs_diff_eq(&other.cos, epsilon) && self.sin.abs_diff_eq(&other.sin, epsilon)
}
}
#[cfg(any(feature = "approx", test))]
impl approx::RelativeEq for Rot2 {
fn default_max_relative() -> f32 {
f32::EPSILON
}
fn relative_eq(&self, other: &Self, epsilon: f32, max_relative: f32) -> bool {
self.cos.relative_eq(&other.cos, epsilon, max_relative)
&& self.sin.relative_eq(&other.sin, epsilon, max_relative)
}
}
#[cfg(any(feature = "approx", test))]
impl approx::UlpsEq for Rot2 {
fn default_max_ulps() -> u32 {
4
}
fn ulps_eq(&self, other: &Self, epsilon: f32, max_ulps: u32) -> bool {
self.cos.ulps_eq(&other.cos, epsilon, max_ulps)
&& self.sin.ulps_eq(&other.sin, epsilon, max_ulps)
}
}
#[cfg(test)]
mod tests {
use approx::assert_relative_eq;
use crate::{Dir2, Rot2, Vec2};
#[test]
fn creation() {
let rotation1 = Rot2::radians(std::f32::consts::FRAC_PI_2);
let rotation2 = Rot2::degrees(90.0);
let rotation3 = Rot2::from_sin_cos(1.0, 0.0);
// All three rotations should be equal
assert_relative_eq!(rotation1.sin, rotation2.sin);
assert_relative_eq!(rotation1.cos, rotation2.cos);
assert_relative_eq!(rotation1.sin, rotation3.sin);
assert_relative_eq!(rotation1.cos, rotation3.cos);
// The rotation should be 90 degrees
assert_relative_eq!(rotation1.as_radians(), std::f32::consts::FRAC_PI_2);
assert_relative_eq!(rotation1.as_degrees(), 90.0);
}
#[test]
fn rotate() {
let rotation = Rot2::degrees(90.0);
assert_relative_eq!(rotation * Vec2::X, Vec2::Y);
assert_relative_eq!(rotation * Dir2::Y, Dir2::NEG_X);
}
#[test]
fn add() {
let rotation1 = Rot2::degrees(90.0);
let rotation2 = Rot2::degrees(180.0);
// 90 deg + 180 deg becomes -90 deg after it wraps around to be within the ]-180, 180] range
assert_eq!((rotation1 * rotation2).as_degrees(), -90.0);
}
#[test]
fn subtract() {
let rotation1 = Rot2::degrees(90.0);
let rotation2 = Rot2::degrees(45.0);
assert_relative_eq!((rotation1 * rotation2.inverse()).as_degrees(), 45.0);
// This should be equivalent to the above
assert_relative_eq!(
rotation2.angle_between(rotation1),
std::f32::consts::FRAC_PI_4
);
}
#[test]
fn length() {
let rotation = Rot2 {
sin: 10.0,
cos: 5.0,
};
assert_eq!(rotation.length_squared(), 125.0);
assert_eq!(rotation.length(), 11.18034);
assert!((rotation.normalize().length() - 1.0).abs() < 10e-7);
}
#[test]
fn is_near_identity() {
assert!(!Rot2::radians(0.1).is_near_identity());
assert!(!Rot2::radians(-0.1).is_near_identity());
assert!(Rot2::radians(0.00001).is_near_identity());
assert!(Rot2::radians(-0.00001).is_near_identity());
assert!(Rot2::radians(0.0).is_near_identity());
}
#[test]
fn normalize() {
let rotation = Rot2 {
sin: 10.0,
cos: 5.0,
};
let normalized_rotation = rotation.normalize();
assert_eq!(normalized_rotation.sin, 0.89442724);
assert_eq!(normalized_rotation.cos, 0.44721362);
assert!(!rotation.is_normalized());
assert!(normalized_rotation.is_normalized());
}
#[test]
fn try_normalize() {
// Valid
assert!(Rot2 {
sin: 10.0,
cos: 5.0,
}
.try_normalize()
.is_some());
// NaN
assert!(Rot2 {
sin: f32::NAN,
cos: 5.0,
}
.try_normalize()
.is_none());
// Zero
assert!(Rot2 { sin: 0.0, cos: 0.0 }.try_normalize().is_none());
// Non-finite
assert!(Rot2 {
sin: f32::INFINITY,
cos: 5.0,
}
.try_normalize()
.is_none());
}
#[test]
fn nlerp() {
let rot1 = Rot2::IDENTITY;
let rot2 = Rot2::degrees(135.0);
assert_eq!(rot1.nlerp(rot2, 1.0 / 3.0).as_degrees(), 28.675055);
assert!(rot1.nlerp(rot2, 0.0).is_near_identity());
assert_eq!(rot1.nlerp(rot2, 0.5).as_degrees(), 67.5);
assert_eq!(rot1.nlerp(rot2, 1.0).as_degrees(), 135.0);
let rot1 = Rot2::IDENTITY;
let rot2 = Rot2::from_sin_cos(0.0, -1.0);
assert!(rot1.nlerp(rot2, 1.0 / 3.0).is_near_identity());
assert!(rot1.nlerp(rot2, 0.0).is_near_identity());
// At 0.5, there is no valid rotation, so the fallback is the original angle.
assert_eq!(rot1.nlerp(rot2, 0.5).as_degrees(), 0.0);
assert_eq!(rot1.nlerp(rot2, 1.0).as_degrees().abs(), 180.0);
}
#[test]
fn slerp() {
let rot1 = Rot2::IDENTITY;
let rot2 = Rot2::degrees(135.0);
assert_eq!(rot1.slerp(rot2, 1.0 / 3.0).as_degrees(), 45.0);
assert!(rot1.slerp(rot2, 0.0).is_near_identity());
assert_eq!(rot1.slerp(rot2, 0.5).as_degrees(), 67.5);
assert_eq!(rot1.slerp(rot2, 1.0).as_degrees(), 135.0);
let rot1 = Rot2::IDENTITY;
let rot2 = Rot2::from_sin_cos(0.0, -1.0);
assert!((rot1.slerp(rot2, 1.0 / 3.0).as_degrees() - 60.0).abs() < 10e-6);
assert!(rot1.slerp(rot2, 0.0).is_near_identity());
assert_eq!(rot1.slerp(rot2, 0.5).as_degrees(), 90.0);
assert_eq!(rot1.slerp(rot2, 1.0).as_degrees().abs(), 180.0);
}
}