3.17 角度

一、源码

use crate::approxeq::ApproxEq;
use crate::trig::Trig;

use core::cmp::{Eq, PartialEq};
use core::hash::Hash;
use core::iter::Sum;
use core::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Rem, Sub, SubAssign};

#[cfg(feature = "bytemuck")]
use bytemuck::{Pod, Zeroable};
use num_traits::real::Real;
use num_traits::{Float, FloatConst, NumCast, One, Zero};
#[cfg(feature = "serde")]
use serde::{Deserialize, Serialize};

/// An angle in radians
#[derive(Copy, Clone, Default, Debug, PartialEq, Eq, PartialOrd, Hash)]
#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
pub struct Angle<T> {
    pub radians: T,
}

#[cfg(feature = "bytemuck")]
unsafe impl<T: Zeroable> Zeroable for Angle<T> {}

#[cfg(feature = "bytemuck")]
unsafe impl<T: Pod> Pod for Angle<T> {}

#[cfg(feature = "arbitrary")]
impl<'a, T> arbitrary::Arbitrary<'a> for Angle<T>
where
    T: arbitrary::Arbitrary<'a>,
{
    // This implementation could be derived, but the derive would require an `extern crate std`.
    fn arbitrary(u: &mut arbitrary::Unstructured<'a>) -> arbitrary::Result<Self> {
        Ok(Angle {
            radians: arbitrary::Arbitrary::arbitrary(u)?,
        })
    }

    fn size_hint(depth: usize) -> (usize, Option<usize>) {
        <T as arbitrary::Arbitrary>::size_hint(depth)
    }
}

impl<T> Angle<T> {
    #[inline]
    pub fn radians(radians: T) -> Self {
        Angle { radians }
    }

    #[inline]
    pub fn get(self) -> T {
        self.radians
    }
}

impl<T> Angle<T>
where
    T: Trig,
{
    #[inline]
    pub fn degrees(deg: T) -> Self {
        Angle {
            radians: T::degrees_to_radians(deg),
        }
    }

    #[inline]
    pub fn to_degrees(self) -> T {
        T::radians_to_degrees(self.radians)
    }
}

impl<T> Angle<T>
where
    T: Rem<Output = T> + Sub<Output = T> + Add<Output = T> + Zero + FloatConst + PartialOrd + Copy,
{
    /// Returns this angle in the [0..2*PI[ range.
    pub fn positive(&self) -> Self {
        let two_pi = T::PI() + T::PI();
        let mut a = self.radians % two_pi;
        if a < T::zero() {
            a = a + two_pi;
        }
        Angle::radians(a)
    }

    /// Returns this angle in the ]-PI..PI] range.
    pub fn signed(&self) -> Self {
        Angle::pi() - (Angle::pi() - *self).positive()
    }
}

impl<T> Angle<T>
where
    T: Rem<Output = T>
        + Mul<Output = T>
        + Sub<Output = T>
        + Add<Output = T>
        + One
        + FloatConst
        + Copy,
{
    /// Returns the shortest signed angle between two angles.
    ///
    /// Takes wrapping and signs into account.
    pub fn angle_to(&self, to: Self) -> Self {
        let two = T::one() + T::one();
        let max = T::PI() * two;
        let d = (to.radians - self.radians) % max;

        Angle::radians(two * d % max - d)
    }

    /// Linear interpolation between two angles, using the shortest path.
    pub fn lerp(&self, other: Self, t: T) -> Self {
        *self + self.angle_to(other) * t
    }
}

impl<T> Angle<T>
where
    T: Float,
{
    /// Returns `true` if the angle is a finite number.
    #[inline]
    pub fn is_finite(self) -> bool {
        self.radians.is_finite()
    }
}

impl<T> Angle<T>
where
    T: Real,
{
    /// Returns `(sin(self), cos(self))`.
    pub fn sin_cos(self) -> (T, T) {
        self.radians.sin_cos()
    }
}

impl<T> Angle<T>
where
    T: Zero,
{
    pub fn zero() -> Self {
        Angle::radians(T::zero())
    }
}

impl<T> Angle<T>
where
    T: FloatConst + Add<Output = T>,
{
    pub fn pi() -> Self {
        Angle::radians(T::PI())
    }

    pub fn two_pi() -> Self {
        Angle::radians(T::PI() + T::PI())
    }

    pub fn frac_pi_2() -> Self {
        Angle::radians(T::FRAC_PI_2())
    }

    pub fn frac_pi_3() -> Self {
        Angle::radians(T::FRAC_PI_3())
    }

    pub fn frac_pi_4() -> Self {
        Angle::radians(T::FRAC_PI_4())
    }
}

impl<T> Angle<T>
where
    T: NumCast + Copy,
{
    /// Cast from one numeric representation to another.
    #[inline]
    pub fn cast<NewT: NumCast>(&self) -> Angle<NewT> {
        self.try_cast().unwrap()
    }

    /// Fallible cast from one numeric representation to another.
    pub fn try_cast<NewT: NumCast>(&self) -> Option<Angle<NewT>> {
        NumCast::from(self.radians).map(|radians| Angle { radians })
    }

    // Convenience functions for common casts.

    /// Cast angle to `f32`.
    #[inline]
    pub fn to_f32(&self) -> Angle<f32> {
        self.cast()
    }

    /// Cast angle `f64`.
    #[inline]
    pub fn to_f64(&self) -> Angle<f64> {
        self.cast()
    }
}

impl<T: Add<T, Output = T>> Add for Angle<T> {
    type Output = Self;
    fn add(self, other: Self) -> Self {
        Self::radians(self.radians + other.radians)
    }
}

impl<T: Copy + Add<T, Output = T>> Add<&Self> for Angle<T> {
    type Output = Self;
    fn add(self, other: &Self) -> Self {
        Self::radians(self.radians + other.radians)
    }
}

impl<T: Add + Zero> Sum for Angle<T> {
    fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
        iter.fold(Self::zero(), Add::add)
    }
}

impl<'a, T: 'a + Add + Copy + Zero> Sum<&'a Self> for Angle<T> {
    fn sum<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
        iter.fold(Self::zero(), Add::add)
    }
}

impl<T: AddAssign<T>> AddAssign for Angle<T> {
    fn add_assign(&mut self, other: Angle<T>) {
        self.radians += other.radians;
    }
}

impl<T: Sub<T, Output = T>> Sub<Angle<T>> for Angle<T> {
    type Output = Angle<T>;
    fn sub(self, other: Angle<T>) -> <Self as Sub>::Output {
        Angle::radians(self.radians - other.radians)
    }
}

impl<T: SubAssign<T>> SubAssign for Angle<T> {
    fn sub_assign(&mut self, other: Angle<T>) {
        self.radians -= other.radians;
    }
}

impl<T: Div<T, Output = T>> Div<Angle<T>> for Angle<T> {
    type Output = T;
    #[inline]
    fn div(self, other: Angle<T>) -> T {
        self.radians / other.radians
    }
}

impl<T: Div<T, Output = T>> Div<T> for Angle<T> {
    type Output = Angle<T>;
    #[inline]
    fn div(self, factor: T) -> Angle<T> {
        Angle::radians(self.radians / factor)
    }
}

impl<T: DivAssign<T>> DivAssign<T> for Angle<T> {
    fn div_assign(&mut self, factor: T) {
        self.radians /= factor;
    }
}

impl<T: Mul<T, Output = T>> Mul<T> for Angle<T> {
    type Output = Angle<T>;
    #[inline]
    fn mul(self, factor: T) -> Angle<T> {
        Angle::radians(self.radians * factor)
    }
}

impl<T: MulAssign<T>> MulAssign<T> for Angle<T> {
    fn mul_assign(&mut self, factor: T) {
        self.radians *= factor;
    }
}

impl<T: Neg<Output = T>> Neg for Angle<T> {
    type Output = Self;
    fn neg(self) -> Self {
        Angle::radians(-self.radians)
    }
}

impl<T: ApproxEq<T>> ApproxEq<T> for Angle<T> {
    #[inline]
    fn approx_epsilon() -> T {
        T::approx_epsilon()
    }

    #[inline]
    fn approx_eq_eps(&self, other: &Angle<T>, approx_epsilon: &T) -> bool {
        self.radians.approx_eq_eps(&other.radians, approx_epsilon)
    }
}

#[test]
fn wrap_angles() {
    use core::f32::consts::{FRAC_PI_2, PI};

    assert!(Angle::radians(0.0).positive().approx_eq(&Angle::zero()));
    assert!(Angle::radians(FRAC_PI_2)
        .positive()
        .approx_eq(&Angle::frac_pi_2()));
    assert!(Angle::radians(-FRAC_PI_2)
        .positive()
        .approx_eq(&Angle::radians(3.0 * FRAC_PI_2)));
    assert!(Angle::radians(3.0 * FRAC_PI_2)
        .positive()
        .approx_eq(&Angle::radians(3.0 * FRAC_PI_2)));
    assert!(Angle::radians(5.0 * FRAC_PI_2)
        .positive()
        .approx_eq(&Angle::frac_pi_2()));
    assert!(Angle::radians(2.0 * PI)
        .positive()
        .approx_eq(&Angle::zero()));
    assert!(Angle::radians(-2.0 * PI)
        .positive()
        .approx_eq(&Angle::zero()));
    assert!(Angle::radians(PI).positive().approx_eq(&Angle::pi()));
    assert!(Angle::radians(-PI).positive().approx_eq(&Angle::pi()));

    assert!(Angle::radians(FRAC_PI_2)
        .signed()
        .approx_eq(&Angle::frac_pi_2()));
    assert!(Angle::radians(3.0 * FRAC_PI_2)
        .signed()
        .approx_eq(&-Angle::frac_pi_2()));
    assert!(Angle::radians(5.0 * FRAC_PI_2)
        .signed()
        .approx_eq(&Angle::frac_pi_2()));
    assert!(Angle::radians(2.0 * PI).signed().approx_eq(&Angle::zero()));
    assert!(Angle::radians(-2.0 * PI).signed().approx_eq(&Angle::zero()));
    assert!(Angle::radians(-PI).signed().approx_eq(&Angle::pi()));
    assert!(Angle::radians(PI).signed().approx_eq(&Angle::pi()));
}

#[test]
fn lerp() {
    type A = Angle<f32>;

    let a = A::radians(1.0);
    let b = A::radians(2.0);
    assert!(a.lerp(b, 0.25).approx_eq(&Angle::radians(1.25)));
    assert!(a.lerp(b, 0.5).approx_eq(&Angle::radians(1.5)));
    assert!(a.lerp(b, 0.75).approx_eq(&Angle::radians(1.75)));
    assert!(a
        .lerp(b + A::two_pi(), 0.75)
        .approx_eq(&Angle::radians(1.75)));
    assert!(a
        .lerp(b - A::two_pi(), 0.75)
        .approx_eq(&Angle::radians(1.75)));
    assert!(a
        .lerp(b + A::two_pi() * 5.0, 0.75)
        .approx_eq(&Angle::radians(1.75)));
}

#[test]
fn sum() {
    type A = Angle<f32>;
    let angles = [A::radians(1.0), A::radians(2.0), A::radians(3.0)];
    let sum = A::radians(6.0);
    assert_eq!(angles.iter().sum::<A>(), sum);
}

二、待阅读内容

编号	内容	说明
1.2	components	组件
1.3	systems	系统
1.4	window	窗口
2	core	核心对象
2.1	primitives	图元
2.1.1	Arc	Arc对象
2.1.2	Line	Line对象
3.3	homogen.rs
3.4	length.rs
3.5	point.rs
3.6	scale.rs
3.7	transform2d.rs
3.8	transform3d.rs
3.9	vector.rs
3.10	box3d.rs
3.11	rect.rs
3.12	rigid.rs
3.13	rotation.rs
3.14	side_offsets.rs
3.15	size.rs
3.16	translation.rs
3.18	box2d.rs
3.19	approxord.rs
3.20	num.rs
3.21	macros.rs
4	4 num_traits外部库