[kaka/rust-sdl-test.git] / src / geometry.rs

use std::ops::{Add, AddAssign, Sub, SubAssign, Mul, MulAssign, Div, DivAssign, Neg};

////////// POINT ///////////////////////////////////////////////////////////////

#[macro_export]
macro_rules! point {
    ( $x:expr, $y:expr ) => {
        Point { x: $x, y: $y }
    };
}

#[derive(Debug, Default, Copy, Clone, PartialEq)]
pub struct Point<T> {
    pub x: T,
    pub y: T,
}

impl Point<f64> {
    pub fn length(&self) -> f64 {
        ((self.x * self.x) + (self.y * self.y)).sqrt()
    }

    pub fn normalized(&self) -> Self {
	let l = self.length();
	Self {
	    x: self.x / l,
	    y: self.y / l,
	}
    }

    pub fn to_angle(&self) -> Angle {
	self.y.atan2(self.x).radians()
    }

    pub fn to_i32(self) -> Point<i32> {
	Point {
	    x: self.x as i32,
	    y: self.y as i32,
	}
    }

    pub fn cross_product(&self, p: Self) -> f64 {
        return self.x * p.y - self.y * p.x;
    }

    /// Returns the perpendicular projection of this vector on a line with the specified angle.
    pub fn project_onto(&self, angle: Angle) -> Point<f64> {
	let dot_product = self.length() * (self.to_angle() - angle).to_radians().cos();
	Point::from(angle) * dot_product
    }
}

macro_rules! impl_point_op {
    ($op:tt, $trait:ident($fn:ident), $trait_assign:ident($fn_assign:ident), $rhs:ident = $Rhs:ty => $x:expr, $y:expr) => {
        impl<T: $trait<Output = T>> $trait<$Rhs> for Point<T> {
            type Output = Self;

            fn $fn(self, $rhs: $Rhs) -> Self {
                Self {
                    x: self.x $op $x,
                    y: self.y $op $y,
                }
            }
        }

        impl<T: $trait<Output = T> + Copy> $trait_assign<$Rhs> for Point<T> {
            fn $fn_assign(&mut self, $rhs: $Rhs) {
                *self = Self {
                    x: self.x $op $x,
                    y: self.y $op $y,
                }
            }
        }
    }
}

impl_point_op!(+, Add(add), AddAssign(add_assign), rhs = Point<T> => rhs.x, rhs.y);
impl_point_op!(-, Sub(sub), SubAssign(sub_assign), rhs = Point<T> => rhs.x, rhs.y);
impl_point_op!(*, Mul(mul), MulAssign(mul_assign), rhs = Point<T> => rhs.x, rhs.y);
impl_point_op!(/, Div(div), DivAssign(div_assign), rhs = Point<T> => rhs.x, rhs.y);
impl_point_op!(+, Add(add), AddAssign(add_assign), rhs = (T, T) => rhs.0, rhs.1);
impl_point_op!(-, Sub(sub), SubAssign(sub_assign), rhs = (T, T) => rhs.0, rhs.1);
impl_point_op!(*, Mul(mul), MulAssign(mul_assign), rhs = (T, T) => rhs.0, rhs.1);
impl_point_op!(/, Div(div), DivAssign(div_assign), rhs = (T, T) => rhs.0, rhs.1);
impl_point_op!(*, Mul(mul), MulAssign(mul_assign), rhs = Dimension<T> => rhs.width, rhs.height);
impl_point_op!(/, Div(div), DivAssign(div_assign), rhs = Dimension<T> => rhs.width, rhs.height);

////////// multiply point with scalar //////////////////////////////////////////
impl<T: Mul<Output = T> + Copy> Mul<T> for Point<T> {
    type Output = Self;

    fn mul(self, rhs: T) -> Self {
	Self {
	    x: self.x * rhs,
	    y: self.y * rhs,
	}
    }
}

impl<T: Mul<Output = T> + Copy> MulAssign<T> for Point<T> {
    fn mul_assign(&mut self, rhs: T) {
	*self = Self {
	    x: self.x * rhs,
	    y: self.y * rhs,
	}
    }
}

////////// divide point with scalar ////////////////////////////////////////////
impl<T: Div<Output = T> + Copy> Div<T> for Point<T> {
    type Output = Self;

    fn div(self, rhs: T) -> Self {
	Self {
	    x: self.x / rhs,
	    y: self.y / rhs,
	}
    }
}

impl<T: Div<Output = T> + Copy> DivAssign<T> for Point<T> {
    fn div_assign(&mut self, rhs: T) {
	*self = Self {
	    x: self.x / rhs,
	    y: self.y / rhs,
	}
    }
}

impl<T: Neg<Output = T>> Neg for Point<T> {
    type Output = Self;

    fn neg(self) -> Self {
	Self {
	    x: -self.x,
	    y: -self.y,
	}
    }
}

impl<T> From<(T, T)> for Point<T> {
    fn from(item: (T, T)) -> Self {
        Point {
            x: item.0,
            y: item.1,
        }
    }
}

impl<T> From<Point<T>> for (T, T) {
    fn from(item: Point<T>) -> Self {
        (item.x, item.y)
    }
}

impl From<Angle> for Point<f64> {
    fn from(item: Angle) -> Self {
	Point {
	    x: item.0.cos(),
	    y: item.0.sin(),
	}
    }
}

////////// ANGLE ///////////////////////////////////////////////////////////////

#[derive(Debug, Default, Clone, Copy)]
pub struct Angle(pub f64);

pub trait ToAngle {
    fn radians(self) -> Angle;
    fn degrees(self) -> Angle;
}

macro_rules! impl_angle {
    ($($type:ty),*) => {
	$(
	    impl ToAngle for $type {
		fn radians(self) -> Angle {
		    Angle(self as f64)
		}

		fn degrees(self) -> Angle {
		    Angle((self as f64).to_radians())
		}
	    }

	    impl Mul<$type> for Angle {
		type Output = Self;

		fn mul(self, rhs: $type) -> Self {
		    Angle(self.0 * (rhs as f64))
		}
	    }

	    impl MulAssign<$type> for Angle {
		fn mul_assign(&mut self, rhs: $type) {
		    self.0 *= rhs as f64;
		}
	    }

	    impl Div<$type> for Angle {
		type Output = Self;

		fn div(self, rhs: $type) -> Self {
		    Angle(self.0 / (rhs as f64))
		}
	    }

	    impl DivAssign<$type> for Angle {
		fn div_assign(&mut self, rhs: $type) {
		    self.0 /= rhs as f64;
		}
	    }
	)*
    }
}

impl_angle!(f32, f64, i8, i16, i32, i64, isize, u8, u16, u32, u64, usize);

impl Angle {
    pub fn to_radians(self) -> f64 {
	self.0
    }

    pub fn to_degrees(self) -> f64 {
	self.0.to_degrees()
    }

    /// Returns the reflection of the incident when mirrored along this angle.
    pub fn mirror(&self, incidence: Angle) -> Angle {
	Angle((std::f64::consts::PI + self.0 * 2.0 - incidence.0) % std::f64::consts::TAU)
    }

    pub fn reverse(&self) -> Angle {
	Angle((self.0 + std::f64::consts::PI) % std::f64::consts::TAU)
    }
}

impl PartialEq for Angle {
    fn eq(&self, rhs: &Angle) -> bool {
	self.0 % std::f64::consts::TAU == rhs.0 % std::f64::consts::TAU
    }
}

// addition and subtraction of angles

impl Add<Angle> for Angle {
    type Output = Self;

    fn add(self, rhs: Angle) -> Self {
	Angle(self.0 + rhs.0)
    }
}

impl AddAssign<Angle> for Angle {
    fn add_assign(&mut self, rhs: Angle) {
	self.0 += rhs.0;
    }
}

impl Sub<Angle> for Angle {
    type Output = Self;

    fn sub(self, rhs: Angle) -> Self {
	Angle(self.0 - rhs.0)
    }
}

impl SubAssign<Angle> for Angle {
    fn sub_assign(&mut self, rhs: Angle) {
	self.0 -= rhs.0;
    }
}

////////// INTERSECTION ////////////////////////////////////////////////////////

#[derive(Debug)]
pub enum Intersection {
    Point(Point<f64>),
    //Line(Point<f64>, Point<f64>), // TODO: overlapping collinear
    None,
}

impl Intersection {
    pub fn lines(p1: Point<f64>, p2: Point<f64>, p3: Point<f64>, p4: Point<f64>) -> Intersection {
	let s1 = p2 - p1;
	let s2 = p4 - p3;

	let denomimator = -s2.x * s1.y + s1.x * s2.y;
	if denomimator != 0.0 {
	    let s = (-s1.y * (p1.x - p3.x) + s1.x * (p1.y - p3.y)) / denomimator;
	    let t = ( s2.x * (p1.y - p3.y) - s2.y * (p1.x - p3.x)) / denomimator;

	    if (0.0..=1.0).contains(&s) && (0.0..=1.0).contains(&t) {
		return Intersection::Point(p1 + (s1 * t))
	    }
	}

	Intersection::None
    }
}

////////// DIMENSION ///////////////////////////////////////////////////////////

#[macro_export]
macro_rules! dimen {
    ( $w:expr, $h:expr ) => {
        Dimension { width: $w, height: $h }
    };
}

#[derive(Debug, Default, Copy, Clone, PartialEq)]
pub struct Dimension<T> {
    pub width: T,
    pub height: T,
}

impl<T: Mul<Output = T> + Copy> Dimension<T> {
    #[allow(dead_code)]
    pub fn area(&self) -> T {
        self.width * self.height
    }
}

impl<T> From<(T, T)> for Dimension<T> {
    fn from(item: (T, T)) -> Self {
        Dimension {
            width: item.0,
            height: item.1,
        }
    }
}

impl<T> From<Dimension<T>> for (T, T) {
    fn from(item: Dimension<T>) -> Self {
        (item.width, item.height)
    }
}

////////////////////////////////////////////////////////////////////////////////

#[allow(dead_code)]
pub fn supercover_line_int(p1: Point<isize>, p2: Point<isize>) -> Vec<Point<isize>> {
    let d = p2 - p1;
    let n = point!(d.x.abs(), d.y.abs());
    let step = point!(d.x.signum(), d.y.signum());

    let mut p = p1;
    let mut points = vec!(point!(p.x as isize, p.y as isize));
    let mut i = point!(0, 0);
    while i.x < n.x || i.y < n.y {
        let decision = (1 + 2 * i.x) * n.y - (1 + 2 * i.y) * n.x;
        if decision == 0 { // next step is diagonal
            p.x += step.x;
            p.y += step.y;
            i.x += 1;
            i.y += 1;
        } else if decision < 0 { // next step is horizontal
            p.x += step.x;
	    i.x += 1;
        } else { // next step is vertical
            p.y += step.y;
            i.y += 1;
        }
        points.push(point!(p.x as isize, p.y as isize));
    }

    points
}

/// Calculates all points a line crosses, unlike Bresenham's line algorithm.
/// There might be room for a lot of improvement here.
pub fn supercover_line(mut p1: Point<f64>, mut p2: Point<f64>) -> Vec<Point<isize>> {
    let mut delta = p2 - p1;
    if (delta.x.abs() > delta.y.abs() && delta.x.is_sign_negative()) || (delta.x.abs() <= delta.y.abs() && delta.y.is_sign_negative()) {
	std::mem::swap(&mut p1, &mut p2);
	delta = -delta;
    }

    let mut last = point!(p1.x as isize, p1.y as isize);
    let mut coords: Vec<Point<isize>> = vec!();
    coords.push(last);

    if delta.x.abs() > delta.y.abs() {
	let k = delta.y / delta.x;
	let m = p1.y as f64 - p1.x as f64 * k;
	for x in (p1.x as isize + 1)..=(p2.x as isize) {
	    let y = (k * x as f64 + m).floor();
	    let next = point!(x as isize - 1, y as isize);
	    if next != last {
		coords.push(next);
	    }
	    let next = point!(x as isize, y as isize);
	    coords.push(next);
	    last = next;
	}
    } else {
	let k = delta.x / delta.y;
	let m = p1.x as f64 - p1.y as f64 * k;
	for y in (p1.y as isize + 1)..=(p2.y as isize) {
	    let x = (k * y as f64 + m).floor();
	    let next = point!(x as isize, y as isize - 1);
	    if next != last {
		coords.push(next);
	    }
	    let next = point!(x as isize, y as isize);
	    coords.push(next);
	    last = next;
	}
    }

    let next = point!(p2.x as isize, p2.y as isize);
    if next != last {
	coords.push(next);
    }

    coords
}

////////// TESTS ///////////////////////////////////////////////////////////////

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn immutable_copy_of_point() {
        let a = point!(0, 0);
        let mut b = a; // Copy
        assert_eq!(a, b); // PartialEq
        b.x = 1;
        assert_ne!(a, b); // PartialEq
    }

    #[test]
    fn add_points() {
        let mut a = point!(1, 0);
        assert_eq!(a + point!(2, 2), point!(3, 2)); // Add
        a += point!(2, 2); // AddAssign
        assert_eq!(a, point!(3, 2));
        assert_eq!(point!(1, 0) + (2, 3), point!(3, 3));
    }

    #[test]
    fn sub_points() {
        let mut a = point!(1, 0);
        assert_eq!(a - point!(2, 2), point!(-1, -2));
        a -= point!(2, 2);
        assert_eq!(a, point!(-1, -2));
        assert_eq!(point!(1, 0) - (2, 3), point!(-1, -3));
    }

    #[test]
    fn mul_points() {
        let mut a = point!(1, 2);
        assert_eq!(a * 2, point!(2, 4));
        assert_eq!(a * point!(2, 3), point!(2, 6));
        a *= 2;
        assert_eq!(a, point!(2, 4));
        a *= point!(3, 1);
        assert_eq!(a, point!(6, 4));
        assert_eq!(point!(1, 0) * (2, 3), point!(2, 0));
    }

    #[test]
    fn div_points() {
        let mut a = point!(4, 8);
        assert_eq!(a / 2, point!(2, 4));
        assert_eq!(a / point!(2, 4), point!(2, 2));
        a /= 2;
        assert_eq!(a, point!(2, 4));
        a /= point!(2, 4);
        assert_eq!(a, point!(1, 1));
        assert_eq!(point!(6, 3) / (2, 3), point!(3, 1));
    }

    #[test]
    fn neg_point() {
        assert_eq!(point!(1, 1), -point!(-1, -1));
    }

    #[test]
    fn angles() {
	assert_eq!(0.radians(), 0.degrees());
	assert_eq!(0.degrees(), 360.degrees());
	assert_eq!(180.degrees(), std::f64::consts::PI.radians());
	assert_eq!(std::f64::consts::PI.radians().to_degrees(), 180.0);
	assert!((Point::from(90.degrees()) - point!(0.0, 1.0)).length() < 0.001);
	assert!((Point::from(std::f64::consts::FRAC_PI_2.radians()) - point!(0.0, 1.0)).length() < 0.001);
    }

    #[test]
    fn area_for_dimension_of_multipliable_type() {
        let r: Dimension<_> = (30, 20).into(); // the Into trait uses the From trait
        assert_eq!(r.area(), 30 * 20);
        // let a = Dimension::from(("a".to_string(), "b".to_string())).area(); // this doesn't work, because area() is not implemented for String
    }

    #[test]
    fn intersection_of_lines() {
        let p1 = point!(0.0, 0.0);
        let p2 = point!(2.0, 2.0);
        let p3 = point!(0.0, 2.0);
        let p4 = point!(2.0, 0.0);
	let r = Intersection::lines(p1, p2, p3, p4);
	if let Intersection::Point(p) = r {
            assert_eq!(p, point!(1.0, 1.0));
	} else {
	    panic!();
	}
    }

    #[test]
    fn some_coordinates_on_line() {
	// horizontally up
	let coords = supercover_line(point!(0.0, 0.0), point!(3.3, 2.2));
	assert_eq!(coords.as_slice(), &[point!(0, 0), point!(1, 0), point!(1, 1), point!(2, 1), point!(2, 2), point!(3, 2)]);

	// horizontally down
	let coords = supercover_line(point!(0.0, 5.0), point!(3.3, 2.2));
	assert_eq!(coords.as_slice(), &[point!(0, 5), point!(0, 4), point!(1, 4), point!(1, 3), point!(2, 3), point!(2, 2), point!(3, 2)]);

	// vertically right
	let coords = supercover_line(point!(0.0, 0.0), point!(2.2, 3.3));
	assert_eq!(coords.as_slice(), &[point!(0, 0), point!(0, 1), point!(1, 1), point!(1, 2), point!(2, 2), point!(2, 3)]);

	// vertically left
	let coords = supercover_line(point!(5.0, 0.0), point!(3.0, 3.0));
	assert_eq!(coords.as_slice(), &[point!(5, 0), point!(4, 0), point!(4, 1), point!(3, 1), point!(3, 2), point!(3, 3)]);

	// negative
	let coords = supercover_line(point!(0.0, 0.0), point!(-3.0, -2.0));
	assert_eq!(coords.as_slice(), &[point!(-3, -2), point!(-2, -2), point!(-2, -1), point!(-1, -1), point!(-1, 0), point!(0, 0)]);

	// 
	let coords = supercover_line(point!(0.0, 0.0), point!(2.3, 1.1));
	assert_eq!(coords.as_slice(), &[point!(0, 0), point!(1, 0), point!(2, 0), point!(2, 1)]);
    }
}
Commit	Line	Data
2836f506	1	use std::ops::{Add, AddAssign, Sub, SubAssign, Mul, MulAssign, Div, DivAssign, Neg};
296187ca	2
60058b91 TW	3	////////// POINT ///////////////////////////////////////////////////////////////
60058b91 TW	4
787dbfb4	5	#[macro_export]
296187ca	6	macro_rules! point {
6ba7aef1	7	( $x:expr, $y:expr ) => {
e570927a	8	Point { x: $x, y: $y }
6ba7aef1	9	};
296187ca TW	10	}
296187ca TW	11
b0566120	12	#[derive(Debug, Default, Copy, Clone, PartialEq)]
e570927a	13	pub struct Point<T> {
296187ca TW	14	pub x: T,
	15	pub y: T,
	16	}
	17
e570927a	18	impl Point<f64> {
eca25591	19	pub fn length(&self) -> f64 {
296187ca TW	20	((self.x * self.x) + (self.y * self.y)).sqrt()
296187ca TW	21	}
bf7b5671	22
93fc5734	23	pub fn normalized(&self) -> Self {
eca25591 TW	24	let l = self.length();
	25	Self {
	26	x: self.x / l,
	27	y: self.y / l,
	28	}
	29	}
	30
40742678 TW	31	pub fn to_angle(&self) -> Angle {
40742678 TW	32	self.y.atan2(self.x).radians()
eca25591 TW	33	}
eca25591 TW	34
e570927a TW	35	pub fn to_i32(self) -> Point<i32> {
e570927a TW	36	Point {
bf7b5671 TW	37	x: self.x as i32,
	38	y: self.y as i32,
	39	}
	40	}
b1075e66 TW	41
	42	pub fn cross_product(&self, p: Self) -> f64 {
	43	return self.x * p.y - self.y * p.x;
	44	}
15cda333 TW	45
	46	/// Returns the perpendicular projection of this vector on a line with the specified angle.
	47	pub fn project_onto(&self, angle: Angle) -> Point<f64> {
	48	let dot_product = self.length() * (self.to_angle() - angle).to_radians().cos();
	49	Point::from(angle) * dot_product
	50	}
296187ca TW	51	}
296187ca TW	52
0d75b79e	53	macro_rules! impl_point_op {
6cd86b94	54	($op:tt, $trait:ident($fn:ident), $trait_assign:ident($fn_assign:ident), $rhs:ident = $Rhs:ty => $x:expr, $y:expr) => {
e570927a	55	impl<T: $trait<Output = T>> $trait<$Rhs> for Point<T> {
6cd86b94 TW	56	type Output = Self;
	57
	58	fn $fn(self, $rhs: $Rhs) -> Self {
	59	Self {
	60	x: self.x $op $x,
	61	y: self.y $op $y,
	62	}
	63	}
2836f506	64	}
2836f506	65
e570927a	66	impl<T: $trait<Output = T> + Copy> $trait_assign<$Rhs> for Point<T> {
6cd86b94 TW	67	fn $fn_assign(&mut self, $rhs: $Rhs) {
	68	*self = Self {
	69	x: self.x $op $x,
	70	y: self.y $op $y,
	71	}
	72	}
2836f506 TW	73	}
	74	}
	75	}
	76
0d75b79e TW	77	impl_point_op!(+, Add(add), AddAssign(add_assign), rhs = Point<T> => rhs.x, rhs.y);
	78	impl_point_op!(-, Sub(sub), SubAssign(sub_assign), rhs = Point<T> => rhs.x, rhs.y);
	79	impl_point_op!(*, Mul(mul), MulAssign(mul_assign), rhs = Point<T> => rhs.x, rhs.y);
	80	impl_point_op!(/, Div(div), DivAssign(div_assign), rhs = Point<T> => rhs.x, rhs.y);
	81	impl_point_op!(+, Add(add), AddAssign(add_assign), rhs = (T, T) => rhs.0, rhs.1);
	82	impl_point_op!(-, Sub(sub), SubAssign(sub_assign), rhs = (T, T) => rhs.0, rhs.1);
	83	impl_point_op!(*, Mul(mul), MulAssign(mul_assign), rhs = (T, T) => rhs.0, rhs.1);
	84	impl_point_op!(/, Div(div), DivAssign(div_assign), rhs = (T, T) => rhs.0, rhs.1);
	85	impl_point_op!(*, Mul(mul), MulAssign(mul_assign), rhs = Dimension<T> => rhs.width, rhs.height);
	86	impl_point_op!(/, Div(div), DivAssign(div_assign), rhs = Dimension<T> => rhs.width, rhs.height);
2836f506 TW	87
2836f506 TW	88	////////// multiply point with scalar //////////////////////////////////////////
e570927a	89	impl<T: Mul<Output = T> + Copy> Mul<T> for Point<T> {
2836f506 TW	90	type Output = Self;
	91
	92	fn mul(self, rhs: T) -> Self {
	93	Self {
	94	x: self.x * rhs,
	95	y: self.y * rhs,
	96	}
	97	}
	98	}
	99
e570927a	100	impl<T: Mul<Output = T> + Copy> MulAssign<T> for Point<T> {
2836f506 TW	101	fn mul_assign(&mut self, rhs: T) {
	102	*self = Self {
	103	x: self.x * rhs,
	104	y: self.y * rhs,
	105	}
	106	}
	107	}
	108
2836f506	109	////////// divide point with scalar ////////////////////////////////////////////
e570927a	110	impl<T: Div<Output = T> + Copy> Div<T> for Point<T> {
2836f506 TW	111	type Output = Self;
	112
	113	fn div(self, rhs: T) -> Self {
	114	Self {
	115	x: self.x / rhs,
	116	y: self.y / rhs,
	117	}
	118	}
	119	}
	120
e570927a	121	impl<T: Div<Output = T> + Copy> DivAssign<T> for Point<T> {
2836f506 TW	122	fn div_assign(&mut self, rhs: T) {
	123	*self = Self {
	124	x: self.x / rhs,
	125	y: self.y / rhs,
	126	}
	127	}
	128	}
	129
e570927a	130	impl<T: Neg<Output = T>> Neg for Point<T> {
2836f506 TW	131	type Output = Self;
	132
	133	fn neg(self) -> Self {
	134	Self {
	135	x: -self.x,
	136	y: -self.y,
	137	}
296187ca TW	138	}
	139	}
	140
e570927a	141	impl<T> From<(T, T)> for Point<T> {
b0566120	142	fn from(item: (T, T)) -> Self {
e570927a	143	Point {
b0566120 TW	144	x: item.0,
	145	y: item.1,
	146	}
	147	}
	148	}
	149
e570927a TW	150	impl<T> From<Point<T>> for (T, T) {
e570927a TW	151	fn from(item: Point<T>) -> Self {
bf7b5671 TW	152	(item.x, item.y)
	153	}
	154	}
	155
40742678 TW	156	impl From<Angle> for Point<f64> {
	157	fn from(item: Angle) -> Self {
	158	Point {
	159	x: item.0.cos(),
	160	y: item.0.sin(),
	161	}
e58a1769 TW	162	}
	163	}
	164
40742678	165	////////// ANGLE ///////////////////////////////////////////////////////////////
e58a1769	166
a9eacb2b	167	#[derive(Debug, Default, Clone, Copy)]
40742678	168	pub struct Angle(pub f64);
e58a1769	169
40742678 TW	170	pub trait ToAngle {
	171	fn radians(self) -> Angle;
	172	fn degrees(self) -> Angle;
	173	}
	174
	175	macro_rules! impl_angle {
	176	($($type:ty),*) => {
	177	$(
	178	impl ToAngle for $type {
	179	fn radians(self) -> Angle {
	180	Angle(self as f64)
	181	}
	182
	183	fn degrees(self) -> Angle {
	184	Angle((self as f64).to_radians())
	185	}
	186	}
	187
	188	impl Mul<$type> for Angle {
	189	type Output = Self;
	190
	191	fn mul(self, rhs: $type) -> Self {
	192	Angle(self.0 * (rhs as f64))
	193	}
	194	}
	195
	196	impl MulAssign<$type> for Angle {
	197	fn mul_assign(&mut self, rhs: $type) {
	198	self.0 *= rhs as f64;
	199	}
	200	}
	201
	202	impl Div<$type> for Angle {
	203	type Output = Self;
	204
	205	fn div(self, rhs: $type) -> Self {
	206	Angle(self.0 / (rhs as f64))
	207	}
	208	}
	209
	210	impl DivAssign<$type> for Angle {
	211	fn div_assign(&mut self, rhs: $type) {
	212	self.0 /= rhs as f64;
	213	}
	214	}
	215	)*
e58a1769 TW	216	}
	217	}
	218
40742678 TW	219	impl_angle!(f32, f64, i8, i16, i32, i64, isize, u8, u16, u32, u64, usize);
	220
	221	impl Angle {
	222	pub fn to_radians(self) -> f64 {
	223	self.0
	224	}
	225
	226	pub fn to_degrees(self) -> f64 {
	227	self.0.to_degrees()
e58a1769	228	}
8065e264 TW	229
8065e264 TW	230	/// Returns the reflection of the incident when mirrored along this angle.
40742678 TW	231	pub fn mirror(&self, incidence: Angle) -> Angle {
	232	Angle((std::f64::consts::PI + self.0 * 2.0 - incidence.0) % std::f64::consts::TAU)
	233	}
15cda333 TW	234
	235	pub fn reverse(&self) -> Angle {
	236	Angle((self.0 + std::f64::consts::PI) % std::f64::consts::TAU)
	237	}
40742678 TW	238	}
40742678 TW	239
a9eacb2b TW	240	impl PartialEq for Angle {
	241	fn eq(&self, rhs: &Angle) -> bool {
	242	self.0 % std::f64::consts::TAU == rhs.0 % std::f64::consts::TAU
	243	}
	244	}
40742678 TW	245
	246	// addition and subtraction of angles
	247
	248	impl Add<Angle> for Angle {
	249	type Output = Self;
	250
	251	fn add(self, rhs: Angle) -> Self {
	252	Angle(self.0 + rhs.0)
	253	}
	254	}
	255
	256	impl AddAssign<Angle> for Angle {
	257	fn add_assign(&mut self, rhs: Angle) {
	258	self.0 += rhs.0;
	259	}
	260	}
	261
	262	impl Sub<Angle> for Angle {
	263	type Output = Self;
	264
	265	fn sub(self, rhs: Angle) -> Self {
	266	Angle(self.0 - rhs.0)
	267	}
	268	}
	269
	270	impl SubAssign<Angle> for Angle {
	271	fn sub_assign(&mut self, rhs: Angle) {
	272	self.0 -= rhs.0;
8065e264	273	}
e58a1769 TW	274	}
e58a1769 TW	275
60058b91 TW	276	////////// INTERSECTION ////////////////////////////////////////////////////////
	277
	278	#[derive(Debug)]
	279	pub enum Intersection {
	280	Point(Point<f64>),
	281	//Line(Point<f64>, Point<f64>), // TODO: overlapping collinear
	282	None,
	283	}
	284
	285	impl Intersection {
	286	pub fn lines(p1: Point<f64>, p2: Point<f64>, p3: Point<f64>, p4: Point<f64>) -> Intersection {
	287	let s1 = p2 - p1;
	288	let s2 = p4 - p3;
	289
	290	let denomimator = -s2.x * s1.y + s1.x * s2.y;
	291	if denomimator != 0.0 {
	292	let s = (-s1.y * (p1.x - p3.x) + s1.x * (p1.y - p3.y)) / denomimator;
	293	let t = ( s2.x * (p1.y - p3.y) - s2.y * (p1.x - p3.x)) / denomimator;
	294
0c56b1f7	295	if (0.0..=1.0).contains(&s) && (0.0..=1.0).contains(&t) {
60058b91 TW	296	return Intersection::Point(p1 + (s1 * t))
	297	}
	298	}
	299
	300	Intersection::None
	301	}
	302	}
	303
	304	////////// DIMENSION ///////////////////////////////////////////////////////////
	305
0b5024d1	306	#[macro_export]
1f42d724 TW	307	macro_rules! dimen {
	308	( $w:expr, $h:expr ) => {
	309	Dimension { width: $w, height: $h }
0b5024d1 TW	310	};
	311	}
	312
8012f86b	313	#[derive(Debug, Default, Copy, Clone, PartialEq)]
1f42d724	314	pub struct Dimension<T> {
6edafdc0 TW	315	pub width: T,
	316	pub height: T,
	317	}
	318
1f42d724	319	impl<T: Mul<Output = T> + Copy> Dimension<T> {
6edafdc0 TW	320	#[allow(dead_code)]
6edafdc0 TW	321	pub fn area(&self) -> T {
6ba7aef1	322	self.width * self.height
6edafdc0 TW	323	}
	324	}
	325
1f42d724	326	impl<T> From<(T, T)> for Dimension<T> {
6edafdc0	327	fn from(item: (T, T)) -> Self {
1f42d724	328	Dimension {
6ba7aef1 TW	329	width: item.0,
	330	height: item.1,
	331	}
6edafdc0 TW	332	}
	333	}
	334
8012f86b TW	335	impl<T> From<Dimension<T>> for (T, T) {
	336	fn from(item: Dimension<T>) -> Self {
	337	(item.width, item.height)
	338	}
	339	}
	340
	341	////////////////////////////////////////////////////////////////////////////////
	342
	343	#[allow(dead_code)]
	344	pub fn supercover_line_int(p1: Point<isize>, p2: Point<isize>) -> Vec<Point<isize>> {
	345	let d = p2 - p1;
	346	let n = point!(d.x.abs(), d.y.abs());
bb3eb700	347	let step = point!(d.x.signum(), d.y.signum());
8012f86b	348
0c56b1f7	349	let mut p = p1;
8012f86b TW	350	let mut points = vec!(point!(p.x as isize, p.y as isize));
	351	let mut i = point!(0, 0);
	352	while i.x < n.x \|\| i.y < n.y {
	353	let decision = (1 + 2 * i.x) * n.y - (1 + 2 * i.y) * n.x;
	354	if decision == 0 { // next step is diagonal
	355	p.x += step.x;
	356	p.y += step.y;
	357	i.x += 1;
	358	i.y += 1;
	359	} else if decision < 0 { // next step is horizontal
	360	p.x += step.x;
	361	i.x += 1;
	362	} else { // next step is vertical
	363	p.y += step.y;
	364	i.y += 1;
	365	}
	366	points.push(point!(p.x as isize, p.y as isize));
	367	}
	368
	369	points
	370	}
	371
	372	/// Calculates all points a line crosses, unlike Bresenham's line algorithm.
	373	/// There might be room for a lot of improvement here.
	374	pub fn supercover_line(mut p1: Point<f64>, mut p2: Point<f64>) -> Vec<Point<isize>> {
	375	let mut delta = p2 - p1;
	376	if (delta.x.abs() > delta.y.abs() && delta.x.is_sign_negative()) \|\| (delta.x.abs() <= delta.y.abs() && delta.y.is_sign_negative()) {
	377	std::mem::swap(&mut p1, &mut p2);
	378	delta = -delta;
	379	}
	380
	381	let mut last = point!(p1.x as isize, p1.y as isize);
	382	let mut coords: Vec<Point<isize>> = vec!();
	383	coords.push(last);
	384
	385	if delta.x.abs() > delta.y.abs() {
	386	let k = delta.y / delta.x;
	387	let m = p1.y as f64 - p1.x as f64 * k;
	388	for x in (p1.x as isize + 1)..=(p2.x as isize) {
	389	let y = (k * x as f64 + m).floor();
	390	let next = point!(x as isize - 1, y as isize);
	391	if next != last {
	392	coords.push(next);
	393	}
	394	let next = point!(x as isize, y as isize);
	395	coords.push(next);
	396	last = next;
	397	}
	398	} else {
	399	let k = delta.x / delta.y;
	400	let m = p1.x as f64 - p1.y as f64 * k;
	401	for y in (p1.y as isize + 1)..=(p2.y as isize) {
	402	let x = (k * y as f64 + m).floor();
	403	let next = point!(x as isize, y as isize - 1);
	404	if next != last {
	405	coords.push(next);
	406	}
	407	let next = point!(x as isize, y as isize);
	408	coords.push(next);
	409	last = next;
	410	}
	411	}
	412
	413	let next = point!(p2.x as isize, p2.y as isize);
414	if next != last {
415	coords.push(next);
416	}
417
418	coords
419	}
420
60058b91	421	////////// TESTS ///////////////////////////////////////////////////////////////
249d43ea	422
296187ca TW	423	#[cfg(test)]
	424	mod tests {
	425	use super::*;
	426
	427	#[test]
	428	fn immutable_copy_of_point() {
	429	let a = point!(0, 0);
	430	let mut b = a; // Copy
	431	assert_eq!(a, b); // PartialEq
	432	b.x = 1;
	433	assert_ne!(a, b); // PartialEq
	434	}
	435
	436	#[test]
	437	fn add_points() {
	438	let mut a = point!(1, 0);
	439	assert_eq!(a + point!(2, 2), point!(3, 2)); // Add
	440	a += point!(2, 2); // AddAssign
	441	assert_eq!(a, point!(3, 2));
2836f506 TW	442	assert_eq!(point!(1, 0) + (2, 3), point!(3, 3));
	443	}
	444
	445	#[test]
	446	fn sub_points() {
	447	let mut a = point!(1, 0);
	448	assert_eq!(a - point!(2, 2), point!(-1, -2));
	449	a -= point!(2, 2);
	450	assert_eq!(a, point!(-1, -2));
6cd86b94	451	assert_eq!(point!(1, 0) - (2, 3), point!(-1, -3));
2836f506 TW	452	}
	453
	454	#[test]
	455	fn mul_points() {
	456	let mut a = point!(1, 2);
	457	assert_eq!(a * 2, point!(2, 4));
	458	assert_eq!(a * point!(2, 3), point!(2, 6));
	459	a *= 2;
	460	assert_eq!(a, point!(2, 4));
	461	a *= point!(3, 1);
	462	assert_eq!(a, point!(6, 4));
6cd86b94	463	assert_eq!(point!(1, 0) * (2, 3), point!(2, 0));
2836f506 TW	464	}
	465
	466	#[test]
	467	fn div_points() {
	468	let mut a = point!(4, 8);
	469	assert_eq!(a / 2, point!(2, 4));
	470	assert_eq!(a / point!(2, 4), point!(2, 2));
	471	a /= 2;
	472	assert_eq!(a, point!(2, 4));
	473	a /= point!(2, 4);
	474	assert_eq!(a, point!(1, 1));
6cd86b94	475	assert_eq!(point!(6, 3) / (2, 3), point!(3, 1));
2836f506 TW	476	}
	477
	478	#[test]
	479	fn neg_point() {
	480	assert_eq!(point!(1, 1), -point!(-1, -1));
296187ca	481	}
6edafdc0 TW	482
6edafdc0 TW	483	#[test]
e58a1769	484	fn angles() {
40742678	485	assert_eq!(0.radians(), 0.degrees());
a9eacb2b	486	assert_eq!(0.degrees(), 360.degrees());
40742678 TW	487	assert_eq!(180.degrees(), std::f64::consts::PI.radians());
	488	assert_eq!(std::f64::consts::PI.radians().to_degrees(), 180.0);
	489	assert!((Point::from(90.degrees()) - point!(0.0, 1.0)).length() < 0.001);
	490	assert!((Point::from(std::f64::consts::FRAC_PI_2.radians()) - point!(0.0, 1.0)).length() < 0.001);
e58a1769 TW	491	}
	492
	493	#[test]
1f42d724 TW	494	fn area_for_dimension_of_multipliable_type() {
1f42d724 TW	495	let r: Dimension<_> = (30, 20).into(); // the Into trait uses the From trait
6ba7aef1	496	assert_eq!(r.area(), 30 * 20);
1f42d724	497	// let a = Dimension::from(("a".to_string(), "b".to_string())).area(); // this doesn't work, because area() is not implemented for String
6edafdc0	498	}
60058b91 TW	499
	500	#[test]
	501	fn intersection_of_lines() {
	502	let p1 = point!(0.0, 0.0);
	503	let p2 = point!(2.0, 2.0);
	504	let p3 = point!(0.0, 2.0);
	505	let p4 = point!(2.0, 0.0);
	506	let r = Intersection::lines(p1, p2, p3, p4);
	507	if let Intersection::Point(p) = r {
	508	assert_eq!(p, point!(1.0, 1.0));
	509	} else {
	510	panic!();
	511	}
	512	}
8012f86b TW	513
	514	#[test]
	515	fn some_coordinates_on_line() {
	516	// horizontally up
	517	let coords = supercover_line(point!(0.0, 0.0), point!(3.3, 2.2));
	518	assert_eq!(coords.as_slice(), &[point!(0, 0), point!(1, 0), point!(1, 1), point!(2, 1), point!(2, 2), point!(3, 2)]);
	519
	520	// horizontally down
	521	let coords = supercover_line(point!(0.0, 5.0), point!(3.3, 2.2));
	522	assert_eq!(coords.as_slice(), &[point!(0, 5), point!(0, 4), point!(1, 4), point!(1, 3), point!(2, 3), point!(2, 2), point!(3, 2)]);
	523
	524	// vertically right
	525	let coords = supercover_line(point!(0.0, 0.0), point!(2.2, 3.3));
	526	assert_eq!(coords.as_slice(), &[point!(0, 0), point!(0, 1), point!(1, 1), point!(1, 2), point!(2, 2), point!(2, 3)]);
	527
	528	// vertically left
	529	let coords = supercover_line(point!(5.0, 0.0), point!(3.0, 3.0));
	530	assert_eq!(coords.as_slice(), &[point!(5, 0), point!(4, 0), point!(4, 1), point!(3, 1), point!(3, 2), point!(3, 3)]);
	531
	532	// negative
	533	let coords = supercover_line(point!(0.0, 0.0), point!(-3.0, -2.0));
	534	assert_eq!(coords.as_slice(), &[point!(-3, -2), point!(-2, -2), point!(-2, -1), point!(-1, -1), point!(-1, 0), point!(0, 0)]);
	535
	536	//
	537	let coords = supercover_line(point!(0.0, 0.0), point!(2.3, 1.1));
	538	assert_eq!(coords.as_slice(), &[point!(0, 0), point!(1, 0), point!(2, 0), point!(2, 1)]);
	539	}
296187ca	540	}