--- /dev/null
+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: $y }
+ };
+}
+
+#[derive(Debug, Default, Copy, Clone, PartialEq)]
+pub struct Point<T> {
+ pub x: T,
+ pub y: T,
+}
+
+impl Point<f64> {
+ pub fn length(&self) -> f64 {
+ ((self.x * self.x) + (self.y * self.y)).sqrt()
+ }
+
+ pub fn normalized(&self) -> Self {
+ let l = self.length();
+ Self {
+ x: self.x / l,
+ y: self.y / l,
+ }
+ }
+
+ pub fn to_angle(&self) -> Angle {
+ self.y.atan2(self.x).radians()
+ }
+
+ pub fn to_i32(self) -> Point<i32> {
+ Point {
+ x: self.x as i32,
+ y: self.y as i32,
+ }
+ }
+}
+
+macro_rules! impl_point_op {
+ ($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)
+ }
+}
+
+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!(
+ if d.x > 0 { 1 } else { -1 },
+ if d.y > 0 { 1 } else { -1 }
+ );
+
+ 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)]);
+ }
+}
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