1 use std::ops::{Add, AddAssign, Sub, SubAssign, Mul, MulAssign, Div, DivAssign, Neg};
3 ////////// POINT ///////////////////////////////////////////////////////////////
7 ( $x:expr, $y:expr ) => {
12 #[derive(Debug, Default, Copy, Clone, PartialEq)]
19 pub fn length(&self) -> f64 {
20 ((self.x * self.x) + (self.y * self.y)).sqrt()
23 pub fn normalized(&self) -> Self {
24 let l = self.length();
31 pub fn to_radians(&self) -> Radians {
32 Radians(self.y.atan2(self.x))
35 pub fn to_degrees(&self) -> Degrees {
36 self.to_radians().to_degrees()
39 pub fn to_i32(self) -> Point<i32> {
47 macro_rules! impl_point_op {
48 ($op:tt, $trait:ident($fn:ident), $trait_assign:ident($fn_assign:ident), $rhs:ident = $Rhs:ty => $x:expr, $y:expr) => {
49 impl<T: $trait<Output = T>> $trait<$Rhs> for Point<T> {
52 fn $fn(self, $rhs: $Rhs) -> Self {
60 impl<T: $trait<Output = T> + Copy> $trait_assign<$Rhs> for Point<T> {
61 fn $fn_assign(&mut self, $rhs: $Rhs) {
71 impl_point_op!(+, Add(add), AddAssign(add_assign), rhs = Point<T> => rhs.x, rhs.y);
72 impl_point_op!(-, Sub(sub), SubAssign(sub_assign), rhs = Point<T> => rhs.x, rhs.y);
73 impl_point_op!(*, Mul(mul), MulAssign(mul_assign), rhs = Point<T> => rhs.x, rhs.y);
74 impl_point_op!(/, Div(div), DivAssign(div_assign), rhs = Point<T> => rhs.x, rhs.y);
75 impl_point_op!(+, Add(add), AddAssign(add_assign), rhs = (T, T) => rhs.0, rhs.1);
76 impl_point_op!(-, Sub(sub), SubAssign(sub_assign), rhs = (T, T) => rhs.0, rhs.1);
77 impl_point_op!(*, Mul(mul), MulAssign(mul_assign), rhs = (T, T) => rhs.0, rhs.1);
78 impl_point_op!(/, Div(div), DivAssign(div_assign), rhs = (T, T) => rhs.0, rhs.1);
79 impl_point_op!(*, Mul(mul), MulAssign(mul_assign), rhs = Dimension<T> => rhs.width, rhs.height);
80 impl_point_op!(/, Div(div), DivAssign(div_assign), rhs = Dimension<T> => rhs.width, rhs.height);
82 ////////// multiply point with scalar //////////////////////////////////////////
83 impl<T: Mul<Output = T> + Copy> Mul<T> for Point<T> {
86 fn mul(self, rhs: T) -> Self {
94 impl<T: Mul<Output = T> + Copy> MulAssign<T> for Point<T> {
95 fn mul_assign(&mut self, rhs: T) {
103 ////////// divide point with scalar ////////////////////////////////////////////
104 impl<T: Div<Output = T> + Copy> Div<T> for Point<T> {
107 fn div(self, rhs: T) -> Self {
115 impl<T: Div<Output = T> + Copy> DivAssign<T> for Point<T> {
116 fn div_assign(&mut self, rhs: T) {
124 impl<T: Neg<Output = T>> Neg for Point<T> {
127 fn neg(self) -> Self {
135 impl<T> From<(T, T)> for Point<T> {
136 fn from(item: (T, T)) -> Self {
144 impl<T> From<Point<T>> for (T, T) {
145 fn from(item: Point<T>) -> Self {
150 impl From<Degrees> for Point<f64> {
151 fn from(item: Degrees) -> Self {
152 let r = item.0.to_radians();
160 impl From<Radians> for Point<f64> {
161 fn from(item: Radians) -> Self {
169 #[derive(Debug, Default, PartialEq, Clone, Copy)]
170 pub struct Degrees(pub f64);
171 #[derive(Debug, Default, PartialEq, Clone, Copy)]
172 pub struct Radians(pub f64);
176 pub fn to_radians(&self) -> Radians {
177 Radians(self.0.to_radians())
183 pub fn to_degrees(&self) -> Degrees {
184 Degrees(self.0.to_degrees())
187 /// Returns the reflection of the incident when mirrored along this angle.
188 pub fn mirror(&self, incidence: Radians) -> Radians {
189 Radians((std::f64::consts::PI + self.0 * 2.0 - incidence.0) % std::f64::consts::TAU)
193 ////////// INTERSECTION ////////////////////////////////////////////////////////
196 pub enum Intersection {
198 //Line(Point<f64>, Point<f64>), // TODO: overlapping collinear
203 pub fn lines(p1: Point<f64>, p2: Point<f64>, p3: Point<f64>, p4: Point<f64>) -> Intersection {
207 let denomimator = -s2.x * s1.y + s1.x * s2.y;
208 if denomimator != 0.0 {
209 let s = (-s1.y * (p1.x - p3.x) + s1.x * (p1.y - p3.y)) / denomimator;
210 let t = ( s2.x * (p1.y - p3.y) - s2.y * (p1.x - p3.x)) / denomimator;
212 if s >= 0.0 && s <= 1.0 && t >= 0.0 && t <= 1.0 {
213 return Intersection::Point(p1 + (s1 * t))
221 ////////// DIMENSION ///////////////////////////////////////////////////////////
225 ( $w:expr, $h:expr ) => {
226 Dimension { width: $w, height: $h }
230 #[derive(Debug, Default, Copy, Clone, PartialEq)]
231 pub struct Dimension<T> {
236 impl<T: Mul<Output = T> + Copy> Dimension<T> {
238 pub fn area(&self) -> T {
239 self.width * self.height
243 impl<T> From<(T, T)> for Dimension<T> {
244 fn from(item: (T, T)) -> Self {
252 impl<T> From<Dimension<T>> for (T, T) {
253 fn from(item: Dimension<T>) -> Self {
254 (item.width, item.height)
258 ////////////////////////////////////////////////////////////////////////////////
261 pub fn supercover_line_int(p1: Point<isize>, p2: Point<isize>) -> Vec<Point<isize>> {
263 let n = point!(d.x.abs(), d.y.abs());
265 if d.x > 0 { 1 } else { -1 },
266 if d.y > 0 { 1 } else { -1 }
269 let mut p = p1.clone();
270 let mut points = vec!(point!(p.x as isize, p.y as isize));
271 let mut i = point!(0, 0);
272 while i.x < n.x || i.y < n.y {
273 let decision = (1 + 2 * i.x) * n.y - (1 + 2 * i.y) * n.x;
274 if decision == 0 { // next step is diagonal
279 } else if decision < 0 { // next step is horizontal
282 } else { // next step is vertical
286 points.push(point!(p.x as isize, p.y as isize));
292 /// Calculates all points a line crosses, unlike Bresenham's line algorithm.
293 /// There might be room for a lot of improvement here.
294 pub fn supercover_line(mut p1: Point<f64>, mut p2: Point<f64>) -> Vec<Point<isize>> {
295 let mut delta = p2 - p1;
296 if (delta.x.abs() > delta.y.abs() && delta.x.is_sign_negative()) || (delta.x.abs() <= delta.y.abs() && delta.y.is_sign_negative()) {
297 std::mem::swap(&mut p1, &mut p2);
301 let mut last = point!(p1.x as isize, p1.y as isize);
302 let mut coords: Vec<Point<isize>> = vec!();
305 if delta.x.abs() > delta.y.abs() {
306 let k = delta.y / delta.x;
307 let m = p1.y as f64 - p1.x as f64 * k;
308 for x in (p1.x as isize + 1)..=(p2.x as isize) {
309 let y = (k * x as f64 + m).floor();
310 let next = point!(x as isize - 1, y as isize);
314 let next = point!(x as isize, y as isize);
319 let k = delta.x / delta.y;
320 let m = p1.x as f64 - p1.y as f64 * k;
321 for y in (p1.y as isize + 1)..=(p2.y as isize) {
322 let x = (k * y as f64 + m).floor();
323 let next = point!(x as isize, y as isize - 1);
327 let next = point!(x as isize, y as isize);
333 let next = point!(p2.x as isize, p2.y as isize);
341 ////////// TESTS ///////////////////////////////////////////////////////////////
348 fn immutable_copy_of_point() {
349 let a = point!(0, 0);
350 let mut b = a; // Copy
351 assert_eq!(a, b); // PartialEq
353 assert_ne!(a, b); // PartialEq
358 let mut a = point!(1, 0);
359 assert_eq!(a + point!(2, 2), point!(3, 2)); // Add
360 a += point!(2, 2); // AddAssign
361 assert_eq!(a, point!(3, 2));
362 assert_eq!(point!(1, 0) + (2, 3), point!(3, 3));
367 let mut a = point!(1, 0);
368 assert_eq!(a - point!(2, 2), point!(-1, -2));
370 assert_eq!(a, point!(-1, -2));
371 assert_eq!(point!(1, 0) - (2, 3), point!(-1, -3));
376 let mut a = point!(1, 2);
377 assert_eq!(a * 2, point!(2, 4));
378 assert_eq!(a * point!(2, 3), point!(2, 6));
380 assert_eq!(a, point!(2, 4));
382 assert_eq!(a, point!(6, 4));
383 assert_eq!(point!(1, 0) * (2, 3), point!(2, 0));
388 let mut a = point!(4, 8);
389 assert_eq!(a / 2, point!(2, 4));
390 assert_eq!(a / point!(2, 4), point!(2, 2));
392 assert_eq!(a, point!(2, 4));
394 assert_eq!(a, point!(1, 1));
395 assert_eq!(point!(6, 3) / (2, 3), point!(3, 1));
400 assert_eq!(point!(1, 1), -point!(-1, -1));
405 assert_eq!(Radians(0.0).to_degrees(), Degrees(0.0));
406 assert_eq!(Radians(std::f64::consts::PI).to_degrees(), Degrees(180.0));
407 assert_eq!(Degrees(180.0).to_radians(), Radians(std::f64::consts::PI));
408 assert!((Point::from(Degrees(90.0)) - point!(0.0, 1.0)).length() < 0.001);
409 assert!((Point::from(Radians(std::f64::consts::FRAC_PI_2)) - point!(0.0, 1.0)).length() < 0.001);
413 fn area_for_dimension_of_multipliable_type() {
414 let r: Dimension<_> = (30, 20).into(); // the Into trait uses the From trait
415 assert_eq!(r.area(), 30 * 20);
416 // let a = Dimension::from(("a".to_string(), "b".to_string())).area(); // this doesn't work, because area() is not implemented for String
420 fn intersection_of_lines() {
421 let p1 = point!(0.0, 0.0);
422 let p2 = point!(2.0, 2.0);
423 let p3 = point!(0.0, 2.0);
424 let p4 = point!(2.0, 0.0);
425 let r = Intersection::lines(p1, p2, p3, p4);
426 if let Intersection::Point(p) = r {
427 assert_eq!(p, point!(1.0, 1.0));
434 fn some_coordinates_on_line() {
436 let coords = supercover_line(point!(0.0, 0.0), point!(3.3, 2.2));
437 assert_eq!(coords.as_slice(), &[point!(0, 0), point!(1, 0), point!(1, 1), point!(2, 1), point!(2, 2), point!(3, 2)]);
440 let coords = supercover_line(point!(0.0, 5.0), point!(3.3, 2.2));
441 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)]);
444 let coords = supercover_line(point!(0.0, 0.0), point!(2.2, 3.3));
445 assert_eq!(coords.as_slice(), &[point!(0, 0), point!(0, 1), point!(1, 1), point!(1, 2), point!(2, 2), point!(2, 3)]);
448 let coords = supercover_line(point!(5.0, 0.0), point!(3.0, 3.0));
449 assert_eq!(coords.as_slice(), &[point!(5, 0), point!(4, 0), point!(4, 1), point!(3, 1), point!(3, 2), point!(3, 3)]);
452 let coords = supercover_line(point!(0.0, 0.0), point!(-3.0, -2.0));
453 assert_eq!(coords.as_slice(), &[point!(-3, -2), point!(-2, -2), point!(-2, -1), point!(-1, -1), point!(-1, 0), point!(0, 0)]);
456 let coords = supercover_line(point!(0.0, 0.0), point!(2.3, 1.1));
457 assert_eq!(coords.as_slice(), &[point!(0, 0), point!(1, 0), point!(2, 0), point!(2, 1)]);