1 use std::ops::{Add, AddAssign, Sub, SubAssign, Mul, MulAssign, Div, DivAssign, Neg};
3 ////////// POINT ///////////////////////////////////////////////////////////////
7 ( $x:expr, $y:expr ) => {
12 #[derive(Debug, Default, Copy, Clone, PartialEq)]
19 pub fn length(&self) -> f64 {
20 ((self.x * self.x) + (self.y * self.y)).sqrt()
23 pub fn normalized(&self) -> Self {
24 let l = self.length();
31 pub fn to_angle(&self) -> Angle {
32 self.y.atan2(self.x).radians()
35 pub fn to_i32(self) -> Point<i32> {
42 pub fn cross_product(&self, p: Self) -> f64 {
43 return self.x * p.y - self.y * p.x;
47 macro_rules! impl_point_op {
48 ($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<Angle> for Point<f64> {
151 fn from(item: Angle) -> Self {
159 ////////// ANGLE ///////////////////////////////////////////////////////////////
161 #[derive(Debug, Default, Clone, Copy)]
162 pub struct Angle(pub f64);
165 fn radians(self) -> Angle;
166 fn degrees(self) -> Angle;
169 macro_rules! impl_angle {
172 impl ToAngle for $type {
173 fn radians(self) -> Angle {
177 fn degrees(self) -> Angle {
178 Angle((self as f64).to_radians())
182 impl Mul<$type> for Angle {
185 fn mul(self, rhs: $type) -> Self {
186 Angle(self.0 * (rhs as f64))
190 impl MulAssign<$type> for Angle {
191 fn mul_assign(&mut self, rhs: $type) {
192 self.0 *= rhs as f64;
196 impl Div<$type> for Angle {
199 fn div(self, rhs: $type) -> Self {
200 Angle(self.0 / (rhs as f64))
204 impl DivAssign<$type> for Angle {
205 fn div_assign(&mut self, rhs: $type) {
206 self.0 /= rhs as f64;
213 impl_angle!(f32, f64, i8, i16, i32, i64, isize, u8, u16, u32, u64, usize);
216 pub fn to_radians(self) -> f64 {
220 pub fn to_degrees(self) -> f64 {
224 /// Returns the reflection of the incident when mirrored along this angle.
225 pub fn mirror(&self, incidence: Angle) -> Angle {
226 Angle((std::f64::consts::PI + self.0 * 2.0 - incidence.0) % std::f64::consts::TAU)
230 impl PartialEq for Angle {
231 fn eq(&self, rhs: &Angle) -> bool {
232 self.0 % std::f64::consts::TAU == rhs.0 % std::f64::consts::TAU
236 // addition and subtraction of angles
238 impl Add<Angle> for Angle {
241 fn add(self, rhs: Angle) -> Self {
242 Angle(self.0 + rhs.0)
246 impl AddAssign<Angle> for Angle {
247 fn add_assign(&mut self, rhs: Angle) {
252 impl Sub<Angle> for Angle {
255 fn sub(self, rhs: Angle) -> Self {
256 Angle(self.0 - rhs.0)
260 impl SubAssign<Angle> for Angle {
261 fn sub_assign(&mut self, rhs: Angle) {
266 ////////// INTERSECTION ////////////////////////////////////////////////////////
269 pub enum Intersection {
271 //Line(Point<f64>, Point<f64>), // TODO: overlapping collinear
276 pub fn lines(p1: Point<f64>, p2: Point<f64>, p3: Point<f64>, p4: Point<f64>) -> Intersection {
280 let denomimator = -s2.x * s1.y + s1.x * s2.y;
281 if denomimator != 0.0 {
282 let s = (-s1.y * (p1.x - p3.x) + s1.x * (p1.y - p3.y)) / denomimator;
283 let t = ( s2.x * (p1.y - p3.y) - s2.y * (p1.x - p3.x)) / denomimator;
285 if (0.0..=1.0).contains(&s) && (0.0..=1.0).contains(&t) {
286 return Intersection::Point(p1 + (s1 * t))
294 ////////// DIMENSION ///////////////////////////////////////////////////////////
298 ( $w:expr, $h:expr ) => {
299 Dimension { width: $w, height: $h }
303 #[derive(Debug, Default, Copy, Clone, PartialEq)]
304 pub struct Dimension<T> {
309 impl<T: Mul<Output = T> + Copy> Dimension<T> {
311 pub fn area(&self) -> T {
312 self.width * self.height
316 impl<T> From<(T, T)> for Dimension<T> {
317 fn from(item: (T, T)) -> Self {
325 impl<T> From<Dimension<T>> for (T, T) {
326 fn from(item: Dimension<T>) -> Self {
327 (item.width, item.height)
331 ////////////////////////////////////////////////////////////////////////////////
334 pub fn supercover_line_int(p1: Point<isize>, p2: Point<isize>) -> Vec<Point<isize>> {
336 let n = point!(d.x.abs(), d.y.abs());
337 let step = point!(d.x.signum(), d.y.signum());
340 let mut points = vec!(point!(p.x as isize, p.y as isize));
341 let mut i = point!(0, 0);
342 while i.x < n.x || i.y < n.y {
343 let decision = (1 + 2 * i.x) * n.y - (1 + 2 * i.y) * n.x;
344 if decision == 0 { // next step is diagonal
349 } else if decision < 0 { // next step is horizontal
352 } else { // next step is vertical
356 points.push(point!(p.x as isize, p.y as isize));
362 /// Calculates all points a line crosses, unlike Bresenham's line algorithm.
363 /// There might be room for a lot of improvement here.
364 pub fn supercover_line(mut p1: Point<f64>, mut p2: Point<f64>) -> Vec<Point<isize>> {
365 let mut delta = p2 - p1;
366 if (delta.x.abs() > delta.y.abs() && delta.x.is_sign_negative()) || (delta.x.abs() <= delta.y.abs() && delta.y.is_sign_negative()) {
367 std::mem::swap(&mut p1, &mut p2);
371 let mut last = point!(p1.x as isize, p1.y as isize);
372 let mut coords: Vec<Point<isize>> = vec!();
375 if delta.x.abs() > delta.y.abs() {
376 let k = delta.y / delta.x;
377 let m = p1.y as f64 - p1.x as f64 * k;
378 for x in (p1.x as isize + 1)..=(p2.x as isize) {
379 let y = (k * x as f64 + m).floor();
380 let next = point!(x as isize - 1, y as isize);
384 let next = point!(x as isize, y as isize);
389 let k = delta.x / delta.y;
390 let m = p1.x as f64 - p1.y as f64 * k;
391 for y in (p1.y as isize + 1)..=(p2.y as isize) {
392 let x = (k * y as f64 + m).floor();
393 let next = point!(x as isize, y as isize - 1);
397 let next = point!(x as isize, y as isize);
403 let next = point!(p2.x as isize, p2.y as isize);
411 ////////// TESTS ///////////////////////////////////////////////////////////////
418 fn immutable_copy_of_point() {
419 let a = point!(0, 0);
420 let mut b = a; // Copy
421 assert_eq!(a, b); // PartialEq
423 assert_ne!(a, b); // PartialEq
428 let mut a = point!(1, 0);
429 assert_eq!(a + point!(2, 2), point!(3, 2)); // Add
430 a += point!(2, 2); // AddAssign
431 assert_eq!(a, point!(3, 2));
432 assert_eq!(point!(1, 0) + (2, 3), point!(3, 3));
437 let mut a = point!(1, 0);
438 assert_eq!(a - point!(2, 2), point!(-1, -2));
440 assert_eq!(a, point!(-1, -2));
441 assert_eq!(point!(1, 0) - (2, 3), point!(-1, -3));
446 let mut a = point!(1, 2);
447 assert_eq!(a * 2, point!(2, 4));
448 assert_eq!(a * point!(2, 3), point!(2, 6));
450 assert_eq!(a, point!(2, 4));
452 assert_eq!(a, point!(6, 4));
453 assert_eq!(point!(1, 0) * (2, 3), point!(2, 0));
458 let mut a = point!(4, 8);
459 assert_eq!(a / 2, point!(2, 4));
460 assert_eq!(a / point!(2, 4), point!(2, 2));
462 assert_eq!(a, point!(2, 4));
464 assert_eq!(a, point!(1, 1));
465 assert_eq!(point!(6, 3) / (2, 3), point!(3, 1));
470 assert_eq!(point!(1, 1), -point!(-1, -1));
475 assert_eq!(0.radians(), 0.degrees());
476 assert_eq!(0.degrees(), 360.degrees());
477 assert_eq!(180.degrees(), std::f64::consts::PI.radians());
478 assert_eq!(std::f64::consts::PI.radians().to_degrees(), 180.0);
479 assert!((Point::from(90.degrees()) - point!(0.0, 1.0)).length() < 0.001);
480 assert!((Point::from(std::f64::consts::FRAC_PI_2.radians()) - point!(0.0, 1.0)).length() < 0.001);
484 fn area_for_dimension_of_multipliable_type() {
485 let r: Dimension<_> = (30, 20).into(); // the Into trait uses the From trait
486 assert_eq!(r.area(), 30 * 20);
487 // let a = Dimension::from(("a".to_string(), "b".to_string())).area(); // this doesn't work, because area() is not implemented for String
491 fn intersection_of_lines() {
492 let p1 = point!(0.0, 0.0);
493 let p2 = point!(2.0, 2.0);
494 let p3 = point!(0.0, 2.0);
495 let p4 = point!(2.0, 0.0);
496 let r = Intersection::lines(p1, p2, p3, p4);
497 if let Intersection::Point(p) = r {
498 assert_eq!(p, point!(1.0, 1.0));
505 fn some_coordinates_on_line() {
507 let coords = supercover_line(point!(0.0, 0.0), point!(3.3, 2.2));
508 assert_eq!(coords.as_slice(), &[point!(0, 0), point!(1, 0), point!(1, 1), point!(2, 1), point!(2, 2), point!(3, 2)]);
511 let coords = supercover_line(point!(0.0, 5.0), point!(3.3, 2.2));
512 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)]);
515 let coords = supercover_line(point!(0.0, 0.0), point!(2.2, 3.3));
516 assert_eq!(coords.as_slice(), &[point!(0, 0), point!(0, 1), point!(1, 1), point!(1, 2), point!(2, 2), point!(2, 3)]);
519 let coords = supercover_line(point!(5.0, 0.0), point!(3.0, 3.0));
520 assert_eq!(coords.as_slice(), &[point!(5, 0), point!(4, 0), point!(4, 1), point!(3, 1), point!(3, 2), point!(3, 3)]);
523 let coords = supercover_line(point!(0.0, 0.0), point!(-3.0, -2.0));
524 assert_eq!(coords.as_slice(), &[point!(-3, -2), point!(-2, -2), point!(-2, -1), point!(-1, -1), point!(-1, 0), point!(0, 0)]);
527 let coords = supercover_line(point!(0.0, 0.0), point!(2.3, 1.1));
528 assert_eq!(coords.as_slice(), &[point!(0, 0), point!(1, 0), point!(2, 0), point!(2, 1)]);