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