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