1 | #pragma once |
2 | |
3 | #include <algorithm> |
4 | #include <cassert> |
5 | #include <cmath> |
6 | #include <memory> |
7 | #include <vector> |
8 | |
9 | namespace mapbox { |
10 | |
11 | namespace util { |
12 | |
13 | template <std::size_t I, typename T> struct nth { |
14 | inline static typename std::tuple_element<I, T>::type |
15 | get(const T& t) { return std::get<I>(t); }; |
16 | }; |
17 | |
18 | } |
19 | |
20 | namespace detail { |
21 | |
22 | template <typename N = uint32_t> |
23 | class Earcut { |
24 | public: |
25 | std::vector<N> indices; |
26 | std::size_t vertices = 0; |
27 | |
28 | template <typename Polygon> |
29 | void operator()(const Polygon& points); |
30 | |
31 | private: |
32 | struct Node { |
33 | Node(N index, double x_, double y_) : i(index), x(x_), y(y_) {} |
34 | Node(const Node&) = delete; |
35 | Node& operator=(const Node&) = delete; |
36 | Node(Node&&) = delete; |
37 | Node& operator=(Node&&) = delete; |
38 | |
39 | const N i; |
40 | const double x; |
41 | const double y; |
42 | |
43 | // previous and next vertice nodes in a polygon ring |
44 | Node* prev = nullptr; |
45 | Node* next = nullptr; |
46 | |
47 | // z-order curve value |
48 | int32_t z = 0; |
49 | |
50 | // previous and next nodes in z-order |
51 | Node* prevZ = nullptr; |
52 | Node* nextZ = nullptr; |
53 | |
54 | // indicates whether this is a steiner point |
55 | bool steiner = false; |
56 | }; |
57 | |
58 | template <typename Ring> Node* linkedList(const Ring& points, const bool clockwise); |
59 | Node* filterPoints(Node* start, Node* end = nullptr); |
60 | void earcutLinked(Node* ear, int pass = 0); |
61 | bool isEar(Node* ear); |
62 | bool isEarHashed(Node* ear); |
63 | Node* cureLocalIntersections(Node* start); |
64 | void splitEarcut(Node* start); |
65 | template <typename Polygon> Node* eliminateHoles(const Polygon& points, Node* outerNode); |
66 | void eliminateHole(Node* hole, Node* outerNode); |
67 | Node* findHoleBridge(Node* hole, Node* outerNode); |
68 | void indexCurve(Node* start); |
69 | Node* sortLinked(Node* list); |
70 | int32_t zOrder(const double x_, const double y_); |
71 | Node* getLeftmost(Node* start); |
72 | bool pointInTriangle(double ax, double ay, double bx, double by, double cx, double cy, double px, double py) const; |
73 | bool isValidDiagonal(Node* a, Node* b); |
74 | double area(const Node* p, const Node* q, const Node* r) const; |
75 | bool equals(const Node* p1, const Node* p2); |
76 | bool intersects(const Node* p1, const Node* q1, const Node* p2, const Node* q2); |
77 | bool intersectsPolygon(const Node* a, const Node* b); |
78 | bool locallyInside(const Node* a, const Node* b); |
79 | bool middleInside(const Node* a, const Node* b); |
80 | Node* splitPolygon(Node* a, Node* b); |
81 | template <typename Point> Node* insertNode(std::size_t i, const Point& p, Node* last); |
82 | void removeNode(Node* p); |
83 | |
84 | bool hashing; |
85 | double minX, maxX; |
86 | double minY, maxY; |
87 | double inv_size = 0; |
88 | |
89 | template <typename T, typename Alloc = std::allocator<T>> |
90 | class ObjectPool { |
91 | public: |
92 | ObjectPool() { } |
93 | ObjectPool(std::size_t blockSize_) { |
94 | reset(newBlockSize: blockSize_); |
95 | } |
96 | ~ObjectPool() { |
97 | clear(); |
98 | } |
99 | template <typename... Args> |
100 | T* construct(Args&&... args) { |
101 | if (currentIndex >= blockSize) { |
102 | currentBlock = alloc.allocate(blockSize); |
103 | allocations.emplace_back(currentBlock); |
104 | currentIndex = 0; |
105 | } |
106 | T* object = ¤tBlock[currentIndex++]; |
107 | alloc.construct(object, std::forward<Args>(args)...); |
108 | return object; |
109 | } |
110 | void reset(std::size_t newBlockSize) { |
111 | for (auto allocation : allocations) alloc.deallocate(allocation, blockSize); |
112 | allocations.clear(); |
113 | blockSize = std::max<std::size_t>(a: 1, b: newBlockSize); |
114 | currentBlock = nullptr; |
115 | currentIndex = blockSize; |
116 | } |
117 | void clear() { reset(newBlockSize: blockSize); } |
118 | private: |
119 | T* currentBlock = nullptr; |
120 | std::size_t currentIndex = 1; |
121 | std::size_t blockSize = 1; |
122 | std::vector<T*> allocations; |
123 | Alloc alloc; |
124 | }; |
125 | ObjectPool<Node> nodes; |
126 | }; |
127 | |
128 | template <typename N> template <typename Polygon> |
129 | void Earcut<N>::operator()(const Polygon& points) { |
130 | // reset |
131 | indices.clear(); |
132 | vertices = 0; |
133 | |
134 | if (points.empty()) return; |
135 | |
136 | double x; |
137 | double y; |
138 | int threshold = 80; |
139 | std::size_t len = 0; |
140 | |
141 | for (size_t i = 0; threshold >= 0 && i < points.size(); i++) { |
142 | threshold -= static_cast<int>(points[i].size()); |
143 | len += points[i].size(); |
144 | } |
145 | |
146 | //estimate size of nodes and indices |
147 | nodes.reset(len * 3 / 2); |
148 | indices.reserve(len + points[0].size()); |
149 | |
150 | Node* outerNode = linkedList(points[0], true); |
151 | if (!outerNode) return; |
152 | |
153 | if (points.size() > 1) outerNode = eliminateHoles(points, outerNode); |
154 | |
155 | // if the shape is not too simple, we'll use z-order curve hash later; calculate polygon bbox |
156 | hashing = threshold < 0; |
157 | if (hashing) { |
158 | Node* p = outerNode->next; |
159 | minX = maxX = p->x; |
160 | minY = maxY = p->y; |
161 | do { |
162 | x = p->x; |
163 | y = p->y; |
164 | minX = std::min<double>(a: minX, b: x); |
165 | minY = std::min<double>(a: minY, b: y); |
166 | maxX = std::max<double>(a: maxX, b: x); |
167 | maxY = std::max<double>(a: maxY, b: y); |
168 | p = p->next; |
169 | } while (p != outerNode); |
170 | |
171 | // minX, minY and size are later used to transform coords into integers for z-order calculation |
172 | inv_size = std::max<double>(a: maxX - minX, b: maxY - minY); |
173 | inv_size = inv_size != .0 ? (1. / inv_size) : .0; |
174 | } |
175 | |
176 | earcutLinked(ear: outerNode); |
177 | |
178 | nodes.clear(); |
179 | } |
180 | |
181 | // create a circular doubly linked list from polygon points in the specified winding order |
182 | template <typename N> template <typename Ring> |
183 | typename Earcut<N>::Node* |
184 | Earcut<N>::linkedList(const Ring& points, const bool clockwise) { |
185 | using Point = typename Ring::value_type; |
186 | double sum = 0; |
187 | const std::size_t len = points.size(); |
188 | std::size_t i, j; |
189 | Node* last = nullptr; |
190 | |
191 | // calculate original winding order of a polygon ring |
192 | for (i = 0, j = len > 0 ? len - 1 : 0; i < len; j = i++) { |
193 | const auto& p1 = points[i]; |
194 | const auto& p2 = points[j]; |
195 | const double p20 = util::nth<0, Point>::get(p2); |
196 | const double p10 = util::nth<0, Point>::get(p1); |
197 | const double p11 = util::nth<1, Point>::get(p1); |
198 | const double p21 = util::nth<1, Point>::get(p2); |
199 | sum += (p20 - p10) * (p11 + p21); |
200 | } |
201 | |
202 | // link points into circular doubly-linked list in the specified winding order |
203 | if (clockwise == (sum > 0)) { |
204 | for (i = 0; i < len; i++) last = insertNode(vertices + i, points[i], last); |
205 | } else { |
206 | for (i = len; i-- > 0;) last = insertNode(vertices + i, points[i], last); |
207 | } |
208 | |
209 | if (last && equals(p1: last, p2: last->next)) { |
210 | removeNode(p: last); |
211 | last = last->next; |
212 | } |
213 | |
214 | vertices += len; |
215 | |
216 | return last; |
217 | } |
218 | |
219 | // eliminate colinear or duplicate points |
220 | template <typename N> |
221 | typename Earcut<N>::Node* |
222 | Earcut<N>::filterPoints(Node* start, Node* end) { |
223 | if (!end) end = start; |
224 | |
225 | Node* p = start; |
226 | bool again; |
227 | do { |
228 | again = false; |
229 | |
230 | if (!p->steiner && (equals(p1: p, p2: p->next) || area(p: p->prev, q: p, r: p->next) == 0)) { |
231 | removeNode(p); |
232 | p = end = p->prev; |
233 | |
234 | if (p == p->next) break; |
235 | again = true; |
236 | |
237 | } else { |
238 | p = p->next; |
239 | } |
240 | } while (again || p != end); |
241 | |
242 | return end; |
243 | } |
244 | |
245 | // main ear slicing loop which triangulates a polygon (given as a linked list) |
246 | template <typename N> |
247 | void Earcut<N>::earcutLinked(Node* ear, int pass) { |
248 | if (!ear) return; |
249 | |
250 | // interlink polygon nodes in z-order |
251 | if (!pass && hashing) indexCurve(start: ear); |
252 | |
253 | Node* stop = ear; |
254 | Node* prev; |
255 | Node* next; |
256 | |
257 | int iterations = 0; |
258 | |
259 | // iterate through ears, slicing them one by one |
260 | while (ear->prev != ear->next) { |
261 | iterations++; |
262 | prev = ear->prev; |
263 | next = ear->next; |
264 | |
265 | if (hashing ? isEarHashed(ear) : isEar(ear)) { |
266 | // cut off the triangle |
267 | indices.emplace_back(prev->i); |
268 | indices.emplace_back(ear->i); |
269 | indices.emplace_back(next->i); |
270 | |
271 | removeNode(p: ear); |
272 | |
273 | // skipping the next vertice leads to less sliver triangles |
274 | ear = next->next; |
275 | stop = next->next; |
276 | |
277 | continue; |
278 | } |
279 | |
280 | ear = next; |
281 | |
282 | // if we looped through the whole remaining polygon and can't find any more ears |
283 | if (ear == stop) { |
284 | // try filtering points and slicing again |
285 | if (!pass) earcutLinked(ear: filterPoints(start: ear), pass: 1); |
286 | |
287 | // if this didn't work, try curing all small self-intersections locally |
288 | else if (pass == 1) { |
289 | ear = cureLocalIntersections(start: ear); |
290 | earcutLinked(ear, pass: 2); |
291 | |
292 | // as a last resort, try splitting the remaining polygon into two |
293 | } else if (pass == 2) splitEarcut(start: ear); |
294 | |
295 | break; |
296 | } |
297 | } |
298 | } |
299 | |
300 | // check whether a polygon node forms a valid ear with adjacent nodes |
301 | template <typename N> |
302 | bool Earcut<N>::isEar(Node* ear) { |
303 | const Node* a = ear->prev; |
304 | const Node* b = ear; |
305 | const Node* c = ear->next; |
306 | |
307 | if (area(p: a, q: b, r: c) >= 0) return false; // reflex, can't be an ear |
308 | |
309 | // now make sure we don't have other points inside the potential ear |
310 | Node* p = ear->next->next; |
311 | |
312 | while (p != ear->prev) { |
313 | if (pointInTriangle(ax: a->x, ay: a->y, bx: b->x, by: b->y, cx: c->x, cy: c->y, px: p->x, py: p->y) && |
314 | area(p: p->prev, q: p, r: p->next) >= 0) return false; |
315 | p = p->next; |
316 | } |
317 | |
318 | return true; |
319 | } |
320 | |
321 | template <typename N> |
322 | bool Earcut<N>::isEarHashed(Node* ear) { |
323 | const Node* a = ear->prev; |
324 | const Node* b = ear; |
325 | const Node* c = ear->next; |
326 | |
327 | if (area(p: a, q: b, r: c) >= 0) return false; // reflex, can't be an ear |
328 | |
329 | // triangle bbox; min & max are calculated like this for speed |
330 | const double minTX = std::min<double>(a->x, std::min<double>(b->x, c->x)); |
331 | const double minTY = std::min<double>(a->y, std::min<double>(b->y, c->y)); |
332 | const double maxTX = std::max<double>(a->x, std::max<double>(b->x, c->x)); |
333 | const double maxTY = std::max<double>(a->y, std::max<double>(b->y, c->y)); |
334 | |
335 | // z-order range for the current triangle bbox; |
336 | const int32_t minZ = zOrder(x_: minTX, y_: minTY); |
337 | const int32_t maxZ = zOrder(x_: maxTX, y_: maxTY); |
338 | |
339 | // first look for points inside the triangle in increasing z-order |
340 | Node* p = ear->nextZ; |
341 | |
342 | while (p && p->z <= maxZ) { |
343 | if (p != ear->prev && p != ear->next && |
344 | pointInTriangle(ax: a->x, ay: a->y, bx: b->x, by: b->y, cx: c->x, cy: c->y, px: p->x, py: p->y) && |
345 | area(p: p->prev, q: p, r: p->next) >= 0) return false; |
346 | p = p->nextZ; |
347 | } |
348 | |
349 | // then look for points in decreasing z-order |
350 | p = ear->prevZ; |
351 | |
352 | while (p && p->z >= minZ) { |
353 | if (p != ear->prev && p != ear->next && |
354 | pointInTriangle(ax: a->x, ay: a->y, bx: b->x, by: b->y, cx: c->x, cy: c->y, px: p->x, py: p->y) && |
355 | area(p: p->prev, q: p, r: p->next) >= 0) return false; |
356 | p = p->prevZ; |
357 | } |
358 | |
359 | return true; |
360 | } |
361 | |
362 | // go through all polygon nodes and cure small local self-intersections |
363 | template <typename N> |
364 | typename Earcut<N>::Node* |
365 | Earcut<N>::cureLocalIntersections(Node* start) { |
366 | Node* p = start; |
367 | do { |
368 | Node* a = p->prev; |
369 | Node* b = p->next->next; |
370 | |
371 | // a self-intersection where edge (v[i-1],v[i]) intersects (v[i+1],v[i+2]) |
372 | if (!equals(p1: a, p2: b) && intersects(p1: a, q1: p, p2: p->next, q2: b) && locallyInside(a, b) && locallyInside(a: b, b: a)) { |
373 | indices.emplace_back(a->i); |
374 | indices.emplace_back(p->i); |
375 | indices.emplace_back(b->i); |
376 | |
377 | // remove two nodes involved |
378 | removeNode(p); |
379 | removeNode(p: p->next); |
380 | |
381 | p = start = b; |
382 | } |
383 | p = p->next; |
384 | } while (p != start); |
385 | |
386 | return p; |
387 | } |
388 | |
389 | // try splitting polygon into two and triangulate them independently |
390 | template <typename N> |
391 | void Earcut<N>::splitEarcut(Node* start) { |
392 | // look for a valid diagonal that divides the polygon into two |
393 | Node* a = start; |
394 | do { |
395 | Node* b = a->next->next; |
396 | while (b != a->prev) { |
397 | if (a->i != b->i && isValidDiagonal(a, b)) { |
398 | // split the polygon in two by the diagonal |
399 | Node* c = splitPolygon(a, b); |
400 | |
401 | // filter colinear points around the cuts |
402 | a = filterPoints(start: a, end: a->next); |
403 | c = filterPoints(start: c, end: c->next); |
404 | |
405 | // run earcut on each half |
406 | earcutLinked(ear: a); |
407 | earcutLinked(ear: c); |
408 | return; |
409 | } |
410 | b = b->next; |
411 | } |
412 | a = a->next; |
413 | } while (a != start); |
414 | } |
415 | |
416 | // link every hole into the outer loop, producing a single-ring polygon without holes |
417 | template <typename N> template <typename Polygon> |
418 | typename Earcut<N>::Node* |
419 | Earcut<N>::eliminateHoles(const Polygon& points, Node* outerNode) { |
420 | const size_t len = points.size(); |
421 | |
422 | std::vector<Node*> queue; |
423 | for (size_t i = 1; i < len; i++) { |
424 | Node* list = linkedList(points[i], false); |
425 | if (list) { |
426 | if (list == list->next) list->steiner = true; |
427 | queue.push_back(getLeftmost(start: list)); |
428 | } |
429 | } |
430 | std::sort(queue.begin(), queue.end(), [](const Node* a, const Node* b) { |
431 | return a->x < b->x; |
432 | }); |
433 | |
434 | // process holes from left to right |
435 | for (size_t i = 0; i < queue.size(); i++) { |
436 | eliminateHole(hole: queue[i], outerNode); |
437 | outerNode = filterPoints(start: outerNode, end: outerNode->next); |
438 | } |
439 | |
440 | return outerNode; |
441 | } |
442 | |
443 | // find a bridge between vertices that connects hole with an outer ring and and link it |
444 | template <typename N> |
445 | void Earcut<N>::eliminateHole(Node* hole, Node* outerNode) { |
446 | outerNode = findHoleBridge(hole, outerNode); |
447 | if (outerNode) { |
448 | Node* b = splitPolygon(a: outerNode, b: hole); |
449 | filterPoints(start: b, end: b->next); |
450 | } |
451 | } |
452 | |
453 | // David Eberly's algorithm for finding a bridge between hole and outer polygon |
454 | template <typename N> |
455 | typename Earcut<N>::Node* |
456 | Earcut<N>::findHoleBridge(Node* hole, Node* outerNode) { |
457 | Node* p = outerNode; |
458 | double hx = hole->x; |
459 | double hy = hole->y; |
460 | double qx = -std::numeric_limits<double>::infinity(); |
461 | Node* m = nullptr; |
462 | |
463 | // find a segment intersected by a ray from the hole's leftmost Vertex to the left; |
464 | // segment's endpoint with lesser x will be potential connection Vertex |
465 | do { |
466 | if (hy <= p->y && hy >= p->next->y && p->next->y != p->y) { |
467 | double x = p->x + (hy - p->y) * (p->next->x - p->x) / (p->next->y - p->y); |
468 | if (x <= hx && x > qx) { |
469 | qx = x; |
470 | if (x == hx) { |
471 | if (hy == p->y) return p; |
472 | if (hy == p->next->y) return p->next; |
473 | } |
474 | m = p->x < p->next->x ? p : p->next; |
475 | } |
476 | } |
477 | p = p->next; |
478 | } while (p != outerNode); |
479 | |
480 | if (!m) return 0; |
481 | |
482 | if (hx == qx) return m->prev; |
483 | |
484 | // look for points inside the triangle of hole Vertex, segment intersection and endpoint; |
485 | // if there are no points found, we have a valid connection; |
486 | // otherwise choose the Vertex of the minimum angle with the ray as connection Vertex |
487 | |
488 | const Node* stop = m; |
489 | double tanMin = std::numeric_limits<double>::infinity(); |
490 | double tanCur = 0; |
491 | |
492 | p = m->next; |
493 | double mx = m->x; |
494 | double my = m->y; |
495 | |
496 | while (p != stop) { |
497 | if (hx >= p->x && p->x >= mx && hx != p->x && |
498 | pointInTriangle(ax: hy < my ? hx : qx, ay: hy, bx: mx, by: my, cx: hy < my ? qx : hx, cy: hy, px: p->x, py: p->y)) { |
499 | |
500 | tanCur = std::abs(hy - p->y) / (hx - p->x); // tangential |
501 | |
502 | if ((tanCur < tanMin || (tanCur == tanMin && p->x > m->x)) && locallyInside(a: p, b: hole)) { |
503 | m = p; |
504 | tanMin = tanCur; |
505 | } |
506 | } |
507 | |
508 | p = p->next; |
509 | } |
510 | |
511 | return m; |
512 | } |
513 | |
514 | // interlink polygon nodes in z-order |
515 | template <typename N> |
516 | void Earcut<N>::indexCurve(Node* start) { |
517 | assert(start); |
518 | Node* p = start; |
519 | |
520 | do { |
521 | p->z = p->z ? p->z : zOrder(x_: p->x, y_: p->y); |
522 | p->prevZ = p->prev; |
523 | p->nextZ = p->next; |
524 | p = p->next; |
525 | } while (p != start); |
526 | |
527 | p->prevZ->nextZ = nullptr; |
528 | p->prevZ = nullptr; |
529 | |
530 | sortLinked(list: p); |
531 | } |
532 | |
533 | // Simon Tatham's linked list merge sort algorithm |
534 | // http://www.chiark.greenend.org.uk/~sgtatham/algorithms/listsort.html |
535 | template <typename N> |
536 | typename Earcut<N>::Node* |
537 | Earcut<N>::sortLinked(Node* list) { |
538 | assert(list); |
539 | Node* p; |
540 | Node* q; |
541 | Node* e; |
542 | Node* tail; |
543 | int i, numMerges, pSize, qSize; |
544 | int inSize = 1; |
545 | |
546 | for (;;) { |
547 | p = list; |
548 | list = nullptr; |
549 | tail = nullptr; |
550 | numMerges = 0; |
551 | |
552 | while (p) { |
553 | numMerges++; |
554 | q = p; |
555 | pSize = 0; |
556 | for (i = 0; i < inSize; i++) { |
557 | pSize++; |
558 | q = q->nextZ; |
559 | if (!q) break; |
560 | } |
561 | |
562 | qSize = inSize; |
563 | |
564 | while (pSize > 0 || (qSize > 0 && q)) { |
565 | |
566 | if (pSize == 0) { |
567 | e = q; |
568 | q = q->nextZ; |
569 | qSize--; |
570 | } else if (qSize == 0 || !q) { |
571 | e = p; |
572 | p = p->nextZ; |
573 | pSize--; |
574 | } else if (p->z <= q->z) { |
575 | e = p; |
576 | p = p->nextZ; |
577 | pSize--; |
578 | } else { |
579 | e = q; |
580 | q = q->nextZ; |
581 | qSize--; |
582 | } |
583 | |
584 | if (tail) tail->nextZ = e; |
585 | else list = e; |
586 | |
587 | e->prevZ = tail; |
588 | tail = e; |
589 | } |
590 | |
591 | p = q; |
592 | } |
593 | |
594 | tail->nextZ = nullptr; |
595 | |
596 | if (numMerges <= 1) return list; |
597 | |
598 | inSize *= 2; |
599 | } |
600 | } |
601 | |
602 | // z-order of a Vertex given coords and size of the data bounding box |
603 | template <typename N> |
604 | int32_t Earcut<N>::zOrder(const double x_, const double y_) { |
605 | // coords are transformed into non-negative 15-bit integer range |
606 | int32_t x = static_cast<int32_t>(32767.0 * (x_ - minX) * inv_size); |
607 | int32_t y = static_cast<int32_t>(32767.0 * (y_ - minY) * inv_size); |
608 | |
609 | x = (x | (x << 8)) & 0x00FF00FF; |
610 | x = (x | (x << 4)) & 0x0F0F0F0F; |
611 | x = (x | (x << 2)) & 0x33333333; |
612 | x = (x | (x << 1)) & 0x55555555; |
613 | |
614 | y = (y | (y << 8)) & 0x00FF00FF; |
615 | y = (y | (y << 4)) & 0x0F0F0F0F; |
616 | y = (y | (y << 2)) & 0x33333333; |
617 | y = (y | (y << 1)) & 0x55555555; |
618 | |
619 | return x | (y << 1); |
620 | } |
621 | |
622 | // find the leftmost node of a polygon ring |
623 | template <typename N> |
624 | typename Earcut<N>::Node* |
625 | Earcut<N>::getLeftmost(Node* start) { |
626 | Node* p = start; |
627 | Node* leftmost = start; |
628 | do { |
629 | if (p->x < leftmost->x) leftmost = p; |
630 | p = p->next; |
631 | } while (p != start); |
632 | |
633 | return leftmost; |
634 | } |
635 | |
636 | // check if a point lies within a convex triangle |
637 | template <typename N> |
638 | bool Earcut<N>::pointInTriangle(double ax, double ay, double bx, double by, double cx, double cy, double px, double py) const { |
639 | return (cx - px) * (ay - py) - (ax - px) * (cy - py) >= 0 && |
640 | (ax - px) * (by - py) - (bx - px) * (ay - py) >= 0 && |
641 | (bx - px) * (cy - py) - (cx - px) * (by - py) >= 0; |
642 | } |
643 | |
644 | // check if a diagonal between two polygon nodes is valid (lies in polygon interior) |
645 | template <typename N> |
646 | bool Earcut<N>::isValidDiagonal(Node* a, Node* b) { |
647 | return a->next->i != b->i && a->prev->i != b->i && !intersectsPolygon(a, b) && |
648 | locallyInside(a, b) && locallyInside(a: b, b: a) && middleInside(a, b); |
649 | } |
650 | |
651 | // signed area of a triangle |
652 | template <typename N> |
653 | double Earcut<N>::area(const Node* p, const Node* q, const Node* r) const { |
654 | return (q->y - p->y) * (r->x - q->x) - (q->x - p->x) * (r->y - q->y); |
655 | } |
656 | |
657 | // check if two points are equal |
658 | template <typename N> |
659 | bool Earcut<N>::equals(const Node* p1, const Node* p2) { |
660 | return p1->x == p2->x && p1->y == p2->y; |
661 | } |
662 | |
663 | // check if two segments intersect |
664 | template <typename N> |
665 | bool Earcut<N>::intersects(const Node* p1, const Node* q1, const Node* p2, const Node* q2) { |
666 | if ((equals(p1, p2: q1) && equals(p1: p2, p2: q2)) || |
667 | (equals(p1, p2: q2) && equals(p1: p2, p2: q1))) return true; |
668 | return (area(p: p1, q: q1, r: p2) > 0) != (area(p: p1, q: q1, r: q2) > 0) && |
669 | (area(p: p2, q: q2, r: p1) > 0) != (area(p: p2, q: q2, r: q1) > 0); |
670 | } |
671 | |
672 | // check if a polygon diagonal intersects any polygon segments |
673 | template <typename N> |
674 | bool Earcut<N>::intersectsPolygon(const Node* a, const Node* b) { |
675 | const Node* p = a; |
676 | do { |
677 | if (p->i != a->i && p->next->i != a->i && p->i != b->i && p->next->i != b->i && |
678 | intersects(p1: p, q1: p->next, p2: a, q2: b)) return true; |
679 | p = p->next; |
680 | } while (p != a); |
681 | |
682 | return false; |
683 | } |
684 | |
685 | // check if a polygon diagonal is locally inside the polygon |
686 | template <typename N> |
687 | bool Earcut<N>::locallyInside(const Node* a, const Node* b) { |
688 | return area(p: a->prev, q: a, r: a->next) < 0 ? |
689 | area(p: a, q: b, r: a->next) >= 0 && area(p: a, q: a->prev, r: b) >= 0 : |
690 | area(p: a, q: b, r: a->prev) < 0 || area(p: a, q: a->next, r: b) < 0; |
691 | } |
692 | |
693 | // check if the middle Vertex of a polygon diagonal is inside the polygon |
694 | template <typename N> |
695 | bool Earcut<N>::middleInside(const Node* a, const Node* b) { |
696 | const Node* p = a; |
697 | bool inside = false; |
698 | double px = (a->x + b->x) / 2; |
699 | double py = (a->y + b->y) / 2; |
700 | do { |
701 | if (((p->y > py) != (p->next->y > py)) && p->next->y != p->y && |
702 | (px < (p->next->x - p->x) * (py - p->y) / (p->next->y - p->y) + p->x)) |
703 | inside = !inside; |
704 | p = p->next; |
705 | } while (p != a); |
706 | |
707 | return inside; |
708 | } |
709 | |
710 | // link two polygon vertices with a bridge; if the vertices belong to the same ring, it splits |
711 | // polygon into two; if one belongs to the outer ring and another to a hole, it merges it into a |
712 | // single ring |
713 | template <typename N> |
714 | typename Earcut<N>::Node* |
715 | Earcut<N>::splitPolygon(Node* a, Node* b) { |
716 | Node* a2 = nodes.construct(a->i, a->x, a->y); |
717 | Node* b2 = nodes.construct(b->i, b->x, b->y); |
718 | Node* an = a->next; |
719 | Node* bp = b->prev; |
720 | |
721 | a->next = b; |
722 | b->prev = a; |
723 | |
724 | a2->next = an; |
725 | an->prev = a2; |
726 | |
727 | b2->next = a2; |
728 | a2->prev = b2; |
729 | |
730 | bp->next = b2; |
731 | b2->prev = bp; |
732 | |
733 | return b2; |
734 | } |
735 | |
736 | // create a node and util::optionally link it with previous one (in a circular doubly linked list) |
737 | template <typename N> template <typename Point> |
738 | typename Earcut<N>::Node* |
739 | Earcut<N>::insertNode(std::size_t i, const Point& pt, Node* last) { |
740 | Node* p = nodes.construct(static_cast<N>(i), util::nth<0, Point>::get(pt), util::nth<1, Point>::get(pt)); |
741 | |
742 | if (!last) { |
743 | p->prev = p; |
744 | p->next = p; |
745 | |
746 | } else { |
747 | assert(last); |
748 | p->next = last->next; |
749 | p->prev = last; |
750 | last->next->prev = p; |
751 | last->next = p; |
752 | } |
753 | return p; |
754 | } |
755 | |
756 | template <typename N> |
757 | void Earcut<N>::removeNode(Node* p) { |
758 | p->next->prev = p->prev; |
759 | p->prev->next = p->next; |
760 | |
761 | if (p->prevZ) p->prevZ->nextZ = p->nextZ; |
762 | if (p->nextZ) p->nextZ->prevZ = p->prevZ; |
763 | } |
764 | } |
765 | |
766 | template <typename N = uint32_t, typename Polygon> |
767 | std::vector<N> earcut(const Polygon& poly) { |
768 | mapbox::detail::Earcut<N> earcut; |
769 | earcut(poly); |
770 | return std::move(earcut.indices); |
771 | } |
772 | } |
773 | |