--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/thirdparty/earcut.h Tue Jun 28 19:49:45 2022 +0300
@@ -0,0 +1,828 @@
+#pragma once
+
+#include <algorithm>
+#include <cassert>
+#include <cmath>
+#include <cstddef>
+#include <limits>
+#include <memory>
+#include <utility>
+#include <vector>
+
+namespace mapbox {
+
+namespace util {
+
+template <std::size_t I, typename T> struct nth {
+ inline static typename std::tuple_element<I, T>::type
+ get(const T& t) { return std::get<I>(t); }
+};
+
+}
+
+namespace detail {
+
+template <typename N = uint32_t>
+class Earcut {
+public:
+ std::vector<N> indices;
+ std::size_t vertices = 0;
+
+ template <typename Polygon>
+ void operator()(const Polygon& points);
+
+private:
+ struct Node {
+ Node(N index, double x_, double y_) : i(index), x(x_), y(y_) {}
+ Node(const Node&) = delete;
+ Node& operator=(const Node&) = delete;
+ Node(Node&&) = delete;
+ Node& operator=(Node&&) = delete;
+
+ const N i;
+ const double x;
+ const double y;
+
+ // previous and next vertice nodes in a polygon ring
+ Node* prev = nullptr;
+ Node* next = nullptr;
+
+ // z-order curve value
+ int32_t z = 0;
+
+ // previous and next nodes in z-order
+ Node* prevZ = nullptr;
+ Node* nextZ = nullptr;
+
+ // indicates whether this is a steiner point
+ bool steiner = false;
+ };
+
+ template <typename Ring> Node* linkedList(const Ring& points, const bool clockwise);
+ Node* filterPoints(Node* start, Node* end = nullptr);
+ void earcutLinked(Node* ear, int pass = 0);
+ bool isEar(Node* ear);
+ bool isEarHashed(Node* ear);
+ Node* cureLocalIntersections(Node* start);
+ void splitEarcut(Node* start);
+ template <typename Polygon> Node* eliminateHoles(const Polygon& points, Node* outerNode);
+ Node* eliminateHole(Node* hole, Node* outerNode);
+ Node* findHoleBridge(Node* hole, Node* outerNode);
+ bool sectorContainsSector(const Node* m, const Node* p);
+ void indexCurve(Node* start);
+ Node* sortLinked(Node* list);
+ int32_t zOrder(const double x_, const double y_);
+ Node* getLeftmost(Node* start);
+ bool pointInTriangle(double ax, double ay, double bx, double by, double cx, double cy, double px, double py) const;
+ bool isValidDiagonal(Node* a, Node* b);
+ double area(const Node* p, const Node* q, const Node* r) const;
+ bool equals(const Node* p1, const Node* p2);
+ bool intersects(const Node* p1, const Node* q1, const Node* p2, const Node* q2);
+ bool onSegment(const Node* p, const Node* q, const Node* r);
+ int sign(double val);
+ bool intersectsPolygon(const Node* a, const Node* b);
+ bool locallyInside(const Node* a, const Node* b);
+ bool middleInside(const Node* a, const Node* b);
+ Node* splitPolygon(Node* a, Node* b);
+ template <typename Point> Node* insertNode(std::size_t i, const Point& p, Node* last);
+ void removeNode(Node* p);
+
+ bool hashing;
+ double minX, maxX;
+ double minY, maxY;
+ double inv_size = 0;
+
+ template <typename T, typename Alloc = std::allocator<T>>
+ class ObjectPool {
+ public:
+ ObjectPool() { }
+ ObjectPool(std::size_t blockSize_) {
+ reset(blockSize_);
+ }
+ ~ObjectPool() {
+ clear();
+ }
+ template <typename... Args>
+ T* construct(Args&&... args) {
+ if (currentIndex >= blockSize) {
+ currentBlock = alloc_traits::allocate(alloc, blockSize);
+ allocations.emplace_back(currentBlock);
+ currentIndex = 0;
+ }
+ T* object = ¤tBlock[currentIndex++];
+ alloc_traits::construct(alloc, object, std::forward<Args>(args)...);
+ return object;
+ }
+ void reset(std::size_t newBlockSize) {
+ for (auto allocation : allocations) {
+ alloc_traits::deallocate(alloc, allocation, blockSize);
+ }
+ allocations.clear();
+ blockSize = std::max<std::size_t>(1, newBlockSize);
+ currentBlock = nullptr;
+ currentIndex = blockSize;
+ }
+ void clear() { reset(blockSize); }
+ private:
+ T* currentBlock = nullptr;
+ std::size_t currentIndex = 1;
+ std::size_t blockSize = 1;
+ std::vector<T*> allocations;
+ Alloc alloc;
+ typedef typename std::allocator_traits<Alloc> alloc_traits;
+ };
+ ObjectPool<Node> nodes;
+};
+
+template <typename N> template <typename Polygon>
+void Earcut<N>::operator()(const Polygon& points) {
+ // reset
+ indices.clear();
+ vertices = 0;
+
+ if (points.empty()) return;
+
+ double x;
+ double y;
+ int threshold = 80;
+ std::size_t len = 0;
+
+ for (size_t i = 0; threshold >= 0 && i < points.size(); i++) {
+ threshold -= static_cast<int>(points[i].size());
+ len += points[i].size();
+ }
+
+ //estimate size of nodes and indices
+ nodes.reset(len * 3 / 2);
+ indices.reserve(len + points[0].size());
+
+ Node* outerNode = linkedList(points[0], true);
+ if (!outerNode || outerNode->prev == outerNode->next) return;
+
+ if (points.size() > 1) outerNode = eliminateHoles(points, outerNode);
+
+ // if the shape is not too simple, we'll use z-order curve hash later; calculate polygon bbox
+ hashing = threshold < 0;
+ if (hashing) {
+ Node* p = outerNode->next;
+ minX = maxX = outerNode->x;
+ minY = maxY = outerNode->y;
+ do {
+ x = p->x;
+ y = p->y;
+ minX = std::min<double>(minX, x);
+ minY = std::min<double>(minY, y);
+ maxX = std::max<double>(maxX, x);
+ maxY = std::max<double>(maxY, y);
+ p = p->next;
+ } while (p != outerNode);
+
+ // minX, minY and size are later used to transform coords into integers for z-order calculation
+ inv_size = std::max<double>(maxX - minX, maxY - minY);
+ inv_size = inv_size != .0 ? (1. / inv_size) : .0;
+ }
+
+ earcutLinked(outerNode);
+
+ nodes.clear();
+}
+
+// create a circular doubly linked list from polygon points in the specified winding order
+template <typename N> template <typename Ring>
+typename Earcut<N>::Node*
+Earcut<N>::linkedList(const Ring& points, const bool clockwise) {
+ using Point = typename Ring::value_type;
+ double sum = 0;
+ const std::size_t len = points.size();
+ std::size_t i, j;
+ Node* last = nullptr;
+
+ // calculate original winding order of a polygon ring
+ for (i = 0, j = len > 0 ? len - 1 : 0; i < len; j = i++) {
+ const auto& p1 = points[i];
+ const auto& p2 = points[j];
+ const double p20 = util::nth<0, Point>::get(p2);
+ const double p10 = util::nth<0, Point>::get(p1);
+ const double p11 = util::nth<1, Point>::get(p1);
+ const double p21 = util::nth<1, Point>::get(p2);
+ sum += (p20 - p10) * (p11 + p21);
+ }
+
+ // link points into circular doubly-linked list in the specified winding order
+ if (clockwise == (sum > 0)) {
+ for (i = 0; i < len; i++) last = insertNode(vertices + i, points[i], last);
+ } else {
+ for (i = len; i-- > 0;) last = insertNode(vertices + i, points[i], last);
+ }
+
+ if (last && equals(last, last->next)) {
+ removeNode(last);
+ last = last->next;
+ }
+
+ vertices += len;
+
+ return last;
+}
+
+// eliminate colinear or duplicate points
+template <typename N>
+typename Earcut<N>::Node*
+Earcut<N>::filterPoints(Node* start, Node* end) {
+ if (!end) end = start;
+
+ Node* p = start;
+ bool again;
+ do {
+ again = false;
+
+ if (!p->steiner && (equals(p, p->next) || area(p->prev, p, p->next) == 0)) {
+ removeNode(p);
+ p = end = p->prev;
+
+ if (p == p->next) break;
+ again = true;
+
+ } else {
+ p = p->next;
+ }
+ } while (again || p != end);
+
+ return end;
+}
+
+// main ear slicing loop which triangulates a polygon (given as a linked list)
+template <typename N>
+void Earcut<N>::earcutLinked(Node* ear, int pass) {
+ if (!ear) return;
+
+ // interlink polygon nodes in z-order
+ if (!pass && hashing) indexCurve(ear);
+
+ Node* stop = ear;
+ Node* prev;
+ Node* next;
+
+ int iterations = 0;
+
+ // iterate through ears, slicing them one by one
+ while (ear->prev != ear->next) {
+ iterations++;
+ prev = ear->prev;
+ next = ear->next;
+
+ if (hashing ? isEarHashed(ear) : isEar(ear)) {
+ // cut off the triangle
+ indices.emplace_back(prev->i);
+ indices.emplace_back(ear->i);
+ indices.emplace_back(next->i);
+
+ removeNode(ear);
+
+ // skipping the next vertice leads to less sliver triangles
+ ear = next->next;
+ stop = next->next;
+
+ continue;
+ }
+
+ ear = next;
+
+ // if we looped through the whole remaining polygon and can't find any more ears
+ if (ear == stop) {
+ // try filtering points and slicing again
+ if (!pass) earcutLinked(filterPoints(ear), 1);
+
+ // if this didn't work, try curing all small self-intersections locally
+ else if (pass == 1) {
+ ear = cureLocalIntersections(filterPoints(ear));
+ earcutLinked(ear, 2);
+
+ // as a last resort, try splitting the remaining polygon into two
+ } else if (pass == 2) splitEarcut(ear);
+
+ break;
+ }
+ }
+}
+
+// check whether a polygon node forms a valid ear with adjacent nodes
+template <typename N>
+bool Earcut<N>::isEar(Node* ear) {
+ const Node* a = ear->prev;
+ const Node* b = ear;
+ const Node* c = ear->next;
+
+ if (area(a, b, c) >= 0) return false; // reflex, can't be an ear
+
+ // now make sure we don't have other points inside the potential ear
+ Node* p = ear->next->next;
+
+ while (p != ear->prev) {
+ if (pointInTriangle(a->x, a->y, b->x, b->y, c->x, c->y, p->x, p->y) &&
+ area(p->prev, p, p->next) >= 0) return false;
+ p = p->next;
+ }
+
+ return true;
+}
+
+template <typename N>
+bool Earcut<N>::isEarHashed(Node* ear) {
+ const Node* a = ear->prev;
+ const Node* b = ear;
+ const Node* c = ear->next;
+
+ if (area(a, b, c) >= 0) return false; // reflex, can't be an ear
+
+ // triangle bbox; min & max are calculated like this for speed
+ const double minTX = std::min<double>(a->x, std::min<double>(b->x, c->x));
+ const double minTY = std::min<double>(a->y, std::min<double>(b->y, c->y));
+ const double maxTX = std::max<double>(a->x, std::max<double>(b->x, c->x));
+ const double maxTY = std::max<double>(a->y, std::max<double>(b->y, c->y));
+
+ // z-order range for the current triangle bbox;
+ const int32_t minZ = zOrder(minTX, minTY);
+ const int32_t maxZ = zOrder(maxTX, maxTY);
+
+ // first look for points inside the triangle in increasing z-order
+ Node* p = ear->nextZ;
+
+ while (p && p->z <= maxZ) {
+ if (p != ear->prev && p != ear->next &&
+ pointInTriangle(a->x, a->y, b->x, b->y, c->x, c->y, p->x, p->y) &&
+ area(p->prev, p, p->next) >= 0) return false;
+ p = p->nextZ;
+ }
+
+ // then look for points in decreasing z-order
+ p = ear->prevZ;
+
+ while (p && p->z >= minZ) {
+ if (p != ear->prev && p != ear->next &&
+ pointInTriangle(a->x, a->y, b->x, b->y, c->x, c->y, p->x, p->y) &&
+ area(p->prev, p, p->next) >= 0) return false;
+ p = p->prevZ;
+ }
+
+ return true;
+}
+
+// go through all polygon nodes and cure small local self-intersections
+template <typename N>
+typename Earcut<N>::Node*
+Earcut<N>::cureLocalIntersections(Node* start) {
+ Node* p = start;
+ do {
+ Node* a = p->prev;
+ Node* b = p->next->next;
+
+ // a self-intersection where edge (v[i-1],v[i]) intersects (v[i+1],v[i+2])
+ if (!equals(a, b) && intersects(a, p, p->next, b) && locallyInside(a, b) && locallyInside(b, a)) {
+ indices.emplace_back(a->i);
+ indices.emplace_back(p->i);
+ indices.emplace_back(b->i);
+
+ // remove two nodes involved
+ removeNode(p);
+ removeNode(p->next);
+
+ p = start = b;
+ }
+ p = p->next;
+ } while (p != start);
+
+ return filterPoints(p);
+}
+
+// try splitting polygon into two and triangulate them independently
+template <typename N>
+void Earcut<N>::splitEarcut(Node* start) {
+ // look for a valid diagonal that divides the polygon into two
+ Node* a = start;
+ do {
+ Node* b = a->next->next;
+ while (b != a->prev) {
+ if (a->i != b->i && isValidDiagonal(a, b)) {
+ // split the polygon in two by the diagonal
+ Node* c = splitPolygon(a, b);
+
+ // filter colinear points around the cuts
+ a = filterPoints(a, a->next);
+ c = filterPoints(c, c->next);
+
+ // run earcut on each half
+ earcutLinked(a);
+ earcutLinked(c);
+ return;
+ }
+ b = b->next;
+ }
+ a = a->next;
+ } while (a != start);
+}
+
+// link every hole into the outer loop, producing a single-ring polygon without holes
+template <typename N> template <typename Polygon>
+typename Earcut<N>::Node*
+Earcut<N>::eliminateHoles(const Polygon& points, Node* outerNode) {
+ const size_t len = points.size();
+
+ std::vector<Node*> queue;
+ for (size_t i = 1; i < len; i++) {
+ Node* list = linkedList(points[i], false);
+ if (list) {
+ if (list == list->next) list->steiner = true;
+ queue.push_back(getLeftmost(list));
+ }
+ }
+ std::sort(queue.begin(), queue.end(), [](const Node* a, const Node* b) {
+ return a->x < b->x;
+ });
+
+ // process holes from left to right
+ for (size_t i = 0; i < queue.size(); i++) {
+ outerNode = eliminateHole(queue[i], outerNode);
+ outerNode = filterPoints(outerNode, outerNode->next);
+ }
+
+ return outerNode;
+}
+
+// find a bridge between vertices that connects hole with an outer ring and and link it
+template <typename N>
+typename Earcut<N>::Node*
+Earcut<N>::eliminateHole(Node* hole, Node* outerNode) {
+ Node* bridge = findHoleBridge(hole, outerNode);
+ if (!bridge) {
+ return outerNode;
+ }
+
+ Node* bridgeReverse = splitPolygon(bridge, hole);
+
+ // filter collinear points around the cuts
+ Node* filteredBridge = filterPoints(bridge, bridge->next);
+ filterPoints(bridgeReverse, bridgeReverse->next);
+
+ // Check if input node was removed by the filtering
+ return outerNode == bridge ? filteredBridge : outerNode;
+}
+
+// David Eberly's algorithm for finding a bridge between hole and outer polygon
+template <typename N>
+typename Earcut<N>::Node*
+Earcut<N>::findHoleBridge(Node* hole, Node* outerNode) {
+ Node* p = outerNode;
+ double hx = hole->x;
+ double hy = hole->y;
+ double qx = -std::numeric_limits<double>::infinity();
+ Node* m = nullptr;
+
+ // find a segment intersected by a ray from the hole's leftmost Vertex to the left;
+ // segment's endpoint with lesser x will be potential connection Vertex
+ do {
+ if (hy <= p->y && hy >= p->next->y && p->next->y != p->y) {
+ double x = p->x + (hy - p->y) * (p->next->x - p->x) / (p->next->y - p->y);
+ if (x <= hx && x > qx) {
+ qx = x;
+ if (x == hx) {
+ if (hy == p->y) return p;
+ if (hy == p->next->y) return p->next;
+ }
+ m = p->x < p->next->x ? p : p->next;
+ }
+ }
+ p = p->next;
+ } while (p != outerNode);
+
+ if (!m) return 0;
+
+ if (hx == qx) return m; // hole touches outer segment; pick leftmost endpoint
+
+ // look for points inside the triangle of hole Vertex, segment intersection and endpoint;
+ // if there are no points found, we have a valid connection;
+ // otherwise choose the Vertex of the minimum angle with the ray as connection Vertex
+
+ const Node* stop = m;
+ double tanMin = std::numeric_limits<double>::infinity();
+ double tanCur = 0;
+
+ p = m;
+ double mx = m->x;
+ double my = m->y;
+
+ do {
+ if (hx >= p->x && p->x >= mx && hx != p->x &&
+ pointInTriangle(hy < my ? hx : qx, hy, mx, my, hy < my ? qx : hx, hy, p->x, p->y)) {
+
+ tanCur = std::abs(hy - p->y) / (hx - p->x); // tangential
+
+ if (locallyInside(p, hole) &&
+ (tanCur < tanMin || (tanCur == tanMin && (p->x > m->x || sectorContainsSector(m, p))))) {
+ m = p;
+ tanMin = tanCur;
+ }
+ }
+
+ p = p->next;
+ } while (p != stop);
+
+ return m;
+}
+
+// whether sector in vertex m contains sector in vertex p in the same coordinates
+template <typename N>
+bool Earcut<N>::sectorContainsSector(const Node* m, const Node* p) {
+ return area(m->prev, m, p->prev) < 0 && area(p->next, m, m->next) < 0;
+}
+
+// interlink polygon nodes in z-order
+template <typename N>
+void Earcut<N>::indexCurve(Node* start) {
+ assert(start);
+ Node* p = start;
+
+ do {
+ p->z = p->z ? p->z : zOrder(p->x, p->y);
+ p->prevZ = p->prev;
+ p->nextZ = p->next;
+ p = p->next;
+ } while (p != start);
+
+ p->prevZ->nextZ = nullptr;
+ p->prevZ = nullptr;
+
+ sortLinked(p);
+}
+
+// Simon Tatham's linked list merge sort algorithm
+// http://www.chiark.greenend.org.uk/~sgtatham/algorithms/listsort.html
+template <typename N>
+typename Earcut<N>::Node*
+Earcut<N>::sortLinked(Node* list) {
+ assert(list);
+ Node* p;
+ Node* q;
+ Node* e;
+ Node* tail;
+ int i, numMerges, pSize, qSize;
+ int inSize = 1;
+
+ for (;;) {
+ p = list;
+ list = nullptr;
+ tail = nullptr;
+ numMerges = 0;
+
+ while (p) {
+ numMerges++;
+ q = p;
+ pSize = 0;
+ for (i = 0; i < inSize; i++) {
+ pSize++;
+ q = q->nextZ;
+ if (!q) break;
+ }
+
+ qSize = inSize;
+
+ while (pSize > 0 || (qSize > 0 && q)) {
+
+ if (pSize == 0) {
+ e = q;
+ q = q->nextZ;
+ qSize--;
+ } else if (qSize == 0 || !q) {
+ e = p;
+ p = p->nextZ;
+ pSize--;
+ } else if (p->z <= q->z) {
+ e = p;
+ p = p->nextZ;
+ pSize--;
+ } else {
+ e = q;
+ q = q->nextZ;
+ qSize--;
+ }
+
+ if (tail) tail->nextZ = e;
+ else list = e;
+
+ e->prevZ = tail;
+ tail = e;
+ }
+
+ p = q;
+ }
+
+ tail->nextZ = nullptr;
+
+ if (numMerges <= 1) return list;
+
+ inSize *= 2;
+ }
+}
+
+// z-order of a Vertex given coords and size of the data bounding box
+template <typename N>
+int32_t Earcut<N>::zOrder(const double x_, const double y_) {
+ // coords are transformed into non-negative 15-bit integer range
+ int32_t x = static_cast<int32_t>(32767.0 * (x_ - minX) * inv_size);
+ int32_t y = static_cast<int32_t>(32767.0 * (y_ - minY) * inv_size);
+
+ x = (x | (x << 8)) & 0x00FF00FF;
+ x = (x | (x << 4)) & 0x0F0F0F0F;
+ x = (x | (x << 2)) & 0x33333333;
+ x = (x | (x << 1)) & 0x55555555;
+
+ y = (y | (y << 8)) & 0x00FF00FF;
+ y = (y | (y << 4)) & 0x0F0F0F0F;
+ y = (y | (y << 2)) & 0x33333333;
+ y = (y | (y << 1)) & 0x55555555;
+
+ return x | (y << 1);
+}
+
+// find the leftmost node of a polygon ring
+template <typename N>
+typename Earcut<N>::Node*
+Earcut<N>::getLeftmost(Node* start) {
+ Node* p = start;
+ Node* leftmost = start;
+ do {
+ if (p->x < leftmost->x || (p->x == leftmost->x && p->y < leftmost->y))
+ leftmost = p;
+ p = p->next;
+ } while (p != start);
+
+ return leftmost;
+}
+
+// check if a point lies within a convex triangle
+template <typename N>
+bool Earcut<N>::pointInTriangle(double ax, double ay, double bx, double by,
+double cx, double cy, double px, double py) const {
+ return (cx - px) * (ay - py) - (ax - px) * (cy - py) >= 0 &&
+ (ax - px) * (by - py) - (bx - px) * (ay - py) >= 0 &&
+ (bx - px) * (cy - py) - (cx - px) * (by - py) >= 0;
+}
+
+// check if a diagonal between two polygon nodes is valid (lies in polygon interior)
+template <typename N>
+bool Earcut<N>::isValidDiagonal(Node* a, Node* b) {
+ // dones't intersect other edges
+ return a->next->i != b->i && a->prev->i != b->i && !intersectsPolygon(a, b) &&
+ // locally visible
+ ((locallyInside(a, b) && locallyInside(b, a) && middleInside(a, b) &&
+ // does not create opposite-facing sectors
+ (area(a->prev, a, b->prev) != 0.0 || area(a, b->prev, b) != 0.0)) ||
+ // special zero-length case
+ (equals(a, b) && area(a->prev, a, a->next) > 0 && area(b->prev, b, b->next) > 0));
+}
+
+// signed area of a triangle
+template <typename N>
+double Earcut<N>::area(const Node* p, const Node* q, const Node* r) const {
+ return (q->y - p->y) * (r->x - q->x) - (q->x - p->x) * (r->y - q->y);
+}
+
+// check if two points are equal
+template <typename N>
+bool Earcut<N>::equals(const Node* p1, const Node* p2) {
+ return p1->x == p2->x && p1->y == p2->y;
+}
+
+// check if two segments intersect
+template <typename N>
+bool Earcut<N>::intersects(const Node* p1, const Node* q1, const Node* p2, const Node* q2) {
+ int o1 = sign(area(p1, q1, p2));
+ int o2 = sign(area(p1, q1, q2));
+ int o3 = sign(area(p2, q2, p1));
+ int o4 = sign(area(p2, q2, q1));
+
+ if (o1 != o2 && o3 != o4) return true; // general case
+
+ if (o1 == 0 && onSegment(p1, p2, q1)) return true; // p1, q1 and p2 are collinear and p2 lies on p1q1
+ if (o2 == 0 && onSegment(p1, q2, q1)) return true; // p1, q1 and q2 are collinear and q2 lies on p1q1
+ if (o3 == 0 && onSegment(p2, p1, q2)) return true; // p2, q2 and p1 are collinear and p1 lies on p2q2
+ if (o4 == 0 && onSegment(p2, q1, q2)) return true; // p2, q2 and q1 are collinear and q1 lies on p2q2
+
+ return false;
+}
+
+// for collinear points p, q, r, check if point q lies on segment pr
+template <typename N>
+bool Earcut<N>::onSegment(const Node* p, const Node* q, const Node* r) {
+ return q->x <= std::max<double>(p->x, r->x) &&
+ q->x >= std::min<double>(p->x, r->x) &&
+ q->y <= std::max<double>(p->y, r->y) &&
+ q->y >= std::min<double>(p->y, r->y);
+}
+
+template <typename N>
+int Earcut<N>::sign(double val) {
+ return (0.0 < val) - (val < 0.0);
+}
+
+// check if a polygon diagonal intersects any polygon segments
+template <typename N>
+bool Earcut<N>::intersectsPolygon(const Node* a, const Node* b) {
+ const Node* p = a;
+ do {
+ if (p->i != a->i && p->next->i != a->i && p->i != b->i && p->next->i != b->i &&
+ intersects(p, p->next, a, b)) return true;
+ p = p->next;
+ } while (p != a);
+
+ return false;
+}
+
+// check if a polygon diagonal is locally inside the polygon
+template <typename N>
+bool Earcut<N>::locallyInside(const Node* a, const Node* b) {
+ return area(a->prev, a, a->next) < 0 ?
+ area(a, b, a->next) >= 0 && area(a, a->prev, b) >= 0 :
+ area(a, b, a->prev) < 0 || area(a, a->next, b) < 0;
+}
+
+// check if the middle Vertex of a polygon diagonal is inside the polygon
+template <typename N>
+bool Earcut<N>::middleInside(const Node* a, const Node* b) {
+ const Node* p = a;
+ bool inside = false;
+ double px = (a->x + b->x) / 2;
+ double py = (a->y + b->y) / 2;
+ do {
+ if (((p->y > py) != (p->next->y > py)) && p->next->y != p->y &&
+ (px < (p->next->x - p->x) * (py - p->y) / (p->next->y - p->y) + p->x))
+ inside = !inside;
+ p = p->next;
+ } while (p != a);
+
+ return inside;
+}
+
+// link two polygon vertices with a bridge; if the vertices belong to the same ring, it splits
+// polygon into two; if one belongs to the outer ring and another to a hole, it merges it into a
+// single ring
+template <typename N>
+typename Earcut<N>::Node*
+Earcut<N>::splitPolygon(Node* a, Node* b) {
+ Node* a2 = nodes.construct(a->i, a->x, a->y);
+ Node* b2 = nodes.construct(b->i, b->x, b->y);
+ Node* an = a->next;
+ Node* bp = b->prev;
+
+ a->next = b;
+ b->prev = a;
+
+ a2->next = an;
+ an->prev = a2;
+
+ b2->next = a2;
+ a2->prev = b2;
+
+ bp->next = b2;
+ b2->prev = bp;
+
+ return b2;
+}
+
+// create a node and util::optionally link it with previous one (in a circular doubly linked list)
+template <typename N> template <typename Point>
+typename Earcut<N>::Node*
+Earcut<N>::insertNode(std::size_t i, const Point& pt, Node* last) {
+ Node* p = nodes.construct(static_cast<N>(i), util::nth<0, Point>::get(pt), util::nth<1, Point>::get(pt));
+
+ if (!last) {
+ p->prev = p;
+ p->next = p;
+
+ } else {
+ assert(last);
+ p->next = last->next;
+ p->prev = last;
+ last->next->prev = p;
+ last->next = p;
+ }
+ return p;
+}
+
+template <typename N>
+void Earcut<N>::removeNode(Node* p) {
+ p->next->prev = p->prev;
+ p->prev->next = p->next;
+
+ if (p->prevZ) p->prevZ->nextZ = p->nextZ;
+ if (p->nextZ) p->nextZ->prevZ = p->prevZ;
+}
+}
+
+template <typename N = uint32_t, typename Polygon>
+std::vector<N> earcut(const Polygon& poly) {
+ mapbox::detail::Earcut<N> earcut;
+ earcut(poly);
+ return std::move(earcut.indices);
+}
+}