src/algorithm/earcut.h

changeset 301
8ccd6fdb30dc
parent 300
3a4b132b8353
child 302
d59cb01d8031
--- a/src/algorithm/earcut.h	Tue Jun 28 19:47:34 2022 +0300
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,828 +0,0 @@
-#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 = &currentBlock[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);
-}
-}

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