earcut.hpp

/*
ISC License

Copyright (c) 2015, Mapbox

Permission to use, copy, modify, and/or distribute this software for any purpose
with or without fee is hereby granted, provided that the above copyright notice
and this permission notice appear in all copies.

THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH
REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT,
INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS
OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER
TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF
THIS SOFTWARE.
*/

#pragma once

#include <algorithm>
#include <cassert>
#include <cmath>
#include <memory>
#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;

    template <typename Polygon>
    void operator()(const Polygon& points);
    
    Earcut() { vertices = 0; inv_size = 0; }

private:
    struct Node {
        Node(N index, double x_, double y_) : i(index), x(x_), y(y_) { z = 0; prev = nullptr; next = nullptr; prevZ = nextZ = nullptr; steiner = false; }
        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;
        Node* next;

        // z-order curve value
        int32_t z;

        // previous and next nodes in z-order
        Node* prevZ;
        Node* nextZ;

        // indicates whether this is a steiner point
        bool steiner; 
    };

    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);
    void eliminateHole(Node* hole, Node* outerNode);
    Node* findHoleBridge(Node* hole, Node* outerNode);
    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 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;

    template <typename T> // , typename Alloc = std::allocator<T>>
    class ObjectPool {
    public:
        ObjectPool() { currentIndex = blockSize = 1; currentBlock = nullptr; }
        ObjectPool(std::size_t blockSize_) {
            reset(blockSize_);
        }
        ~ObjectPool() {
            clear();
        }
        template <typename... Args>
        T* construct(Args&&... args) {
            if (currentIndex >= blockSize) {
                currentBlock = (T*) new char[sizeof(T) * blockSize];
                // alloc_traits::allocate(alloc, blockSize);
                allocations.emplace_back(currentBlock);
                currentIndex = 0;
            }
            T* object = &currentBlock[currentIndex++];
            // alloc_traits::construct(alloc, object, std::forward<Args>(args)...);
            ::new (static_cast<void*>(object)) T(std::forward<Args>(args)...);
            return object;
        }
        void reset(std::size_t newBlockSize) {
            for (auto allocation : allocations) {
                // alloc_traits::deallocate(alloc, allocation, blockSize);                
                delete[] allocation;
            }
            allocations.clear();
            blockSize = std::max<std::size_t>(1, newBlockSize);
            currentBlock = nullptr;
            currentIndex = blockSize;
        }
        void clear() { reset(blockSize); }
    private:
        T* currentBlock;
        std::size_t currentIndex;
        std::size_t blockSize;
        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) {
    typedef typename Ring::value_type Point;
    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(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 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++) {
        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>
void Earcut<N>::eliminateHole(Node* hole, Node* outerNode) {
    outerNode = findHoleBridge(hole, outerNode);
    if (outerNode) {
        Node* b = splitPolygon(outerNode, hole);
        filterPoints(b, b->next);
    }
}

// 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->prev;

    // 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->next;
    double mx = m->x;
    double my = m->y;

    while (p != stop) {
        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 ((tanCur < tanMin || (tanCur == tanMin && p->x > m->x)) && locallyInside(p, hole)) {
                m = p;
                tanMin = tanCur;
            }
        }

        p = p->next;
    }

    return m;
}

// 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) {
    return a->next->i != b->i && a->prev->i != b->i && !intersectsPolygon(a, b) &&
           locallyInside(a, b) && locallyInside(b, a) && middleInside(a, b);
}

// 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) {
    if ((equals(p1, q1) && equals(p2, q2)) ||
        (equals(p1, q2) && equals(p2, q1))) return true;
    return (area(p1, q1, p2) > 0) != (area(p1, q1, q2) > 0) &&
           (area(p2, q2, p1) > 0) != (area(p2, q2, q1) > 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);
}
}