Working Triangulization with Hole

src/earcut.hpp

@@ -0,0 +1,932 @@
+#pragma once
+
+#include "godot_cpp/variant/vector2.hpp"
+#include <algorithm>
+#include <cassert>
+#include <cmath>
+#include <cstddef>
+#include <cstdint>
+#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 util
+
+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_) : x(x_), y(y_), i(index), steiner(0) {}
+    Node(const Node &) = delete;
+    Node &operator=(const Node &) = delete;
+    Node(Node &&) = delete;
+    Node &operator=(Node &&) = delete;
+
+    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;
+
+    // original index in polygon
+    const N i : (sizeof(N) * 8 - 1);
+
+    // indicates whether this is a steiner point
+    N steiner : 1;
+
+    // previous and next nodes in z-order
+    Node *prevZ = nullptr;
+    Node *nextZ = nullptr;
+  };
+
+  // Cache-optimized Triangle structure for repeated geometric tests
+  struct Triangle {
+    const double ax, ay;
+    const double bx, by;
+    const double cx, cy;
+
+    Triangle(const Node *a, const Node *b, const Node *c)
+        : ax(a->x), ay(a->y), bx(b->x), by(b->y), cx(c->x), cy(c->y) {}
+
+    inline double area() const {
+      return (by - ay) * (cx - bx) - (bx - ax) * (cy - by);
+    }
+
+    inline bool containsPoint(double px, double py) const {
+      return (cx - px) * (ay - py) >= (ax - px) * (cy - py) &&
+             (ax - px) * (by - py) >= (bx - px) * (ay - py) &&
+             (bx - px) * (cy - py) >= (cx - px) * (by - py);
+    }
+  };
+
+  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() { allocateNewBlock(256); }
+    ObjectPool(std::size_t blockSize_) : baseBlockSize(blockSize_) {
+      allocateNewBlock(std::max<std::size_t>(blockSize_, 256));
+    }
+    ~ObjectPool() { clear(); }
+    template <typename... Args> T *construct(Args &&...args) {
+      // If current block is full, move to next block or allocate new one
+      if (currentIndex >= baseBlockSize) {
+        currentBlockIndex++;
+        if (currentBlockIndex < memoryBlocks.size()) {
+          // Reuse existing block
+          currentIndex = 0;
+        } else {
+          // Allocate a new one
+          allocateNewBlock(baseBlockSize);
+        }
+      }
+
+      T *object = memoryBlocks[currentBlockIndex].get() + currentIndex;
+      alloc_traits::construct(alloc, object, std::forward<Args>(args)...);
+      totalObjects++;
+      currentIndex++;
+      return object;
+    }
+    void reset() { clear(); }
+    void clear() {
+      // Destroy all objects, but keep blocks allocated for reuse
+      std::size_t objectsDestroyed = 0;
+      for (std::size_t blockIdx = 0;
+           blockIdx < memoryBlocks.size() && objectsDestroyed < totalObjects;
+           ++blockIdx) {
+        // check if we are in the last block
+        std::size_t objectsInThisBlock =
+            std::min(baseBlockSize, totalObjects - objectsDestroyed);
+        for (std::size_t i = 0; i < objectsInThisBlock; ++i) {
+          T *object = memoryBlocks[blockIdx].get() + i;
+          alloc_traits::destroy(alloc, object);
+        }
+        objectsDestroyed += objectsInThisBlock;
+      }
+      // Reset to start from first block again
+      currentBlockIndex = 0;
+      currentIndex = 0;
+      totalObjects = 0;
+    }
+
+  private:
+    Alloc alloc;
+    typedef typename std::allocator_traits<Alloc> alloc_traits;
+
+    // Custom deleter that uses the allocator
+    struct AllocDeleter {
+      Alloc alloc;
+      std::size_t capacity;
+      void operator()(T *ptr) {
+        alloc_traits::deallocate(alloc, ptr, capacity);
+      }
+    };
+
+    std::vector<std::unique_ptr<T[], AllocDeleter>> memoryBlocks;
+    std::vector<std::size_t> blockCapacities;
+    std::size_t currentBlockIndex = 0;
+    std::size_t currentIndex = 0;
+    std::size_t totalObjects = 0;
+    std::size_t baseBlockSize = 256;
+
+    void allocateNewBlock(std::size_t capacity) {
+      T *rawMemory = alloc_traits::allocate(alloc, capacity);
+      auto newBlock = std::unique_ptr<T[], AllocDeleter>(
+          rawMemory, AllocDeleter{alloc, capacity});
+      memoryBlocks.push_back(std::move(newBlock));
+      blockCapacities.push_back(capacity);
+      currentBlockIndex = memoryBlocks.size() - 1;
+      currentIndex = 0;
+    }
+  };
+
+  std::unique_ptr<ObjectPool<Node>> nodes;
+  std::vector<Node *> holeQueue;
+};
+
+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
+  if (!nodes) {
+    std::size_t estimatedNodes = len * 3 / 2;
+    nodes = std::make_unique<ObjectPool<Node>>(
+        std::max<std::size_t>(estimatedNodes, 256));
+  }
+  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 inv_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 ? (32767. / inv_size) : .0;
+  }
+
+  earcutLinked(outerNode);
+
+  nodes->clear();
+  holeQueue.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;
+
+  // iterate through ears, slicing them one by one
+  while (ear->prev != ear->next) {
+    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;
+
+  // Create triangle with cached coordinates and bounding box
+  const Triangle tri(a, b, c);
+  if (tri.area() >= 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 (tri.containsPoint(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;
+
+  // Create triangle with cached coordinates and bounding box
+  const Triangle tri(a, b, c);
+  if (tri.area() >= 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>(tri.ax, std::min<double>(tri.bx, tri.cx));
+  const double minTY =
+      std::min<double>(tri.ay, std::min<double>(tri.by, tri.cy));
+  const double maxTX =
+      std::max<double>(tri.ax, std::max<double>(tri.bx, tri.cx));
+  const double maxTY =
+      std::max<double>(tri.ay, std::max<double>(tri.by, tri.cy));
+
+  // 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 && tri.containsPoint(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 && tri.containsPoint(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();
+
+  holeQueue.clear();
+  for (size_t i = 1; i < len; i++) {
+    Node *list = linkedList(points[i], false);
+    if (list) {
+      if (list == list->next)
+        list->steiner = true;
+      holeQueue.push_back(getLeftmost(list));
+    }
+  }
+  std::sort(holeQueue.begin(), holeQueue.end(),
+            [](const Node *a, const Node *b) { return a->x < b->x; });
+
+  // process holes from left to right
+  for (size_t i = 0; i < holeQueue.size(); i++) {
+    outerNode = eliminateHole(holeQueue[i], outerNode);
+  }
+
+  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
+  filterPoints(bridgeReverse, bridgeReverse->next);
+
+  // Check if input node was removed by the filtering
+  return filterPoints(bridge, bridge->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;
+        m = p->x < p->next->x ? p : p->next;
+        if (x == hx)
+          return m; // hole touches outer segment; pick leftmost endpoint
+      }
+    }
+    p = p->next;
+  } while (p != outerNode);
+
+  if (!m)
+    return 0;
+
+  // 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>((x_ - minX) * inv_size);
+  int32_t y = static_cast<int32_t>((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) &&
+         (ax - px) * (by - py) >= (bx - px) * (ay - py) &&
+         (bx - px) * (cy - py) >= (cx - px) * (by - py);
+}
+
+// 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) && // dones't intersect other edges
+         ((locallyInside(a, b) && locallyInside(b, a) &&
+           middleInside(a, b) && // locally visible
+           (area(a->prev, a, b->prev) != 0.0 ||
+            area(a, b->prev, b) !=
+                0.0)) || // does not create opposite-facing sectors
+          (equals(a, b) && area(a->prev, a, a->next) > 0 &&
+           area(b->prev, b, b->next) > 0)); // special zero-length case
+}
+
+// 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;
+}
+} // namespace detail
+
+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);
+}
+} // namespace mapbox

src/gdexample.cpp

@@ -1,24 +0,0 @@
-#include "gdexample.h"
-#include <godot_cpp/core/class_db.hpp>
-
-using namespace godot;
-
-void GDExample::_bind_methods() {}
-
-GDExample::GDExample() {
-  // Initialize any variables here.
-  time_passed = 0.0;
-}
-
-GDExample::~GDExample() {
-  // Add your cleanup here.
-}
-
-void GDExample::_process(double delta) {
-  time_passed += delta;
-
-  Vector2 new_position = Vector2(10.0 + (10.0 * sin(time_passed * 2.0)),
-                                 10.0 + (10.0 * cos(time_passed * 1.5)));
-
-  set_position(new_position);
-}

src/gdexample.h

@@ -1,23 +0,0 @@
-#pragma once
-
-#include <godot_cpp/classes/sprite2d.hpp>
-
-namespace godot {
-
-class GDExample : public Sprite2D {
-	GDCLASS(GDExample, Sprite2D)
-
-private:
-	double time_passed;
-
-protected:
-	static void _bind_methods();
-
-public:
-	GDExample();
-	~GDExample();
-
-	void _process(double delta) override;
-};
-
-} // namespace godot

src/register_types.cpp

@@ -1,6 +1,6 @@
 #include "register_types.h"
-
-#include "gdexample.h"
+#include "godot_cpp/core/class_db.hpp"
+#include "triangulization.hpp"
 
 #include <gdextension_interface.h>
 #include <godot_cpp/core/defs.hpp>
@@ -13,7 +13,7 @@ void initialize_triangulation_module(ModuleInitializationLevel p_level) {
     return;
   }
 
-  GDREGISTER_RUNTIME_CLASS(GDExample);
+  GDREGISTER_CLASS(Triangulization)
 }
 
 void uninitialize_triangulation_module(ModuleInitializationLevel p_level) {

src/triangulization.cpp

@@ -0,0 +1,61 @@
+#include "triangulization.hpp"
+#include "earcut.hpp"
+#include "godot_cpp/classes/polygon2d.hpp"
+#include "godot_cpp/core/class_db.hpp"
+#include "godot_cpp/variant/array.hpp"
+#include "godot_cpp/variant/packed_int32_array.hpp"
+#include "godot_cpp/variant/packed_vector2_array.hpp"
+#include "godot_cpp/variant/string.hpp"
+#include "godot_cpp/variant/utility_functions.hpp"
+#include "godot_cpp/variant/vector2.hpp"
+#include <array>
+#include <cstdint>
+#include <vector>
+
+Triangulization::Triangulization() {}
+
+void Triangulization::_bind_methods() {
+  ClassDB::bind_method(
+      godot::D_METHOD("triangulate_with_holes", "outer", "inner"),
+      &Triangulization::triangulate_with_holes);
+}
+
+std::vector<std::array<double, 2>>
+_convert_to_std_vec(const godot::PackedVector2Array &packed_array) {
+  std::vector<std::array<double, 2>> std_vec;
+  std_vec.reserve(packed_array.size());
+
+  for (int i = 0; i < packed_array.size(); i++) {
+    Vector2 tmp = packed_array[i];
+    std_vec.push_back({tmp.x, tmp.y});
+  }
+
+  return std_vec;
+}
+
+PackedInt32Array Triangulization::triangulate_with_holes(Polygon2D *outer,
+                                                         Polygon2D *inner) {
+  std::vector<std::vector<std::array<double, 2>>> p;
+
+  p.push_back(_convert_to_std_vec(outer->get_polygon()));
+  p.push_back(_convert_to_std_vec(inner->get_polygon()));
+
+  // for (int i = 0; i < p.size(); i++) {
+  //   for (int j = 0; j < p[i].size(); j++) {
+  //     UtilityFunctions::print(String("Value: "),
+  //     String::num_uint64(p[i][j][0]),
+  //                             String(","), String::num_uint64(p[i][j][1]));
+  //   }
+  // }
+
+  std::vector<uint32_t> indices = mapbox::earcut<uint32_t>(p);
+  // reverse to counter clockwise creating of triangles
+  std::reverse(indices.begin(), indices.end());
+
+  PackedInt32Array return_values;
+  for (int i = 0; i < indices.size(); i++) {
+    return_values.push_back(indices[i]);
+  }
+
+  return return_values;
+};

src/triangulization.hpp

@@ -0,0 +1,21 @@
+#pragma once
+
+#include "godot_cpp/classes/wrapped.hpp"
+#include "godot_cpp/variant/packed_int32_array.hpp"
+#include <godot_cpp/classes/object.hpp>
+#include <godot_cpp/classes/polygon2d.hpp>
+
+using namespace godot;
+
+class Triangulization : public Object {
+  GDCLASS(Triangulization, Object);
+
+protected:
+  static void _bind_methods();
+
+public:
+  Triangulization();
+
+  PackedInt32Array triangulate_with_holes(godot::Polygon2D *inner,
+                                          godot::Polygon2D *outer);
+};