using System; using System.Collections.Generic; using Mapbox.VectorTile.Geometry; using UnityEngine; namespace Assets.Mapbox.Unity.MeshGeneration.Modifiers.MeshModifiers { public static class EarcutLibrary { public static List Earcut(List data, List holeIndices, int dim) { dim = Math.Max(dim, 2); var hasHoles = holeIndices.Count; var outerLen = hasHoles > 0 ? holeIndices[0] * dim : data.Count; var outerNode = linkedList(data, 0, outerLen, dim, true); var triangles = new List((int)(outerNode.i * 1.5)); if (outerNode == null) return triangles; var minX = 0f; var minY = 0f; var maxX = 0f; var maxY = 0f; var x = 0f; var y = 0f; var size = 0f; if (hasHoles > 0) outerNode = EliminateHoles(data, holeIndices, outerNode, dim); // if the shape is not too simple, we'll use z-order curve hash later; calculate polygon bbox if (data.Count > 80 * dim) { minX = maxX = data[0]; minY = maxY = data[1]; for (var i = dim; i < outerLen; i += dim) { x = data[i]; y = data[i + 1]; if (x < minX) minX = x; if (y < minY) minY = y; if (x > maxX) maxX = x; if (y > maxY) maxY = y; } // minX, minY and size are later used to transform coords into integers for z-order calculation size = Math.Max(maxX - minX, maxY - minY); } earcutLinked(outerNode, triangles, dim, minX, minY, size); return triangles; } private static void earcutLinked(Node ear, List triangles, int dim, float minX, float minY, float size, int pass = 0) { if (ear == null) return; // interlink polygon nodes in z-order if (pass == 0 && size > 0) indexCurve(ear, minX, minY, size); var 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 (size > 0 ? isEarHashed(ear, minX, minY, size) : isEar(ear)) { // cut off the triangle triangles.Add(prev.i / dim); triangles.Add(next.i / dim); triangles.Add(ear.i / dim); 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 == 0) { earcutLinked(FilterPoints(ear, null), triangles, dim, minX, minY, size, 1); // if this didn't work, try curing all small self-intersections locally } else if (pass == 1) { ear = cureLocalIntersections(ear, triangles, dim); earcutLinked(ear, triangles, dim, minX, minY, size, 2); // as a last resort, try splitting the remaining polygon into two } else if (pass == 2) { splitEarcut(ear, triangles, dim, minX, minY, size); } break; } } } private static bool isEarHashed(Node ear, float minX, float minY, float size) { var a = ear.prev; var b = ear; var 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 var minTX = a.x < b.x ? (a.x < c.x ? a.x : c.x) : (b.x < c.x ? b.x : c.x); var minTY = a.y < b.y ? (a.y < c.y ? a.y : c.y) : (b.y < c.y ? b.y : c.y); var maxTX = a.x > b.x ? (a.x > c.x ? a.x : c.x) : (b.x > c.x ? b.x : c.x); var maxTY = a.y > b.y ? (a.y > c.y ? a.y : c.y) : (b.y > c.y ? b.y : c.y); // z-order range for the current triangle bbox; var minZ = zOrder(minTX, minTY, minX, minY, size); var maxZ = zOrder(maxTX, maxTY, minX, minY, size); // first look for points inside the triangle in increasing z-order var p = ear.nextZ; while (p != null && p.mZOrder <= 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 != null && p.mZOrder >= 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; } private static int zOrder(float x, float y, float minX, float minY, float size) { //TODO casting here might be wrong x = 32767 * (x - minX) / size; y = 32767 * (y - minY) / size; x = ((int)x | ((int)x << 8)) & 0x00FF00FF; x = ((int)x | ((int)x << 4)) & 0x0F0F0F0F; x = ((int)x | ((int)x << 2)) & 0x33333333; x = ((int)x | ((int)x << 1)) & 0x55555555; y = ((int)y | ((int)y << 8)) & 0x00FF00FF; y = ((int)y | ((int)y << 4)) & 0x0F0F0F0F; y = ((int)y | ((int)y << 2)) & 0x33333333; y = ((int)y | ((int)y << 1)) & 0x55555555; return (int)x | ((int)y << 1); } private static void splitEarcut(Node start, List triangles, int dim, float minX, float minY, float size) { var a = start; do { var b = a.next.next; while (b != a.prev) { if (a.i != b.i && isValidDiagonal(a, b)) { // split the polygon in two by the diagonal var 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, triangles, dim, minX, minY, size); earcutLinked(c, triangles, dim, minX, minY, size); return; } b = b.next; } a = a.next; } while (a != start); } private static bool 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); } private static bool middleInside(Node a, Node b) { var p = a; var inside = false; var px = (a.x + b.x) / 2; var 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; } private static bool intersectsPolygon(Node a, Node b) { var 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; } private static Node cureLocalIntersections(Node start, List triangles, int dim) { var p = start; do { var a = p.prev; var b = p.next.next; if (!equals(a, b) && intersects(a, p, p.next, b) && locallyInside(a, b) && locallyInside(b, a)) { triangles.Add(a.i / dim); triangles.Add(p.i / dim); triangles.Add(b.i / dim); // remove two nodes involved removeNode(p); removeNode(p.next); p = start = b; } p = p.next; } while (p != start); return p; } private static bool intersects(Node p1, Node q1, Node p2, 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; } private static bool isEar(Node ear) { var a = ear.prev; var b = ear; var 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 var 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; } private static void indexCurve(Node start, float minX, float minY, float size) { var p = start; do { if (p.mZOrder == 0) p.mZOrder = zOrder(p.x, p.y, minX, minY, size); p.prevZ = p.prev; p.nextZ = p.next; p = p.next; } while (p != start); p.prevZ.nextZ = null; p.prevZ = null; sortLinked(p); } private static Node sortLinked(Node list) { var i = 0; Node p; Node q; Node e; Node tail; var numMerges = 0; ; var pSize = 0; var qSize = 0; var inSize = 1; do { p = list; list = null; tail = null; numMerges = 0; while (p != null) { numMerges++; q = p; pSize = 0; for (i = 0; i < inSize; i++) { pSize++; q = q.nextZ; if (q == null) break; } qSize = inSize; while (pSize > 0 || (qSize > 0 && q != null)) { if (pSize != 0 && (qSize == 0 || q == null || p.mZOrder <= q.mZOrder)) { e = p; p = p.nextZ; pSize--; } else { e = q; q = q.nextZ; qSize--; } if (tail != null) tail.nextZ = e; else list = e; e.prevZ = tail; tail = e; } p = q; } tail.nextZ = null; inSize *= 2; } while (numMerges > 1); return list; } private static Node EliminateHoles(List data, List holeIndices, Node outerNode, int dim) { var i = 0; var len = holeIndices.Count; var start = 0; var end = 0; Node list = null; var queue = new List(len); for (i = 0; i < len; i++) { start = holeIndices[i] * dim; end = i < len - 1 ? holeIndices[i + 1] * dim : data.Count; list = linkedList(data, start, end, dim, false); if (list == list.next) list.steiner = true; queue.Add(getLeftmost(list)); } queue.Sort(delegate (Node a, Node b) { return (int)Math.Ceiling(a.x - b.x); }); // process holes from left to right for (i = 0; i < queue.Count; i++) { EliminateHole(queue[i], outerNode); outerNode = FilterPoints(outerNode, outerNode.next); } return outerNode; } private static void EliminateHole(Node hole, Node outerNode) { outerNode = FindHoleBridge(hole, outerNode); if (outerNode != null) { var b = SplitPolygon(outerNode, hole); FilterPoints(b, b.next); } } private static Node FilterPoints(Node start, Node end) { if (start == null) return start; if (end == null) end = start; var p = start; bool again = true; 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) return null; again = true; } else { p = p.next; } } while (again || p != end); return end; } private static Node SplitPolygon(Node a, Node b) { var a2 = new Node(a.i, a.x, a.y); var b2 = new Node(b.i, b.x, b.y); var an = a.next; var 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; } private static Node FindHoleBridge(Node hole, Node outerNode) { var p = outerNode; var hx = hole.x; var hy = hole.y; var qx = float.MinValue; Node m = null; // find a segment intersected by a ray from the hole's leftmost point to the left; // segment's endpoint with lesser x will be potential connection point do { if (hy <= p.y && hy >= p.next.y && p.next.y != p.y) { var 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 == null) return null; if (hx == qx) return m.prev; // hole touches outer segment; pick lower endpoint // look for points inside the triangle of hole point, segment intersection and endpoint; // if there are no points found, we have a valid connection; // otherwise choose the point of the minimum angle with the ray as connection point var stop = m; var mx = m.x; var my = m.y; var tanMin = float.MaxValue; float tan = 0f; p = m.next; 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)) { tan = Math.Abs(hy - p.y) / (hx - p.x); // tangential if ((tan < tanMin || (tan == tanMin && p.x > m.x)) && locallyInside(p, hole)) { m = p; tanMin = tan; } } p = p.next; } return m; } private static bool locallyInside(Node a, 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; } private static float area(Node p, Node q, Node r) { return (q.y - p.y) * (r.x - q.x) - (q.x - p.x) * (r.y - q.y); } private static bool pointInTriangle(float ax, float ay, float bx, float by, float cx, float cy, float px, float py) { 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; } private static Node getLeftmost(Node start) { var p = start; var leftmost = start; do { if (p.x < leftmost.x) leftmost = p; p = p.next; } while (p != start); return leftmost; } // create a circular doubly linked list from polygon points in the specified winding order private static Node linkedList(List data, int start, int end, int dim, bool clockwise) { var i = 0; Node last = null; if (clockwise == (signedArea(data, start, end, dim) > 0)) { for (i = start; i < end; i += dim) last = insertNode(i, data[i], data[i + 1], last); } else { for (i = end - dim; i >= start; i -= dim) last = insertNode(i, data[i], data[i + 1], last); } if (last != null && equals(last, last.next)) { removeNode(last); last = last.next; } return last; } private static void removeNode(Node p) { p.next.prev = p.prev; p.prev.next = p.next; if (p.prevZ != null) p.prevZ.nextZ = p.nextZ; if (p.nextZ != null) p.nextZ.prevZ = p.prevZ; } private static bool equals(Node p1, Node p2) { return p1.x == p2.x && p1.y == p2.y; } private static float signedArea(List data, int start, int end, int dim) { var sum = 0f; var j = end - dim; for (var i = start; i < end; i += dim) { sum += (data[j] - data[i]) * (data[i + 1] + data[j + 1]); j = i; } return sum; } private static Node insertNode(int i, float x, float y, Node last) { var p = new Node(i, x, y); if (last == null) { p.prev = p; p.next = p; } else { p.next = last.next; p.prev = last; last.next.prev = p; last.next = p; } return p; } public static Data Flatten(List> data) { var dataCount = data.Count; var totalVertCount = 0; for (int i = 0; i < dataCount; i++) { totalVertCount += data[i].Count; } var result = new Data() { Dim = 2 }; result.Vertices = new List(totalVertCount * 2); var holeIndex = 0; for (var i = 0; i < dataCount; i++) { var subCount = data[i].Count; for (var j = 0; j < subCount; j++) { result.Vertices.Add(data[i][j][0]); result.Vertices.Add(data[i][j][2]); } if (i > 0) { holeIndex += data[i - 1].Count; result.Holes.Add(holeIndex); } } return result; } } public class Data { public List Vertices; public List Holes; public int Dim; public Data() { Holes = new List(); Dim = 2; } } public class Node { /* Member Variables. */ public int i; public float x; public float y; public int mZOrder; public Node prev; public Node next; public Node prevZ; public Node nextZ; public bool steiner; public Node(int ind, float pX, float pY) { /* Initialize Member Variables. */ this.i = ind; this.x = pX; this.y = pY; this.mZOrder = 0; this.prev = null; this.next = null; this.prevZ = null; this.nextZ = null; } protected void setPreviousNode(Node pNode) { this.prev = pNode; } protected Node getPreviousNode() { return this.prev; } protected void setNextNode(Node pNode) { this.next = pNode; } protected Node getNextNode() { return this.next; } protected void setZOrder(int pZOrder) { this.mZOrder = pZOrder; } protected int getZOrder() { return this.mZOrder; } protected void setPreviousZNode(Node pNode) { this.prevZ = pNode; } protected Node getPreviousZNode() { return this.prevZ; } protected void setNextZNode(Node pNode) { this.nextZ = pNode; } protected Node getNextZNode() { return this.nextZ; } } }