(function (global, factory) { typeof exports === 'object' && typeof module !== 'undefined' ? module.exports = factory() : typeof define === 'function' && define.amd ? define(factory) : (global = global || self, global.Delaunator = factory()); }(this, function () { 'use strict'; var EPSILON = Math.pow(2, -52); var EDGE_STACK = new Uint32Array(512); var Delaunator = function Delaunator(coords) { var n = coords.length >> 1; if (n > 0 && typeof coords[0] !== 'number') { throw new Error('Expected coords to contain numbers.'); } this.coords = coords; // arrays that will store the triangulation graph var maxTriangles = Math.max(2 * n - 5, 0); this._triangles = new Uint32Array(maxTriangles * 3); this._halfedges = new Int32Array(maxTriangles * 3); // temporary arrays for tracking the edges of the advancing convex hull this._hashSize = Math.ceil(Math.sqrt(n)); this._hullPrev = new Uint32Array(n); // edge to prev edge this._hullNext = new Uint32Array(n); // edge to next edge this._hullTri = new Uint32Array(n); // edge to adjacent triangle this._hullHash = new Int32Array(this._hashSize).fill(-1); // angular edge hash // temporary arrays for sorting points this._ids = new Uint32Array(n); this._dists = new Float64Array(n); this.update(); }; Delaunator.from = function from (points, getX, getY) { if ( getX === void 0 ) getX = defaultGetX; if ( getY === void 0 ) getY = defaultGetY; var n = points.length; var coords = new Float64Array(n * 2); for (var i = 0; i < n; i++) { var p = points[i]; coords[2 * i] = getX(p); coords[2 * i + 1] = getY(p); } return new Delaunator(coords); }; Delaunator.prototype.update = function update () { var ref = this; var coords = ref.coords; var hullPrev = ref._hullPrev; var hullNext = ref._hullNext; var hullTri = ref._hullTri; var hullHash = ref._hullHash; var n = coords.length >> 1; // populate an array of point indices; calculate input data bbox var minX = Infinity; var minY = Infinity; var maxX = -Infinity; var maxY = -Infinity; for (var i = 0; i < n; i++) { var x = coords[2 * i]; var y = coords[2 * i + 1]; if (x < minX) { minX = x; } if (y < minY) { minY = y; } if (x > maxX) { maxX = x; } if (y > maxY) { maxY = y; } this._ids[i] = i; } var cx = (minX + maxX) / 2; var cy = (minY + maxY) / 2; var minDist = Infinity; var i0, i1, i2; // pick a seed point close to the center for (var i$1 = 0; i$1 < n; i$1++) { var d = dist(cx, cy, coords[2 * i$1], coords[2 * i$1 + 1]); if (d < minDist) { i0 = i$1; minDist = d; } } var i0x = coords[2 * i0]; var i0y = coords[2 * i0 + 1]; minDist = Infinity; // find the point closest to the seed for (var i$2 = 0; i$2 < n; i$2++) { if (i$2 === i0) { continue; } var d$1 = dist(i0x, i0y, coords[2 * i$2], coords[2 * i$2 + 1]); if (d$1 < minDist && d$1 > 0) { i1 = i$2; minDist = d$1; } } var i1x = coords[2 * i1]; var i1y = coords[2 * i1 + 1]; var minRadius = Infinity; // find the third point which forms the smallest circumcircle with the first two for (var i$3 = 0; i$3 < n; i$3++) { if (i$3 === i0 || i$3 === i1) { continue; } var r = circumradius(i0x, i0y, i1x, i1y, coords[2 * i$3], coords[2 * i$3 + 1]); if (r < minRadius) { i2 = i$3; minRadius = r; } } var i2x = coords[2 * i2]; var i2y = coords[2 * i2 + 1]; if (minRadius === Infinity) { // order collinear points by dx (or dy if all x are identical) // and return the list as a hull for (var i$4 = 0; i$4 < n; i$4++) { this._dists[i$4] = (coords[2 * i$4] - coords[0]) || (coords[2 * i$4 + 1] - coords[1]); } quicksort(this._ids, this._dists, 0, n - 1); var hull = new Uint32Array(n); var j = 0; for (var i$5 = 0, d0 = -Infinity; i$5 < n; i$5++) { var id = this._ids[i$5]; if (this._dists[id] > d0) { hull[j++] = id; d0 = this._dists[id]; } } this.hull = hull.subarray(0, j); this.triangles = new Uint32Array(0); this.halfedges = new Uint32Array(0); return; } // swap the order of the seed points for counter-clockwise orientation if (orient(i0x, i0y, i1x, i1y, i2x, i2y)) { var i$6 = i1; var x$1 = i1x; var y$1 = i1y; i1 = i2; i1x = i2x; i1y = i2y; i2 = i$6; i2x = x$1; i2y = y$1; } var center = circumcenter(i0x, i0y, i1x, i1y, i2x, i2y); this._cx = center.x; this._cy = center.y; for (var i$7 = 0; i$7 < n; i$7++) { this._dists[i$7] = dist(coords[2 * i$7], coords[2 * i$7 + 1], center.x, center.y); } // sort the points by distance from the seed triangle circumcenter quicksort(this._ids, this._dists, 0, n - 1); // set up the seed triangle as the starting hull this._hullStart = i0; var hullSize = 3; hullNext[i0] = hullPrev[i2] = i1; hullNext[i1] = hullPrev[i0] = i2; hullNext[i2] = hullPrev[i1] = i0; hullTri[i0] = 0; hullTri[i1] = 1; hullTri[i2] = 2; hullHash.fill(-1); hullHash[this._hashKey(i0x, i0y)] = i0; hullHash[this._hashKey(i1x, i1y)] = i1; hullHash[this._hashKey(i2x, i2y)] = i2; this.trianglesLen = 0; this._addTriangle(i0, i1, i2, -1, -1, -1); for (var k = 0, xp = (void 0), yp = (void 0); k < this._ids.length; k++) { var i$8 = this._ids[k]; var x$2 = coords[2 * i$8]; var y$2 = coords[2 * i$8 + 1]; // skip near-duplicate points if (k > 0 && Math.abs(x$2 - xp) <= EPSILON && Math.abs(y$2 - yp) <= EPSILON) { continue; } xp = x$2; yp = y$2; // skip seed triangle points if (i$8 === i0 || i$8 === i1 || i$8 === i2) { continue; } // find a visible edge on the convex hull using edge hash var start = 0; for (var j$1 = 0, key = this._hashKey(x$2, y$2); j$1 < this._hashSize; j$1++) { start = hullHash[(key + j$1) % this._hashSize]; if (start !== -1 && start !== hullNext[start]) { break; } } start = hullPrev[start]; var e = start, q = (void 0); while (q = hullNext[e], !orient(x$2, y$2, coords[2 * e], coords[2 * e + 1], coords[2 * q], coords[2 * q + 1])) { e = q; if (e === start) { e = -1; break; } } if (e === -1) { continue; } // likely a near-duplicate point; skip it // add the first triangle from the point var t = this._addTriangle(e, i$8, hullNext[e], -1, -1, hullTri[e]); // recursively flip triangles from the point until they satisfy the Delaunay condition hullTri[i$8] = this._legalize(t + 2); hullTri[e] = t; // keep track of boundary triangles on the hull hullSize++; // walk forward through the hull, adding more triangles and flipping recursively var n$1 = hullNext[e]; while (q = hullNext[n$1], orient(x$2, y$2, coords[2 * n$1], coords[2 * n$1 + 1], coords[2 * q], coords[2 * q + 1])) { t = this._addTriangle(n$1, i$8, q, hullTri[i$8], -1, hullTri[n$1]); hullTri[i$8] = this._legalize(t + 2); hullNext[n$1] = n$1; // mark as removed hullSize--; n$1 = q; } // walk backward from the other side, adding more triangles and flipping if (e === start) { while (q = hullPrev[e], orient(x$2, y$2, coords[2 * q], coords[2 * q + 1], coords[2 * e], coords[2 * e + 1])) { t = this._addTriangle(q, i$8, e, -1, hullTri[e], hullTri[q]); this._legalize(t + 2); hullTri[q] = t; hullNext[e] = e; // mark as removed hullSize--; e = q; } } // update the hull indices this._hullStart = hullPrev[i$8] = e; hullNext[e] = hullPrev[n$1] = i$8; hullNext[i$8] = n$1; // save the two new edges in the hash table hullHash[this._hashKey(x$2, y$2)] = i$8; hullHash[this._hashKey(coords[2 * e], coords[2 * e + 1])] = e; } this.hull = new Uint32Array(hullSize); for (var i$9 = 0, e$1 = this._hullStart; i$9 < hullSize; i$9++) { this.hull[i$9] = e$1; e$1 = hullNext[e$1]; } // trim typed triangle mesh arrays this.triangles = this._triangles.subarray(0, this.trianglesLen); this.halfedges = this._halfedges.subarray(0, this.trianglesLen); }; Delaunator.prototype._hashKey = function _hashKey (x, y) { return Math.floor(pseudoAngle(x - this._cx, y - this._cy) * this._hashSize) % this._hashSize; }; Delaunator.prototype._legalize = function _legalize (a) { var ref = this; var triangles = ref._triangles; var halfedges = ref._halfedges; var coords = ref.coords; var i = 0; var ar = 0; // recursion eliminated with a fixed-size stack while (true) { var b = halfedges[a]; /* if the pair of triangles doesn't satisfy the Delaunay condition * (p1 is inside the circumcircle of [p0, pl, pr]), flip them, * then do the same check/flip recursively for the new pair of triangles * * pl pl * /||\ / \ * al/ || \bl al/\a * / || \ / \ * / a||b \flip/___ar___\ * p0\ || /p1 => p0\---bl---/p1 * \ || / \ / * ar\ || /br b\/br * \||/ \ / * pr pr */ var a0 = a - a % 3; ar = a0 + (a + 2) % 3; if (b === -1) { // convex hull edge if (i === 0) { break; } a = EDGE_STACK[--i]; continue; } var b0 = b - b % 3; var al = a0 + (a + 1) % 3; var bl = b0 + (b + 2) % 3; var p0 = triangles[ar]; var pr = triangles[a]; var pl = triangles[al]; var p1 = triangles[bl]; var illegal = inCircle( coords[2 * p0], coords[2 * p0 + 1], coords[2 * pr], coords[2 * pr + 1], coords[2 * pl], coords[2 * pl + 1], coords[2 * p1], coords[2 * p1 + 1]); if (illegal) { triangles[a] = p1; triangles[b] = p0; var hbl = halfedges[bl]; // edge swapped on the other side of the hull (rare); fix the halfedge reference if (hbl === -1) { var e = this._hullStart; do { if (this._hullTri[e] === bl) { this._hullTri[e] = a; break; } e = this._hullPrev[e]; } while (e !== this._hullStart); } this._link(a, hbl); this._link(b, halfedges[ar]); this._link(ar, bl); var br = b0 + (b + 1) % 3; // don't worry about hitting the cap: it can only happen on extremely degenerate input if (i < EDGE_STACK.length) { EDGE_STACK[i++] = br; } } else { if (i === 0) { break; } a = EDGE_STACK[--i]; } } return ar; }; Delaunator.prototype._link = function _link (a, b) { this._halfedges[a] = b; if (b !== -1) { this._halfedges[b] = a; } }; // add a new triangle given vertex indices and adjacent half-edge ids Delaunator.prototype._addTriangle = function _addTriangle (i0, i1, i2, a, b, c) { var t = this.trianglesLen; this._triangles[t] = i0; this._triangles[t + 1] = i1; this._triangles[t + 2] = i2; this._link(t, a); this._link(t + 1, b); this._link(t + 2, c); this.trianglesLen += 3; return t; }; // monotonically increases with real angle, but doesn't need expensive trigonometry function pseudoAngle(dx, dy) { var p = dx / (Math.abs(dx) + Math.abs(dy)); return (dy > 0 ? 3 - p : 1 + p) / 4; // [0..1] } function dist(ax, ay, bx, by) { var dx = ax - bx; var dy = ay - by; return dx * dx + dy * dy; } // return 2d orientation sign if we're confident in it through J. Shewchuk's error bound check function orientIfSure(px, py, rx, ry, qx, qy) { var l = (ry - py) * (qx - px); var r = (rx - px) * (qy - py); return Math.abs(l - r) >= 3.3306690738754716e-16 * Math.abs(l + r) ? l - r : 0; } // a more robust orientation test that's stable in a given triangle (to fix robustness issues) function orient(rx, ry, qx, qy, px, py) { var sign = orientIfSure(px, py, rx, ry, qx, qy) || orientIfSure(rx, ry, qx, qy, px, py) || orientIfSure(qx, qy, px, py, rx, ry); return sign < 0; } function inCircle(ax, ay, bx, by, cx, cy, px, py) { var dx = ax - px; var dy = ay - py; var ex = bx - px; var ey = by - py; var fx = cx - px; var fy = cy - py; var ap = dx * dx + dy * dy; var bp = ex * ex + ey * ey; var cp = fx * fx + fy * fy; return dx * (ey * cp - bp * fy) - dy * (ex * cp - bp * fx) + ap * (ex * fy - ey * fx) < 0; } function circumradius(ax, ay, bx, by, cx, cy) { var dx = bx - ax; var dy = by - ay; var ex = cx - ax; var ey = cy - ay; var bl = dx * dx + dy * dy; var cl = ex * ex + ey * ey; var d = 0.5 / (dx * ey - dy * ex); var x = (ey * bl - dy * cl) * d; var y = (dx * cl - ex * bl) * d; return x * x + y * y; } function circumcenter(ax, ay, bx, by, cx, cy) { var dx = bx - ax; var dy = by - ay; var ex = cx - ax; var ey = cy - ay; var bl = dx * dx + dy * dy; var cl = ex * ex + ey * ey; var d = 0.5 / (dx * ey - dy * ex); var x = ax + (ey * bl - dy * cl) * d; var y = ay + (dx * cl - ex * bl) * d; return {x: x, y: y}; } function quicksort(ids, dists, left, right) { if (right - left <= 20) { for (var i = left + 1; i <= right; i++) { var temp = ids[i]; var tempDist = dists[temp]; var j = i - 1; while (j >= left && dists[ids[j]] > tempDist) { ids[j + 1] = ids[j--]; } ids[j + 1] = temp; } } else { var median = (left + right) >> 1; var i$1 = left + 1; var j$1 = right; swap(ids, median, i$1); if (dists[ids[left]] > dists[ids[right]]) { swap(ids, left, right); } if (dists[ids[i$1]] > dists[ids[right]]) { swap(ids, i$1, right); } if (dists[ids[left]] > dists[ids[i$1]]) { swap(ids, left, i$1); } var temp$1 = ids[i$1]; var tempDist$1 = dists[temp$1]; while (true) { do { i$1++; } while (dists[ids[i$1]] < tempDist$1); do { j$1--; } while (dists[ids[j$1]] > tempDist$1); if (j$1 < i$1) { break; } swap(ids, i$1, j$1); } ids[left + 1] = ids[j$1]; ids[j$1] = temp$1; if (right - i$1 + 1 >= j$1 - left) { quicksort(ids, dists, i$1, right); quicksort(ids, dists, left, j$1 - 1); } else { quicksort(ids, dists, left, j$1 - 1); quicksort(ids, dists, i$1, right); } } } function swap(arr, i, j) { var tmp = arr[i]; arr[i] = arr[j]; arr[j] = tmp; } function defaultGetX(p) { return p[0]; } function defaultGetY(p) { return p[1]; } return Delaunator; }));