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-
- const EPSILON = Math.pow(2, -52);
- const EDGE_STACK = new Uint32Array(512);
-
- import {orient2d} from 'robust-predicates';
-
- export default class Delaunator {
-
- static from(points, getX = defaultGetX, getY = defaultGetY) {
- const n = points.length;
- const coords = new Float64Array(n * 2);
-
- for (let i = 0; i < n; i++) {
- const p = points[i];
- coords[2 * i] = getX(p);
- coords[2 * i + 1] = getY(p);
- }
-
- return new Delaunator(coords);
- }
-
- constructor(coords) {
- const 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
- const 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); // angular edge hash
-
- // temporary arrays for sorting points
- this._ids = new Uint32Array(n);
- this._dists = new Float64Array(n);
-
- this.update();
- }
-
- update() {
- const {coords, _hullPrev: hullPrev, _hullNext: hullNext, _hullTri: hullTri, _hullHash: hullHash} = this;
- const n = coords.length >> 1;
-
- // populate an array of point indices; calculate input data bbox
- let minX = Infinity;
- let minY = Infinity;
- let maxX = -Infinity;
- let maxY = -Infinity;
-
- for (let i = 0; i < n; i++) {
- const x = coords[2 * i];
- const 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;
- }
- const cx = (minX + maxX) / 2;
- const cy = (minY + maxY) / 2;
-
- let i0, i1, i2;
-
- // pick a seed point close to the center
- for (let i = 0, minDist = Infinity; i < n; i++) {
- const d = dist(cx, cy, coords[2 * i], coords[2 * i + 1]);
- if (d < minDist) {
- i0 = i;
- minDist = d;
- }
- }
- const i0x = coords[2 * i0];
- const i0y = coords[2 * i0 + 1];
-
- // find the point closest to the seed
- for (let i = 0, minDist = Infinity; i < n; i++) {
- if (i === i0) continue;
- const d = dist(i0x, i0y, coords[2 * i], coords[2 * i + 1]);
- if (d < minDist && d > 0) {
- i1 = i;
- minDist = d;
- }
- }
- let i1x = coords[2 * i1];
- let i1y = coords[2 * i1 + 1];
-
- let minRadius = Infinity;
-
- // find the third point which forms the smallest circumcircle with the first two
- for (let i = 0; i < n; i++) {
- if (i === i0 || i === i1) continue;
- const r = circumradius(i0x, i0y, i1x, i1y, coords[2 * i], coords[2 * i + 1]);
- if (r < minRadius) {
- i2 = i;
- minRadius = r;
- }
- }
- let i2x = coords[2 * i2];
- let 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 (let i = 0; i < n; i++) {
- this._dists[i] = (coords[2 * i] - coords[0]) || (coords[2 * i + 1] - coords[1]);
- }
- quicksort(this._ids, this._dists, 0, n - 1);
- const hull = new Uint32Array(n);
- let j = 0;
- for (let i = 0, d0 = -Infinity; i < n; i++) {
- const id = this._ids[i];
- const d = this._dists[id];
- if (d > d0) {
- hull[j++] = id;
- d0 = d;
- }
- }
- 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 (orient2d(i0x, i0y, i1x, i1y, i2x, i2y) < 0) {
- const i = i1;
- const x = i1x;
- const y = i1y;
- i1 = i2;
- i1x = i2x;
- i1y = i2y;
- i2 = i;
- i2x = x;
- i2y = y;
- }
-
- const center = circumcenter(i0x, i0y, i1x, i1y, i2x, i2y);
- this._cx = center.x;
- this._cy = center.y;
-
- for (let i = 0; i < n; i++) {
- this._dists[i] = dist(coords[2 * i], coords[2 * i + 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;
- let 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 (let k = 0, xp, yp; k < this._ids.length; k++) {
- const i = this._ids[k];
- const x = coords[2 * i];
- const y = coords[2 * i + 1];
-
- // skip near-duplicate points
- if (k > 0 && Math.abs(x - xp) <= EPSILON && Math.abs(y - yp) <= EPSILON) continue;
- xp = x;
- yp = y;
-
- // skip seed triangle points
- if (i === i0 || i === i1 || i === i2) continue;
-
- // find a visible edge on the convex hull using edge hash
- let start = 0;
- for (let j = 0, key = this._hashKey(x, y); j < this._hashSize; j++) {
- start = hullHash[(key + j) % this._hashSize];
- if (start !== -1 && start !== hullNext[start]) break;
- }
-
- start = hullPrev[start];
- let e = start, q;
- while (q = hullNext[e], orient2d(x, y, coords[2 * e], coords[2 * e + 1], coords[2 * q], coords[2 * q + 1]) >= 0) {
- 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
- let t = this._addTriangle(e, i, hullNext[e], -1, -1, hullTri[e]);
-
- // recursively flip triangles from the point until they satisfy the Delaunay condition
- hullTri[i] = 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
- let n = hullNext[e];
- while (q = hullNext[n], orient2d(x, y, coords[2 * n], coords[2 * n + 1], coords[2 * q], coords[2 * q + 1]) < 0) {
- t = this._addTriangle(n, i, q, hullTri[i], -1, hullTri[n]);
- hullTri[i] = this._legalize(t + 2);
- hullNext[n] = n; // mark as removed
- hullSize--;
- n = q;
- }
-
- // walk backward from the other side, adding more triangles and flipping
- if (e === start) {
- while (q = hullPrev[e], orient2d(x, y, coords[2 * q], coords[2 * q + 1], coords[2 * e], coords[2 * e + 1]) < 0) {
- t = this._addTriangle(q, i, 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] = e;
- hullNext[e] = hullPrev[n] = i;
- hullNext[i] = n;
-
- // save the two new edges in the hash table
- hullHash[this._hashKey(x, y)] = i;
- hullHash[this._hashKey(coords[2 * e], coords[2 * e + 1])] = e;
- }
-
- this.hull = new Uint32Array(hullSize);
- for (let i = 0, e = this._hullStart; i < hullSize; i++) {
- this.hull[i] = e;
- e = hullNext[e];
- }
-
- // trim typed triangle mesh arrays
- this.triangles = this._triangles.subarray(0, this.trianglesLen);
- this.halfedges = this._halfedges.subarray(0, this.trianglesLen);
- }
-
- _hashKey(x, y) {
- return Math.floor(pseudoAngle(x - this._cx, y - this._cy) * this._hashSize) % this._hashSize;
- }
-
- _legalize(a) {
- const {_triangles: triangles, _halfedges: halfedges, coords} = this;
-
- let i = 0;
- let ar = 0;
-
- // recursion eliminated with a fixed-size stack
- while (true) {
- const 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
- */
- const a0 = a - a % 3;
- ar = a0 + (a + 2) % 3;
-
- if (b === -1) { // convex hull edge
- if (i === 0) break;
- a = EDGE_STACK[--i];
- continue;
- }
-
- const b0 = b - b % 3;
- const al = a0 + (a + 1) % 3;
- const bl = b0 + (b + 2) % 3;
-
- const p0 = triangles[ar];
- const pr = triangles[a];
- const pl = triangles[al];
- const p1 = triangles[bl];
-
- const 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;
-
- const hbl = halfedges[bl];
-
- // edge swapped on the other side of the hull (rare); fix the halfedge reference
- if (hbl === -1) {
- let 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);
-
- const 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;
- }
-
- _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
- _addTriangle(i0, i1, i2, a, b, c) {
- const 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) {
- const p = dx / (Math.abs(dx) + Math.abs(dy));
- return (dy > 0 ? 3 - p : 1 + p) / 4; // [0..1]
- }
-
- function dist(ax, ay, bx, by) {
- const dx = ax - bx;
- const dy = ay - by;
- return dx * dx + dy * dy;
- }
-
- function inCircle(ax, ay, bx, by, cx, cy, px, py) {
- const dx = ax - px;
- const dy = ay - py;
- const ex = bx - px;
- const ey = by - py;
- const fx = cx - px;
- const fy = cy - py;
-
- const ap = dx * dx + dy * dy;
- const bp = ex * ex + ey * ey;
- const 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) {
- const dx = bx - ax;
- const dy = by - ay;
- const ex = cx - ax;
- const ey = cy - ay;
-
- const bl = dx * dx + dy * dy;
- const cl = ex * ex + ey * ey;
- const d = 0.5 / (dx * ey - dy * ex);
-
- const x = (ey * bl - dy * cl) * d;
- const y = (dx * cl - ex * bl) * d;
-
- return x * x + y * y;
- }
-
- function circumcenter(ax, ay, bx, by, cx, cy) {
- const dx = bx - ax;
- const dy = by - ay;
- const ex = cx - ax;
- const ey = cy - ay;
-
- const bl = dx * dx + dy * dy;
- const cl = ex * ex + ey * ey;
- const d = 0.5 / (dx * ey - dy * ex);
-
- const x = ax + (ey * bl - dy * cl) * d;
- const y = ay + (dx * cl - ex * bl) * d;
-
- return {x, y};
- }
-
- function quicksort(ids, dists, left, right) {
- if (right - left <= 20) {
- for (let i = left + 1; i <= right; i++) {
- const temp = ids[i];
- const tempDist = dists[temp];
- let j = i - 1;
- while (j >= left && dists[ids[j]] > tempDist) ids[j + 1] = ids[j--];
- ids[j + 1] = temp;
- }
- } else {
- const median = (left + right) >> 1;
- let i = left + 1;
- let j = right;
- swap(ids, median, i);
- if (dists[ids[left]] > dists[ids[right]]) swap(ids, left, right);
- if (dists[ids[i]] > dists[ids[right]]) swap(ids, i, right);
- if (dists[ids[left]] > dists[ids[i]]) swap(ids, left, i);
-
- const temp = ids[i];
- const tempDist = dists[temp];
- while (true) {
- do i++; while (dists[ids[i]] < tempDist);
- do j--; while (dists[ids[j]] > tempDist);
- if (j < i) break;
- swap(ids, i, j);
- }
- ids[left + 1] = ids[j];
- ids[j] = temp;
-
- if (right - i + 1 >= j - left) {
- quicksort(ids, dists, i, right);
- quicksort(ids, dists, left, j - 1);
- } else {
- quicksort(ids, dists, left, j - 1);
- quicksort(ids, dists, i, right);
- }
- }
- }
-
- function swap(arr, i, j) {
- const tmp = arr[i];
- arr[i] = arr[j];
- arr[j] = tmp;
- }
-
- function defaultGetX(p) {
- return p[0];
- }
- function defaultGetY(p) {
- return p[1];
- }
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