483 lines
15 KiB
JavaScript
483 lines
15 KiB
JavaScript
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const EPSILON = Math.pow(2, -52);
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const EDGE_STACK = new Uint32Array(512);
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import {orient2d} from 'robust-predicates';
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export default class Delaunator {
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static from(points, getX = defaultGetX, getY = defaultGetY) {
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const n = points.length;
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const coords = new Float64Array(n * 2);
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for (let i = 0; i < n; i++) {
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const p = points[i];
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coords[2 * i] = getX(p);
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coords[2 * i + 1] = getY(p);
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}
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return new Delaunator(coords);
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}
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constructor(coords) {
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const n = coords.length >> 1;
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if (n > 0 && typeof coords[0] !== 'number') throw new Error('Expected coords to contain numbers.');
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this.coords = coords;
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// arrays that will store the triangulation graph
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const maxTriangles = Math.max(2 * n - 5, 0);
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this._triangles = new Uint32Array(maxTriangles * 3);
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this._halfedges = new Int32Array(maxTriangles * 3);
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// temporary arrays for tracking the edges of the advancing convex hull
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this._hashSize = Math.ceil(Math.sqrt(n));
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this._hullPrev = new Uint32Array(n); // edge to prev edge
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this._hullNext = new Uint32Array(n); // edge to next edge
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this._hullTri = new Uint32Array(n); // edge to adjacent triangle
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this._hullHash = new Int32Array(this._hashSize).fill(-1); // angular edge hash
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// temporary arrays for sorting points
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this._ids = new Uint32Array(n);
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this._dists = new Float64Array(n);
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this.update();
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}
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update() {
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const {coords, _hullPrev: hullPrev, _hullNext: hullNext, _hullTri: hullTri, _hullHash: hullHash} = this;
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const n = coords.length >> 1;
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// populate an array of point indices; calculate input data bbox
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let minX = Infinity;
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let minY = Infinity;
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let maxX = -Infinity;
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let maxY = -Infinity;
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for (let i = 0; i < n; i++) {
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const x = coords[2 * i];
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const y = coords[2 * i + 1];
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if (x < minX) minX = x;
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if (y < minY) minY = y;
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if (x > maxX) maxX = x;
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if (y > maxY) maxY = y;
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this._ids[i] = i;
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}
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const cx = (minX + maxX) / 2;
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const cy = (minY + maxY) / 2;
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let minDist = Infinity;
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let i0, i1, i2;
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// pick a seed point close to the center
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for (let i = 0; i < n; i++) {
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const d = dist(cx, cy, coords[2 * i], coords[2 * i + 1]);
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if (d < minDist) {
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i0 = i;
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minDist = d;
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}
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}
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const i0x = coords[2 * i0];
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const i0y = coords[2 * i0 + 1];
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minDist = Infinity;
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// find the point closest to the seed
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for (let i = 0; i < n; i++) {
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if (i === i0) continue;
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const d = dist(i0x, i0y, coords[2 * i], coords[2 * i + 1]);
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if (d < minDist && d > 0) {
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i1 = i;
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minDist = d;
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}
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}
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let i1x = coords[2 * i1];
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let i1y = coords[2 * i1 + 1];
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let minRadius = Infinity;
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// find the third point which forms the smallest circumcircle with the first two
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for (let i = 0; i < n; i++) {
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if (i === i0 || i === i1) continue;
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const r = circumradius(i0x, i0y, i1x, i1y, coords[2 * i], coords[2 * i + 1]);
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if (r < minRadius) {
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i2 = i;
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minRadius = r;
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}
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}
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let i2x = coords[2 * i2];
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let i2y = coords[2 * i2 + 1];
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if (minRadius === Infinity) {
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// order collinear points by dx (or dy if all x are identical)
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// and return the list as a hull
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for (let i = 0; i < n; i++) {
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this._dists[i] = (coords[2 * i] - coords[0]) || (coords[2 * i + 1] - coords[1]);
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}
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quicksort(this._ids, this._dists, 0, n - 1);
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const hull = new Uint32Array(n);
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let j = 0;
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for (let i = 0, d0 = -Infinity; i < n; i++) {
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const id = this._ids[i];
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if (this._dists[id] > d0) {
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hull[j++] = id;
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d0 = this._dists[id];
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}
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}
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this.hull = hull.subarray(0, j);
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this.triangles = new Uint32Array(0);
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this.halfedges = new Uint32Array(0);
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return;
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}
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// swap the order of the seed points for counter-clockwise orientation
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if (orient2d(i0x, i0y, i1x, i1y, i2x, i2y) < 0) {
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const i = i1;
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const x = i1x;
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const y = i1y;
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i1 = i2;
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i1x = i2x;
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i1y = i2y;
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i2 = i;
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i2x = x;
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i2y = y;
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}
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const center = circumcenter(i0x, i0y, i1x, i1y, i2x, i2y);
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this._cx = center.x;
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this._cy = center.y;
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for (let i = 0; i < n; i++) {
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this._dists[i] = dist(coords[2 * i], coords[2 * i + 1], center.x, center.y);
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}
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// sort the points by distance from the seed triangle circumcenter
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quicksort(this._ids, this._dists, 0, n - 1);
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// set up the seed triangle as the starting hull
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this._hullStart = i0;
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let hullSize = 3;
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hullNext[i0] = hullPrev[i2] = i1;
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hullNext[i1] = hullPrev[i0] = i2;
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hullNext[i2] = hullPrev[i1] = i0;
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hullTri[i0] = 0;
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hullTri[i1] = 1;
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hullTri[i2] = 2;
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hullHash.fill(-1);
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hullHash[this._hashKey(i0x, i0y)] = i0;
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hullHash[this._hashKey(i1x, i1y)] = i1;
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hullHash[this._hashKey(i2x, i2y)] = i2;
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this.trianglesLen = 0;
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this._addTriangle(i0, i1, i2, -1, -1, -1);
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for (let k = 0, xp, yp; k < this._ids.length; k++) {
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const i = this._ids[k];
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const x = coords[2 * i];
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const y = coords[2 * i + 1];
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// skip near-duplicate points
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if (k > 0 && Math.abs(x - xp) <= EPSILON && Math.abs(y - yp) <= EPSILON) continue;
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xp = x;
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yp = y;
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// skip seed triangle points
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if (i === i0 || i === i1 || i === i2) continue;
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// find a visible edge on the convex hull using edge hash
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let start = 0;
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for (let j = 0, key = this._hashKey(x, y); j < this._hashSize; j++) {
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start = hullHash[(key + j) % this._hashSize];
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if (start !== -1 && start !== hullNext[start]) break;
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}
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start = hullPrev[start];
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let e = start, q;
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while (q = hullNext[e], orient2d(x, y, coords[2 * e], coords[2 * e + 1], coords[2 * q], coords[2 * q + 1]) >= 0) {
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e = q;
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if (e === start) {
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e = -1;
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break;
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}
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}
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if (e === -1) continue; // likely a near-duplicate point; skip it
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// add the first triangle from the point
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let t = this._addTriangle(e, i, hullNext[e], -1, -1, hullTri[e]);
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// recursively flip triangles from the point until they satisfy the Delaunay condition
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hullTri[i] = this._legalize(t + 2);
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hullTri[e] = t; // keep track of boundary triangles on the hull
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hullSize++;
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// walk forward through the hull, adding more triangles and flipping recursively
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let n = hullNext[e];
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while (q = hullNext[n], orient2d(x, y, coords[2 * n], coords[2 * n + 1], coords[2 * q], coords[2 * q + 1]) < 0) {
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t = this._addTriangle(n, i, q, hullTri[i], -1, hullTri[n]);
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hullTri[i] = this._legalize(t + 2);
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hullNext[n] = n; // mark as removed
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hullSize--;
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n = q;
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}
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// walk backward from the other side, adding more triangles and flipping
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if (e === start) {
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while (q = hullPrev[e], orient2d(x, y, coords[2 * q], coords[2 * q + 1], coords[2 * e], coords[2 * e + 1]) < 0) {
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t = this._addTriangle(q, i, e, -1, hullTri[e], hullTri[q]);
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this._legalize(t + 2);
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hullTri[q] = t;
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hullNext[e] = e; // mark as removed
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hullSize--;
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e = q;
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}
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}
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// update the hull indices
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this._hullStart = hullPrev[i] = e;
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hullNext[e] = hullPrev[n] = i;
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hullNext[i] = n;
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// save the two new edges in the hash table
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hullHash[this._hashKey(x, y)] = i;
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hullHash[this._hashKey(coords[2 * e], coords[2 * e + 1])] = e;
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}
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this.hull = new Uint32Array(hullSize);
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for (let i = 0, e = this._hullStart; i < hullSize; i++) {
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this.hull[i] = e;
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e = hullNext[e];
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}
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// trim typed triangle mesh arrays
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this.triangles = this._triangles.subarray(0, this.trianglesLen);
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this.halfedges = this._halfedges.subarray(0, this.trianglesLen);
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}
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_hashKey(x, y) {
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return Math.floor(pseudoAngle(x - this._cx, y - this._cy) * this._hashSize) % this._hashSize;
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}
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_legalize(a) {
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const {_triangles: triangles, _halfedges: halfedges, coords} = this;
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let i = 0;
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let ar = 0;
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// recursion eliminated with a fixed-size stack
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while (true) {
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const b = halfedges[a];
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/* if the pair of triangles doesn't satisfy the Delaunay condition
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* (p1 is inside the circumcircle of [p0, pl, pr]), flip them,
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* then do the same check/flip recursively for the new pair of triangles
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*
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* pl pl
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* /||\ / \
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* al/ || \bl al/ \a
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* / || \ / \
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* / a||b \ flip /___ar___\
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* p0\ || /p1 => p0\---bl---/p1
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* \ || / \ /
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* ar\ || /br b\ /br
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* \||/ \ /
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* pr pr
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*/
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const a0 = a - a % 3;
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ar = a0 + (a + 2) % 3;
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if (b === -1) { // convex hull edge
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if (i === 0) break;
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a = EDGE_STACK[--i];
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continue;
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}
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const b0 = b - b % 3;
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const al = a0 + (a + 1) % 3;
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const bl = b0 + (b + 2) % 3;
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const p0 = triangles[ar];
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const pr = triangles[a];
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const pl = triangles[al];
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const p1 = triangles[bl];
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const illegal = inCircle(
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coords[2 * p0], coords[2 * p0 + 1],
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coords[2 * pr], coords[2 * pr + 1],
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coords[2 * pl], coords[2 * pl + 1],
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coords[2 * p1], coords[2 * p1 + 1]);
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if (illegal) {
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triangles[a] = p1;
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triangles[b] = p0;
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const hbl = halfedges[bl];
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// edge swapped on the other side of the hull (rare); fix the halfedge reference
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if (hbl === -1) {
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let e = this._hullStart;
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do {
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if (this._hullTri[e] === bl) {
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this._hullTri[e] = a;
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break;
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}
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e = this._hullPrev[e];
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} while (e !== this._hullStart);
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}
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this._link(a, hbl);
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this._link(b, halfedges[ar]);
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this._link(ar, bl);
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const br = b0 + (b + 1) % 3;
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// don't worry about hitting the cap: it can only happen on extremely degenerate input
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if (i < EDGE_STACK.length) {
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EDGE_STACK[i++] = br;
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}
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} else {
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if (i === 0) break;
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a = EDGE_STACK[--i];
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}
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}
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return ar;
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}
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_link(a, b) {
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this._halfedges[a] = b;
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if (b !== -1) this._halfedges[b] = a;
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}
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// add a new triangle given vertex indices and adjacent half-edge ids
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_addTriangle(i0, i1, i2, a, b, c) {
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const t = this.trianglesLen;
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|
|
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];
|
||
|
|
}
|