@xtor/cga.js
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Xtor Compute Geometry Algorithm Libary 计算几何算法库
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JavaScript
"use strict";
Object.defineProperty(exports, "__esModule", { value: true });
exports.Delaunator = void 0;
var EPSILON = Math.pow(2, -52);
var EDGE_STACK = new Uint32Array(512);
var Delaunator = /** @class */ (function () {
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 (points) {
var n = points.length;
var coords = new Float64Array(n);
for (var i = 0; i < n; i++) {
var p = points[i];
coords[i] = p;
}
return new Delaunator(coords);
};
Delaunator.fromVecs = function (points) {
var ps = [];
for (var i = 0; i < points.length; i++) {
ps.push(points[i].x, points[i].y);
}
return Delaunator.from(ps);
};
Delaunator.prototype.update = function () {
var _a = this, coords = _a.coords, hullPrev = _a._hullPrev, hullNext = _a._hullNext, hullTri = _a._hullTri, hullHash = _a._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 = 0, i1 = 0, i2 = 0;
// pick a seed point close to the center
for (var i = 0; i < n; i++) {
var d = dist(cx, cy, coords[2 * i], coords[2 * i + 1]);
if (d < minDist) {
i0 = i;
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 = 0; i < n; i++) {
if (i === i0)
continue;
var d = dist(i0x, i0y, coords[2 * i], coords[2 * i + 1]);
if (d < minDist && d > 0) {
i1 = i;
minDist = d;
}
}
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 = 0; i < n; i++) {
if (i === i0 || i === i1)
continue;
var r = circumradius(i0x, i0y, i1x, i1y, coords[2 * i], coords[2 * i + 1]);
if (r < minRadius) {
i2 = i;
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 = 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);
var hull = new Uint32Array(n);
var j = 0;
for (var i = 0, d0 = -Infinity; i < n; i++) {
var id = this._ids[i];
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 = i1;
var x = i1x;
var y = i1y;
i1 = i2;
i1x = i2x;
i1y = i2y;
i2 = i;
i2x = x;
i2y = y;
}
var center = circumcenter(i0x, i0y, i1x, i1y, i2x, i2y);
this._cx = center.x;
this._cy = center.y;
for (var 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;
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 = this._ids[k];
var x = coords[2 * i];
var y = coords[2 * i + 1];
// skip near-duplicate points
if (k > 0)
if (xp !== undefined && yp !== undefined) {
if (Math.abs(x - xp) <= EPSILON && Math.abs(y - yp) <= EPSILON)
continue;
}
else
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
var start = 0;
for (var 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];
var e = start, q = void 0;
while (q = hullNext[e], !orient(x, y, 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, 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
var n_1 = hullNext[e];
while (q = hullNext[n_1], orient(x, y, coords[2 * n_1], coords[2 * n_1 + 1], coords[2 * q], coords[2 * q + 1])) {
t = this._addTriangle(n_1, i, q, hullTri[i], -1, hullTri[n_1]);
hullTri[i] = 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, y, coords[2 * q], coords[2 * q + 1], coords[2 * e], coords[2 * e + 1])) {
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_1] = i;
hullNext[i] = n_1;
// 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 (var 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);
};
Delaunator.prototype._hashKey = function (x, y) {
return Math.floor(pseudoAngle(x - this._cx, y - this._cy) * this._hashSize) % this._hashSize;
};
Delaunator.prototype._legalize = function (a) {
var _a = this, triangles = _a._triangles, halfedges = _a._halfedges, coords = _a.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 (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 (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;
};
return Delaunator;
}());
exports.Delaunator = Delaunator;
// 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) {
return (orientIfSure(px, py, rx, ry, qx, qy) ||
orientIfSure(rx, ry, qx, qy, px, py) ||
orientIfSure(qx, qy, px, py, rx, ry)) < 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 = left + 1;
var 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);
var temp = ids[i];
var 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) {
var tmp = arr[i];
arr[i] = arr[j];
arr[j] = tmp;
}