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yalmar
Published
Edited
Jan 21, 2021
Fork of 2D Triangulation
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md`# 2D Regular Triangulation`
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mutable EDGE_STACK = new Uint32Array(512);
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mutable EPSILON = Math.pow(2, -52);
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// 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]
}

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function dist(ax, ay, bx, by) {
const dx = ax - bx;
const dy = ay - by;
return dx * dx + dy * dy;
}
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// 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) {
const l = (ry - py) * (qx - px);
const r = (rx - px) * (qy - py);
return Math.abs(l - r) >= 3.3306690738754716e-16 * Math.abs(l + r) ? l - r : 0;
}
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// 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;
}

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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;
}
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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;
}

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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};
}

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function swap(arr, i, j) {
const tmp = arr[i];
arr[i] = arr[j];
arr[j] = tmp;
}

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function defaultGetX(p) {
return p[0];
}
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function defaultGetY(p) {
return p[1];
}
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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);
}
}
}

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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).fill(-1); // 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 minDist = Infinity;
let i0, i1, i2;

// pick a seed point close to the center
for (let i = 0; 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];

minDist = Infinity;

// find the point closest to the seed
for (let i = 0; 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];
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)) {
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], !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
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], orient(x, y, coords[2 * n], coords[2 * n + 1], coords[2 * q], coords[2 * q + 1])) {
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], 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] = 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;
}
}
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import {Vector, Curve, MBR} from "@yalmar/2d-geometry-utils"
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Vec = (x,y)=>new Vector(x,y)
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function pt_inside_poly(point, vs) {
// ray-casting algorithm based on
// http://www.ecse.rpi.edu/Homepages/wrf/Research/Short_Notes/pnpoly.html
var x = point[0], y = point[1];
var inside = false;
for (var i = 0, j = vs.length - 1; i < vs.length; j = i++) {
var xi = vs[i][0], yi = vs[i][1];
var xj = vs[j][0], yj = vs[j][1];
var intersect = ((yi > y) != (yj > y))
&& (x < (xj - xi) * (y - yi) / (yj - yi) + xi);
if (intersect) inside = !inside;
}
return inside;
}
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mutable curve = new Curve(Vec(100,100),Vec(300,300),Vec(500,200))
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function len_seg(p, q){
let x = q[0]-p[0];
let y = q[1]-p[1];
return Math.sqrt(x*x+y*y);
}
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