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ISC License
Copyright (c) 2017, Mapbox
Permission to use, copy, modify, and/or distribute this software for any purpose
with or without fee is hereby granted, provided that the above copyright notice
and this permission notice appear in all copies.
THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH
REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT,
INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS
OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER
TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF
THIS SOFTWARE.

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# Delaunator [![Build Status](https://travis-ci.org/mapbox/delaunator.svg?branch=master)](https://travis-ci.org/mapbox/delaunator) [![](https://img.shields.io/badge/simply-awesome-brightgreen.svg)](https://github.com/mourner/projects)
An incredibly fast JavaScript library for
[Delaunay triangulation](https://en.wikipedia.org/wiki/Delaunay_triangulation) of 2D points.
- [Interactive Demo](https://mapbox.github.io/delaunator/demo.html)
- [Guide to data structures](https://mapbox.github.io/delaunator/)
### Projects based on Delaunator
- [d3-delaunay](https://github.com/d3/d3-delaunay) for Voronoi diagrams, search, traversal and rendering.
- [d3-geo-voronoi](https://github.com/Fil/d3-geo-voronoi) for Delaunay triangulations and Voronoi diagrams on a sphere (e.g. for geographic locations).
### Ports to other languages
- [delaunator-rs](https://github.com/mourner/delaunator-rs) (Rust)
- [fogleman/delaunay](https://github.com/fogleman/delaunay) (Go)
- [delaunator-cpp](https://github.com/delfrrr/delaunator-cpp) (C++)
<img src="delaunator.png" alt="Delaunay triangulation example" width="600" />
## Example
```js
const points = [[168, 180], [168, 178], [168, 179], [168, 181], [168, 183], ...];
const delaunay = Delaunator.from(points);
console.log(delaunay.triangles);
// [623, 636, 619, 636, 444, 619, ...]
```
## Install
Install with NPM (`npm install delaunator`) or Yarn (`yarn add delaunator`), then:
```js
// import as an ES module
import Delaunator from 'delaunator';
// or require in Node / Browserify
const Delaunator = require('delaunator');
```
Or use a browser build directly:
```html
<script src="https://unpkg.com/delaunator@4.0.0/delaunator.min.js"></script> <!-- minified build -->
<script src="https://unpkg.com/delaunator@4.0.0/delaunator.js"></script> <!-- dev build -->
```
## API Reference
#### Delaunator.from(points[, getX, getY])
Constructs a delaunay triangulation object given an array of points (`[x, y]` by default).
`getX` and `getY` are optional functions of the form `(point) => value` for custom point formats.
Duplicate points are skipped.
#### new Delaunator(coords)
Constructs a delaunay triangulation object given an array of point coordinates of the form:
`[x0, y0, x1, y1, ...]` (use a typed array for best performance).
#### delaunay.triangles
A `Uint32Array` array of triangle vertex indices (each group of three numbers forms a triangle).
All triangles are directed counterclockwise.
To get the coordinates of all triangles, use:
```js
for (let i = 0; i < triangles.length; i += 3) {
coordinates.push([
points[triangles[i]],
points[triangles[i + 1]],
points[triangles[i + 2]]
]);
}
```
#### delaunay.halfedges
A `Int32Array` array of triangle half-edge indices that allows you to traverse the triangulation.
`i`-th half-edge in the array corresponds to vertex `triangles[i]` the half-edge is coming from.
`halfedges[i]` is the index of a twin half-edge in an adjacent triangle
(or `-1` for outer half-edges on the convex hull).
The flat array-based data structures might be counterintuitive,
but they're one of the key reasons this library is fast.
#### delaunay.hull
A `Uint32Array` array of indices that reference points on the convex hull of the input data, counter-clockwise.
#### delaunay.coords
An array of input coordinates in the form `[x0, y0, x1, y1, ....]`,
of the type provided in the constructor (or `Float64Array` if you used `Delaunator.from`).
#### delaunay.update()
Updates the triangulation if you modified `delaunay.coords` values in place, avoiding expensive memory allocations.
Useful for iterative relaxation algorithms such as [Lloyd's](https://en.wikipedia.org/wiki/Lloyd%27s_algorithm).
## Performance
Benchmark results against other Delaunay JS libraries
(`npm run bench` on Macbook Pro Retina 15" 2017, Node v10.10.0):
&nbsp; | uniform 100k | gauss 100k | grid 100k | degen 100k | uniform 1&nbsp;million | gauss 1&nbsp;million | grid 1&nbsp;million | degen 1&nbsp;million
:-- | --: | --: | --: | --: | --: | --: | --: | --:
**delaunator** | 82ms | 61ms | 66ms | 25ms | 1.07s | 950ms | 830ms | 278ms
[faster&#8209;delaunay](https://github.com/Bathlamos/delaunay-triangulation) | 473ms | 411ms | 272ms | 68ms | 4.27s | 4.62s | 4.3s | 810ms
[incremental&#8209;delaunay](https://github.com/mikolalysenko/incremental-delaunay) | 547ms | 505ms | 172ms | 528ms | 5.9s | 6.08s | 2.11s | 6.09s
[d3&#8209;voronoi](https://github.com/d3/d3-voronoi) | 972ms | 909ms | 358ms | 720ms | 15.04s | 13.86s | 5.55s | 11.13s
[delaunay&#8209;fast](https://github.com/ironwallaby/delaunay) | 3.8s | 4s | 12.57s | timeout | 132s | 138s | 399s | timeout
[delaunay](https://github.com/darkskyapp/delaunay) | 4.85s | 5.73s | 15.05s | timeout | 156s | 178s | 326s | timeout
[delaunay&#8209;triangulate](https://github.com/mikolalysenko/delaunay-triangulate) | 2.24s | 2.04s | OOM | 1.51s | OOM | OOM | OOM | OOM
[cdt2d](https://github.com/mikolalysenko/cdt2d) | 45s | 51s | 118s | 17s | timeout | timeout | timeout | timeout
## Papers
The algorithm is based on ideas from the following papers:
- [A simple sweep-line Delaunay triangulation algorithm](http://www.academicpub.org/jao/paperInfo.aspx?paperid=15630), 2013, Liu Yonghe, Feng Jinming and Shao Yuehong
- [S-hull: a fast radial sweep-hull routine for Delaunay triangulation](http://www.s-hull.org/paper/s_hull.pdf), 2010, David Sinclair
- [A faster circle-sweep Delaunay triangulation algorithm](http://cglab.ca/~biniaz/papers/Sweep%20Circle.pdf), 2011, Ahmad Biniaz and Gholamhossein Dastghaibyfard

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(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;
}));

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const EPSILON = Math.pow(2, -52);
const EDGE_STACK = new Uint32Array(512);
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).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;
}
}
// 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;
}
// 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;
}
// a more robust orientation test that's stable in a given triangle (to fix robustness issues)
function orient(rx, ry, qx, qy, px, py) {
const 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) {
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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{
"_from": "delaunator@4",
"_id": "delaunator@4.0.1",
"_inBundle": false,
"_integrity": "sha512-WNPWi1IRKZfCt/qIDMfERkDp93+iZEmOxN2yy4Jg+Xhv8SLk2UTqqbe1sfiipn0and9QrE914/ihdx82Y/Giag==",
"_location": "/delaunator",
"_phantomChildren": {},
"_requested": {
"type": "range",
"registry": true,
"raw": "delaunator@4",
"name": "delaunator",
"escapedName": "delaunator",
"rawSpec": "4",
"saveSpec": null,
"fetchSpec": "4"
},
"_requiredBy": [
"/d3-delaunay"
],
"_resolved": "https://registry.npmjs.org/delaunator/-/delaunator-4.0.1.tgz",
"_shasum": "3d779687f57919a7a418f8ab947d3bddb6846957",
"_spec": "delaunator@4",
"_where": "/home/prabhatdev/Documents/opensource/gitHubStats/waka-readme-stats/node_modules/d3-delaunay",
"author": {
"name": "Vladimir Agafonkin"
},
"bugs": {
"url": "https://github.com/mapbox/delaunator/issues"
},
"bundleDependencies": false,
"dependencies": {},
"deprecated": false,
"description": "An incredibly fast JavaScript library for Delaunay triangulation of 2D points",
"devDependencies": {
"c8": "^5.0.1",
"eslint": "^6.2.2",
"eslint-config-mourner": "^3.0.0",
"esm": "^3.2.25",
"rollup": "^1.20.3",
"rollup-plugin-buble": "^0.19.8",
"rollup-plugin-terser": "^5.1.1",
"tape": "^4.11.0"
},
"eslintConfig": {
"extends": "mourner",
"rules": {
"no-sequences": 0
}
},
"files": [
"index.js",
"delaunator.js",
"delaunator.min.js"
],
"homepage": "https://github.com/mapbox/delaunator#readme",
"jsdelivr": "delaunator.min.js",
"keywords": [
"delaunay triangulation",
"computational geometry",
"algorithms"
],
"license": "ISC",
"main": "delaunator.js",
"module": "index.js",
"name": "delaunator",
"repository": {
"type": "git",
"url": "git+https://github.com/mapbox/delaunator.git"
},
"scripts": {
"bench": "node -r esm bench.js",
"build": "rollup -c",
"cov": "c8 node -r esm test/test.js && c8 report -r html",
"lint": "eslint index.js test/test.js bench.js rollup.config.js docs/diagrams.js",
"prepublishOnly": "npm test && npm run build",
"pretest": "npm run lint",
"start": "rollup -cw",
"test": "node -r esm test/test.js"
},
"unpkg": "delaunator.min.js",
"version": "4.0.1"
}