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Nuno Coração
+15
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ISC License
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Copyright (c) 2017, Mapbox
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Permission to use, copy, modify, and/or distribute this software for any purpose
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with or without fee is hereby granted, provided that the above copyright notice
|
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and this permission notice appear in all copies.
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|
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THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH
|
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REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
|
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FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT,
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INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS
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OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER
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TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF
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THIS SOFTWARE.
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# Delaunator [](https://travis-ci.org/mapbox/delaunator) [](https://github.com/mourner/projects) [](https://unpkg.com/delaunator)
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An incredibly fast JavaScript library for
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[Delaunay triangulation](https://en.wikipedia.org/wiki/Delaunay_triangulation) of 2D points.
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- [Interactive Demo](https://mapbox.github.io/delaunator/demo.html)
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- [Guide to data structures](https://mapbox.github.io/delaunator/)
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<img src="delaunator.png" alt="Delaunay triangulation example" width="600" />
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### Projects based on Delaunator
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- [d3-delaunay](https://github.com/d3/d3-delaunay) for Voronoi diagrams, search, traversal and rendering (a part of [D3](https://d3js.org)).
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- [d3-geo-voronoi](https://github.com/Fil/d3-geo-voronoi) for Delaunay triangulations and Voronoi diagrams on a sphere (e.g. for geographic locations).
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### Ports to other languages
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- [delaunator-rs](https://github.com/mourner/delaunator-rs) (Rust)
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- [fogleman/delaunay](https://github.com/fogleman/delaunay) (Go)
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- [delaunator-cpp](https://github.com/abellgithub/delaunator-cpp) (C++)
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||||
- [delaunator-sharp](https://github.com/nol1fe/delaunator-sharp) (C#)
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- [delaunator-ruby](https://github.com/hendrixfan/delaunator-ruby) (Ruby)
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- [Delaunator-Python](https://github.com/HakanSeven12/Delaunator-Python) (Python)
|
||||
- [hx-delaunator](https://github.com/dmitryhryppa/hx-delaunator) (Haxe)
|
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- [ricardomatias/delaunator](https://github.com/ricardomatias/delaunator) (Kotlin)
|
||||
|
||||
## Example
|
||||
|
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```js
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const points = [[168, 180], [168, 178], [168, 179], [168, 181], [168, 183], ...];
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const delaunay = Delaunator.from(points);
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console.log(delaunay.triangles);
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// [623, 636, 619, 636, 444, 619, ...]
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```
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|
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## Install
|
||||
|
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Install with NPM (`npm install delaunator`) or Yarn (`yarn add delaunator`), then:
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```js
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// import as an ES module
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import Delaunator from 'delaunator';
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|
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// or require in Node / Browserify
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const Delaunator = require('delaunator');
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```
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|
||||
Or use a browser build directly:
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|
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```html
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<script src="https://unpkg.com/delaunator@4.0.1/delaunator.min.js"></script> <!-- minified build -->
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<script src="https://unpkg.com/delaunator@4.0.1/delaunator.js"></script> <!-- dev build -->
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```
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|
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## API Reference
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#### Delaunator.from(points[, getX, getY])
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Constructs a delaunay triangulation object given an array of points (`[x, y]` by default).
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`getX` and `getY` are optional functions of the form `(point) => value` for custom point formats.
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Duplicate points are skipped.
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#### new Delaunator(coords)
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Constructs a delaunay triangulation object given an array of point coordinates of the form:
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`[x0, y0, x1, y1, ...]` (use a typed array for best performance).
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|
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#### delaunay.triangles
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A `Uint32Array` array of triangle vertex indices (each group of three numbers forms a triangle).
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All triangles are directed counterclockwise.
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To get the coordinates of all triangles, use:
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|
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```js
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for (let i = 0; i < triangles.length; i += 3) {
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coordinates.push([
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points[triangles[i]],
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||||
points[triangles[i + 1]],
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points[triangles[i + 2]]
|
||||
]);
|
||||
}
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```
|
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|
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#### delaunay.halfedges
|
||||
|
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A `Int32Array` array of triangle half-edge indices that allows you to traverse the triangulation.
|
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`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,
|
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but they're one of the key reasons this library is fast.
|
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|
||||
#### delaunay.hull
|
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A `Uint32Array` array of indices that reference points on the convex hull of the input data, counter-clockwise.
|
||||
|
||||
#### delaunay.coords
|
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An array of input coordinates in the form `[x0, y0, x1, y1, ....]`,
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of the type provided in the constructor (or `Float64Array` if you used `Delaunator.from`).
|
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|
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#### delaunay.update()
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Updates the triangulation if you modified `delaunay.coords` values in place, avoiding expensive memory allocations.
|
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Useful for iterative relaxation algorithms such as [Lloyd's](https://en.wikipedia.org/wiki/Lloyd%27s_algorithm).
|
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|
||||
## Performance
|
||||
|
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Benchmark results against other Delaunay JS libraries
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(`npm run bench` on Macbook Pro Retina 15" 2017, Node v10.10.0):
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|
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| uniform 100k | gauss 100k | grid 100k | degen 100k | uniform 1 million | gauss 1 million | grid 1 million | degen 1 million
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:-- | --: | --: | --: | --: | --: | --: | --: | --:
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**delaunator** | 82ms | 61ms | 66ms | 25ms | 1.07s | 950ms | 830ms | 278ms
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[faster‑delaunay](https://github.com/Bathlamos/delaunay-triangulation) | 473ms | 411ms | 272ms | 68ms | 4.27s | 4.62s | 4.3s | 810ms
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[incremental‑delaunay](https://github.com/mikolalysenko/incremental-delaunay) | 547ms | 505ms | 172ms | 528ms | 5.9s | 6.08s | 2.11s | 6.09s
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[d3‑voronoi](https://github.com/d3/d3-voronoi) | 972ms | 909ms | 358ms | 720ms | 15.04s | 13.86s | 5.55s | 11.13s
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[delaunay‑fast](https://github.com/ironwallaby/delaunay) | 3.8s | 4s | 12.57s | timeout | 132s | 138s | 399s | timeout
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[delaunay](https://github.com/darkskyapp/delaunay) | 4.85s | 5.73s | 15.05s | timeout | 156s | 178s | 326s | timeout
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[delaunay‑triangulate](https://github.com/mikolalysenko/delaunay-triangulate) | 2.24s | 2.04s | OOM | 1.51s | OOM | OOM | OOM | OOM
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||||
[cdt2d](https://github.com/mikolalysenko/cdt2d) | 45s | 51s | 118s | 17s | timeout | timeout | timeout | timeout
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||||
|
||||
## Papers
|
||||
|
||||
The algorithm is based on ideas from the following papers:
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||||
|
||||
- [A simple sweep-line Delaunay triangulation algorithm](http://www.academicpub.org/jao/paperInfo.aspx?paperid=15630), 2013, Liu Yonghe, Feng Jinming and Shao Yuehong
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||||
- [S-hull: a fast radial sweep-hull routine for Delaunay triangulation](http://www.s-hull.org/paper/s_hull.pdf), 2010, David Sinclair
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||||
- [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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+757
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(function (global, factory) {
|
||||
typeof exports === 'object' && typeof module !== 'undefined' ? module.exports = factory() :
|
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typeof define === 'function' && define.amd ? define(factory) :
|
||||
(global = typeof globalThis !== 'undefined' ? globalThis : global || self, global.Delaunator = factory());
|
||||
}(this, (function () { 'use strict';
|
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|
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const epsilon = 1.1102230246251565e-16;
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const splitter = 134217729;
|
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const resulterrbound = (3 + 8 * epsilon) * epsilon;
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|
||||
// fast_expansion_sum_zeroelim routine from oritinal code
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function sum(elen, e, flen, f, h) {
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let Q, Qnew, hh, bvirt;
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let enow = e[0];
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let fnow = f[0];
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let eindex = 0;
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let findex = 0;
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if ((fnow > enow) === (fnow > -enow)) {
|
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Q = enow;
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enow = e[++eindex];
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} else {
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Q = fnow;
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fnow = f[++findex];
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}
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let hindex = 0;
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if (eindex < elen && findex < flen) {
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if ((fnow > enow) === (fnow > -enow)) {
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Qnew = enow + Q;
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hh = Q - (Qnew - enow);
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enow = e[++eindex];
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} else {
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Qnew = fnow + Q;
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hh = Q - (Qnew - fnow);
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fnow = f[++findex];
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}
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Q = Qnew;
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if (hh !== 0) {
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h[hindex++] = hh;
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}
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while (eindex < elen && findex < flen) {
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if ((fnow > enow) === (fnow > -enow)) {
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Qnew = Q + enow;
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bvirt = Qnew - Q;
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hh = Q - (Qnew - bvirt) + (enow - bvirt);
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enow = e[++eindex];
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} else {
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Qnew = Q + fnow;
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bvirt = Qnew - Q;
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hh = Q - (Qnew - bvirt) + (fnow - bvirt);
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fnow = f[++findex];
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||||
}
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Q = Qnew;
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if (hh !== 0) {
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h[hindex++] = hh;
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}
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}
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}
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while (eindex < elen) {
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Qnew = Q + enow;
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bvirt = Qnew - Q;
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hh = Q - (Qnew - bvirt) + (enow - bvirt);
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enow = e[++eindex];
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Q = Qnew;
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if (hh !== 0) {
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h[hindex++] = hh;
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}
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}
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while (findex < flen) {
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Qnew = Q + fnow;
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bvirt = Qnew - Q;
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hh = Q - (Qnew - bvirt) + (fnow - bvirt);
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fnow = f[++findex];
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Q = Qnew;
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if (hh !== 0) {
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h[hindex++] = hh;
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}
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}
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if (Q !== 0 || hindex === 0) {
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h[hindex++] = Q;
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}
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return hindex;
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}
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function estimate(elen, e) {
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let Q = e[0];
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for (let i = 1; i < elen; i++) Q += e[i];
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return Q;
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}
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function vec(n) {
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return new Float64Array(n);
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}
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const ccwerrboundA = (3 + 16 * epsilon) * epsilon;
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const ccwerrboundB = (2 + 12 * epsilon) * epsilon;
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const ccwerrboundC = (9 + 64 * epsilon) * epsilon * epsilon;
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const B = vec(4);
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const C1 = vec(8);
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const C2 = vec(12);
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const D = vec(16);
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const u = vec(4);
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function orient2dadapt(ax, ay, bx, by, cx, cy, detsum) {
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let acxtail, acytail, bcxtail, bcytail;
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let bvirt, c, ahi, alo, bhi, blo, _i, _j, _0, s1, s0, t1, t0, u3;
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const acx = ax - cx;
|
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const bcx = bx - cx;
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const acy = ay - cy;
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const bcy = by - cy;
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s1 = acx * bcy;
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c = splitter * acx;
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ahi = c - (c - acx);
|
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alo = acx - ahi;
|
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c = splitter * bcy;
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bhi = c - (c - bcy);
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blo = bcy - bhi;
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s0 = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
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t1 = acy * bcx;
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c = splitter * acy;
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ahi = c - (c - acy);
|
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alo = acy - ahi;
|
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c = splitter * bcx;
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bhi = c - (c - bcx);
|
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blo = bcx - bhi;
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t0 = alo * blo - (t1 - ahi * bhi - alo * bhi - ahi * blo);
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_i = s0 - t0;
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bvirt = s0 - _i;
|
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B[0] = s0 - (_i + bvirt) + (bvirt - t0);
|
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_j = s1 + _i;
|
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bvirt = _j - s1;
|
||||
_0 = s1 - (_j - bvirt) + (_i - bvirt);
|
||||
_i = _0 - t1;
|
||||
bvirt = _0 - _i;
|
||||
B[1] = _0 - (_i + bvirt) + (bvirt - t1);
|
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u3 = _j + _i;
|
||||
bvirt = u3 - _j;
|
||||
B[2] = _j - (u3 - bvirt) + (_i - bvirt);
|
||||
B[3] = u3;
|
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|
||||
let det = estimate(4, B);
|
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let errbound = ccwerrboundB * detsum;
|
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if (det >= errbound || -det >= errbound) {
|
||||
return det;
|
||||
}
|
||||
|
||||
bvirt = ax - acx;
|
||||
acxtail = ax - (acx + bvirt) + (bvirt - cx);
|
||||
bvirt = bx - bcx;
|
||||
bcxtail = bx - (bcx + bvirt) + (bvirt - cx);
|
||||
bvirt = ay - acy;
|
||||
acytail = ay - (acy + bvirt) + (bvirt - cy);
|
||||
bvirt = by - bcy;
|
||||
bcytail = by - (bcy + bvirt) + (bvirt - cy);
|
||||
|
||||
if (acxtail === 0 && acytail === 0 && bcxtail === 0 && bcytail === 0) {
|
||||
return det;
|
||||
}
|
||||
|
||||
errbound = ccwerrboundC * detsum + resulterrbound * Math.abs(det);
|
||||
det += (acx * bcytail + bcy * acxtail) - (acy * bcxtail + bcx * acytail);
|
||||
if (det >= errbound || -det >= errbound) return det;
|
||||
|
||||
s1 = acxtail * bcy;
|
||||
c = splitter * acxtail;
|
||||
ahi = c - (c - acxtail);
|
||||
alo = acxtail - ahi;
|
||||
c = splitter * bcy;
|
||||
bhi = c - (c - bcy);
|
||||
blo = bcy - bhi;
|
||||
s0 = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
|
||||
t1 = acytail * bcx;
|
||||
c = splitter * acytail;
|
||||
ahi = c - (c - acytail);
|
||||
alo = acytail - ahi;
|
||||
c = splitter * bcx;
|
||||
bhi = c - (c - bcx);
|
||||
blo = bcx - bhi;
|
||||
t0 = alo * blo - (t1 - ahi * bhi - alo * bhi - ahi * blo);
|
||||
_i = s0 - t0;
|
||||
bvirt = s0 - _i;
|
||||
u[0] = s0 - (_i + bvirt) + (bvirt - t0);
|
||||
_j = s1 + _i;
|
||||
bvirt = _j - s1;
|
||||
_0 = s1 - (_j - bvirt) + (_i - bvirt);
|
||||
_i = _0 - t1;
|
||||
bvirt = _0 - _i;
|
||||
u[1] = _0 - (_i + bvirt) + (bvirt - t1);
|
||||
u3 = _j + _i;
|
||||
bvirt = u3 - _j;
|
||||
u[2] = _j - (u3 - bvirt) + (_i - bvirt);
|
||||
u[3] = u3;
|
||||
const C1len = sum(4, B, 4, u, C1);
|
||||
|
||||
s1 = acx * bcytail;
|
||||
c = splitter * acx;
|
||||
ahi = c - (c - acx);
|
||||
alo = acx - ahi;
|
||||
c = splitter * bcytail;
|
||||
bhi = c - (c - bcytail);
|
||||
blo = bcytail - bhi;
|
||||
s0 = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
|
||||
t1 = acy * bcxtail;
|
||||
c = splitter * acy;
|
||||
ahi = c - (c - acy);
|
||||
alo = acy - ahi;
|
||||
c = splitter * bcxtail;
|
||||
bhi = c - (c - bcxtail);
|
||||
blo = bcxtail - bhi;
|
||||
t0 = alo * blo - (t1 - ahi * bhi - alo * bhi - ahi * blo);
|
||||
_i = s0 - t0;
|
||||
bvirt = s0 - _i;
|
||||
u[0] = s0 - (_i + bvirt) + (bvirt - t0);
|
||||
_j = s1 + _i;
|
||||
bvirt = _j - s1;
|
||||
_0 = s1 - (_j - bvirt) + (_i - bvirt);
|
||||
_i = _0 - t1;
|
||||
bvirt = _0 - _i;
|
||||
u[1] = _0 - (_i + bvirt) + (bvirt - t1);
|
||||
u3 = _j + _i;
|
||||
bvirt = u3 - _j;
|
||||
u[2] = _j - (u3 - bvirt) + (_i - bvirt);
|
||||
u[3] = u3;
|
||||
const C2len = sum(C1len, C1, 4, u, C2);
|
||||
|
||||
s1 = acxtail * bcytail;
|
||||
c = splitter * acxtail;
|
||||
ahi = c - (c - acxtail);
|
||||
alo = acxtail - ahi;
|
||||
c = splitter * bcytail;
|
||||
bhi = c - (c - bcytail);
|
||||
blo = bcytail - bhi;
|
||||
s0 = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
|
||||
t1 = acytail * bcxtail;
|
||||
c = splitter * acytail;
|
||||
ahi = c - (c - acytail);
|
||||
alo = acytail - ahi;
|
||||
c = splitter * bcxtail;
|
||||
bhi = c - (c - bcxtail);
|
||||
blo = bcxtail - bhi;
|
||||
t0 = alo * blo - (t1 - ahi * bhi - alo * bhi - ahi * blo);
|
||||
_i = s0 - t0;
|
||||
bvirt = s0 - _i;
|
||||
u[0] = s0 - (_i + bvirt) + (bvirt - t0);
|
||||
_j = s1 + _i;
|
||||
bvirt = _j - s1;
|
||||
_0 = s1 - (_j - bvirt) + (_i - bvirt);
|
||||
_i = _0 - t1;
|
||||
bvirt = _0 - _i;
|
||||
u[1] = _0 - (_i + bvirt) + (bvirt - t1);
|
||||
u3 = _j + _i;
|
||||
bvirt = u3 - _j;
|
||||
u[2] = _j - (u3 - bvirt) + (_i - bvirt);
|
||||
u[3] = u3;
|
||||
const Dlen = sum(C2len, C2, 4, u, D);
|
||||
|
||||
return D[Dlen - 1];
|
||||
}
|
||||
|
||||
function orient2d(ax, ay, bx, by, cx, cy) {
|
||||
const detleft = (ay - cy) * (bx - cx);
|
||||
const detright = (ax - cx) * (by - cy);
|
||||
const det = detleft - detright;
|
||||
|
||||
if (detleft === 0 || detright === 0 || (detleft > 0) !== (detright > 0)) return det;
|
||||
|
||||
const detsum = Math.abs(detleft + detright);
|
||||
if (Math.abs(det) >= ccwerrboundA * detsum) return det;
|
||||
|
||||
return -orient2dadapt(ax, ay, bx, by, cx, cy, detsum);
|
||||
}
|
||||
|
||||
const EPSILON = Math.pow(2, -52);
|
||||
const EDGE_STACK = new Uint32Array(512);
|
||||
|
||||
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 (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];
|
||||
}
|
||||
|
||||
return Delaunator;
|
||||
|
||||
})));
|
||||
+1
File diff suppressed because one or more lines are too long
+482
@@ -0,0 +1,482 @@
|
||||
|
||||
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).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 (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];
|
||||
}
|
||||
+58
@@ -0,0 +1,58 @@
|
||||
{
|
||||
"name": "delaunator",
|
||||
"version": "5.0.0",
|
||||
"description": "An incredibly fast JavaScript library for Delaunay triangulation of 2D points",
|
||||
"main": "index.js",
|
||||
"module": "index.js",
|
||||
"type": "module",
|
||||
"jsdelivr": "delaunator.min.js",
|
||||
"unpkg": "delaunator.min.js",
|
||||
"sideEffects": false,
|
||||
"dependencies": {
|
||||
"robust-predicates": "^3.0.0"
|
||||
},
|
||||
"devDependencies": {
|
||||
"@rollup/plugin-node-resolve": "^11.2.0",
|
||||
"c8": "^7.6.0",
|
||||
"eslint": "^7.22.0",
|
||||
"eslint-config-mourner": "^3.0.0",
|
||||
"rollup": "^2.42.4",
|
||||
"rollup-plugin-terser": "^7.0.2",
|
||||
"tape": "^5.2.2"
|
||||
},
|
||||
"repository": {
|
||||
"type": "git",
|
||||
"url": "https://github.com/mapbox/delaunator.git"
|
||||
},
|
||||
"scripts": {
|
||||
"lint": "eslint index.js test/test.js bench.js rollup.config.js docs/diagrams.js",
|
||||
"pretest": "npm run lint",
|
||||
"test": "node test/test.js",
|
||||
"cov": "c8 node test/test.js && c8 report -r html",
|
||||
"bench": "node bench.js",
|
||||
"build": "rollup -c",
|
||||
"start": "rollup -cw",
|
||||
"prepublishOnly": "npm test && npm run build"
|
||||
},
|
||||
"files": [
|
||||
"index.js",
|
||||
"delaunator.js",
|
||||
"delaunator.min.js"
|
||||
],
|
||||
"eslintConfig": {
|
||||
"extends": "mourner",
|
||||
"rules": {
|
||||
"no-sequences": 0
|
||||
},
|
||||
"parserOptions": {
|
||||
"ecmaVersion": 2020
|
||||
}
|
||||
},
|
||||
"keywords": [
|
||||
"delaunay triangulation",
|
||||
"computational geometry",
|
||||
"algorithms"
|
||||
],
|
||||
"author": "Vladimir Agafonkin",
|
||||
"license": "ISC"
|
||||
}
|
||||
Reference in New Issue
Block a user