# Delaunator [](https://travis-ci.org/mapbox/delaunator) [](https://github.com/mourner/projects) [](https://unpkg.com/delaunator)
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 (a part of [D3](https://d3js.org)).
- [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/abellgithub/delaunator-cpp) (C++)
- [delaunator-sharp](https://github.com/nol1fe/delaunator-sharp) (C#)
- [delaunator-ruby](https://github.com/hendrixfan/delaunator-ruby) (Ruby)
- [Delaunator-Python](https://github.com/HakanSeven12/Delaunator-Python) (Python)
- [hx-delaunator](https://github.com/dmitryhryppa/hx-delaunator) (Haxe)
- [ricardomatias/delaunator](https://github.com/ricardomatias/delaunator) (Kotlin)
## 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
```
## 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):
| uniform 100k | gauss 100k | grid 100k | degen 100k | uniform 1 million | gauss 1 million | grid 1 million | degen 1 million
:-- | --: | --: | --: | --: | --: | --: | --: | --:
**delaunator** | 82ms | 61ms | 66ms | 25ms | 1.07s | 950ms | 830ms | 278ms
[faster‑delaunay](https://github.com/Bathlamos/delaunay-triangulation) | 473ms | 411ms | 272ms | 68ms | 4.27s | 4.62s | 4.3s | 810ms
[incremental‑delaunay](https://github.com/mikolalysenko/incremental-delaunay) | 547ms | 505ms | 172ms | 528ms | 5.9s | 6.08s | 2.11s | 6.09s
[d3‑voronoi](https://github.com/d3/d3-voronoi) | 972ms | 909ms | 358ms | 720ms | 15.04s | 13.86s | 5.55s | 11.13s
[delaunay‑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‑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