What is delaunator?
The delaunator npm package is a fast library for Delaunay triangulation of 2D points. It is used to triangulate a set of points into a mesh of triangles, which is a fundamental operation in many geometric algorithms. The package is particularly useful in graphics, geographical information systems (GIS), and for performing various computational geometry tasks.
What are delaunator's main functionalities?
Triangulation
This feature allows you to perform Delaunay triangulation on an array of points. The 'triangles' property of the resulting object contains the indices of the points that form the triangles.
const Delaunator = require('delaunator');
const points = [[0, 0], [1, 0], [1, 1], [0, 1]];
const delaunay = Delaunator.from(points);
console.log(delaunay.triangles);
Hull
This feature provides the convex hull of the input points as an array of point indices that are in the hull. The hull is the outermost 'shell' of the triangulation.
const Delaunator = require('delaunator');
const points = [[0, 0], [1, 0], [1, 1], [0, 1]];
const delaunay = Delaunator.from(points);
console.log(delaunay.hull);
Coordinates Conversion
Delaunator can also take a flat array of coordinates and perform triangulation. This is useful when working with data that is not already structured as an array of points.
const Delaunator = require('delaunator');
const coords = [0, 0, 1, 0, 1, 1, 0, 1];
const delaunay = Delaunator.from(coords);
console.log(delaunay.triangles);
Other packages similar to delaunator
earcut
Earcut is a fast, header-only polygon triangulation library. It's similar to delaunator but focuses on converting polygons to triangles, which is useful for rendering complex shapes in computer graphics.
trianglify
Trianglify is a library for generating colorful triangle meshes that can be used as SVG images and CSS backgrounds. While delaunator focuses on the triangulation algorithm, Trianglify builds on top of it to create visually appealing patterns.
p2t
Poly2Tri is a 2D constrained Delaunay triangulation library. Unlike delaunator, which only works with point sets, Poly2Tri can handle complex polygons with holes and Steiner points, making it more suitable for certain GIS applications.
Delaunator
![](https://badgen.net/bundlephobia/minzip/delaunator)
An incredibly fast JavaScript library for
Delaunay triangulation of 2D points.
Projects based on Delaunator
- d3-delaunay for Voronoi diagrams, search, traversal and rendering (a part of D3).
- d3-geo-voronoi for Delaunay triangulations and Voronoi diagrams on a sphere (e.g. for geographic locations).
Ports to other languages
Example
const points = [[168, 180], [168, 178], [168, 179], [168, 181], [168, 183], ...];
const delaunay = Delaunator.from(points);
console.log(delaunay.triangles);
Install
Install with NPM (npm install delaunator
) or Yarn (yarn add delaunator
), then:
import Delaunator from 'delaunator';
const Delaunator = require('delaunator');
Or use a browser build directly:
<script src="https://unpkg.com/delaunator@4.0.1/delaunator.min.js"></script>
<script src="https://unpkg.com/delaunator@4.0.1/delaunator.js"></script>
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:
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.
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 | 473ms | 411ms | 272ms | 68ms | 4.27s | 4.62s | 4.3s | 810ms |
incremental‑delaunay | 547ms | 505ms | 172ms | 528ms | 5.9s | 6.08s | 2.11s | 6.09s |
d3‑voronoi | 972ms | 909ms | 358ms | 720ms | 15.04s | 13.86s | 5.55s | 11.13s |
delaunay‑fast | 3.8s | 4s | 12.57s | timeout | 132s | 138s | 399s | timeout |
delaunay | 4.85s | 5.73s | 15.05s | timeout | 156s | 178s | 326s | timeout |
delaunay‑triangulate | 2.24s | 2.04s | OOM | 1.51s | OOM | OOM | OOM | OOM |
cdt2d | 45s | 51s | 118s | 17s | timeout | timeout | timeout | timeout |
Papers
The algorithm is based on ideas from the following papers: