@thi.ng/geom-voronoi
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Fast, incremental 2D Delaunay & Voronoi mesh implementation
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# 
[](https://www.npmjs.com/package/@thi.ng/geom-voronoi)
[](https://mastodon.thi.ng/@toxi)
> [!NOTE]
> This is one of 205 standalone projects, maintained as part
> of the [.ng/umbrella](https://github.com/thi-ng/umbrella/) monorepo
> and anti-framework.
>
> 🚀 Please help me to work full-time on these projects by [sponsoring me on
> GitHub](https://github.com/sponsors/postspectacular). Thank you! ❤️
- [About](#about)
- [Status](#status)
- [Related packages](#related-packages)
- [Installation](#installation)
- [Dependencies](#dependencies)
- [Usage examples](#usage-examples)
- [API](#api)
- [Authors](#authors)
- [License](#license)
## About
Fast, incremental 2D Delaunay & Voronoi mesh implementation, based on
the
[.ng/quad-edge](https://github.com/thi-ng/umbrella/tree/develop/packages/quad-edge)
data structure after Guibas & Stolfi and partially ported from C++
versions by Dani Lischinski, Paul Heckbert et al:
References:
- http://www.cs.cmu.edu/afs/andrew/scs/cs/15-463/2001/pub/src/a2/quadedge.html
- http://www.cs.cmu.edu/afs/andrew/scs/cs/15-463/2001/pub/src/a2/lischinski/114.ps
Construction speed: 20k random points ([poisson disc samples, even
distribution](https://github.com/thi-ng/umbrella/tree/develop/packages/poisson))
in ~850ms (Chrome 72, MBP 2016)
## Status
**STABLE** - used in production
[Search or submit any issues for this package](https://github.com/thi-ng/umbrella/issues?q=%5Bgeom-voronoi%5D+in%3Atitle)
## Related packages
- [.ng/quad-edge](https://github.com/thi-ng/umbrella/tree/develop/packages/quad-edge) - Quadedge data structure after Guibas & Stolfi
## Installation
```bash
yarn add .ng/geom-voronoi
```
ESM import:
```ts
import * as gv from "@thi.ng/geom-voronoi";
```
Browser ESM import:
```html
<script type="module" src="https://esm.run/@thi.ng/geom-voronoi"></script>
```
[JSDelivr documentation](https://www.jsdelivr.com/)
For Node.js REPL:
```js
const gv = await import("@thi.ng/geom-voronoi");
```
Package sizes (brotli'd, pre-treeshake): ESM: 1.45 KB
## Dependencies
- [.ng/api](https://github.com/thi-ng/umbrella/tree/develop/packages/api)
- [.ng/bitfield](https://github.com/thi-ng/umbrella/tree/develop/packages/bitfield)
- [.ng/checks](https://github.com/thi-ng/umbrella/tree/develop/packages/checks)
- [.ng/geom-clip-line](https://github.com/thi-ng/umbrella/tree/develop/packages/geom-clip-line)
- [.ng/geom-clip-poly](https://github.com/thi-ng/umbrella/tree/develop/packages/geom-clip-poly)
- [.ng/geom-isec](https://github.com/thi-ng/umbrella/tree/develop/packages/geom-isec)
- [.ng/geom-poly-utils](https://github.com/thi-ng/umbrella/tree/develop/packages/geom-poly-utils)
- [.ng/math](https://github.com/thi-ng/umbrella/tree/develop/packages/math)
- [.ng/quad-edge](https://github.com/thi-ng/umbrella/tree/develop/packages/quad-edge)
- [.ng/vectors](https://github.com/thi-ng/umbrella/tree/develop/packages/vectors)
Note: .ng/api is in _most_ cases a type-only import (not used at runtime)
## Usage examples
Three projects in this repo's
[/examples](https://github.com/thi-ng/umbrella/tree/develop/examples)
directory are using this package:
| Screenshot | Description | Live demo | Source |
|:------------------------------------------------------------------------------------------------------------------------|:---------------------------------------------------------------------------------|:-------------------------------------------------------|:------------------------------------------------------------------------------------|
| <img src="https://raw.githubusercontent.com/thi-ng/umbrella/develop/assets/examples/geom-voronoi-mst.jpg" width="240"/> | Poisson-disk shape-aware sampling, Voronoi & Minimum Spanning Tree visualization | [Demo](https://demo.thi.ng/umbrella/geom-voronoi-mst/) | [Source](https://github.com/thi-ng/umbrella/tree/develop/examples/geom-voronoi-mst) |
| <img src="https://raw.githubusercontent.com/thi-ng/umbrella/develop/assets/examples/quasi-lattice.png" width="240"/> | Quasi-random lattice generator | [Demo](https://demo.thi.ng/umbrella/quasi-lattice/) | [Source](https://github.com/thi-ng/umbrella/tree/develop/examples/quasi-lattice) |
| <img src="https://raw.githubusercontent.com/thi-ng/umbrella/develop/assets/examples/rotating-voronoi.jpg" width="240"/> | Animated Voronoi diagram, cubic splines & SVG download | [Demo](https://demo.thi.ng/umbrella/rotating-voronoi/) | [Source](https://github.com/thi-ng/umbrella/tree/develop/examples/rotating-voronoi) |
## API
[Generated API docs](https://docs.thi.ng/umbrella/geom-voronoi/)
```ts
import * as g from "@thi.ng/geom";
import { DVMesh } from "@thi.ng/geom-voronoi";
import { repeatedly } from "@thi.ng/transducers";
import { randNorm2 } from "@thi.ng/vectors";
const pts = [...repeatedly(() => randNorm2([], Math.random() * 250), 1000)];
const mesh = new DVMesh(pts);
// raw polygons of primary or dual mesh
mesh.delaunay()
mesh.voronoi()
// ...or clipped & filtered polygons within convex polygon boundary
const bounds = g.vertices(g.center(g.rect(500)));
// [ [ -250, -250 ], [ 250, -250 ], [ 250, 250 ], [ -250, 250 ] ]
const cells = mesh.voronoi(bounds);
document.body.innerHtml = g.asSvg(
g.svgDoc({ fill: "none", "stroke-width": 0.25 },
g.group({ stroke: "blue" }, mesh.delaunay(bounds).map((p) => g.polygon(p))),
g.group({ stroke: "red" }, mesh.voronoi(bounds).map((p) => g.polygon(p)))
)
);
```
## Authors
- [Karsten Schmidt](https://thi.ng)
If this project contributes to an academic publication, please cite it as:
```bibtex
{thing-geom-voronoi,
title = "@thi.ng/geom-voronoi",
author = "Karsten Schmidt",
note = "https://thi.ng/geom-voronoi",
year = 2016
}
```
## License
© 2016 - 2025 Karsten Schmidt // Apache License 2.0