Please be advised this library is in the process of a complete rewrite, which will be released during October–November 2020. The new 1.x tier will deprecate everything in the 0.x tier. Version 1.x will bring a completely new approach, which is even more efficient, more robust, and natively allows for tangent circles – the new version will set new state of the art benchmarks for performance.

A blazingly fast solution for computing all regions in a 2D plane resulted from intersecting any number of circles, in any configuration. This is essentially the engine inside Harrison Hogg's wonderful "circles" art project – check it out live here; the algorithm is described on HHogg's website. I also saved the algorithm description on the Wayback Machine, in case he decides to drop it off the website for some reason.

The library works both in NodeJS, and as a stand-alone, browser library (use the browser approach below to test it on Runkit).

Install it with

npm install circle-regions

And use it

"use strict";
const circleRegions = require('circle-regions');

console.log(circleRegions.getIntersectionRegions([
  {
    x: 0,
    y: 0,
    radius: 1
  },
  {
    x: 0.5,
    y:0.5,
    radius: 1
  }
]));

Typescript is also supported; the definitions are bundled with the npm package.

Generate the JavaScript bundle

npm run browserify

This will produce a plain JavaScript file called circle-regions.Bundle.js, which you can load in your HTML file. You can then use it

console.log(circleRegions.getIntersectionRegions([
  {
    x: 0,
    y: 0,
    radius: 1
  },
  {
    x: 0.5,
    y:0.5,
    radius: 1
  }
]));