Smallest Circle (Typescript)

Iterative and recursive two-dimensional implementations of Welzl's algorithm for computing the smallest circle that encloses a set of points.

This problem is also known as the smallest enclosing circle problem, minimum covering circle problem, or bounding circle problem. The implementation is based on the following work(s):

Welzl, E. (1991). Smallest enclosing disks (balls and ellipsoids).
In New results and new trends in computer science (pp. 359-370).
Springer, Berlin, Heidelberg.

Welzl's algorithm solves this problem in expected O(n) runtime. The original algorithm was formulated as recursive program, leading to a call stack overflow for a moderately large amount of points. Thus, the iterative implementation in this crate should be preferred. However, the recursive version is provided for demonstration purposes.

Please note that the expected runtime only holds for randomized inputs (i.e., you may want to shuffle your input stream in advance).

This is a port of the corresponding Rust implementation rust-smallest-enclosing-circle.

Install

npm install smallest-circle

Usage Examples

The smallestCircle function takes an array of points and returns an object specifying the smallest enclosing circle for the given input. You can use the provided circleCenter and circleRadius methods to determine the circle's center point and radius. Optionally randomize your input data with the provided in-place shuffle function.

import { circleCenter, circleRadius, smallestCircle, shuffle } from 'smallest-circle'

const points = [[0, 0], [8, 0], [2.5, 3], [1.5, -2], [4, 1], [7, -1]]
shuffle(points)
const circle = smallestCircle(points)
const center = circleCenter(circle)
const radius = circleRadius(circle)

console.log(center) // [ 4, 0 ]
console.log(radius) // 4

The API for the recursive version is identical (however it is discouraged to be used in real-world applications for its tendency to exceed call stack size):

import { circleCenter, circleRadius, shuffle, smallestCircleRecursive } from 'smallest-circle'

const points = [[0, 0], [8, 0], [2.5, 3], [1.5, -2], [4, 1], [7, -1]]
shuffle(points)
const circle = smallestCircleRecursive(points)
const center = circleCenter(circle)
const radius = circleRadius(circle)

console.log(center) // [ 4, 0 ]
console.log(radius) // 4