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Copy pathConvexHullGraham.js
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103 lines (90 loc) · 2.34 KB
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/**
* Author: Arnab Ray
* ConvexHull using Graham Scan
* Wikipedia: https://en.wikipedia.org/wiki/Graham_scan
* Given a set of points in the plane. The Convex hull of the set is the smallest
* convex polygon that contains all the points of it.
*/
function compare(a, b) {
// Compare Function to Sort the points, a and b are points to compare
if (a.x < b.x) return -1
if (a.x === b.x && a.y < b.y) return -1
return 1
}
function orientation(a, b, c) {
// Check orientation of Line(a, b) and Line(b, c)
const alpha = (b.y - a.y) / (b.x - a.x)
const beta = (c.y - b.y) / (c.x - b.x)
// Clockwise
if (alpha > beta) return 1
// Anticlockwise
else if (beta > alpha) return -1
// Colinear
return 0
}
function convexHull(points) {
const pointsLen = points.length
if (pointsLen <= 2) {
throw new Error('Minimum of 3 points is required to form closed polygon!')
}
points.sort(compare)
const p1 = points[0]
const p2 = points[pointsLen - 1]
// Divide Hull in two halves
const upperPoints = []
const lowerPoints = []
upperPoints.push(p1)
lowerPoints.push(p1)
for (let i = 1; i < pointsLen; i++) {
if (i === pointsLen - 1 || orientation(p1, points[i], p2) !== -1) {
let upLen = upperPoints.length
while (
upLen >= 2 &&
orientation(
upperPoints[upLen - 2],
upperPoints[upLen - 1],
points[i]
) === -1
) {
upperPoints.pop()
upLen = upperPoints.length
}
upperPoints.push(points[i])
}
if (i === pointsLen - 1 || orientation(p1, points[i], p2) !== 1) {
let lowLen = lowerPoints.length
while (
lowLen >= 2 &&
orientation(
lowerPoints[lowLen - 2],
lowerPoints[lowLen - 1],
points[i]
) === 1
) {
lowerPoints.pop()
lowLen = lowerPoints.length
}
lowerPoints.push(points[i])
}
}
const hull = []
for (let i = 1; i < upperPoints.length - 1; i++) {
hull.push(upperPoints[i])
}
for (let i = lowerPoints.length - 1; i >= 0; i--) {
hull.push(lowerPoints[i])
}
return hull
}
export { convexHull }
// Example
// const points = [
// { x: 0, y: 3 },
// { x: 1, y: 1 },
// { x: 2, y: 2 },
// { x: 4, y: 4 },
// { x: 0, y: 0 },
// { x: 1, y: 2 },
// { x: 3, y: 1 },
// { x: 3, y: 3 }]
// convexHull(points)