/*
* Convex hull algorithm - Library (TypeScript)
*
* Copyright (c) 2021 Project Nayuki
* https://www.nayuki.io/page/convex-hull-algorithm
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program (see COPYING.txt and COPYING.LESSER.txt).
* If not, see
(points: Readonly {
let newPoints: Array = points.slice();
newPoints.sort(convexhull.POINT_COMPARATOR);
return convexhull.makeHullPresorted(newPoints);
}
// Returns the convex hull, assuming that each points[i] <= points[i + 1]. Runs in O(n) time.
export function makeHullPresorted (points: Readonly {
if (points.length <= 1)
return points.slice();
// Andrew's monotone chain algorithm. Positive y coordinates correspond to "up"
// as per the mathematical convention, instead of "down" as per the computer
// graphics convention. This doesn't affect the correctness of the result.
let upperHull: Array = [];
for (let i = 0; i < points.length; i++) {
const p: P = points[i];
while (upperHull.length >= 2) {
const q: P = upperHull[upperHull.length - 1];
const r: P = upperHull[upperHull.length - 2];
if ((q.x - r.x) * (p.y - r.y) >= (q.y - r.y) * (p.x - r.x))
upperHull.pop();
else
break;
}
upperHull.push(p);
}
upperHull.pop();
let lowerHull: Array = [];
for (let i = points.length - 1; i >= 0; i--) {
const p: P = points[i];
while (lowerHull.length >= 2) {
const q: P = lowerHull[lowerHull.length - 1];
const r: P = lowerHull[lowerHull.length - 2];
if ((q.x - r.x) * (p.y - r.y) >= (q.y - r.y) * (p.x - r.x))
lowerHull.pop();
else
break;
}
lowerHull.push(p);
}
lowerHull.pop();
if (upperHull.length == 1 && lowerHull.length == 1 && upperHull[0].x == lowerHull[0].x && upperHull[0].y == lowerHull[0].y)
return upperHull;
else
return upperHull.concat(lowerHull);
}
export function POINT_COMPARATOR(a: Point, b: Point): number {
if (a.x < b.x)
return -1;
else if (a.x > b.x)
return +1;
else if (a.y < b.y)
return -1;
else if (a.y > b.y)
return +1;
else
return 0;
}
}