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/*
* 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 <http://www.gnu.org/licenses/>.
*/
// Returns a new array of points representing the convex hull of
// the given set of points. The convex hull excludes collinear points.
// This algorithm runs in O(n log n) time.
export function makeHull(points) {
const newPoints = points.slice();
newPoints.sort(POINT_COMPARATOR);
return makeHullPresorted(newPoints);
}
// Returns the convex hull, assuming that each points[i] <= points[i + 1]. Runs in O(n) time.
export function makeHullPresorted(points) {
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.
const upperHull = [];
for (let i = 0; i < points.length; i++) {
const p = points[i];
while (upperHull.length >= 2) {
const q = upperHull[upperHull.length - 1];
const r = 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();
const lowerHull = [];
for (let i = points.length - 1; i >= 0; i--) {
const p = points[i];
while (lowerHull.length >= 2) {
const q = lowerHull[lowerHull.length - 1];
const r = 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, b) {
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;
}
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