/* 
 * 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/>.
 */


interface Point {
	x: number;
	y: number;
}


namespace convexhull {
	
	// 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<P extends Point>(points: Readonly<Array<P>>): Array<P> {
		let newPoints: Array<P> = 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<P extends Point>(points: Readonly<Array<P>>): Array<P> {
		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<P> = [];
		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<P> = [];
		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;
	}
	
}