/*
 * © Copyright 2014 – Urheberrechtshinweis
 * Alle Rechte vorbehalten / All Rights Reserved
 *
 * Programmcode ist urheberrechtlich geschuetzt.
 * Das Urheberrecht liegt, soweit nicht ausdruecklich anders gekennzeichnet, bei Frank Ebner.
 * Keine Verwendung ohne explizite Genehmigung.
 * (vgl. § 106 ff UrhG / § 97 UrhG)
 */

#ifndef GEO_CONVEXHULL2_H
#define GEO_CONVEXHULL2_H

#include "Point2.h"

#include <algorithm>
#include <vector>

/**
 * get a convex-hull around a set of 2D points
 * https://en.wikibooks.org/wiki/Algorithm_Implementation/Geometry/Convex_hull/Monotone_chain
 */
class ConvexHull2 {

public:

	//using namespace std;

	typedef double coord_t;		// coordinate type
	typedef double coord2_t;	// must be big enough to hold 2*max(|coordinate|)^2

	// 2D cross product of OA and OB vectors, i.e. z-component of their 3D cross product.
	// Returns a positive value, if OAB makes a counter-clockwise turn,
	// negative for clockwise turn, and zero if the points are collinear.
	static inline coord2_t cross(const Point2 O, const Point2 A, const Point2 B) {
		return (A.x - O.x) * (B.y - O.y) - (A.y - O.y) * (B.x - O.x);
	}

	// Returns a list of points on the convex hull in counter-clockwise order.
	// Note: the last point in the returned list is the same as the first one.
	static inline std::vector<Point2> get(std::vector<Point2> P) {

		auto comp = [] (const Point2 p1, const Point2 p2) {
			return p1.x < p2.x || (p1.x == p2.x && p1.y < p2.y);
		};

		int n = P.size(), k = 0;
		if (n == 1) return P;
		std::vector<Point2> H(2*n);

		// Sort points lexicographically
		std::sort(P.begin(), P.end(), comp);

		// Build lower hull
		for (int i = 0; i < n; ++i) {
			while (k >= 2 && cross(H[k-2], H[k-1], P[i]) <= 0) k--;
			H[k++] = P[i];
		}

		// Build upper hull
		for (int i = n-2, t = k+1; i >= 0; i--) {
			while (k >= t && cross(H[k-2], H[k-1], P[i]) <= 0) k--;
			H[k++] = P[i];
		}

		H.resize(k-1);
		return H;

	}


};

#endif // GEO_CONVEXHULL2_H