/* * Convex hull algorithm - Library (C++) * * 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 . */ #include #include "ConvexHull.hpp" using std::vector; bool Point::operator==(const Point &other) const { return x == other.x && y == other.y; } bool Point::operator!=(const Point &other) const { return x != other.x || y != other.y; } bool Point::operator<(const Point &other) const { if (x != other.x) return x < other.x; else return y < other.y; } bool Point::operator>(const Point &other) const { if (x != other.x) return x > other.x; else return y > other.y; } bool Point::operator<=(const Point &other) const { if (x != other.x) return x < other.x; else return y <= other.y; } bool Point::operator>=(const Point &other) const { if (x != other.x) return x > other.x; else return y >= other.y; } vector makeConvexHull(vector points) { std::sort(points.begin(), points.end()); return makeConvexHullPresorted(points); } vector makeConvexHullPresorted(const vector &points) { if (points.size() <= 1) return vector(points); // 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. vector upperHull; for (const Point &p : points) { while (upperHull.size() >= 2) { const Point &q = *(upperHull.cend() - 1); // Same as .back() const Point &r = *(upperHull.cend() - 2); if ((q.x - r.x) * (p.y - r.y) >= (q.y - r.y) * (p.x - r.x)) upperHull.pop_back(); else break; } upperHull.push_back(p); } upperHull.pop_back(); vector lowerHull; for (vector::const_reverse_iterator it = points.crbegin(); it != points.crend(); ++it) { const Point &p = *it; while (lowerHull.size() >= 2) { const Point &q = *(lowerHull.cend() - 1); // Same as .back() const Point &r = *(lowerHull.cend() - 2); if ((q.x - r.x) * (p.y - r.y) >= (q.y - r.y) * (p.x - r.x)) lowerHull.pop_back(); else break; } lowerHull.push_back(p); } lowerHull.pop_back(); if (!(upperHull.size() == 1 && upperHull == lowerHull)) upperHull.insert(upperHull.end(), lowerHull.cbegin(), lowerHull.cend()); return upperHull; }