/*
* Convex hull algorithm - Library (C#)
*
* Copyright (c) 2017 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 .
*/
using System;
using System.Collections.Generic;
using System.Linq;
public sealed class ConvexHull {
// Returns a new list 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.
public static IList MakeHull(IList points) {
List newPoints = new List(points);
newPoints.Sort();
return MakeHullPresorted(newPoints);
}
// Returns the convex hull, assuming that each points[i] <= points[i + 1]. Runs in O(n) time.
public static IList MakeHullPresorted(IList points) {
if (points.Count <= 1)
return new List(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.
List upperHull = new List();
foreach (Point p in points) {
while (upperHull.Count >= 2) {
Point q = upperHull[upperHull.Count - 1];
Point r = upperHull[upperHull.Count - 2];
if ((q.x - r.x) * (p.y - r.y) >= (q.y - r.y) * (p.x - r.x))
upperHull.RemoveAt(upperHull.Count - 1);
else
break;
}
upperHull.Add(p);
}
upperHull.RemoveAt(upperHull.Count - 1);
IList lowerHull = new List();
for (int i = points.Count - 1; i >= 0; i--) {
Point p = points[i];
while (lowerHull.Count >= 2) {
Point q = lowerHull[lowerHull.Count - 1];
Point r = lowerHull[lowerHull.Count - 2];
if ((q.x - r.x) * (p.y - r.y) >= (q.y - r.y) * (p.x - r.x))
lowerHull.RemoveAt(lowerHull.Count - 1);
else
break;
}
lowerHull.Add(p);
}
lowerHull.RemoveAt(lowerHull.Count - 1);
if (!(upperHull.Count == 1 && Enumerable.SequenceEqual(upperHull, lowerHull)))
upperHull.AddRange(lowerHull);
return upperHull;
}
}
public struct Point : IComparable {
public double x;
public double y;
public Point(double x, double y) {
this.x = x;
this.y = y;
}
public int CompareTo(Point other) {
if (x < other.x)
return -1;
else if (x > other.x)
return +1;
else if (y < other.y)
return -1;
else if (y > other.y)
return +1;
else
return 0;
}
}