mcs/class/Mono.C5/UserGuideExamples/GConvexHull.cs

   1 /*
   2  Copyright (c) 2003-2006 Niels Kokholm and Peter Sestoft
   3  Permission is hereby granted, free of charge, to any person obtaining a copy
   4  of this software and associated documentation files (the "Software"), to deal
   5  in the Software without restriction, including without limitation the rights
   6  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
   7  copies of the Software, and to permit persons to whom the Software is
   8  furnished to do so, subject to the following conditions:
   9
  10  The above copyright notice and this permission notice shall be included in
  11  all copies or substantial portions of the Software.
  12
  13  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  14  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  15  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  16  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  17  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  18  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  19  SOFTWARE.
  20 */
  21
  22 // Compile with
  23 //    csc /r:C5.dll GConvexHull.cs
  24
  25 using System;
  26 using C5;
  27
  28 namespace GConvexHull
  29 {
  30 // Find the convex hull of a point set in the plane
  31
  32 // An implementation of Graham's (1972) point elimination algorithm,
  33 // as modified by Andrew (1979) to find lower and upper hull separately.
  34
  35 // This implementation correctly handle duplicate points, and
  36 // multiple points with the same x-coordinate.
  37
  38 // 1. Sort the points lexicographically by increasing (x,y), thus
  39 //    finding also a leftmost point L and a rightmost point R.
  40 // 2. Partition the point set into two lists, upper and lower, according as
  41 //    point is above or below the segment LR.  The upper list begins with
  42 //    L and ends with R; the lower list begins with R and ends with L.
  43 // 3. Traverse the point lists clockwise, eliminating all but the extreme
  44 //    points (thus eliminating also duplicate points).
  45 // 4. Join the point lists (in clockwise order) in an array,
  46 //    leaving out L from lower and R from upper.
  47
  48   public class Convexhull
  49   {
  50     public static Point[] ConvexHull(Point[] pts)
  51     {
  52       // 1. Sort points lexicographically by increasing (x, y)
  53       int N = pts.Length;
  54       Array.Sort(pts);
  55       Point left = pts[0], right = pts[N - 1];
  56       // 2. Partition into lower hull and upper hull
  57       IList<Point> lower = new LinkedList<Point>(),
  58         upper = new LinkedList<Point>();
  59       lower.InsertFirst(left); upper.InsertLast(left);
  60       for (int i = 0; i < N; i++)
  61       {
  62         double det = Point.Area2(left, right, pts[i]);
  63         if (det < 0)
  64           lower.InsertFirst(pts[i]);
  65         else if (det > 0)
  66           upper.InsertLast(pts[i]);
  67       }
  68       lower.InsertFirst(right);
  69       upper.InsertLast(right);
  70       // 3. Eliminate points not on the hull
  71       Eliminate(lower);
  72       Eliminate(upper);
  73       // 4. Join the lower and upper hull, leaving out lower.Last and upper.Last
  74       Point[] res = new Point[lower.Count + upper.Count - 2];
  75       lower[0, lower.Count - 1].CopyTo(res, 0);
  76       upper[0, upper.Count - 1].CopyTo(res, lower.Count - 1);
  77       return res;
  78     }
  79
  80     // Graham's scan
  81     public static void Eliminate(IList<Point> lst)
  82     {
  83       IList<Point> view = lst.View(0, 0);
  84       int slide = 0;
  85       while (view.TrySlide(slide, 3))
  86         if (Point.Area2(view[0], view[1], view[2]) < 0)   // right turn
  87           slide = 1;
  88         else
  89         {                                                 // left or straight
  90           view.RemoveAt(1);
  91           slide = view.Offset != 0 ? -1 : 0;
  92         }
  93     }
  94   }
  95
  96 // ------------------------------------------------------------
  97
  98 // Points in the plane
  99
 100   public class Point : IComparable<Point>
 101   {
 102     private static readonly C5Random rnd = new C5Random(42);
 103
 104     public readonly double x, y;
 105
 106     public Point(double x, double y)
 107     {
 108       this.x = x; this.y = y;
 109     }
 110
 111     public override string ToString()
 112     {
 113       return "(" + x + ", " + y + ")";
 114     }
 115
 116     public static Point Random(int w, int h)
 117     {
 118       return new Point(rnd.Next(w), rnd.Next(h));
 119     }
 120
 121     public bool Equals(Point p2)
 122     {
 123       return x == p2.x && y == p2.y;
 124     }
 125
 126     public int CompareTo(Point p2)
 127     {
 128       int major = x.CompareTo(p2.x);
 129       return major != 0 ? major : y.CompareTo(p2.y);
 130     }
 131
 132     // Twice the signed area of the triangle (p0, p1, p2)
 133     public static double Area2(Point p0, Point p1, Point p2)
 134     {
 135       return p0.x * (p1.y - p2.y) + p1.x * (p2.y - p0.y) + p2.x * (p0.y - p1.y);
 136     }
 137   }
 138
 139 // ------------------------------------------------------------
 140
 141   class GConvexHull
 142   {
 143     static void Main(String[] args)
 144     {
 145       if (args.Length == 1)
 146       {
 147         string arg = args[0];
 148         int N = int.Parse(arg);
 149         Point[] pts = new Point[N];
 150         for (int i = 0; i < N; i++)
 151           pts[i] = Point.Random(500, 500);
 152         Point[] chpts = Convexhull.ConvexHull(pts);
 153         Console.WriteLine("Area is " + Area(chpts));
 154         Print(chpts);
 155       }
 156       else
 157         Console.WriteLine("Usage: GConvexHull <pointcount>\n");
 158     }
 159
 160     // The area of a polygon (represented by an array of ordered vertices)
 161     public static double Area(Point[] pts)
 162     {
 163       int N = pts.Length;
 164       Point origo = new Point(0, 0);
 165       double area2 = 0;
 166       for (int i = 0; i < N; i++)
 167         area2 += Point.Area2(origo, pts[i], pts[(i + 1) % N]);
 168       return Math.Abs(area2 / 2);
 169     }
 170
 171     public static void Print(Point[] pts)
 172     {
 173       int N = pts.Length;
 174       for (int i = 0; i < N; i++)
 175         Console.WriteLine(pts[i]);
 176     }
 177   }
 178 }