Douglas Peucker算法的C#实现

一、算法原理

Douglas-Peucker算法

在数字化过程中,需要对曲线进行采样简化,即在曲线上取有限个点,将其变为折线,并且能够在一定程度

上保持原有的形状。

经典的Douglas-Peucker算法描述如下:

(1)在曲线首尾两点A,B之间连接一条直线AB,该直线为曲线的弦;

(2)得到曲线上离该直线段距离最大的点C,计算其与AB的距离D;

(3)比较该距离与预先给定的阈值threshold的大小,如果小于threshold,则该直线段作为曲线的近似,该段曲线处理完毕。

(4)如果距离大于阈值,则用C将曲线分为两段AC和BC,并分别对两段取信进行1~3的处理。

(5)当所有曲线都处理完毕时,依次连接各个分割点形成的折线,即可以作为曲线的近似。

 

二、算法C#实现

 1 using System;
 2 using System.Collections.Generic;
 3 using System.Linq;
 4 using System.Text;
 5 
 6 namespace ConsoleApplication2
 7 {
 8     public struct cvPoint
 9     {
10         public int X;
11         public int Y;
12         public cvPoint(int x, int y)
13         {
14             X = x;
15             Y = y;
16         }
17     }
18     class Program
19     {
20         static void Main(string[] args)
21         {
22             var points = new List<cvPoint>();
23             points.Add(new cvPoint(1, 1));
24             points.Add(new cvPoint(2, 2));
25             points.Add(new cvPoint(3, 3));
26             points.Add(new cvPoint(4, 3));
27             points.Add(new cvPoint(5, 3));
28             points.Add(new cvPoint(6, 3));
29             points.Add(new cvPoint(5, 3));
30             points.Add(new cvPoint(6, 3));
31             points.Add(new cvPoint(7, 3));
32             points.Add(new cvPoint(8, 3));
33             var epsilon = 0.8d;
34             var filteredPoints = new List<cvPoint>();
35             DouglasPeucker(points, epsilon, ref filteredPoints);
36             Console.WriteLine("Filtered points:");
37             foreach (var f in filteredPoints)
38             {
39                 Console.WriteLine(string.Format("{0},{1}", f.X, f.Y));
40             }
41             Console.ReadKey();
42         }
43         private static double distanceToSegment(cvPoint p, cvPoint start, cvPoint end)
44         {
45             var m1 = ((double)(end.Y - start.Y)) / ((double)(end.X - start.X));
46             var c1 = start.Y - m1 * start.X;
47             var interPointX = 0d;
48             var interPointY = 0d;
49             if (m1 == 0)
50             {
51                 interPointX = p.X;
52                 interPointY = c1;
53 
54             }
55             else
56             {
57                 var m2 = -1 / m1;
58                 var c2 = p.Y - m2 * p.X;
59                 interPointX = (c1 - c2) / (m2 - m1);
60                 interPointY = m2 * interPointX + c2;
61             }
62             return Math.Sqrt(Math.Pow(p.X - interPointX, 2) + Math.Pow(p.Y - interPointY, 2));
63         }
64 
65         private static void DouglasPeucker(IList<cvPoint> PointList, double epsilon, ref List<cvPoint> filteredPoints)
66         {
67             var dmax = 0d;
68             int index = 0;
69             int length = PointList.Count;
70             for (int i = 1; i < length - 1; i++)
71             {
72                 var d = distanceToSegment(PointList[i], PointList[0], PointList[length - 1]);
73                 Console.WriteLine(string.Format("{0}.distence:{1}", i, d));
74                 if (d > dmax)
75                 {
76                     index = i;
77                     dmax = d;
78                 }
79             }
80             Console.WriteLine(string.Format("dMax:{0}", dmax));
81             // If max distance is greater than epsilon, recursively simplify
82             if (dmax > epsilon)
83             {
84                 filteredPoints.Add(PointList[0]);
85                 filteredPoints.Add(PointList[index]);
86                 filteredPoints.Add(PointList[length - 1]);
87                 DouglasPeucker(PointList.Take(index + 1).ToList(), epsilon, ref filteredPoints);
88                 DouglasPeucker(PointList.Skip(index + 1).Take(PointList.Count - index - 1).ToList(), epsilon, ref filteredPoints);
89             }
90         }
91     }
92 }

 

三、算法验证
近似前:

近似后的线段:

 

本文地址: http://www.cnblogs.com/deepleo/p/Douglas-Peucker.html

参考:http://www.codeproject.com/Articles/18936/A-C-Implementation-of-Douglas-Peucker-Line-Approxi

posted @ 2014-12-02 11:28 夜の魔王 阅读(...) 评论(...) 编辑 收藏