GIS算法之多边形面积求解

多边形面积求解的方法很多，其中比较多见的就是增加一个点P，然后分别连接多边形各个定点与P点，然后计算每个三角形的符号面积（面积有正负之分），求和就可以计算出面积。

代码

1 private double GetAreaOfPolyGon(List<Point> points)
2 {
3 double area = 0;
4 if (points.Count < 3)
5 {
6 throw new Exception("至少需要3个点才有面积");
7 }
8
9 Point p1 = points[0];
10 for (int i = 1; i < points.Count - 1; i++)
11 {
12 Point p2 = points[i];
13 Point p3 = points[i + 1];
14 //构造向量
15 Point vecP1P2 = new Point(p2.X - p1.X, p2.Y - p1.Y);
16 Point vecP2P3 = new Point(p3.X - p2.X, p3.Y - p2.Y);
17 double vecMult = vecP1P2.X * vecP2P3.Y - vecP1P2.Y * vecP2P3.X;//用于判断顺时针还是逆时针
18 int sign = 0;
19 if (vecMult > 0)
20 {
21 sign = 1;
22 }
23 else if (vecMult < 0)
24 {
25 sign = -1;
26 }
27 double triArea = GetAreaOfTriangle(p1, p2, p3)*sign;
28 area += triArea;
29 }
30 return Math.Abs(area);
31 }
32
33 private double GetAreaOfTriangle(Point p1, Point p2, Point p3)
34 {
35 double area = 0;
36 double p1p2 = GetLineLength(p1, p2);
37 double p2p3 = GetLineLength(p2,p3);
38 double p3p1 = GetLineLength(p3, p1);
39 double s = (p1p2 + p2p3 + p3p1) / 2;
40 area = s * (s - p1p2) * (s - p2p3) * (s - p3p1);
41 area = Math.Sqrt(area);
42 return area;
43 }
44
45 private double GetLineLength(Point p1, Point p2)
46 {
47 double length;
48 length = Convert.ToDouble((p1.X - p2.X) * (p1.X - p2.X) + (p1.Y - p2.Y) * (p1.Y - p2.Y));
49 length = Math.Sqrt(length);
50 return length;
51 }