C# 编程实现非自相交多边形质心

计算公式公式: http://en.wikipedia.org/wiki/Centroid#Centroid_of_polygon

多边形的质心：

一个非自相交的n个顶点的多边形(x₀,y₀), (x₁,y₁), ..., (x_n−1,y_n−1) 的质心 (C_x, C_y):

A是多边形的有向面积：

在这些公式中，顶点被假定为沿多边形周长编号。此外，顶点（xn，yn）与（x0，y0）是相同的，意味着对最后一次循环的i + 1 会回到i = 0.
注意，如果点按顺时针方向进行编号，按上述方法计算，会出现一个无法预知的结果；但在这种情况下质心坐标也会是正确的。

In these formulas, the vertices are assumed to be numbered in order of their occurrence along the polygon's perimeter. Furthermore, the vertex ( x_n, y_n ) is assumed to be the same as ( x₀, y₀ ), meaning i + 1 on the last case must loop around to i = 0. Note that if the points are numbered in clockwise order the areaA, computed as above, will have a negative sign; but the centroid coordinates will be correct even in this case.

对于那些难以理解这些公式∑符号，下面给出C#的实现代码：

class Program

{

    static void Main(string[] args)

    {

        List<Point> vertices = new List<Point>();

        vertices.Add(new Point() { X = 1, Y = 1 });

        vertices.Add(new Point() { X = 1, Y = 10 });

        vertices.Add(new Point() { X = 2, Y = 10 });

        vertices.Add(new Point() { X = 2, Y = 2 });

        vertices.Add(new Point() { X = 10, Y = 2 });

        vertices.Add(new Point() { X = 10, Y = 1 });

        vertices.Add(new Point() { X = 1, Y = 1 });

        Point centroid = Compute2DPolygonCentroid(vertices);

    }

    static Point Compute2DPolygonCentroid(List<Point> vertices)

    {

        Point centroid = new Point() { X = 0.0, Y = 0.0 };

        double signedArea = 0.0;

        double x0 = 0.0; // Current vertex X

        double y0 = 0.0; // Current vertex Y

        double x1 = 0.0; // Next vertex X

        double y1 = 0.0; // Next vertex Y

        double a = 0.0;  // Partial signed area

        // For all vertices except last

        int i=0;

        for (i = 0; i < vertices.Count - 1; ++i)

        {

            x0 = vertices[i].X;

            y0 = vertices[i].Y;

            x1 = vertices[i+1].X;

            y1 = vertices[i+1].Y;

            a = x0*y1 - x1*y0;

            signedArea += a;

            centroid.X += (x0 + x1)*a;

            centroid.Y += (y0 + y1)*a;

        }

        // Do last vertex

        x0 = vertices[i].X;

        y0 = vertices[i].Y;

        x1 = vertices[0].X;

        y1 = vertices[0].Y;

        a = x0*y1 - x1*y0;

        signedArea += a;

        centroid.X += (x0 + x1)*a;

        centroid.Y += (y0 + y1)*a;

        signedArea *= 0.5;

        centroid.X /= (6*signedArea);

        centroid.Y /= (6*signedArea);

        return centroid;

    }

}

public class Point

{

    public double X { get; set; }

    public double Y { get; set; }

}

巴特西

C# 编程实现非自相交多边形质心

计算公式公式: http://en.wikipedia.org/wiki/Centroid#Centroid_of_polygon

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