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

多邊形的質心：

一個非自相交的n個頂點的多邊形(x₀,y₀), (x₁,y₁), ..., (x_n?1,y_n?1) 的質心 (C_x,?C_y):

A是多邊形的有向面積：

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在這些公式中，頂點被假定為沿多邊形周長編號。此外，頂點（xn，yn）與（x0，y0）是相同的，意味著 對最后一次循環的i + 1?會回到i = 0.
注意，如果點按順時針方向進行編號，按上述方法計算，會出現一個無法預知的結果；但在這種情況下質心坐標也會是正確的。

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.

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對于那些難以理解這些公式∑符號，下面給出C#的實現代碼：

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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 Xdouble y0 = 0.0; // Current vertex Ydouble x1 = 0.0; // Next vertex Xdouble y1 = 0.0; // Next vertex Ydouble a = 0.0; // Partial signed area// For all vertices except lastint 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 vertexx0 = 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; } }

　　

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轉載于:https://www.cnblogs.com/thunderpanda/p/6233250.html

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