1         /// <summary>
 2         /// 获取顶三角形坐标
 3         /// </summary>
 4         /// <param name="r">外接圆半径（顶点到中心的距离）</param>
 5         /// <param name="n">N角星</param>
 6         /// <param name="x1">左横坐标</param>
 7         /// <param name="y1">纵坐标</param>
 8         /// <param name="x2">又横坐标</param>
 9         private void GetCoordinate(double r, int n, out double x1, out double y1, out double x2)
10         {
11             double unitAngle = 0;
12             if(n < 5)
13             {
14                 //奇数角星锐角30，偶数角星锐角和为45
15                 unitAngle = n % 2 == 1 ? 30 : 45;
16             }
17             else
18             {
19                 //奇数角星锐角和为180，偶数角星锐角和为360
20                 unitAngle = n % 2 == 1 ? 180 / n : 360 / n;
21             }
22             double l = Math.PI / 180;    //弧度单位
23             double a = Math.Sin(360 / (2 * n) * l),         //多角芒星各角连中心分割所得的夹角的一半
24                 b = Math.Sin(unitAngle/2 * l),           //芒星内角锐角的一半
25                 c = Math.Sin((180 - 360 / (2 * n) - unitAngle/2) * l),  //芒星除了内锐角的其他内角与中心点连线的夹角
26                 d = Math.Cos((360 / (2 * n)) * l);
27             x1 = (a * r * b) / c;         //正弦定理
28             y1 = (d * r * b) / c;
29             x2 = r - x1;    //x2与x1关于中心点垂线对称,右移r个长度
30             x1 += r;        //右移r个长度
31             y1 -= r;        //下移r个长度
32             //取正数
33             x1 = x1 < 0 ? x1 * (-1) : x1;
34             y1 = y1 < 0 ? y1 * (-1) : y1;
35             x2 = x2 < 0 ? x2 * (-1) : x2;
36         }

 1         /// <summary>
 2         /// 画多角芒星,正多角星
 3         /// </summary>
 4         /// <param name="r">外接圆半径</param>
 5         /// <param name="n">角数量</param>
 6         /// <returns>返回包含正多角星的Canvas</returns>
 7         private Canvas DrawingPentacle(double r, int n)
 8         {
 9             double x1, x2, y1;
10             GetCoordinate(r, n, out x1, out y1, out x2);
11             Canvas canvas = new Canvas() { Width = 100, Height = 100 };
12             //重复N次画出N个三角形斜边
13             for (int i = 1; i <= n; i++)
14             {
15                 DrawingVisual dv = new DrawingVisual();
16                 using (DrawingContext dc = dv.RenderOpen())
17                 {
18                     dc.DrawGeometry(Brushes.LightBlue, new Pen(Brushes.BlueViolet, 1), Geometry.Parse(string.Format("M {0},0 L{1},{2} M 50,0 L{3},{2}", r, x1, y1, x2)));
19                 }
20                 //顺时针旋转
21                 dv.Transform = new RotateTransform(i * 360 / n, 50, 50);
22
23                 //作为图片资源放到图片控件中
24                 RenderTargetBitmap rtb = new RenderTargetBitmap(100, 100, 0, 0, PixelFormats.Default);
25                 rtb.Render(dv);
26                 Image image = new Image() { Source = rtb };
27                 canvas.Children.Add(image);
28             }
29             return canvas;
30         }