WPF画N角芒星，正N角星

计算顶部三角形坐标方法：

        /// <summary>
        /// 获取顶三角形坐标
        /// </summary>
        /// <param name="r">外接圆半径（顶点到中心的距离）</param>
        /// <param name="n">N角星</param>
        /// <param name="x1">左横坐标</param>
        /// <param name="y1">纵坐标</param>
        /// <param name="x2">又横坐标</param>
        private void GetCoordinate(double r, int n, out double x1, out double y1, out double x2)
        {
            double unitAngle = 0;
            if(n < 5)
            {
                //奇数角星锐角30，偶数角星锐角和为45
                unitAngle = n % 2 == 1 ? 30 : 45;
            }
            else
            {
                //奇数角星锐角和为180，偶数角星锐角和为360
                unitAngle = n % 2 == 1 ? 180 / n : 360 / n;
            }
            double l = Math.PI / 180;    //弧度单位
            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
                b = Math.Sin(unitAngle/2 * l),           //芒星内角锐角的一半
                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
                d = Math.Cos((360 / (2 * n)) * l);
            x1 = (a * r * b) / c;         //正弦定理
            y1 = (d * r * b) / c;
            x2 = r - x1;    //x2与x1关于中心点垂线对称,右移r个长度
            x1 += r;        //右移r个长度
            y1 -= r;        //下移r个长度
            //取正数
            x1 = x1 < 0 ? x1 * (-1) : x1;  
            y1 = y1 < 0 ? y1 * (-1) : y1;
            x2 = x2 < 0 ? x2 * (-1) : x2;
        }

1、画空心正N角星

思路：通过计算得到顶部一个三角形的坐标，画出三角形，再画出三角形顺时针旋转一周的其他N-1个三角形。组合起来得到一个伪的多角芒星。

        /// <summary>
        /// 画多角芒星,正多角星
        /// </summary>
        /// <param name="r">外接圆半径</param>
        /// <param name="n">角数量</param>
        /// <returns>返回包含正多角星的Canvas</returns>
        private Canvas DrawingPentacle(double r, int n)
        {
            double x1, x2, y1;
            GetCoordinate(r, n, out x1, out y1, out x2);
            Canvas canvas = new Canvas() { Width = 100, Height = 100 };
            //重复N次画出N个三角形斜边
            for (int i = 1; i <= n; i++)
            {
                DrawingVisual dv = new DrawingVisual();
                using (DrawingContext dc = dv.RenderOpen())
                {
                    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)));
                }
                //顺时针旋转
                dv.Transform = new RotateTransform(i * 360 / n, 50, 50);

                //作为图片资源放到图片控件中
                RenderTargetBitmap rtb = new RenderTargetBitmap(100, 100, 0, 0, PixelFormats.Default);
                rtb.Render(dv);
                Image image = new Image() { Source = rtb };
                canvas.Children.Add(image);
            }
            return canvas;
        }