C#写的雪花分形

 1 public partial class Form1 : Form  2     {  3         public Form1()  4         {  5             InitializeComponent();  6         }  7   8         private void Form1_Paint(object sender, PaintEventArgs e)  9         { 10             DrawKochSnow(e.Graphics); 11         } 12  13         private void ZheXian(Point p1, Point p2, Graphics g)    // 4条基本线段组成的折线 14         { 15             Point p3 = new Point(p1.X + (p2.X - p1.X) / 3, p1.Y + (p2.Y - p1.Y) / 3);    // 三等分点坐标 16             Point p4 = new Point(p1.X + (p2.X - p1.X) * 2 / 3, p1.Y + (p2.Y - p1.Y) * 2 / 3);    // 三等分点坐标 17             Point p4XD3 = new Point(p4.X - p3.X, p4.Y - p3.Y);    // p4相对于p3点的坐标 18             //int x = (int)(p4XD3.X * Math.Cos(Math.PI / 3) - p4XD3.Y * Math.Sin(Math.PI / 3)); 19             //int y = (int)(p4XD3.X * Math.Sin(Math.PI / 3) + p4XD3.Y * Math.Cos(Math.PI / 3)); 20             // 注意计算机的屏幕垂直坐标和数学上相反，所以数学上逆时针旋转在计算机上相当于顺时针旋转 21             int x = (int)Math.Round(p4XD3.X * Math.Cos(Math.PI / 3) + p4XD3.Y * Math.Sin(Math.PI / 3)); 22             int y = (int)Math.Round(p4XD3.Y * Math.Cos(Math.PI / 3) - p4XD3.X * Math.Sin(Math.PI / 3)); 23             Point p5XD3 = new Point(x, y);    // 凸起点p5相对于p3点的坐标 24             Point p5 = new Point(p3.X + x, p3.Y + y);    // p5相对于原点的坐标 25             Pen pen = new Pen(Brushes.Black, 1); 26             double length = Math.Sqrt(Math.Pow(p2.X - p1.X, 2) + Math.Pow(p2.Y - p1.Y, 2)) / 3; 27             //Console.WriteLine(length); 28             if (length > 20)    // 通过最终线段长度可以控制迭代 29             { 30                 ZheXian(p1, p3, g); 31                 ZheXian(p3, p5, g); 32                 ZheXian(p5, p4, g); 33                 ZheXian(p4, p2, g); 34             } 35             else 36             { 37                 g.DrawLine(pen, p1, p3); 38                 g.DrawLine(pen, p3, p5); 39                 g.DrawLine(pen, p5, p4); 40                 g.DrawLine(pen, p4, p2); 41             } 42         } 43  44         private void DrawKochSnow(Graphics g)    // 科赫雪花(瑞典人科赫于1904年提出了著名的“雪花”曲线) 45         { 46             int length = 480; 47             Point origin = new Point(this.ClientSize.Width / 2, this.ClientSize.Height / 2); 48             g.FillEllipse(Brushes.Blue, new RectangleF(origin, new Size(10, 10))); 49             // 计算三角形的顶点让其中心和窗体的中心重合 50             Point A = new Point(origin.X - length / 2, (int)(origin.Y + length / (2 * Math.Sqrt(3)))); 51             Point B = new Point(origin.X, (int)(origin.Y - length / Math.Sqrt(3))); 52             Point C = new Point(origin.X + length / 2, (int)(origin.Y + length / (2 * Math.Sqrt(3)))); 53             ZheXian(A, B, g); 54             ZheXian(B, C, g); 55             ZheXian(C, A, g); 56         } 57     }