koch曲线与koch雪花的MATLAB实现

代码

 1 % 2016-4-3
 2 function koch(Ax, Ay, Bx, By)
 3 % 控制递归深度
 4 Deepth = 20;
 5 % 控制图画大小
 6 Size = 100;
 7 if ((Bx-Ax)^2 + (By-Ay)^2) < Deepth
 8    plot([Ax, Bx], [Ay, By], '-r') 
 9    hold on
10    axis([0 Size 0 Size]);
11 else
12     Cx = Ax + (Bx-Ax)/3;
13     Cy = Ay + (By-Ay)/3;
14     Dx = Bx - (Bx-Ax)/3;
15     Dy = By - (By-Ay)/3;
16     
17     koch(Ax, Ay, Cx, Cy);
18     koch(Dx, Dy, Bx, By);
19     
20     L = sqrt((Dx-Cx)^2 + (Dy-Cy)^2);
21     alpha = atan((Dy-Cy)/(Dx-Cx));
22     % 数学
23     if (alpha>=0 && Dx-Cx<0) || (alpha<0 && (Dx-Cx)<0)
24        alpha = alpha + pi;
25     end
26     
27     Ex = Cx + cos(alpha + pi/3)*L;
28     Ey = Cy + sin(alpha + pi/3)*L;
29     
30     koch(Cx, Cy, Ex, Ey);
31     koch(Ex, Ey, Dx, Dy);
32 end
33 end
34 
35 % matlab的单步调试有助于理解该递归
36 % 可通过设置断点观察图形是如何一步一步被画出来的

koch曲线

koch雪花