万花尺的动态模拟程序

helendcany

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万花尺的动态模拟程序

萬花尺原理：
& x: X( W8 j& b萬花尺有著一個普遍的公式，即 。其中，R為大圓半徑，r為小圓半徑。若這樣的k 和M存在，則稱為k圈M花尺。其中k為小圓圓心繞大圓圓心轉過的圈數，M為花瓣的個數。
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• function flowers(a,b,r,mode,N,gifname)
• %万花尺程序
• %input -a 大圆半径 -b 小圆半径 -r 画笔距小圆圆心的距离
• % -mode ：非0 表示小圆沿大圆内侧转动
• % 0 表示小圆沿大圆外侧转动
• % a = 4;b = 1.2;mode =1;r = b;%10花尺
• % a = 4;b = 2;mode =1;r = 3;%2花尺
• % a = 4;b = 1;mode =1;r = b;%4花尺
• % a = 4;b = 1.5;mode =1;r = b;%8花尺
• % a = 4;b = 0.75;mode =1;r = b;%16花尺
• % a = 4;b = 8/3;mode =1;r = b;%6花尺
• % a = 4;b = 8/9;mode =1;r = b;%9花尺
• % a = 4;b = 4/3;mode =1;r = b/2;%3花尺
• % a = 4;b = 1;mode =1;r = b/2;%4花尺
• % a = 4;b = 2;mode =1;r = b;%2花尺
• if nargin < 3,r = b;end
• if nargin < 4 || mode,mode = -1;else mode = 1;end
• if nargin < 5,N = 10;end
• if nargin < 6,gifname = 'flowers.gif';end
• [k,m] = cylnumber(a,b,N);
• t = 0:pi/200:2*k*pi;
• tt = 0:pi/200:2*pi;
• x1 = a+mode*b;
• xx = a*cos(tt); yy = a*sin(tt);
• plot(xx,yy);
• xm = a+abs(abs(r)+mode*b);
• axis equal off
• title([num2str(m),'花尺'])
• %设置颜色、标记、标记尺寸、擦除模式
• h = line('Color','k','Marker','*',...
•     'MarkerSize',1,'EraseMode','xor');
• h2 = line('Color','k','Marker','.',...
•     'MarkerSize',8,'EraseMode','xor');
• h1 = line('Color','r','Marker','.',...
•     'MarkerSize',20,'EraseMode','xor');
• n = length(t);
• if mode == -1,nk = n:-1:1;else nk = 1:n;end
• for k = 1:n
•     x = x1*cos(t(k))+r*cos(x1/b*t(nk(k)));
•     y = x1*sin(t(k))+r*sin(x1/b*t(nk(k)));
•     x2 = x1*cos(t); y2 = x1*sin(t);
•     x3 = x2(k)+b*cos(tt); y3 = y2(k)+b*sin(tt);
•     hold on
•     set(h,'xdata',x3,'ydata',y3); %画图、画线设置
•     plot(x,y,'r.');
•     set(h2,'xdata',[x x2(k)],'ydata',[y y2(k)]);
•     set(h1,'xdata',[x x],'ydata',[y y]);
•     axis([-xm,xm,-xm,xm]);
•     try
•         f = getframe;
•         imind = frame2im(f); %将单帧图像转化为RGB图像
•         [imind,cm] = rgb2ind(imind,256);
•         if k ~= 1
•             imwrite(imind,cm,gifname,'gif','WriteMode','append','DelayTime',.05)
•         else
•             imwrite(imind,cm,gifname,'gif','Loopcount',inf,'DelayTime',.05)
•         end
•     end
•     pause(0.00001)
• end
• function [k,m] = cylnumber(a,b,N)
• k = 1;
• m = a/b;
• while rem(m,1) && k < N
•     k = k + 1;
•     m = k*a/b;
• end
  

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wuke8

厉害了，图说明的很明了