利用MATLAB实现管状几何体的绘制

ulppknot

3 m: U' t' j! i$ l8 L. ^利用MATLAB绘制管状几何体，所谓管状几何体就是中空的像水管一样的几何体。我编了一个MATLAB函数TubeLike，可以根据管道中心线坐标及各点处管道半径绘制管状几何体。下面结合具体例子介绍TubeLike函数的用法。
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8 F$ n0 E6 q7 W5 ~, C" [5 v【例1】绘制扭结
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• % Example1：扭结
• n = 100;
• r = 0.75;
• q = floor(n/3);
• t = (0:n)/n;
• a = 2; b = 3; c = 1.5;
• q1=2; q2=4;
• f0 = sin(q1*pi*t) + a*sin(q2*pi*t) - ...
•     b*cos(4*pi*t)/2 + c*sin(6*pi*t);
• f0 = [ f0(1:n) f0(1:n) ];
• x = f0(1:n+1);
• y = f0(q+1:q+n+1);
• z = f0(2*q+1:2*q+n+1);
• figure(1)
• TubeLike(x,y,z,r)
• shading interp;
• light
• lighting gouraud
• view(2)
• axis equal off
• axis vis3d
  

【例2】绘制双鱼

• % Example2：双鱼
• t = linspace(0,2*pi,50);
• x = sin(t);
• y = cos(t);
• z = cos(t/2);
• r = sin(t);
• figure(2)
• TubeLike(x,y,z,r)
  

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【例3】绘制田螺
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• % Example3：田螺
• t = linspace(0,7*pi,200);
• x = t.*cos(t)*0.1;
• y = t.*sin(t)*0.1;
• z = [1:numel(t)]*0.01;
• r = sqrt([0:numel(t)-1]*0.004);
• figure(3)
• TubeLike(x,y,z,r)
• view(-44,-52)
• axis equal off
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【例4】绘制风车(或章鱼)
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• % Example4：风车(或章鱼)
• x0 = linspace(0,2*pi,60)';
• y0 = sin(x0);
• t = 0:pi/4:7*pi/4;
• x = x0*cos(t)+y0*sin(t);
• y = -x0*sin(t)+y0*cos(t);
• z = zeros(size(x0));
• figure(4)
• hold on
• for i = 1:numel(t)
•     [X,Y,Z] = TubeLike(x(:,i),y(:,i),z,0.5);
•    suRF(X,Y,Z,'FaceColor',rand(1,3),'LineStyle','none');
• end
• hold off
• view(3)
• axis equal off
• light
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利用MATLAB实现管状几何体的绘制

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利用MATLAB实现管状几何体的绘制