Figure Asymptote graph3 -- 001

Posted on 2011-01-01 Edited on 2025-04-20 In Tech , Programming , Asymptote , Examples 3D , Graph3.asy

An Asymptote code and the generated picture graph3--001.

🔗This picture comes from the Asymptote gallery of topic graph3

Figure graph3 001 Generated with Asymptote

A MÃ¶bius strip of half-width $w$ with midcircle of radius

$R$ and at height $z=0$ can be represented parametrically byÂ :

\begin{cases}%
x=\left(R+s\times\cos \left(\frac{t}{2}\right)\right)\cos(t)\\
y=\left(R+s\times\cos \left(\frac{t}{2}\right)\right)\sin(t)\\
z=s\times\sin \left(\frac{t}{2}\right)
\end{cases}

for $s$ in $[-w\,;\,w]$ and $t$ in $[0\,;\,2\pi]$ . In this parametrization, the MÃ¶bius strip is therefore a cubic surface with equation

$-R$ ^2y+x2y+y^3-2Rxz-2x2z-2y^2z+yz2=0

Source

Show graph3/fig0010.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Graph3.asy
Tags : #Graph (3D) | #Surface | #Level set (3D)

import graph3;
ngraph=200;
size(12cm,0);
currentprojection=orthographic(-4,-4,5);

real x(real t), y(real t), z(real t);

real R=2;
void xyzset(real s){
  x=new real(real t){return (R+s*cos(t/2))*cos(t);};
  y=new real(real t){return (R+s*cos(t/2))*sin(t);};
  z=new real(real t){return s*sin(t/2);};
}


int n=ngraph;
real w=1;
real s=-w, st=2w/n;
path3 p;
triple[][] ts;
for (int i=0; i <= n; ++i) {
  xyzset(s);
  p=graph(x,y,z,0,2pi);

  ts.push(new triple[] {});
  for (int j=0; j <= ngraph; ++j) {
    ts[i].push(point(p,j));
  }
  s += st;
}

pen[] pens={black, yellow, red, yellow, black};
draw(surface(ts, new bool[][]{}), lightgrey);
for (int i=0; i <= 4; ++i) {
  xyzset(-w+i*w/2);
  draw(graph(x,y,z,0,2pi), 2bp+pens[i]);
}