Indy Telecom & Industrial Media

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The usual immersion of this surface is given by the equation:

The famous “figure 8” immersion can be expressed in parametric equations as:

The renders shown below are of the latter, done in Scilab. Click to view the larger versions.

And as always, here is the code for the above render:

//Klein Bottle
clear;
stacksize (10000000);
num_points = 50;
u = linspace (0, 2*(%pi), num_points);
v= linspace (0, 2*(%pi), num_points);
[U, V] = meshgrid (u, v);
x = cos(U).*(cos(U./2).*(sqrt(2)+cos(V))+(sin(U./2).*sin(V).*cos(V)));
y = sin(U).*(cos(U./2).*(sqrt(2)+cos(V))+(sin(U./2).*sin(V).*cos(V)));
z = -1.*sin(U./2).*(sqrt(2)+cos(V))+cos(U./2).*sin(V).*cos(V);
surf(x, y, z,’edgecol’,'gre’);

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