"Sebastian H." wrote:
> 
> Herman Serras wrote:
> > Dini's surface (or a twisted pseudosphere) is a surface of negative
> > constant curvature.
> > The equations depend on two parameters. This animation (animated
> > giffile) has been obtained by fixing one of the parameters and varying
> > the second parameter.
> >
> This is beautiful, looks like a flower.
> Could you post the function, please?
> 
> Regards,
> Sebastian H.

The parametric equations for the Dini surface are:

#declare fx=function(x,y) { a*cos(u)*sin(v) };
#declare fy=function(x,y) { a*(cos(v)+ln(tan((v/2))))+b*u };
#declare fz=function(x,y) { a*sin(u)*sin(v) };

u varies between 0 and 4*pi, v varies between 0.0001 and pi/2.
The parameter b was fixed at 0.2 and the animation was obtained by
varying the parameter a from 0.1 to 1.1.
I didn't use the "parametric" possibilities in Povray 5.5, because I
found the rendering was to slow but furthermore the sharp peak in the
images was cut off. I used the method explained by Tore Nordstand,
http://www.uib.no/People/nfytn/mathgal.htm
using smooth triangles, but adopted his program to use #declare fx =
function.... etc.
I also had to change other thing in his program.

As I'm not at all an advanced user of Povray I had to trie a lot about
placing the camera and the lightsources!

Friendly greetings,

-- 
Herman Serras
Gent (Belgium)
http://cage.rug.ac.be/~hs/

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