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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.
--
Herman Serras
Gent (Belgium)
http://cage.rug.ac.be/~hs/
Post a reply to this message
Attachments:
Download 'dinianimop.gif' (78 KB)
Preview of image 'dinianimop.gif'
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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.
Post a reply to this message
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"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/
Post a reply to this message
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> 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.
>
Thanks!
New stuff for some some playaround...
> As I'm not at all an advanced user of Povray I had to trie a lot about
> placing the camera and the lightsources!
>
Always a question of how you like it best ;-)
Regards,
Sebastian H.
Post a reply to this message
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On Tue, 20 Aug 2002 19:02:58 +0200, "Sebastian H." <seb### [at] web de> wrote:
> This is beautiful, looks like a flower.
> Could you post the function, please?
http://mathworld.wolfram.com/DinisSurface.html
ABX
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