POV-Ray : Newsgroups : povray.binaries.images : Faux Dupin Cyclide : Re: Faux Dupin Cyclide Server Time
7 Nov 2024 00:19:29 EST (-0500)
  Re: Faux Dupin Cyclide  
From: Le Forgeron
Date: 18 May 2017 10:26:49
Message: <591daf29@news.povray.org>
Le 18/05/2017 à 13:57, Bald Eagle a écrit :
> I did a bit of work on this last night, and thanks to
> 
> figures 12.21 and 12.22   here:
>
http://what-when-how.com/computer-graphics-and-geometric-modeling/surfaces-in-computer-graphics-geometric-modeling-part-7/
> 
> I was able to work out some of the circles that lie on the face of the algebraic
> surface, the inner ellipse, and the hyperboloid that the surface is tangent to.
> 
> It's not perfect - I think there's a little bit of difference due to the scaling
> in the z direction due to B=A*0.98, but most of the hard stuff is worked out.

Thanks to your link, I would say:

A = R
C = abs(r-rho)/2
B = sqrt(A^2-C^2)
D = (r+rho)/2

with R the traditional radius (major) of the torus
r & rho the two different minor radius

and voila!

Here with 3,2 & 1  (and still the white sphere of radius 1 at origin)


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