

Thank you to Peter Popov and Ron Parker for the information that you gave me
on CSG, that were of great utility.
I have another question, does somebody know how is expressed a torus
mathematically?, the other figures don't represent a real problem, but does
it seem that the torus is a compound figure, how can I calculate the normal,
the intersections, etc. for a torus?, does exist a torus mathematical
formula?...
Again, thank you for your time.
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majucatur <maj### [at] yahoocom> wrote:
: does exist a torus mathematical formula?...
The torus function is:
sqrt((sqrt(x^2+z^2)Rmaj)^2 + y^2)  Rmin = 0

#macro M(A,N,D,L)plane{z,9pigment{mandel L*9translate N color_map{[0rgb x]
[1rgb 9]}scale<D,D*3D>*1e3}rotate y*A*8}#end M(3<1.206434.28623>70,7)M(
1<.7438.1795>1,20)M(1<.77595.13699>30,20)M(3<.75923.07145>80,99)//  Warp 
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majucatur wrote:
>
> Thank you to Peter Popov and Ron Parker for the information that you gave me
> on CSG, that were of great utility.
>
> I have another question, does somebody know how is expressed a torus
> mathematically?, the other figures don't represent a real problem, but does
> it seem that the torus is a compound figure, how can I calculate the normal,
> the intersections, etc. for a torus?, does exist a torus mathematical
> formula?...
For answers to some of your questions, you
may have a look into these posts of mine:
http://news.povray.org/povray.advancedusers/20922/138919
http://news.povray.org/3C292BC5.5A6AB4A6%40hotmail.com
http://news.povray.org/povray.advancedusers/20922/145305
http://news.povray.org/3C4B045F.DFBD5D79%40hotmail.com
And at this page you'll find a polynomial
equation for the torus:
http://www.nada.kth.se/hacks/doc/PoVRay/pov122.html
Here's a macro that will return a quartic torus:
#macro QuarticTorus(Rmaj, Rmin)
#local rxz = 2*(Rmaj^2 + Rmin^2);
#local ry = 2*(Rmaj^2  Rmin^2);
#local rr = (Rmaj^2  Rmin^2)^2;
quartic {
<
1, 0, 0, 0, 2, 0, 0, 2, 0, rxz,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 2, 0, ry, 0, 0, 0, 0,
1, 0, rxz, 0, rr
>
sturm
}
#end // macro QuarticTorus
Tor Olav
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