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Tor Olav Kristensen wrote:
> But I can not tell my macros to go and use an external utility...
>
> ... Or can I ? :)
...but there is no reason why you cannot create the points for your
lathe object first and then utilize them in your macro.
--
Ken Tyler - 1400+ POV-Ray, Graphics, 3D Rendering, and Raytracing Links:
http://home.pacbell.net/tylereng/index.html http://www.povray.org/links/
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Tor Olav Kristensen wrote:
> Btw.: Will such a lathe render slower than my "cigar" shape ?
Lathes can render quickly if you use a linear or quadratic spline.
Cubic splines are little slower. A lot of it depends on how many
points for the spline are specified and how well behaved it is.
If you specify a lot of points or require sharp bends from the
spline is can slow things down. For a simple cigar shape I see
no reason why it would not render in an acceptable amount of
time.
--
Ken Tyler - 1400+ POV-Ray, Graphics, 3D Rendering, and Raytracing Links:
http://home.pacbell.net/tylereng/index.html http://www.povray.org/links/
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Tor Olav Kristensen wrote:
>
> Chris Huff wrote:
> >
> > Ken wrote:
> >
> > > Tor Olav Kristensen wrote:
> > > > ...How are we supposed to model such cigar shapes then?
> > >
> > > A lathe can do it with ease and can also be used in CSG operations.
> >
> > You can also do it with the poly or quartic objects, and it is quite
> > easy to do with the isosurface object.
>
> I have been thinking about that, but I have not found the
> proper equation for that yet.
>
> (Where the minor and major radii are a part of the equation.)
>
> Any suggestions?
>
Maybe this is what you are asking about?
Equations for a torus,
major radius R>0 centered at (x,y,z)=(0,0,0)
minor radius r>0 (any value: r<R, r=R, or r>R, all OK)
rotational symmetry axis = z-axis
Parametric equations, depending on parameters s and t from 0 to 2*Pi:
x:=(R+r*cos(t))*cos(s);
y:=(R+r*cos(t))*sin(s);
z:=r*sin(t);
Implicit quartic equation:
0 = (x^2+y^2+z^2+R^2-r^2)^2-4*R^2*(x^2+y^2)
which expands to:
0 = r^4 - 2*x^2*r^2 - 2*y^2*r^2 - 2*r^2*R^2 - 2*r^2*z^2 + R^4 -
2*R^2*x^2 - 2*y^2*R^2 + 2*R^2*z^2 + x^4 + 2*x^2*y^2 + 2*x^2*z^2 +
2*y^2*z^2 + z^4 + y^4
I gave an example of this when replying to a post in this newsgroup by
D. Fontaine, 12-19-99.
Adam C.
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Adam Coffman wrote:
>
> Maybe this is what you are asking about?
>
> Equations for a torus,
> ...
Yes. That helped a lot!
Thank you.
> I gave an example of this when replying to a post in this newsgroup by
> D. Fontaine, 12-19-99.
Sorry.
I had not discovered these news groups at that time.
Tor Olav
--
mailto:tor### [at] hotmail com
http://www.crosswinds.net/~tok/tokrays.html
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