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Isn't the equation for a 2D oval/ellips something like
(x^2)/a + (y^2)/b = 0? A circle is x^2+y^2=0.
Couldn't we find the part of the torus discription
that deals with the major radius and add the division
parts?
Nieminen Juha wrote:
> Mark Wagner <mar### [at] gte net> wrote:
> : A true oval cannot be created by scaling a torus.
>
> Perhaps I'll think about how to do it with a poly-object. It looks like
> it will need a 6th degree polynomial (since the regular torus need a 4th
> degree one)...
>
> --
> main(i,_){for(_?--i,main(i+2,"FhhQHFIJD|FQTITFN]zRFHhhTBFHhhTBFysdB"[i]
> ):5;i&&_>1;printf("%s",_-70?_&1?"[]":" ":(_=0,"\n")),_/=2);} /*- Warp -*/
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Mr. Art wrote in message <37CD54FE.76230D45@gci.net>...
>Isn't the equation for a 2D oval/ellips something like
>(x^2)/a + (y^2)/b = 0? A circle is x^2+y^2=0.
>Couldn't we find the part of the torus discription
>that deals with the major radius and add the division
>parts?
An oval is not an ellipse, they just look similar. An oval is easier to
draw freehand, but an ellipse is easier to create mathematically.
Mark
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Point taken. But is there someone out there that can point out the
places in the code to put the values a and b in something like
this?
// Torus having major radius sqrt(40), minor radius sqrt(12)
#declare Torus=
quartic {
<
1, 0, 0, 0, 2, 0, 0,
2, 0,-104, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 1,
0, 0, 2, 0, 56, 0, 0,
0, 0, 1, 0, -104, 0, 784
>
sturm
pigment{White}
}
This is almost stright form the docs.
Mark Wagner wrote:
> Mr. Art wrote in message <37CD54FE.76230D45@gci.net>...
> >Isn't the equation for a 2D oval/ellips something like
> >(x^2)/a + (y^2)/b = 0? A circle is x^2+y^2=0.
> >Couldn't we find the part of the torus discription
> >that deals with the major radius and add the division
> >parts?
>
> An oval is not an ellipse, they just look similar. An oval is easier to
> draw freehand, but an ellipse is easier to create mathematically.
>
> Mark
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Mr. Art <mr.### [at] gcinet> wrote:
: Point taken. But is there someone out there that can point out the
: places in the code to put the values a and b in something like
: this?
It's not as easy as "putting the values a and b in this".
I have been calculating polynomials (man, I wish I got some mathematical
program to help me; typing polynomials by hand is tedious) and it seems
to be impossible.
If I'm correct, a perfect elliptical torus would require a 8th degree
polynomial (a very simple explanation of this is that it's because the torus
is a 4th degree polynomial and you have to raise it to the power of 2).
Povray can only handle polynomials up to the 7th degree. Bad luck.
A non-perfect elliptical torus (ie. the minor radius does not stay
constant along the torus) may require only a 6th degree polynomial (note:
this torus is not the same as a scaled torus; the minor radius would be
the same at both axes of symmetry; the radius will differ at the "corners").
--
main(i,_){for(_?--i,main(i+2,"FhhQHFIJD|FQTITFN]zRFHhhTBFHhhTBFysdB"[i]
):5;i&&_>1;printf("%s",_-70?_&1?"[]":" ":(_=0,"\n")),_/=2);} /*- Warp -*/
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How about a "sweep" object of some kind?
Bob Hughes <inv### [at] aolcom> wrote in message
news:37cc138e@news.povray.org...
> An oval using the torus is not going to turn out right unless you use
> Kens second method. Uneven scaling is one thing, procedural-type
> scaling is another, of which POV-Ray is unable to do. Another
> possibility is to string together spheres or blob components along a
> spline path, just not as efficient.
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You need a copy of Mathematica!
I can't use more than a fraction of what it does, but it's too cool to give
up so I won't give it away <g>. Maybe you can get a special student price?
Nieminen Juha <war### [at] cctutfi> wrote in message
news:37ce25b1@news.povray.org...
> I have been calculating polynomials (man, I wish I got some mathematical
> program to help me; typing polynomials by hand is tedious) and it seems
> to be impossible.
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If you mean in official Pov, don't think that would be any different
than trying to scale a torus, ie. 'lathe', 'sor' etc. are still
circular, so I don't see any way other than some CSG method. Keep in
mind I do not know all there is to know by far.
Bob
John M. Dlugosz <joh### [at] dlugoszcom> wrote in message
news:37ceeb75@news.povray.org...
> How about a "sweep" object of some kind?
>
> Bob Hughes <inv### [at] aolcom> wrote in message
> news:37cc138e@news.povray.org...
> > An oval using the torus is not going to turn out right unless you
use
> > Kens second method. Uneven scaling is one thing, procedural-type
> > scaling is another, of which POV-Ray is unable to do. Another
> > possibility is to string together spheres or blob components along
a
> > spline path, just not as efficient.
>
>
>
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Nieminen Juha wrote in message <37ce25b1@news.povray.org>...
>Mr. Art <mr.### [at] gcinet> wrote:
>: Point taken. But is there someone out there that can point out the
>: places in the code to put the values a and b in something like
>: this?
>
> It's not as easy as "putting the values a and b in this".
> I have been calculating polynomials (man, I wish I got some mathematical
>program to help me; typing polynomials by hand is tedious) and it seems
>to be impossible.
> If I'm correct, a perfect elliptical torus would require a 8th degree
>polynomial (a very simple explanation of this is that it's because the
torus
>is a 4th degree polynomial and you have to raise it to the power of 2).
>Povray can only handle polynomials up to the 7th degree.
Can the isosurface functions handle an 8th degree polynomial?
Mark
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Mark Wagner <mar### [at] gtenet> wrote:
: Can the isosurface functions handle an 8th degree polynomial?
I suppose so.
--
main(i,_){for(_?--i,main(i+2,"FhhQHFIJD|FQTITFN]zRFHhhTBFHhhTBFysdB"[i]
):5;i&&_>1;printf("%s",_-70?_&1?"[]":" ":(_=0,"\n")),_/=2);} /*- Warp -*/
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John M. Dlugosz <joh### [at] dlugoszcom> wrote:
: You need a copy of Mathematica!
But not an illegal one, that's for sure.
: Maybe you can get a special student price?
AFAIK they don't sell students licenses for mathematica here at TUT. But
I have to ask. Maple is another possibility.
--
main(i,_){for(_?--i,main(i+2,"FhhQHFIJD|FQTITFN]zRFHhhTBFHhhTBFysdB"[i]
):5;i&&_>1;printf("%s",_-70?_&1?"[]":" ":(_=0,"\n")),_/=2);} /*- Warp -*/
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