http://www.mhri.edu.au/~pdb/modelling/supertoroid/

	The supertoriod is one I would find quite useful. In fact I had
been trying to figure out how to fake one before I ran across
this link. 

	I can go the round ones with a lathe but not the others. 

	Look at fourth row, second from right,suitably bounded, a pagoda
"roof." 

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Finally up on 99/06/22

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Matt Giwer wrote:
> 
> http://www.mhri.edu.au/~pdb/modelling/supertoroid/
> 
>         The supertoriod is one I would find quite useful. In fact I had
> been trying to figure out how to fake one before I ran across
> this link.

See the thread below from this group about this subject. It was discussed
in some detail.

    Subject:  Check this out!!!
       Date:  Mon, 22 Feb 1999 22:44:26 -0500
       From:  Anthony Bennett <ben### [at] panamaphoenixnet>
 Newsgroups: povray.general

-- 
Ken Tyler

mailto://tylereng@pacbell.net

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> See the thread below from this group about this subject. It was discussed
> in some detail.
> 
>     Subject:  Check this out!!!
>        Date:  Mon, 22 Feb 1999 22:44:26 -0500
>        From:  Anthony Bennett <ben### [at] panamaphoenixnet>
>  Newsgroups: povray.general

	Thanks, the wheel has been rediscovered. 

	So what is needed is the equation for the intersection of a line
and this thing. That should be the same as for the intersection
of a line and a common torus simply extended for n not equal to
2. I'll put looking into that on my to do stack. 

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Finally up on 99/06/22 updated 06/28

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Matt Giwer <mgi### [at] giwersworldorg> wrote in message
news:377969C4.90D5C3EE@giwersworld.org...
> > See the thread below from this group about this subject. It was
discussed
> > in some detail.
> >
> >     Subject:  Check this out!!!
> >        Date:  Mon, 22 Feb 1999 22:44:26 -0500
> >        From:  Anthony Bennett <ben### [at] panamaphoenixnet>
> >  Newsgroups: povray.general
>
> Thanks, the wheel has been rediscovered.
>
> So what is needed is the equation for the intersection of a line
> and this thing. That should be the same as for the intersection
> of a line and a common torus simply extended for n not equal to
> 2. I'll put looking into that on my to do stack.


Actually, I was looking into this last night. I have some basic pov code -
but be warned, it DOES NOT work properly.  depending on the values, it only
shows quarter of a torus, due to degenerate triangles. (warning! do NOT put
spheres at the vertices for values that give you degen. triangles. That's a
REALLY good way to lock up Pov. )

The code that I have is here: http://24.108.7.134/supertoroid.pov

Also, looking into the pov code, the torii that are used in pov are actually
4th order polys, so modifying that isn't as easy as you would think.

I even thought of adding another keyword to the torus code.....


Twyst

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Twyst wrote:
> 
> Matt Giwer <mgi### [at] giwersworldorg> wrote in message
> news:377969C4.90D5C3EE@giwersworld.org...
> > > See the thread below from this group about this subject. It was
> discussed
> > > in some detail.
> > >
> > >     Subject:  Check this out!!!
> > >        Date:  Mon, 22 Feb 1999 22:44:26 -0500
> > >        From:  Anthony Bennett <ben### [at] panamaphoenixnet>
> > >  Newsgroups: povray.general
> >
> > Thanks, the wheel has been rediscovered.
> >
> > So what is needed is the equation for the intersection of a line
> > and this thing. That should be the same as for the intersection
> > of a line and a common torus simply extended for n not equal to
> > 2. I'll put looking into that on my to do stack.
> 
> Actually, I was looking into this last night. I have some basic pov code -
> but be warned, it DOES NOT work properly.  depending on the values, it only
> shows quarter of a torus, due to degenerate triangles. (warning! do NOT put
> spheres at the vertices for values that give you degen. triangles. That's a
> REALLY good way to lock up Pov. )
> 
> The code that I have is here: http://24.108.7.134/supertoroid.pov
> 
> Also, looking into the pov code, the torii that are used in pov are actually
> 4th order polys, so modifying that isn't as easy as you would think.
> 
> I even thought of adding another keyword to the torus code.....

Note: a buch of interesting information on the toriodal variant of the
superquadric appeared in one of the Graphics Gems books.

Unlike the normal torus, you won't find an exact (general) solution for
the intersection of a ray with the surface.  This thing is way worse
than an three variable polynomial with integral powers.

For someone with time on their hands, what you need to do is to follow
the example of what I did in the superquadric code.  Chop the surface
into octants, find intersections with the bounding box+planes that
chopped it, then do a N-R solution.

The difficulty with this particular surface is that it doesn't guarantee
just one solution per octant.  Even worse, there is no simple way to
slice the octant to make that happen (yes, I thought about this one a
few years back and didn't think it was worth the time).

I suppose an interval arithmetic approach would work pretty well, but
that requires adding quite a bit of code.

Triangles are probably best here...

Xander

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> Note: a buch of interesting information on the toriodal variant of the
> superquadric appeared in one of the Graphics Gems books.
>
> Unlike the normal torus, you won't find an exact (general) solution for
> the intersection of a ray with the surface.  This thing is way worse
> than an three variable polynomial with integral powers.
>
> For someone with time on their hands, what you need to do is to follow
> the example of what I did in the superquadric code.  Chop the surface
> into octants, find intersections with the bounding box+planes that
> chopped it, then do a N-R solution.
>
> The difficulty with this particular surface is that it doesn't guarantee
> just one solution per octant.  Even worse, there is no simple way to
> slice the octant to make that happen (yes, I thought about this one a
> few years back and didn't think it was worth the time).
>
> I suppose an interval arithmetic approach would work pretty well, but
> that requires adding quite a bit of code.
>
> Triangles are probably best here...


Yes, but the problem is twofold, when it comes to triangles.
a) Can't CSG.
b) degenerate triangles.

I might simply take the C code on that page, and make a DXF-outputting mesh
generator/ (DXF supports quad meshes...)

I truly wish povray had a 'quad mesh' - less chance of degenerate triangles
(Note: it might work as a variant on the polygon code - simply stipulate
that all points are coplanar. )


Twyst
>
> Xander

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Oh yea... one more thing - as I stated in the initial message, pov will lock
up if you place spheres at the vertices when you get degenerate triangles.
Any idea why? It just works on one point instead of three(so duplicate
points shouldn't matter..) ... but it sits there churning over the bounding
boxes.. (at least in the superpatch...)

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> I truly wish povray had a 'quad mesh' - less chance of degenerate
triangles
> (Note: it might work as a variant on the polygon code - simply stipulate
> that all points are coplanar. )

Doh!
I seem to have been smoking the good stuff!


polygon

5,
p1,p2,p3,p4,p1
}

does the trick. I missed the fact that it's a 3-point vector, as all the
examples are 2-point...

However...
instead of degenerate triangles, I'm getting colinear points.
<sigh>
This is one evil shape.


>
>
> Twyst
> >
> > Xander
>
>

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