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28 Jul 2024 16:16:31 EDT (-0400)
  creating calabi-yau manifolds (Message 1 to 3 of 3)  
From: smirkingman
Subject: creating calabi-yau manifolds
Date: 21 Aug 2008 05:55:01
Message: <web.48ad3b17bd3c71ece62335cd0@news.povray.org>
I would like to use POVRay to create (hopefully pleasing) images of calabi-yau
manifolds, like http://en.wikipedia.org/wiki/Calabi-Yau_manifold.

I'm a complete newbie, so any pointers to .pov files or tuts would be most
appreciated.

Thanks in advance and best regards,
Maurice


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From: Mike Williams
Subject: Re: creating calabi-yau manifolds
Date: 21 Aug 2008 08:47:56
Message: <8l4ELSBKLWrIFwGd@econym.demon.co.uk>
Wasn't it smirkingman who wrote:
>I would like to use POVRay to create (hopefully pleasing) images of calabi-yau
>manifolds, like http://en.wikipedia.org/wiki/Calabi-Yau_manifold.
>
>I'm a complete newbie, so any pointers to .pov files or tuts would be most
>appreciated.

POVRay doesn't solve 6-dimensional polynomials of complex variables, so
you'll need to find a way to express a 3-dimensional cross section of
the manifold using only expressions that are available in POVRay.

If you end up with something that can be expressed as a polynomial of x,
y and z, then you can use the poly object.

If you end up with something that can be expressed as
        F(x,y,z) = 0
where F is a function that uses only trig functions, hyperbolic trig
functions, logs, powers and simple arithmetic on real variables, then
you can use an isosurface.

If you end up with something that can be expressed as
        x = Fx(u,v)
        y = Fy(u,v)
        z = Fy(u,v)
Then you can use a parametric object. Parametric objects can be
extremely slow, but you can use Ingo Janssen's Param.inc to approximate
them with smooth meshes.

-- 
Mike Williams
Gentleman of Leisure


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From: smirkingman
Subject: Re: creating calabi-yau manifolds
Date: 21 Aug 2008 17:00:00
Message: <web.48add6224a9a9f045afe6fd0@news.povray.org>
Mike Williams <nos### [at] econymdemoncouk> wrote:
> Wasn't it smirkingman who wrote:
> >I would like to use POVRay to create (hopefully pleasing) images of calabi-yau
> >manifolds, like http://en.wikipedia.org/wiki/Calabi-Yau_manifold.
> >
> >I'm a complete newbie, so any pointers to .pov files or tuts would be most
> >appreciated.
>
> POVRay doesn't solve 6-dimensional polynomials of complex variables, so
> you'll need to find a way to express a 3-dimensional cross section of
> the manifold using only expressions that are available in POVRay.
>
> If you end up with something that can be expressed as a polynomial of x,
> y and z, then you can use the poly object.
>
> If you end up with something that can be expressed as
>         F(x,y,z) = 0
> where F is a function that uses only trig functions, hyperbolic trig
> functions, logs, powers and simple arithmetic on real variables, then
> you can use an isosurface.
>
> If you end up with something that can be expressed as
>         x = Fx(u,v)
>         y = Fy(u,v)
>         z = Fy(u,v)
> Then you can use a parametric object. Parametric objects can be
> extremely slow, but you can use Ingo Janssen's Param.inc to approximate
> them with smooth meshes.
>
> --
> Mike Williams
> Gentleman of Leisure

Thank you for taking the time to reply so promptly, I'm very grateful.
I'll explore what you suggested and see if a solution is possible.
Best regards,
Maurice


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