Two words: HOLY and COW.  How long was the parse time?
"Tor Olav Kristensen" <tor### [at] hotmailcom> wrote in message
news:3CBDEADA.E12E0676@hotmail.com...
>
> - is used to place the spheres in this image.
>
> A NURBS surface is a made with a bivariate function.
> I.e. the value of the functions varies according
> to 2 variables; e.g.  u and v
>
> (A curve is a univariate function. It's value
> varies along with a single variable; e.g.  t)
>
> The value of a trivariate function varies along with
> 3 variables; e.g.   u, v and w   or   x, y and z
>
> So a trivariate function can be used to build solid
> shapes in 3D (that has a volume; like we do with
> isosurfaces).
>
> The image enclosed shows a quick try at doing this
> with a trivariate NURBS function that controls
> the positions of spheres in a 3D grid. (The tone
> range in the image is adjusted after rendering.)
>
> But trivariates can also be used to control other
> things, like e.g. density, pigments, light,
> directions of movement/acceleration, refraction
> index, temperature, humidity, vector fields
> (gradients) and so on...
>
> Later I'll try to find time to show how trivariate
> B-splines can be used to do a kind of 3D morphing
> of shapes made from meshes.
>
> I also hope that POV-Ray will render fast enough
> to calculate some interesting isosurfaces made
> with (simple) trivariate B-splines.
>
> Higher dimensional multivariate B-spline functions
> are interesting too, but I fear that the slow
> speed of POV's parsing will prevent us from
> exploring the possibilities that they provide.
>
>
> Tor Olav


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