Gert Van den Eynde wrote:
> Hi all,
>
> I would like to use povray to model some scientific data: I have a
> (large) set <x,y,z,data> vectors in which the data scalar can be
> represented using a color. Between the given data, an interpolation
> mechanism should provide continuity. How could I model this in Povray
> (speed of trace is not that important) ?

This can be very tricky to get good results.  The best method will depend on
what sort of data you have and what you want it to look like.

In terms of final result, are you expecting a closed opaque solid that
completely covers all data points?  Are you expecting it to be nice smooth
curved surfaces or sharp angular plane facets?  Or do you want it to only
cover some of the data points (eg "data>5.0" bit like an isosurface).  Or do
you want semi-transparent "layers" to show the data, a bit like a 3D medical
image where they can make the bone show up as solid and then the skin and
muscles semi-transparent with different colours.

And as for the input, is is on a regular grid?  Are all the data points
"inside" the object you want to see?

As a first suggestion, radial basis functions tend to be quite good at
interpolating between data points, Google will turn up some info I expect.
Then once you have your interpolated function you have to decide what you
are going to do with it.  Maybe an iso-surface will do, but render times
will be ridiculous if you have more than a handful of data points.

The alternative is to triangulate the interpolated function, not a
straightforward task.  You could use something like marching cubes (although
I'm sure there's better, marching cubes/tetrahedra are the only ones I
learnt!) and then you could colour-code each vertex depending on the "data"
value too.

Or, a very simple method would be to just stick a sphere at each data point.
You could play with the size/colour/transparency until something looked
good.

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