jarbee wrote:
> 

> news:3BB18755.31FE7049@atosorigin.com...
> > jarbee wrote:
> > >
> > > Meshes could also be interpolated from point density data using (almost)
> the
> > > same algorithm.
> >
> > Please explain, I really have no clue what you are writing about.
> 
> Well, OK - I'm writing about doing a hundred things with th one program. Say
> you had a 3d mesh made of 1000 polygons. 

That's not a lot (1000)...

> Couldn't you use either the vertex
> points, or the point at the centre of each polygon as input to a SOM,

Please avoid using abbreviation when explaining things to poor brain like
mine. I do not know what SOM is. Surface Of M... ???

> 'mapping' each polygon to, say, all triangles of a certain size and, say,
> 500 polygons? Obviously the result would be an estimate of the original
> mesh, rather than a reduction as you outlined.

I do not understand what you want : Reducing the number of polygon ? 
First keep in mind that Pov does not support mesh of polygons (Yet ???).
Next, a convex polygon can always be replaced by a set of triangles, 
BUT if uv-mapping was used, the texture will get bogus.

Why reducing the number of polygons/triangles ?
Mesh are generally generated from an abstract object, so I believe
it would be far easier to raise the size of the triangle/polygon when
generating the mesh than at a later stage.

Let's me do a parallel with Music/Sound.

The abstract object is the sound you can hear, fully analogic,
full of details.
The representation with a mesh of triangles/polygons is a 
digitalisation of that sound, at a given frequency. (CD quality, 44.1 kHz,
stereo).
Reducing the number of triangles/polygons is either 
 - asking for a lower frequency of sampling, which is really easy
   to perform if you have the analog record, but which required very
   complex maths to do it CORRECTLY directly from the digital data.
   (at least in the generic case when the new frequency is not a 
    multiple/divider of the old frequency).

 - asking for an MP3 compression (with some loose). Alas, MP3 takes
   a lot of studies and commitees before publication. May be someone
   as already publish things like that on the web, I do not know of any.

Moreover, this parallel is not exact, because sound can be considered
as 1D, and the mesh is 3D, which only add to the math complexity and
may provide you with unresolvable trouble.

(For instance, when moving randomly in 1D, the probability to get back
around the original point at some time is 1, whereas in 3D it is 0,
So adding dimensions to a problem may change the tools you could have used).

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