In article <421b4484$1@news.povray.org>,
 "William Peska" <wil### [at] yahoocom> wrote:

> > As it is, you're essentially asking for "magic".
> Is the above algorithm mathematically impossible(analytically and
> numerically)?

Yes. You could come up with a numeric method for finding separate 
surfaces, but only with great difficulty and it would be either very 
unreliable or very slow. (One method that comes to mind would be 
building a voxel map and searching for disconnected regions of voxels. 
Another would require tessellating the isosurface and searching for 
unconnected groups of triangles. Neither would succeed if you have a 
contiguous surface enclosing multiple separate volumes.)

Once you have that, you've still got the first "magic" step of finding a 
sensible mapping between spatial coordinates and surface coordinates. So 
you pick an origin point and two basis vectors...where do you go from 
there? As far as I can tell, that's only enough for "height field" type 
isosurfaces, a simple sheet displaced vertically without any overhangs. 
There are many surfaces that simply can't be seamlessly mapped to a 2D 
plane. The sphere is the simplest example. How would your hypothetical 
algorithm UV map a sphere?

And assuming you finally figure out how to automatically define a 
mapping, you'll just get something that doesn't make any sense to a 
human. If the mapping is unpredictable, it's useless. The only practical 
option is to design the mapping specifically for the object and intended 
purpose, and doing so is impossible for something as flexible as an 
isosurface.

-- 
Christopher James Huff <cja### [at] gmailcom>
http://home.earthlink.net/~cjameshuff/
POV-Ray TAG: <chr### [at] tagpovrayorg>
http://tag.povray.org/

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