On Thu, 22 Feb 2001 17:56:21 +0100, Christoph Hormann wrote:
>
>
>Ron Parker wrote:
>> 
>> Isosurfaces can be viewed as basic mathematical objects for the sake of
>> this exercise, since the approximation is purely visual.  The problem
>> of determining whether two "basic mathematical objects" overlap reduces
>> to a simple matter of solving a set of simultaneous equations and looking
>> for solutions within given ranges.  Unfortunately, the equations you're
>> solving aren't necessarily linear or even polynomial.  Presumably it's
>> possible to solve such a system for any given combination of objects
>> (though not necessarily) but it's either impossible or ridiculously
>> difficult to automate the process for any two arbitrary objects.
>> 
>
>Seems you are right if you want to make it work for any CSG.  Anyway if
>you only need the objects themselves (or unions) it could be reduced to a
>set of independent equations.  

Yes and no.  Some objects, like isosurfaces, blobs, and polys, are fairly
ugly even then.  Other objects, like cubes and cones and cylinders, can 
get fairly ugly after you apply transformations to them.

Even CSG intersections could be handled, if you could handle the solution of
the independent equations.  The problem is that that solution is not easy.

-- 
Ron Parker   http://www2.fwi.com/~parkerr/traces.html
My opinions.  Mine.  Not anyone else's.

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