Alan Walkington wrote:
> "Achill" <ach### [at] matumde> wrote in message
> news:3EA### [at] matumde...
> <snip>
> 
>>Adding mesh approximations of solids should be possible, like adding
>>polytopes. The "vertices" and some more useless points (which have to be
>>excluded, for example with the help of a "convex hull algorithm") are
>>given by all possible sums of vertices from the input sets.
>>
>>That seems to be a bigger project though... :-)
>>
> 
> Bigger than what?

I guess it would take some time to implement and develop corresponding 
algorithms for meshes (with certain nice properties). So it is "bigger" 
than anything that I could realize within the next few years...



> You are suggesting to create a "sum of a set A with a sphere of radius r,
> centered at <0,0,0>, which gives the set of all points "within distance
> r of A".

That was only a very special example of a "sum of two sets".



> Aren't there an infinite number of points within a solid, or for that
> matter, on the surface of a solid?
> That sounds like a pretty big project to me. ...

That is why I suggested to use an approximation with meshes.


> You will have to use some approximation ... some definition of a smallest
> cell .. to give yourself a finite number of points within the solid.  A mesh
> is just doing that to the surface rather than the volume. How is that more
> complicated?

Mesh approximations of the surface of a solid is all you need to build 
an approximation of the sum. This is not "more complicated". It is the 
only idea I have for the moment, which could lead to a general sum 
(approximation) of solids. Might be an illusion...?!?

Achill

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