>>> Question: is the intersection of the 3D projections of the 8 
>>> hyperplanes equal to the 3D projection of the intersection of the 8 
>>> hyperplanes?
>>
>>
>> No. and that is not a feature unique to 4D->3D. An example in 2D-1D:
>> Consider the normal vectors (1,1) and (1,-1) and work it out. Another
>> example: Take the sets {(0,0),(1,1)} and {(0,1),(1,0)}. Projection, then
>> intersection yields {0,1}, while the other way around you obtain the 
>> empty
>> set. The first collects all 1D-points that can be extended to some point
>> in each of the original sets. The second collects all 1D-point that have
>> one extension that pertains to both sets simultaneously.
> 
> 
> Right...
> 
> So figuring out how to project the 8 hyperplanes into 3D and then asking 
> POV-Ray for the intersection will get me nowhere fast. (I was already 
> beginning to suspect this conclusion, which is why I asked! ;-)

Here's another question... what about slicing? If I choose a particular 
value for the 4th ordinate and fix that, can I *then* do the 
intersection on 3D? (Taking a slice is after all a set intersection 
operation - and I *believe* those things are associative...)

Andrew @ home.

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