Am 28.02.2011 18:57, schrieb Trevor G Quayle:

> For any CSG, a bounding box is made as a single object that is known to contain
> everything in the CSG.  So for an intersection operation, the bounding box will
> be big enough to contain both (or all) your objects, regardless of how big the
> remaining part is.  This is espescially an issue if one or mor objects doesn't
> interesect, as it still gets included in the ray testing.

No; actually it's just the other way round: An intersection's bounding 
box will be computed as the intersection of all its elements' bounding 
boxes, with the effect that all elements' bounding boxes include the 
/full/ intersection's bounding box.

For instance, the intersection of a sphere {<0,0,0>,1} and a 
sphere{<0,0,1>,0.5} would be computed as follows:

1st sphere bounding box = box { <-1,-1,-1>, <1,1,1> }
2nd sphere bounding box = box { <-0.5,-0.5,0.5>, <0.5,0.5,1.5> }

intersection bounding box = box {
   <max(-1,-0.5),max(-1,-0.5),max(-1,0.5)>,
   <min(1,0.5),min(1,0.5),min(1,1.5)>
}
= box { <-0.5,-0.5,0.5>, <0.5,0.5,1> }

However, if the elements' bounding boxes don't have a common 
intersection at all, this doesn't work out; e.g.:

1st element bounding box = box { <-1,-1,-1>, <1,1,1> }
2nd element bounding box = box { <-0.5,-0.5,1.5>, <0.5,0.5,2.5> }

intersection bounding box = box {
   <max(-1,-0.5),max(-1,-0.5),max(-1,1.5)>,
   <min(1,0.5),min(1,0.5),min(1,2.5)>
}
= box { <-0.5,-0.5,1.5>, <0.5,0.5,1> }

which has a "smallest z" larger than its "largest z", which 
mathematically doesn't make any sense. My first guess would be that this 
is exactly what POV-Ray computes, but that it doesn't recognize it as 
bullshit.

> This is even more extreme in difference operations as POV treats them as an
> intersection of the first object with inverses of the subtracting objects.
> Essentially the subtractiong objects are infinite in size.  (Try rendering a
> plate with 10000 round holes in it for example.)

Not exactly; with differences, the problem is not that the difference's 
bounding box would be infinite (it isn't, because the volume covered by 
the difference is obviously at most the volume of the main object), nor 
that the subtracted objects would have an infinite bounding box (they 
actually don't either, because AFAIK the bounding boxes actually don't 
contain "all that is part of the object", but "all that is part of the 
object's surface"); instead, the problem is that for each intersection 
found with the main object, each and every differenced-away element is 
tested for insideness, without using any bounding box hierarchy that 
might speed things up. (Using the full scene's bounding hierarchy might 
be too expensive with large scenes, and individual CSG objects don't 
have any "private" bounding hierarchy.)

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