[comp.graphics] Box/Plane-Set test

erich@eye.com ( Eric Haines) (12/07/90)

I've recently been looking at the following problem:

	Given an orthogonal (axis-aligned) box and a set of planes defining a
	space (e.g. a polyhedron, a view frustum, etc), find if the box is
	entirely inside, entirely outside, or overlapping the plane-set space.
	Note that the space defined by the planes is convex.

A practical example of this would be finding if an object was inside, outside,
or overlapping a view frustum.  The trick is I want a general answer (it has
to work for more that view frustums, i.e. for any set of planes defining a
space).

Such an algorithm would have a lot of potential uses, e.g. it would certainly
be handy for Arvo & Kirk's formation of candidate lists for their 5D ray
tracing efficiency scheme.  I know of the techniques mentioned in A & K's
article - has anyone found anything faster for this particular sub-problem?  I
thought I'd ask before trying to refine and write up an idea I had, so that I
don't get "you silly fool, this problem was solved long ago by Euclid" notices.

Interested to hear from you all,

Eric Haines