# Shape from a set of bounding planes

Given a set of planes having normals facing away from a point, it seems possible to carve out a region of space and call it a shape (even if part of the shape would be infinite). For example, 6 planes could be used to construct a cuboid.

What is the method for finding the minimum bounding volume represented by the planes? Also, whether the shape has an infinite dimension?

-
What do you mean by “minimum bounding volume”, as opposed to simply “volume”? – MvG Oct 17 '12 at 20:27
I think you need to narrow your focus, here. You are asking a lot of very different questions. You are allowed to ask multiple questions, but it's better to ask them in multiple posts :) – rschwieb Oct 18 '12 at 13:52
Oh, sorry, maybe a better way to say it would be the smallest volume containing the point. – Jake Oct 18 '12 at 14:02
I asked both in the same place since they're closely related. For example, two planes could describe an infinite wedge which would have infinite volume. – Jake Oct 18 '12 at 14:09