Pyramids That Bound Surface Patches

This paper describes how to construct a pyramid which has the property that if its vertex is translated to any point on a given rational Bezier surface patch with positive weights, the patch will lie completely outside the pyramid. This pyramid can facilitate operations such as loop detection in surface intersection. Earlier literature asserted that the complement of a normal bounding cone or pyramid is a surface bounding cone or pyramid. This paper proves that the reverse of this statement is always true, but that the statement itself is true only under certain conditions spelled out in the paper.