A Bound on the Implicit Degree of Polygonal Bézier Surfaces

Recent work has shown that the triangular rational Bezier surface representation can be used to create polygonal surface patches. The key to the construction is the judicious use of zero weights in creating the surface parameterization. These zero weights introduce base points into the resulting rational parameterizations. Base points also lower the degree of the implicit representation of these polygonal surface patches. This paper states and proves in a simple, constructive manner a bound on the implicit degree of these rational surfaces.