A Multisided Generalization of Bezier Surfaces

Charles Loop, Tony D. DeRose

Abstract:

In this paper we introduce a class of surface patch representations, called S-patches, that unify and generalize triangular and tensor product Bezier surfaces by allowing patches to be defined over any convex polygonal domain; hence, S-patches may have any number of boundary curves. Other properties of S-patches are geometrically meaningful control points, separate control over positions and derivatives along boundary curves, and a geometric construction algorithm based on de Casteljau's algorithm. Of special interest are the regular S-patches, that is, S-patches defined on regular domain polygons. Also presented is an algorithm for smoothly joining together these surfaces with Ck continuity.

Available in Transactions on Graphics, Vol 8, No 3, July 1989.