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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.