A multisided generalization of Bézier surfaces

Charles T. Loop, Tony D. DeRose
1989 ACM Transactions on Graphics  
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
more » ... hm. 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 C" continuity.
doi:10.1145/77055.77059 fatcat:gmascpgiajactjoagm7urcsu5q