A multisided generalization of Bézier surfaces
- 1 July 1989
- journal article
- Published by Association for Computing Machinery (ACM) in ACM Transactions on Graphics
- Vol. 8 (3) , 204-234
- https://doi.org/10.1145/77055.77059
Abstract
In this paper we introduce a class of surface patch representations, called S-patches, that unify and generalize triangular and tensor product Bézier 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.Keywords
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