Journal for Geometry and Graphics 09 (2005), No. 1, 001--009
Copyright Heldermann Verlag 2005
Examples of Bézier-Surfaces of Revolution
Calin-Serban Barbat
Berliner Str. 15, 85221 Dachau, Germany
calin.barbat@web.de
[Abstract-pdf]
This paper gives examples of polynomially parametrizable surfaces of revolution. The first section presents examples which have the additional property of being ruled surfaces. The second section presents a simple and direct approach for the construction of a class of polynomial surfaces of revolution, based on the mapping $f \colon C \to C$, $w \mapsto w^m$ for $m \in {\mathbb N}$. The property of being polynomially parametrizable makes this type of surfaces useful in mathematics not only for studying the solution sets of certain diophantine equations but also in the field of CAGD, especially when B\'ezier-surfaces of revolution are needed.
Keywords: Ruled surfaces, surfaces of revolution, Bezier-polynomial surfaces.
MSC: 53A05; 68U05
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