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Linear convexity conditions for parametric tensor-product Bézier surface patches. (English) Zbl 0965.65027

Goodman, Tim (ed.) et al., The mathematics of surfaces. VII. Proceedings of the 7th conference, Dundee, Great Britain, September 1996. Winchester: Information Geometers, Limited. 189-208 (1997).
Summary: In the first part of this article we present a method for generating linear sufficient conditions which guarantee the convexity of parametric tensor-product Bézier surfaces. The linearized conditions can be adapted to any strongly convex surface patch.
In the second part we discuss the so-called lifting problem for convex surfaces. With the help of the linearized convexity conditions this task be formulated as a simple optimization problem.
For the entire collection see [Zbl 0952.00040].

MSC:

65D17 Computer-aided design (modeling of curves and surfaces)