DOI: 10.1007/978-3-642-11620-9_9
View full text

Abstract: We use ideas from algebraic geometry and dynamical systems to explain some ways that control points influence the shape of a Bézier curve or patch. In particular, we establish a generalization of Birch's Theorem and use it to deduce sufficient conditions on the control points for a patch to be injective. We also explain a way that the control points influence the shape via degenerations to regular control polytopes. The natural objects of this investigation are irrational patches, which are a generalization o…

Expand abstract