Some Geometrical Aspects of Control Points for Toric Patches Conference Paper

abstract

• We use ideas from algebraic geometry and dynamical systems to explain some ways that control points influence the shape of a Bzier 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 of Krasauskas's toric patches, and include Bzier and tensor product patches as important special cases. 2010 Springer.

authors

• Sottile, Frank

published proceedings

• Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

author list (cited authors)

• Craciun, G., Garca-Puente, L. D., & Sottile, F.

citation count

• 27

complete list of authors

• Craciun, Gheorghe||García-Puente, Luis David||Sottile, Frank

publication date

• April 2010

publisher

• Springer Nature  Publisher

published in

• Lecture Notes in Computer Science  Journal

keywords

• 46 Information And Computing Sciences

Digital Object Identifier (DOI)

• 10.1007/978-3-642-11620-9_9

International Standard Book Number (ISBN) 10

• 3642116191

International Standard Book Number (ISBN) 13

• 9783642116193

start page

• 111

end page

• 135

volume

• 5862

URL

• http://dx.doi.org/10.1007/978-3-642-11620-9_9