English

Toric degenerations of Bezier patches

Graphics 2011-01-04 v2 Algebraic Geometry

Abstract

The control polygon of a Bezier curve is well-defined and has geometric significance---there is a sequence of weights under which the limiting position of the curve is the control polygon. For a Bezier surface patch, there are many possible polyhedral control structures, and none are canonical. We propose a not necessarily polyhedral control structure for surface patches, regular control surfaces, which are certain C^0 spline surfaces. While not unique, regular control surfaces are exactly the possible limiting positions of a Bezier patch when the weights are allowed to vary.

Keywords

Cite

@article{arxiv.1006.4903,
  title  = {Toric degenerations of Bezier patches},
  author = {Luis David Garcia-Puente and Frank Sottile and Chungang Zhu},
  journal= {arXiv preprint arXiv:1006.4903},
  year   = {2011}
}

Comments

21 pages, many .eps figures