Toric degenerations of Bézier patches

Authors:
Luis David Garc'ia-Puente;Frank Sottile;Chungang Zhu
Affiliations:
Sam Houston State University, Huntsville, TX;Texas A&M University, College Station, TX;Dalian University of Technology, Dalian, China
Venue:
ACM Transactions on Graphics (TOG)
Year:
2011

Citing 2
Cited 0

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Some geometrical aspects of control points for toric patches

MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces

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Abstract

The control polygon of a rational Bézier 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 rational Bézier surface patch, there are many possible polyhedral control structures, and none is canonical. We propose a not necessarily polyhedral control structure for rational surface patches, regular control surfaces, which are certain C0 spline surfaces. While not unique, regular control surfaces are exactly the possible limiting positions of a rational Bézier patch when the weights vary.