Toric degenerations of Bezier patches

Details Toric degenerations of Bezier patches Toric degenerations of Bezier patches

2010-06-25

arxiv.org/abs/1006.4903v2

Computer Science

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21 pages, many .eps figures

Scientific paper

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.

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