Toric degenerations of Bezier patches Institutional Repository Document uri icon

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.

author list (cited authors)

  • Garcia-Puente, L. D., Sottile, F., & Zhu, C.

complete list of authors

  • Garcia-Puente, Luis David||Sottile, Frank||Zhu, Chungang

Book Title

  • arXiv

publication date

  • June 2010