Toric degenerations of Bézier patches Academic Article uri icon


  • 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. © 2011 ACM.

author list (cited authors)

  • Garc'ia-Puente, L. D., Sottile, F., & Zhu, C.

citation count

  • 15

publication date

  • October 2011