Toric degenerations of Bzier patches Academic Article uri icon


  • The control polygon of a rational Bzier 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 Bzier 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 C 0 spline surfaces. While not unique, regular control surfaces are exactly the possible limiting positions of a rational Bzier patch when the weights vary.

published proceedings

  • ACM Transactions on Graphics

author list (cited authors)

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

citation count

  • 17

complete list of authors

  • Garc'ia-Puente, Luis David||Sottile, Frank||Zhu, Chungang

publication date

  • October 2011