Toric Degenerations of Bezier Patches
The control polygon of a rational 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 rational Bezier 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 Bezier patch when the weights vary.
bezier patch design theory control polytope toric variety