Today I read a paper titled “Toric degenerations of Bezier patches”
The abstract is:
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