Toric degeneration of Bézier surfaces

  The control polygon of a Bézier curve is well-defined and meaningful---there is a sequence of weights under which the limiting position of the curve is the control polygon. For a Bézier 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 C⁰ spline surfaces. While not unique, regular control surfaces are exactly the possible limiting positions of a Bézier patch when the weights are allowed to vary, but the control points are fixed.