Robust Simulation of Small-Scale Thin Features in SPH-based Free Surface Flows

The control polygon of a Bezier 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 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, but the control points are fixed.