On Geometric Evolution and Cascadic Multigrid in Subdivision

A new approach to subdivision based on the evolution of surfaces under curvature motion is presented. Such an evolution can be understood as a natural geometric filter process where time corresponds to the filter width. Thus, subdivision can be interpreted as the application of a geometric filter on an initial surface. The approach closely connects subdivision to surface fairing concerning the geometric smoothing and to cascadic multigrid methods with respect to the actual numerical procedure. The derived method does not distinguish between different valences of nodes nor between different mesh refinement types.