author = {Diewald, U. and Morigi, S. and Rumpf, M.},
  title = {A Cascadic Geometric Filtering Approach to Subdivision},
  journal = {Computer Aided Geometric Design},
  year = {2002},
  volume = {19},
  pages = {675--694},
  abstract = {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 concrete scheme
	is a model of such a filtering based on a successively improved spatial
	approximation starting with some initial coarse mesh and leading
	to a smooth limit surface.\par In every subdivision step the underlying
	grid is refined by some regular refinement rule and a linear finite
	element problem is either solved exactly or, especially on fine grid
	levels, one confines to a small number of smoothing steps within
	the corresponding iterative linear solver. 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. Furthermore,
	the method comes along with a new approach for the theoretical treatment
	of subdivision.},
  pdf = { 1}