The Analysis and Design of Subdivision Schemes

constructing smooth surfaces from coarse polyhedral meshes. At each
step of the process new vertices are connected with edges and faces to
the old ones, producing a finer mesh, until in the limit we obtain a
smooth surface. The mini-course will describe the state of the art in
subdivision, with particular emphasis on:

-- Continuity and Convergence of curve schemes

-- Artifacts of curves and surfaces

-- Tuning for good behaviour at extraordinary points

-- Geometry sensitivity via Mean Curvatures

The mini-course will demonstrate that we are now at the stage where we
can analyze a lot of properties of the subdivision surfaces as a
routine process. With this understanding the research should now focus
on finding ways to engineer the subdivision process to obtain
subdivision schemes that are a lot easier to use than NURBS and give
surfaces of comparable or better quality.

The lecturer is one of the pioneers of subdivision surfaces. His first
paper on the subject, dating back in 1978, describes the Doo-Sabin
subdivision surfaces and introduces the spectral analysis of the
subdivision matrix as a tool for analyzing the properties of the
subdivision surfaces at the extraordinary points. His subsequent
numerous papers on the subject deal with most of the aspects related
to subdivision surfaces.