Date:	Mon, March 11, 2013
Time:	17:15
Place:	Research II Lecture Hall

Abstract: Subdivision offers attractive and simple iterative methods to efficiently generate freeform surfaces. Although subdivision schemes are simple to implement, their results, the so called subdivision surfaces are difficult to analyze. Much progress has been made, but still we see further development and a growing understanding. In this talk, I present an overview over this development from its beginnings in 1974 till today. I point out central directions of research in this field and, in more detail, describe subdivision for arbitrary non-regular meshes. Understanding the smoothness of subdivision surfaces is of great importance. I will cover well-known results and a new geometric technique that allows analyzing the infinite class of midpoint subdivision schemes of any order. The technique can also be used to show first order smoothness for other classes of subdivision schemes based on simple convex combinations. Modifying midpoint subdivision, one can even obtain arbitrarily smooth subdivision surfaces. I conclude the talk discussing the existence of Ck algorithms and shape artifacts of general subdivision surfaces.