Subdivision, multiresolution and the construction of scalable algorithms in computer graphics

Abstract

Multiresolution representations are a critical tool in addressing complexity issues (time and memory) for the large scenes typically found in computer graphics applications. Many of these techniques are based on classical subdivision techniques and their generalizations. In this chapter we review two exemplary applications from this area, multiresolution surface editing and semi-regular remeshing. The former is directed towards building algorithms which are fast enough for interactive manipulation of complex surfaces of arbitrary topology. The latter is concerned with constructing smooth parameterizations for arbitrary topology surfaces as they typically arise from 3D scanning techniques. Remeshing such surfaces then allows the use of classical subdivision ideas. We focus in particular on the practical aspects of making the well-understood mathematical machinery applicable and accessible to the very general settings encountered in practice.