A discrete approach to multiresolution curves and surfaces

Abstract

Subdivision surfaces have been widely adopted in modeling in part because they introduce a separation between the surface and the underlying basis functions. This separation allows for simple general-topology subdivision schemes. Multiresolution representations based on subdivision, however, incongruently return to continuous functional spaces in their construction and analysis. In this paper, we propose a discrete multiresolution framework applicable to many subdivision schemes and based only on the subdivision rules. Noting that a compact representation can only afford to store a subset of the detail information, our construction enforces a constraint between adjacent detail terms. In this way, all detail information is recoverable for reconstruction, and a decomposition approach is implied by the constraint. Our framework is demonstrated with case studies in Dyn-Levin-Gregory curves and Catmull-Clark surfaces, each of which our method produces results on par with earlier methods. It is further shown that our construction can be interpreted as biorthogonal wavelet systems. © 2009 Springer-Verlag Berlin Heidelberg.