Adaptive subdivision curves and surfaces

Abstract

Well-known schemes of subdivision curves and surfaces are modified so that they allow an adaptive refinement. Adaptation is controlled by an error measure which indicates for the vertices of a mesh whether the approximation is sufficient. The adaptive constructions are based on local operations of refining or coarsening. They allow to reach all other subdivisions, in particular the non-adaptive ones, from any given subdivision. The local operations also make possible, besides static top-down and bottom-up calculations, the fully dynamic adaptation of a given mesh to varying error conditions, for instance caused by changes of view during visualization of the curve or surface. The adaptive constructions reduce the computational requirements.