WAVELETS FOR ADAPTIVELY REFINED 2~(1/3)-SUBDIVISION MESHES

摘要

For view-dependent visualization, adaptively refined volumetric meshes are used to adapt resolution to given error constraints. A mesh hierarchy based on the 2~(1/3)-subdivision scheme produces structured grids with the highest adaptivity. Downsampling filters reduce aliasing effects and lead to higher quality data representation (in terms of lower approximation error) at coarser levels of resolution. We present a method for applying wavelet based downsampling filters to adaptively refined meshes. We use a linear B-spline wavelet lifting scheme to derive narrow filter masks. Using these narrow masks, the wavelet filters are applicable to adaptively refined meshes without imposing any restrictions on the adaptivity of the meshes, such that all wavelet filtering operations can be performed without further subdivision steps. We define rules for vertex dependencies in wavelet-based adaptive refinement and resolve them in an unambiguous manner. We use the wavelet filters for view-dependent visualization in order to demonstrate the functionality and the benefits of our approach. When using wavelet filters, the approximation quality is higher at each resolution level. Thus, less polyhedra need to be traversed by a visualization method to meet certain error bounds/quality measures.