Wavelets for adaptively refined '3rd-root-of-2'-subdivision meshes
For view-dependent visualization, adaptively refined volumetric meshes are used to adapt resolution to given error constraints. A mesh hierarchy based on the '3rd-root-of-2'-subdivision scheme produces structured grids with 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. These masks are applicable to adaptively refined meshes without imposing any restrictions on the adaptivity of the meshes, i.\,e., 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, less polyhedra need to be traversed by a visualization method and less triangles need to be drawn to satisfy a certain error bound.