Wavelets for Adaptively Refined 3√2-subdivision Meshes

L. Linsen, B. Hamann, and K.I. Joy (USA)


View-dependent visualization, multiresolution modeling,B-spline wavelets, lifting, downsampling filter, data approximation.


For view-dependent visualization, adaptively refined vol umetric meshes are used to adapt resolution to given error constraints. A mesh hierarchy based on the -subdivision scheme produces structured grids with highest adaptivity. Downsampling filters reduce aliasing effects and lead to higher-quality data representation (in terms of lower ap proximation error) at coarser levels of resolution. We present a method for applying wavelet-based downsam pling filters to adaptively refined meshes. We use a lin ear B-spline wavelet lifting scheme to derive narrow filter masks. These masks are applicable to adaptively refined meshes without imposing any restrictions on the adaptiv ity 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 re finement 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 tri angles need to be drawn to satisfy a certain error bound.

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