TitleHierarchical Large-scale Volume Representation with 3rd-root-of-2 Subdivision and Trivariate B-spline Wavelets (Tech Report)
Author(s) Lars Linsen, Jevan Gray, Valerio Pascucci, Mark A. Duchaineau, Bernd Hamann, Ken Joy
Year 2002
InstitutionDepartment of Computer Science, University of California, Davis
Abstract Multiresolution methods provide a means for representing data at multiple levels of detail. They are typically based on a hierarchical data organization scheme and update rules needed for data value computation. We use a data organization that is based on what we call $\sqrt[n]{2}$ subdivision. The main advantage of $\sqrt[n]{2}$ subdivision, compared to quadtree (n=2) or octree (n=3) organizations, is that the number of vertices is only doubled in each subdivision step instead of multiplied by a factor of four or eight, respectively. To update data values we use n-variate B-spline wavelets, which yield better approximations for each level of detail. We develop a lifting scheme for n=2 and n=3 based on the $\sqrt[n]{2}$-subdivision scheme. We obtain narrow masks that provide a basis for out-of-core techniques as well as view-dependent visualization and adaptive, localized refinement.