TitleHierarchical Large-scale Volume Representation with 32 Subdivision and Trivariate B-spline Wavelets (In Book)
inGeometric Modeling for Scientific Visualization
Author(s) Lars Linsen, Jevan Gray, Valerio Pascucci, Mark A. Duchaineau, Bernd Hamann, Ken Joy
Editor(s) Guido Brunette, Bernd Hamann, Heinrich Mueller, Lars Linsen
Year 2004
SeriesMathematics + Visualization
PublisherSpringer Verlag
AddressHeidelberg, Germany
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 'nth-root-of-2' subdivision, where n is the dimension of the data set. The main advantage of 'nth-root-of-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 2^n, i.\,e., 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 'nth-root-of-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.