Institute for Data Analysis and Visualization

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.