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Hierarchical Large-scale Volume Representation with 3rd-root-of-2 Subdivision and Trivariate B-spline Wavelets

  • Author(s): Linsen, Lars
  • Gray, Jevan
  • Pascucci, Valerio
  • Duchaineau, Mark A.
  • Hamann, Bernd
  • Joy, Ken
  • et al.
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.

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