Adaptive Multilinear Tensor Product Wavelets


Many foundational visualization techniques together with isosurfacing, direct volume rendering and texture mapping depend on piecewise multilinear interpolation over the cells of a mesh. However, there has not been much focus at intervals the visualization community on techniques that efficiently generate and encode globally continuous functions outlined by the union of multilinear cells. Wavelets give a wealthy context for analyzing and processing difficult datasets. During this paper, we have a tendency to exploit adaptive regular refinement as a suggests that of representing and evaluating functions described by a subset of their nonzero wavelet coefficients. We tend to analyze the dependencies concerned in the wavelet remodel and describe how to get and represent the coarsest adaptive mesh with nodal perform values such that the inverse wavelet remodel is exactly reproduced via easy interpolation (subdivision) over the mesh parts. This permits for an adaptive, sparse representation of the perform with on-demand analysis at any point within the domain. We have a tendency to specialize in the popular wavelets shaped by tensor products of linear B-splines, ensuing in an adaptive, nonconforming but crack-free quadtree (2D) or octree (3D) mesh that permits reproducing globally continuous functions via multilinear interpolation over its cells.

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