Adaptive projection operators in multiresolution scientificvisualization

摘要

Recently, multiresolution visualization methods have become annindispensable ingredient of real-time interactive postprocessing. Thenenormous databases, typically coming along with some hierarchicalnstructure, are locally resolved on different levels of detail to achievena significant savings of CPU and rendering time. In this paper, thenmethod of adaptive projection and the corresponding operators on datanfunctions, respectively, are introduced. They are defined and discussednas mathematically rigorous foundations for multiresolution datananalysis. Keeping in mind data from efficient numerical multigridnmethods, this approach applies to hierarchical nested grids consistingnof elements which are any tensor product of simplices, generatednrecursively by an arbitrary, finite set of refinement rules from somencoarse grid. The corresponding visualization algorithms, e.g. colornshading on slices or isosurface rendering, are confined to annappropriate depth-first traversal of the grid hierarchy. A continuousnprojection of the data onto an adaptive, extracted subgrid is therebyncalculated recursively. The presented concept covers different methodsnof local error measurement, time-dependent data which have to beninterpolated from a sequence of key frames, and a tool for local datanfocusing. Furthermore, it allows for a continuous level of detail