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Mario Ohlberger, Martin Rumpf, "Adaptive Projection Operators in Multiresolution Scientific Visualization," IEEE Transactions on Visualization and Computer Graphics, vol. 4, no. 4, pp. 344364, OctoberDecember, 1998.  
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@article{ 10.1109/2945.765328, author = {Mario Ohlberger and Martin Rumpf}, title = {Adaptive Projection Operators in Multiresolution Scientific Visualization}, journal ={IEEE Transactions on Visualization and Computer Graphics}, volume = {4}, number = {4}, issn = {10772626}, year = {1998}, pages = {344364}, doi = {http://doi.ieeecomputersociety.org/10.1109/2945.765328}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Visualization and Computer Graphics TI  Adaptive Projection Operators in Multiresolution Scientific Visualization IS  4 SN  10772626 SP344 EP364 EPD  344364 A1  Mario Ohlberger, A1  Martin Rumpf, PY  1998 KW  Adaptive projection operators KW  multiresolution KW  efficient data analysis KW  error indicators KW  hierarchical grids KW  visualization of large data sets. VL  4 JA  IEEE Transactions on Visualization and Computer Graphics ER   
Abstract—Recently, multiresolution visualization methods have become an indispensable ingredient of realtime interactive postprocessing. The enormous databases, typically coming along with some hierarchical structure, are locally resolved on different levels of detail to achieve a significant savings of CPU and rendering time. Here, the method of adaptive projection and the corresponding operators on data functions, respectively, are introduced. They are defined and discussed as mathematically rigorous foundations for multiresolution data analysis. Keeping in mind data from efficient numerical multigrid methods, this approach applies to hierarchical nested grids consisting of elements which are any tensor product of simplices, generated recursively by an arbitrary, finite set of refinement rules from some coarse grid. The corresponding visualization algorithms, e.g., color shading on slices or isosurface rendering, are confined to an appropriate depthfirst traversal of the grid hierarchy. A continuous projection of the data onto an adaptive, extracted subgrid is thereby calculated recursively. The presented concept covers different methods of local error measurement, timedependent data which have to be interpolated from a sequence of key frames, and a tool for local data focusing. Furthermore, it allows for a continuous level of detail.
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