Multi-dimensional and multi-resolution geometric data-structures for scientific visualization.

摘要

This dissertation investigates multi-resolution and multi-dimensional geometric techniques oriented to the visualization of scientific data. The main focus is on the display of scalar fields represented as single valued functions defined on unstructured geometric domains, like simplicial complexes, or structured geometric domains, like rectilinear grids. Previous isosurface approaches can be roughly categorized in two major groups: (i) those that build off-line multi-resolution representations from the finest detail and (ii) those that build single-resolution adaptive levels of detail satisfying each time one specific error tolerance. This dissertation introduces a new on-line technique that allows one to combine the advantages of these two classes of approaches by building progressively a multi-resolution representation of the output isosurface. The scheme constructs a multi-resolution isosurface and provides at any intermediate stage continuously improved approximated representations.; One important related problem is the fast selection of particularly “meaningful” isosurfaces, like the boundaries separating different materials in a CT scan. This dissertation introduces an approach called Contour Spectrum that provides the user with a simple set of 1-dimensional plots representing exactly fundamental integral properties of the input field. For certain classes of data the Contour Spectrum reduces the number of “meaningful” isovalues that need to be tested. The user does not need to explore the entire range of scalar values of the field. The Contour Spectrum has proved valuable also for static workload analysis in the computation of high resolution isosurfaces. From the latter analysis one can determine a data partitioning scheme that guarantees both (i) good load balancing in parallel computations and (ii) minimal I/O overhead in out-of-core computations.; The last part of the dissertation addresses the problem of producing fast and intuitive rendering of scalar fields of dimension higher than three. The approach has been tested, for example, in the case of a five-dimensional molecular interaction potential. Using this rendering scheme the user can explore interactively the global structure of the potential field with respect to both translational and rotational degrees of freedom at the same time.