Multiresolution modeling for scientific visualization

Interactive visualization and exploration of large-scale scientific data sets is an important application for the analysis of data obtained from computational fluid dynamics (CFD), computerized tomography (CT), and laser-range scans. These data sets are typically defined by discrete samples, either aligned on regular grids or randomly scattered in space, describing an underlying shape or a volumetric field function. Examples are isosurfaces and shock waves in CFD, height maps for terrain data, and three-dimensional scanned objects in reverse engineering. Starting with discrete samples, a continuous geometric model is built, that closely approximates an underlying shape. Multiresolution representations are essential for displaying large-scale surface and volume models within minimal computation time, satisfying certain error bounds or bounds on complexity. This dissertation is concerned with the efficient construction of multiresolution surface and volume models for high-quality approximation of scientific data. We present two adaptive clustering methods used for scattered data approximation. The first method uses hierarchical Voronoi diagrams and Sibson's interpolant for multiresolution surface modeling. The second approach is based on binary space-partition trees and quadratic polynomial approximation used as intermediate representation for the construction of triangulated surfaces. For multiresolution representation and compression of data sets defined on regular grids, we construct biorthogonal lifted B-spline wavelets with small filters. A major contribution is the construction of new symmetric lifted B-spline subdivision-surface wavelets with finite filters for representing surfaces of arbitrary topology defined by irregular polygonal base meshes. Regular mesh subdivision results in smooth limit surfaces with the option of sharp features and boundary curves represented by modified subdivision rules. These new wavelet constructions are used for approximation and compression of isosurfaces taken from a high-resolution turbulent-mixing hydrodynamics simulation. A similar approach is used to define wavelets on planar tessellations.

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