Multiresolution modeling of curvilinear grids
Junwon Sung · 1997
Most data sets in scientific visualization, which can be either physical measurements or be created by a mathematical simulation, are numerous. Therefore, an important issue of scientific visualization system is the management of these data sets. The goal of data management is to reduce the storage space and access time of these data sets to speed up the visualization process. In recent years, multiresolution analysis and wavelets have received considerable attention since they provide a useful and efficient tool for representing shape and analyzing features at multiple levels of detail. From approximation at lower resolution, brief outlines of features can be extracted in short periods of time and partial reconstruction is a good framework for data management in scientific visualization. The basic assumption of the multiresolution analysis is that the data are uniformly distributed in the domain since classic wavelets are constructed using the Fourier transform. Therefore, the wavelet transform designed by the Fourier transform cannot properly work for irregularly sampled data. A non-orthogonal grid, curvilinear grid is an irregular grid since nodes of each direction are located non-uniformly along the grid lines. Using the lifting scheme, which is a new method to construct wavelets, a new non-tensor product biorthogonal wavelet transform for the curvilinear grid data will be introduced. The new wavelet transform provides progressive transmission and the local control of levels of detail without changing the boundaries of the objects that are embedded inside the curvilinear grid through all different levels.