Multiresolution data modelling for irregular data fields based on wavelets

In many applications of scientific visualization, the data fields are so large that they are very expensive to store, transmit and render. Multiresolution offers a promising new approach for addressing these difficulties on a simple, unified way. Wavelets provide an extremely useful mathematical toolkit for hierarchically decomposing functions in ways that are both efficient and theoretically sound. This paper focuses on extension of wavelet based multiresolution to arbitrary topological data grid. Using wavelet transform, the method proposed here obtains a unique shape description of an irregular data field. A biorthogonal volume wavelet is constructed. Recursive subdivision is applied to irregular data field and leads to a collection of refinable scaling functions and hence to a sequence of nested linear spaces, as required by multiresolution. In order to overcome the subdivision connectivity restriction, an applicable method is presented to convert the completely arbitrary data field to multiresolution so that the technique for creating multiresolution can be used