Multi - resolution Modeling of Discrete Scalar Fields

Thanks to improvement in simulation, high resolution scanning facilities and multidimensional medical imaging, the size of geometrical dataset is rapidly increasing, and huge datasets are commonly available. The purpose of this thesis is dealing with large sets of twoor three-dimensional discrete data sets describing scalar fields, by using a multiresolution approach. Specifically our aim is in designing and implementing data structures and algorithms for multi-resolution models of scalar fields described by large data sets for scientific data analysis and visualization. To achieve this goal we have identified and developed three tasks, namely, design and development of compact data structures for multiresolution models which operate in main memory, design and development of out-of-core algorithms for building and querying multi-resolution models, as well as out-of-core data structures for implementing such models, and design and development of multi-resolution models of scalar fields which take into account the underlying field morphology. In this thesis, we have first developed and experimented compact data structures for multiresolution models for two-dimensional scalar fields based on triangle meshes and built through iterative vertex insertion/removal. Such representations can be also applied to encode multi-resolution models of free-form triangulated surfaces. We have designed and developed multi-resolution data structures for multi-resolution models for 3D scalar fields, based on vertex insertion/removal, and on half-edge collapse. We have performed an extensive experimental comparisons with a multi-resolution model built through full-edge collapse and a multi-resolution model based on regular nested tetrahedral meshes Largest datasets exceed main memory even if compact data structures are adopted. For these reasons, we have investigated out-of core approaches for encoding and manipulating multi-resolution models for 3D shapes, twoand three-dimensional scalar fields, independently of the simplification strategy used to generate the LOD model. The major issue here has been investigating and experimenting effective techniques for clustering the modifications forming the multi-resolution model. In our research, we have developed out-of-core algorithms for generating and querying multi-resolution models out-of-core, which can be coupled with different representations for the modifications in the model. One of the major motivations in using multi-resolution models based on unstructured meshes for describing a scalar field lies in their ability of encompassing morphological information. This is the first step towards development of more powerful multi-resolution models based on the combined representation of the geometry and the morphology of the field. To this aim, we have developed techniques for extracting morphological information from a scalar field and we have developed an algorithm for a generating a multi-resolution representation of a two-dimensional scalar field which maintains the morphology of the field at different levels of resolution.