| Scientific visualization provides useful insights and analysis for scientists through graphical representations of data. As numerical simulations become more sophisticated, interpretation of the underlying physical phenomena requires new tools to be developed that perform complex feature analysis and cross correlation of data parameters. Towards this end, this thesis presents two new frameworks that contribute to more effective data understanding. The first is a segmentation framework that can be used to effectively identify regions of interest in data sets. A format of higher-level data is defined from which meaningful derived features can be efficiently extracted and visualized. Furthermore, a higher-order interpolation scheme is presented that allows for extraction of smoother feature surfaces from scalar data. The second framework robustly computes cross parameterizations between two triangulated meshes of arbitrary and possibly unequal genus. Cross parameterizations can be used to describe the evolution of surfaces over time as well as to establish a shape deviation metric. Results are presented that demonstrate the effectiveness of both of the frameworks in a variety of data analysis applications. |
