Topological analysis of scalar functions for scientific data visualization
Vijay Natarajan, Herbert Edelsbrunner · 2004
Scientists attempt to understand physical phenomena by studying various quanti-ties measured over the region of interest. A majority of these quantities are scalar (real-valued) functions. These functions are typically studied using traditional visual-ization techniques like isosurface extraction, volume rendering etc. As the data grows in size and becomes increasingly complex, these techniques are no longer effective. State of the art visualization methods attempt to automatically extract features and annotate a display of the data with a visualization of its features. In this thesis, we study and extract the topological features of the data and use them for visualization. We have three results: • An algorithm that simplifies a scalar function defined over a tetrahedral mesh. In addition to minimizing the error introduced by the approximation of the function, the algorithm improves the mesh quality and preserves the topology of the domain. We perform an extensive set of experiments to study the effect of requiring better mesh quality on the approximation error and the level of sim-