Scientific Visualization based on Simplicial Complexes

Cignoni P.

Scientific Visualization  Computational Geometry 

The main objective of the thesis is the development of a complete and efficient set of solutions for the Scientific Visualization (SciViz), the computer science field which deals with the study, design and implementation of algorithms and data structures for the visualization of scientific data. We propose the adoption of the simplicial complexes as the unifying geometric structure and we show how the choice of this structure as kernel geometric primitive is effective both for the theoretical and practical aspects of SciViz. The contents of the thesis can be summarized as follows. We interpret the diversified SciViz process as a two-steps mapping problem: a modeling step, in which data are mapped into geometry with visual attributes, and a rendering step where geometry and visual attributes are transformed into images. As unifying geometric structure for the modeling step we propose the adoption of the simplicial complexes. To validate our approach we define new algorithms and data structures for the SciViz problems, based on the use of the simplicial complex as basic geometric representation scheme. In particular the thesis supplies original solutions and results to the following problems: 1. Visualization of scalar volume datasets: optimizing techniques for the extraction of isosurface and for the direct volume rendering; 2. Depth sorting of simplicial complexes (a fundamental topic for the efficient and correct use of direct volume rendering based on projective techniques); 3. Integration of isosurface extraction techniques and direct volume rendering techniques. Definition of the concept of discontinuous transfer functions; 4. Simplification of the geometric complexity of simplicial complexes (in order to speed up the visualization process) while minimizing the introduced error; 5. Multiresolution representation schemes for simplicial complexes. These schemes permit both the visualization of complexes at different levels of details and the visualization of a single complex in which different parts are at different resolution.