Three-Dimensional Second-Order Tensor Fields: Exploratory Visualization and Anisotropic Sampling

  • Tensors provide a powerful mathematical language to describe physical phenomena. Consequently, they have a long tradition in physics and appear in various application areas, either as intermediate product or as output of simulations or measurements. The potential of tensors to describe complex anisotropic behavior, however, concurrently complicates their interpretation. The central research question of this thesis is how three-dimensional tensor fields of second order are visualized effectively so that, as a long term goal, their interpretation becomes easier. The focus of this thesis lies on the class of indefinite tensors. The methods that are proposed in this thesis fall into two main categories: (1.) the interactive exploration of the three-dimensional tensor data, and (2.) the geometric reduction of the data to two-dimensional planes or triangulated surfaces. In both cases, possible visualization approaches are presented. For interactive exploration of the data, we propose to combine diagram views with three-dimensional hybrid visualizations. We show that this facilitates familiarizing with the data and leads to exciting analytic queries. If a geometric data reduction is possible, we focus on glyph- and texture-based methods. In this context, the thesis is concerned with methods to improve their quality. Therefore, we propose two algorithms for the efficient creation of anisotropic sample distributions. Moreover, we present a novel visualization method that works on planar slices as well as on triangulated surfaces. The basic idea of this method is to use anisotropic sample distributions for the efficient computation of anisotropic Voronoi cells, which then are used as base elements for texture mapping. Hence, the usage of textures to encode the tensor’s various degrees of freedom becomes possible. We evaluate our methods for the interactive exploration on stress tensor fields from structure simulations. To show the ffectiveness of novel visualization methods, various datasets are presented.
Metadaten
Author:Andrea Kratz
Document Type:Doctoral Thesis
Tag:anisotropic sampling of tensor fields; exploratory visualization; tensors of second order; visualization
Granting Institution:Freie Universität Berlin
Advisor:Dr. Ingrid Hotz, Prof. Dr. Markus Hadwiger
Date of final exam:2013/05/02
Publishing Institution:Freie Universität Berlin
Date of first Publication:2013/07/03
Pagenumber:XIV, 157 S.
URL:http://www.diss.fu-berlin.de/diss/receive/FUDISS_thesis_000000094629