Auer, Cornelia
[VerfasserIn]
;
auercornelia@gmx.de
[MitwirkendeR];
w
[MitwirkendeR];
Ingrid Hotz
[MitwirkendeR];
Hans Hagen
[MitwirkendeR]
Visualization of fundamental structures in two dimensional second order tensor fields on planar and curved surfaces ; Visualisierung fundamentaler Strukturen in zweidimensionalen Tensorfeldern zweiter Ordnung auf planaren und gekrümmten Mannigfaltigkeiten
Titel:
Visualization of fundamental structures in two dimensional second order tensor fields on planar and curved surfaces ; Visualisierung fundamentaler Strukturen in zweidimensionalen Tensorfeldern zweiter Ordnung auf planaren und gekrümmten Mannigfaltigkeiten
Beteiligte:
Auer, Cornelia
[VerfasserIn]
Erschienen:
Freie Universität Berlin: Refubium (FU Berlin), 2014
Anmerkungen:
Diese Datenquelle enthält auch Bestandsnachweise, die nicht zu einem Volltext führen.
Beschreibung:
Tensors provide a powerful and at the same time concise mathematical formalism to encode intricate physical phenomena. They describe multi-linear functions independently of a frame of reference and capture anisotropic properties which vary as function of direction. However, the wealth of information contained in tensor data can be a mixed blessing as in return this can heavily aggravate their interpretation. This thesis is concerned with analysis and visualization methods to support the interpretation of second order tensors per se and fields of such tensors. The focus is on tensor fields from engineering and mechanics. We present visualization concepts for indefinite symmetric tensors as well as asymmetric tensors which both bring about their individual properties and requirements. The aim is to truthfully reflect the specific properties in the tensor fields and at the same time to support an immediate understanding by the user. The presented methods are developed for two dimensional second order tensor fields defined on planar or curved surfaces. These tensor fields naturally occur e.g. on boundary surfaces but also if the data is analyzed on cuts extracted from three dimensional data. This facilitates to inspect the intrinsic properties on these geometries in full detail. One primary constituent of this work is to find expressive structures in order to present the tensor data in a condensed and simplified manner. The results are given as explicit geometries which can be used for further processing such as tracking over time or statistical inquiry. For symmetric second order tensor fields we extract the topology which captures all essential structural features in a strongly reduced graph structure. This graph structure is used as a basis to develop enriched visualization methods. In this vein, a complete segmentation is presented that partitions the field into regions of homogeneous eigenvector and eigenvalue behavior. This segmentation serves as well defined framework for rich visualizations – texture mapping ...