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Summary: CURVATURE MEASURES OF 3D VECTOR FIELDS AND
THEIR APPLICATIONS
T. Weinkauf
H. Theisel
Zuse Institute Berlin, Scientific Visualization Group, Takustr. 7, D-14343 Berlin, Germany
weinkauf@zib.de, http://www.zib.de/visual/
University of Rostock, Computer Science Department, D-18051 Rostock, Germany
theisel@informatik.uni-rostock.de, http://wwwicg.informatik.uni-rostock.de/
ABSTRACT
Tangent curves are a powerful tool for analyzing and visualizing vector fields. In this paper two
of their most important properties are examined: their curvature and torsion. Furthermore, the
concept of normal surfaces is introduced to the theory of 3D vector fields, and their Gaussian
and mean curvature are analyzed. It is shown that those four curvature measures tend to infinity
near critical points of a 3D vector field. Applications utilizing this behaviour for the (topological)
treatment of critical points are discussed.
Keywords: flow visualization, vector fields, tangent curves, curvature, topology
1 INTRODUCTION AND RELATED
WORK
The treatment and visualization of vector fields
is of great importance to a wide area of sciences.
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