Issue No. 02 - April-June (1998 vol. 4)

ISSN: 1077-2626

pp: 109-116

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/2945.694953

ABSTRACT

<p><b>Abstract</b>—We present our results on the visualization of nonlinear vector field topology. The underlying mathematics is done in Clifford algebra, a system describing geometry by extending the usual vector space by a multiplication of vectors. We started with the observation that all known algorithms for vector field topology are based on piecewise linear or bilinear approximation, and that these methods destroy the local topology if nonlinear behavior is present. Our algorithm looks for such situations, chooses an appropriate polynomial approximation in these areas, and, finally, visualizes the topology. This overcomes the problem, and the algorithm is still very fast because we are using linear approximation outside these small but important areas. The paper contains a detailed description of the algorithm and a basic introduction to Clifford algebra.</p>

INDEX TERMS

Vector field topology, Clifford algebra, visualization.

CITATION

Gerik Scheuermann, Martin Menzel, Alyn P. Rockwood, Heinz Krüger, "Visualizing Nonlinear Vector Field Topology",

*IEEE Transactions on Visualization & Computer Graphics*, vol. 4, no. , pp. 109-116, April-June 1998, doi:10.1109/2945.694953SEARCH