Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
1998 | 10.1109/2945.694953 | IEEE Trans. Vis. Comput. Graph. |
Keywords | Field | DocType |
known algorithm,bilinear approximation,linear approximation,appropriate polynomial approximation,vector field topology,clifford algebra,visualizing nonlinear vector field,nonlinear behavior,nonlinear vector field topology,local topology,usual vector space,piecewise linear,vectors,polynomials,data visualisation,vector space,computational geometry,visualization | Topology,Discrete mathematics,Weak topology (polar topology),Weak topology,General topology,Computer science,Theoretical computer science,Initial topology,Product topology,Extension topology,Particular point topology,Computational topology | Journal |
Volume | Issue | ISSN |
4 | 2 | 1077-2626 |
Citations | PageRank | References |
60 | 4.18 | 3 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Gerik Scheuermann | 1 | 1382 | 112.65 |
| Heinz Kr?ˉ? Uger | 2 | 66 | 5.19 |
| Martin Menzel | 3 | 60 | 4.18 |
| Alyn Rockwood | 4 | 950 | 179.19 |