Visualizing nonlinear vector field topology

摘要

We present our results on the visualization of nonlinear vectornfield topology. The underlying mathematics is done in Clifford algebra,na system describing geometry by extending the usual vector space by anmultiplication of vectors. We started with the observation that allnknown algorithms for vector field topology are based on piecewise linearnor bilinear approximation, and that these methods destroy the localntopology if nonlinear behavior is present. Our algorithm looks for suchnsituations, chooses an appropriate polynomial approximation in thesenareas, and, finally, visualizes the topology. This overcomes thenproblem, and the algorithm is still very fast because we are usingnlinear approximation outside these small but important areas. The paperncontains a detailed description of the algorithm and a basicnintroduction to Clifford algebra