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In this paper, the authors present an approach for monitoring the positions of vector field singularities in time-dependent datasets. The concept of singularity index is discussed and extended from the well-understood planar case to the more intricate three-dimensional setting. Assuming a tetrahedral grid with linear interpolation in space and time, vector field singularities obey rules imposed by fundamental invariants (Poincare index), which they use as a basis for an efficient tracking algorithm. They apply the presented algorithm to CFD datasets to illustrate its purpose in the examination of structures that exhibit topological variations with time and describe some of the insight gained with this method.
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