(a) 184 first order critical points. The box around the molecule represents the chosen area for topological simplification. (b) Topologically simplified representation with one higher order critical point elucidates the far field behavior of the benzene.  This paper presents an approach to extracting and classifying higher order critical points of 3D vector fields. To do so, we place a closed convex surface s around the area of interest. Then we show that the complete 3D classification of a critical point into areas of different flow behavior is equivalent to extracting the topological skeleton of an appropriate 2D vector field on s, if each critical point is equipped with an additional Bit of information. Out of this skeleton, we create an icon which replaces the complete topological structure inside s for the visualization. We apply our method to find a simplified visual representation of clusters of critical points, leading to expressive visualizations of topologically complex 3D vector fields.
Weinkauf et al. REF introduced a topological simplification technique for 3D vector fields based on the extraction of higher-order critical points.
Extracting higher order critical points and topological simplification of 3D vector fields
VIS 05. IEEE Visualization, 2005.
VIS 05. IEEE Visualization, 2005.
Computer Science Mathematics