Topological Methods in Data Analysis and Visualization II

Part of the series Mathematics and Visualization pp 47-59


Combinatorial Vector Field Topology in Three Dimensions

  • Wieland ReichAffiliated withUniversity of Leipzig Email author 
  • , Dominic SchneiderAffiliated withUniversity of Leipzig
  • , Christian HeineAffiliated withUniversity of Leipzig
  • , Alexander WiebelAffiliated withMax-Planck-Institut for Human Cognitive and Brian Sciences, Leipzig
  • , Guoning ChenAffiliated withUniversity of Utah
  • , Gerik ScheuermannAffiliated withUniversity of Leipzig

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In this paper, we present two combinatorial methods to process 3-D steady vector fields, which both use graph algorithms to extract features from the underlying vector field. Combinatorial approaches are known to be less sensitive to noise than extracting individual trajectories. Both of the methods are a straightforward extension of an existing 2-D technique to 3-D fields. We observed that the first technique can generate overly coarse results and therefore we present a second method that works using the same concepts but produces more detailed results. We evaluate our method on a CFD-simulation of a gas furnace chamber. Finally, we discuss several possibilities for categorizing the invariant sets with respect to the flow.