Summary: IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 1
Fast Combinatorial Vector Field Topology
Jan Reininghaus, Christian L¨owen, and Ingrid Hotz
Abstract--This paper introduces a novel approximation algorithm for the fundamental graph problem of combinatorial vector
field topology (CVT). CVT is a combinatorial approach based on a sound theoretical basis given by Forman's work on a
discrete Morse theory for dynamical systems. A computational framework for this mathematical model of vector field topology
has been developed recently. The applicability of this framework is however severely limited by the quadratic complexity of its
main computational kernel. In this work we present an approximation algorithm for CVT with a significantly lower complexity.
This new algorithm reduces the runtime by several orders of magnitude, and maintains the main advantages of CVT over the
continuous approach. Due to the simplicity of our algorithm it can be easily parallelized to improve the runtime further.
Index Terms--9.VI.IX.II Flow Visualization, 7.II.II.I Graph algorithms
TOPOLOGICAL data analysis has been proven
successful for the visualization of vector fields.
The topology of a vector field is derived from
the homotopy classes of its streamlines. Standard
algorithms for the extraction of this topological
skeleton involve many numerical challenges: finding
all zeros, integrating streamlines and streamsurfaces,