 
Summary: Combinatorial 2D Vector Field Topology
Extraction and Simplification
Jan Reininghaus1
, Ingrid Hotz2
1
Zuse Institute Berlin (ZIB), Germany. reininghaus@zib.de
2
Zuse Institute Berlin (ZIB), Germany. hotz@zib.de
Summary: This paper investigates a combinatorial approach to vector field
topology. The theoretical basis is given by Robin Forman's work on a combinato
rial Morse theory for dynamical systems defined on general simplicial complexes.
We formulate Forman's theory in a graph theoretic setting and provide a simple
algorithm for the construction and topological simplification of combinatorial
vector fields on 2D manifolds. Given a combinatorial vector field we are able to
extract its topological skeleton including all periodic orbits. Due to the solid the
oretical foundation we know that the resulting structure is always topologically
consistent. We explore the applicability and limitations of this combinatorial
approach with several examples and determine its robustness with respect to
noise.
1 Introduction
