Topology Preserving Thinning of Vector Fields on Triangular Meshes

We consider the topology of piecewise linear vector fields whose domain is a piecewise linear 2-manifold, i.e. a triangular mesh. Such vector fields can describe simulated 2-dimensional flows, or they may reflect geometric properties of the underlying mesh. We introduce a thinning technique which preserves the complete topology of the vector field, i.e. the critical points and separatrices. As the theoretical foundation, we have shown in an earlier paper that for local modifications of a vector field, it is possible to decide entirely by a local analysis whether or not the global topology is preserved. This result is applied in a number of compression algorithms which are based on a repeated local modification of the vector field – namely a repeated edge-collapse of the underlying piecewise linear domain.