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#### Topology Preserving Thinning of Vector Fields on Triangular Meshes

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##### Citation

Theisel, H., Rössl, C., & Seidel, H.-P. (2004). Topology Preserving Thinning of
Vector Fields on Triangular Meshes. In N. A. Dodgson, M. S. Floater, & M. A. Sabin (*Advances in Multiresolution for Geometric Modelling* (pp. 353-366). Berlin, Germany: Springer.

Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-2B61-D

##### Abstract

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 modiØcations 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.