Theisel, H.2015-02-162015-02-1620021467-8659https://doi.org/10.1111/1467-8659.t01-1-00710We introduce a scheme of control polygons to design topological skeletons for vector fields of arbitrary topology. Based on this we construct piecewise linear vector fields of exactly the topology specified by the control polygons. This way a controlled construction of vector fields of any topology is possible. Finally we apply this method for topology-preserving compression of vector fields consisting of a simple topology.10.1111/1467-8659.t01-1-00710595-604