Topology-Preserving Smoothing of Vector Fields

In this paper we propose a technique for topology preserving smoothing of sampled vector fields. In this technique, the vector field data is first converted into a scalar level-set representation. We then locally analyze the dynamic behavior of level-sets by placing geometric primitives in the scalar field and by subsequently distorting these primitives with respect to local variations in this field. Geometrical and topological considerations are then combined to successively smooth the vector data. Using the resulting algorithm, we have built a visualization system that enables us to effectively smooth dense flow fields at the same time retaining their topological structure.