Streamline Embedding for 3D Vector Field Exploration

We propose a new technique for visual exploration of streamlines in 3D vector fields. We construct a map from the space of all streamlines to points in IRⁿ based on the preservation of the Hausdorff metric in streamline space. The image of a vector field under this map is a set of 2-manifolds in IRⁿ with characteristic geometry and topology. Then standard clustering methods applied to the point sets in IRⁿ yield a segmentation of the original vector field. Our approach provides a global analysis of 3D vector fields which incorporates the topological segmentation but yields additional information. In addition to a pure segmentation, the established map provides a natural "parametrization” visualized by the manifolds. We test our approach on a number of synthetic and real-world data sets.