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Issue No.03 - March (2012 vol.18)
pp: 407-420
Christian Rössl , Otto-von-Guericke-Universität, Magdeburg
Holger Theisel , Otto-von-Guericke-Universität, Magdeburg
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 {\hbox{\rlap{I}\kern 2.0pt{\hbox{R}}}}^n 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 {\hbox{\rlap{I}\kern 2.0pt{\hbox{R}}}}^n with characteristic geometry and topology. Then standard clustering methods applied to the point sets in {\hbox{\rlap{I}\kern 2.0pt{\hbox{R}}}}^n 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.
Vector fields, streamline embedding, clustering.
Christian Rössl, Holger Theisel, "Streamline Embedding for 3D Vector Field Exploration", IEEE Transactions on Visualization & Computer Graphics, vol.18, no. 3, pp. 407-420, March 2012, doi:10.1109/TVCG.2011.78
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