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Rüdiger Westermann, Christopher Johnson, Thomas Ertl, "TopologyPreserving Smoothing of Vector Fields," IEEE Transactions on Visualization and Computer Graphics, vol. 7, no. 3, pp. 222229, JulySeptember, 2001.  
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@article{ 10.1109/2945.942690, author = {Rüdiger Westermann and Christopher Johnson and Thomas Ertl}, title = {TopologyPreserving Smoothing of Vector Fields}, journal ={IEEE Transactions on Visualization and Computer Graphics}, volume = {7}, number = {3}, issn = {10772626}, year = {2001}, pages = {222229}, doi = {http://doi.ieeecomputersociety.org/10.1109/2945.942690}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Visualization and Computer Graphics TI  TopologyPreserving Smoothing of Vector Fields IS  3 SN  10772626 SP222 EP229 EPD  222229 A1  Rüdiger Westermann, A1  Christopher Johnson, A1  Thomas Ertl, PY  2001 KW  Flow visualization. VL  7 JA  IEEE Transactions on Visualization and Computer Graphics ER   
Abstract—In this paper, we propose a technique for topologypreserving smoothing of sampled vector fields. The vector field data is first converted into a scalar representation in which time surfaces implicitly exist as levelsets. We then locally analyze the dynamic behavior of levelsets by placing geometric primitives in the scalar field and by subsequently distorting these primitives with respect to local variations in this field. From the distorted primitives, we calculate the curvature normal and we use the normal magnitude and its direction to separate distinct flow features. Geometrical and topological considerations are then combined to successively smooth dense flow fields, at the same time retaining their topological structure.
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