Abstract
Topological methods are important for flow visualization, and many of them involve the detection and classification of critical points. Traditionally, the critical points are detected and classified by error-prone numerical methods, until Bhatia et al. (Topological methods in data analysis and visualization III, Springer, 2014) proposed the robust method for detecting simplices containing critical points. In this paper, we will extend Bhatia’s idea to compute the Poincaré index of critical points in piecewise linear vector fields. All kinds of simplical complexes are considered, including 2D/3D triangulated meshes, and also triangulated surfaces. We test our algorithm on both synthetic and simulation data sets, which show the efficiency and accuracy of our methods.
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Acknowledgements
This work is supported by Chinese 973 Program (2015CB755604) and the National Science Foundation of China (61202335). We would like to thank Dr. He Ouyang for his guidance.
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Wang, W., Wang, W. & Li, S. Detection and classification of critical points in piecewise linear vector fields. J Vis 21, 147–161 (2018). https://doi.org/10.1007/s12650-017-0438-2
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DOI: https://doi.org/10.1007/s12650-017-0438-2