Journal of Visualization

, Volume 21, Issue 1, pp 147–161 | Cite as

Detection and classification of critical points in piecewise linear vector fields

  • Wentao Wang
  • Wenke Wang
  • Sikun Li
Regular Paper


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.

Graphical Abstract


Flow visualization Critical points Poincaré index Brouwer degree Simulation of simplicity 



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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Copyright information

© The Visualization Society of Japan 2017

Authors and Affiliations

  1. 1.College of ComputerNational University of Defense TechnologyChangshaChina
  2. 2.State Key Laboratory of High Performance ComputingNational University of Defense TechnologyChangshaChina
  3. 3.Institute of Ocean Science and EngineeringNational University of Defense TechnologyChangshaChina

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