Detection and classification of critical points in piecewise linear vector fields

作者：Wang, Wentao; Wang, Wenke^*; Li, Sikun

来源：Journal of Visualization, 2018, 21(1): 147-161.

DOI：10.1007/s12650-017-0438-2

• Flow visualization
• Critical points
• Poincare index
• Brouwer degree
• Simulation of simplicity

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 Poincar, 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.

• 出版日期2018-2
• 单位中国人民解放军国防科学技术大学