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Introduction to Vector Field Topology

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Topological Methods in Data Analysis and Visualization VI

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

Flow visualization is a research discipline that is concerned with the visual exploration and analysis of vector fields. An important class of methods are the topology-based techniques, which concentrate on individual structures in the domain that govern, constrain or guide the behavior of particles in the vector field. In this chapter, we give an overview of existing techniques for steady and unsteady vector fields in 2D and 3D. For time-dependent flows, we describe streamline-oriented and pathline-oriented approaches, eventually leading us to closely related feature-based visualization concepts such as reference frame invariance and Lagrangian coherent structures.

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Acknowledgements

This work was supported by the Swiss National Science Foundation (SNSF) Ambizione grant no. PZ00P2_180114 and by ETH Research Grant ETH-07 18-1.

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  1. Tobias Günther

    Present address: Department of Computer Science, ETH Zürich, Zürich, Switzerland

Authors and Affiliations

  1. Department of Computer Science, ETH Zürich, Zürich, Switzerland

    Irene Baeza Rojo

  2. FAU Erlangen-Nürnberg, Erlangen, Germany

    Tobias Günther

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  1. Tobias Günther
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  2. Irene Baeza Rojo
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Correspondence to Tobias Günther .

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Editors and Affiliations

  1. Department of Science and Technology, Linköping University, Norrköping, Sweden

    Ingrid Hotz

  2. Department of Science and Technology, Linköping University, Norrköping, Sweden

    Talha Bin Masood

  3. Heidelberg University, IWR, Heidelberg, Germany

    Filip Sadlo

  4. CNRS, Department of Scientific Computing, Sorbonne Université, Paris, France

    Julien Tierny

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Günther, T., Baeza Rojo, I. (2021). Introduction to Vector Field Topology. In: Hotz, I., Bin Masood, T., Sadlo, F., Tierny, J. (eds) Topological Methods in Data Analysis and Visualization VI. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-030-83500-2_15

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