From numerics to combinatorics: a survey of topological methods for vector field visualization

Topological methods are important tools for data analysis, and recently receiving more and more attention in vector field visualization. In this paper, we give an introductory description to some important topological methods in vector field visualization. Besides traditional methods of vector field...

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Bibliographic Details
Published in:Journal of visualization Vol. 19; no. 4; pp. 727 - 752
Main Authors: Wang, Wentao, Wang, Wenke, Li, Sikun
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2016
Springer Nature B.V
Subjects:
Classical and Continuum Physics
Combinatorial analysis
Computer Imaging
Data analysis
Decomposition
Engineering
Engineering Fluid Dynamics
Engineering Thermodynamics
Fields (mathematics)
Heat and Mass Transfer
Liapunov exponents
Numerical methods
Pattern Recognition and Graphics
Regular Paper
Topology
Vision
Visualization
Hodge decomposition
Morse decomposition
Discrete Morse theory
Conley index
Vector field visualization
Degree
Robustness
Topology
ISSN:1343-8875, 1875-8975
Online Access:Get full text
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Summary:Topological methods are important tools for data analysis, and recently receiving more and more attention in vector field visualization. In this paper, we give an introductory description to some important topological methods in vector field visualization. Besides traditional methods of vector field topology, space-time method and finite-time Lyapunov exponent, we also include in this survey Hodge decomposition, combinatorial vector field topology, Morse decomposition, and robustness, etc. In addition to familiar numerical techniques, more and more combinatorial tools emerge in vector field visualization. The numerical methods often rely on error-prone interpolations and interpolations, while combinatorial techniques produce robust but coarse features. In this survey, we clarify the relevant concepts and hope to guide future topological research in vector field visualization. Graphical abstract
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ISSN:1343-8875
1875-8975
DOI:10.1007/s12650-016-0348-8