Towards Multifield Scalar Topology Based on Pareto Optimality

How can the notion of topological structures for single scalar fields be extended to multifields? In this paper we propose a definition for such structures using the concepts of Pareto optimality and Pareto dominance. Given a set of piecewise‐linear, scalar functions over a common simplical complex...

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Bibliographic Details
Published in:Computer graphics forum Vol. 32; no. 3pt3; pp. 341 - 350
Main Authors: Huettenberger, L., Heine, C., Carr, H., Scheuermann, G., Garth, C.
Format: Journal Article
Language:English
Published: Oxford, UK Blackwell Publishing Ltd 01.06.2013
Subjects:
Analysis
and systems
Computational fluid dynamics
Computer graphics
Computer simulation
Data processing
Dominance
I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Geometric algorithms
I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Geometric algorithms, languages, and systems
languages
Mathematical analysis
Pareto optimality
Scalars
Studies
Topological manifolds
Topology
Visualization
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary:How can the notion of topological structures for single scalar fields be extended to multifields? In this paper we propose a definition for such structures using the concepts of Pareto optimality and Pareto dominance. Given a set of piecewise‐linear, scalar functions over a common simplical complex of any dimension, our method finds regions of “consensus” among single fields’ critical points and their connectivity relations. We show that our concepts are useful to data analysis on real‐world examples originating from fluid‐flow simulations; in two cases where the consensus of multiple scalar vortex predictors is of interest and in another case where one predictor is studied under different simulation parameters. We also compare the properties of our approach with current alternatives.
Bibliography:istex:37C4799BD1365EDC96AEAF150050EDEEC321A0BB
ArticleID:CGF12121
ark:/67375/WNG-HXS3D873-D
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ObjectType-Feature-1
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.12121