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Topological segmentation in three-dimensional vector fields

K. Mahrous, J. Bennett, G. Scheuermann, B. Hamann, K.I. Joy
2004 IEEE Transactions on Visualization and Computer Graphics  
We present a new method for topological segmentation in steady three-dimensional vector fields.  ...  The resulting partitions can be visualized using standard techniques for a visualization of a vector field at a higher level of abstraction.  ...  Most visualization techniques for three-dimensional flow fields concentrate on streamline and streamsurface representations, however these techniques do not give a clear illustration of the field's topological  ... 
doi:10.1109/tvcg.2004.1260771 pmid:15384644 fatcat:24ir6hgt75d6bhid3c7cwi7uuy

Visualization and criticality of magnetotail field topology in a three-dimensional particle simulation

DongSheng Cai, Yaoting Li, Taizi Ichikawai, Chijic Xiao, Ken-ichi Nishikawa
2001 Earth, Planets and Space  
The skeleton that includes the critical points, characteristic curves, and surfaces provides the three-dimensional topological structure of the reconnection.  ...  We present the temporal evolution of magnetic field topology in the magnetotail with a southward IMF in order to identify the magnetic reconnection.  ...  Visualizing Magnetotail Field Topology in a Three-Dimensional Particle Simulation We visualize the magnetic field topology in the magnetotail using the data sets obtained by the three-dimensional full  ... 
doi:10.1186/bf03351698 fatcat:nx5bq5imhvgkxcj77xore4tvge

Scale-Space Tracking of Critical Points in 3D Vector Fields [chapter]

Thomas Klein, Thomas Ertl
2007 Mathematics and Visualization  
In this paper, we investigate an approach based on scale-space hierarchies of three-dimensional vector fields.  ...  In general, the same properties hold for vector fields such as flow data.  ...  Acknowledgments This work was funded by the German Research Council (DFG) as part of project SFB 382.  ... 
doi:10.1007/978-3-540-70823-0_3 fatcat:n4usr3exdzabngesmxmbu2y6by

MVF Designer: Design and Visualization of Morse Vector Fields [article]

Youjia Zhou, Janis Lazovskis, Michael J. Catanzaro, Matthew Zabka, Bei Wang
2019 arXiv   pre-print
In this paper, we consider the idea of vector field design with a new motivation from computational topology.  ...  To achieve such a goal, we present MVF Designer, a new interactive design system that provides fine-grained control over vector field geometry, enables the editing of vector field topology, and supports  ...  Discussions Inspired by topological data analysis, the MVF Designer gives the user a tool to design and visualize Morse vector fields on the sphere.  ... 
arXiv:1912.09580v1 fatcat:v6sru5u3dzawvmww436cdhd6z4

Bicubic subdivision-surface wavelets for large-scale isosurface representation and visualization

Janine Bennett, Karim Mahrous, Bernd Hamann, Kenneth I. Joy
2003 Proceedings of the 18th spring conference on Computer graphics - SCCG '03  
We illustrate this framework with examples from scalar-and vector-field visualization.  ...  , and the effective visual representation of the extracted data.  ...  We thank the members of the Visualization Group at the Center for Image Processing and Integrated Computing (CIPIC) at the University of California, Davis for their support.  ... 
doi:10.1145/984952.984954 dblp:conf/sccg/BennettMHJ03 fatcat:m2eh4koh2zc3fbih3h2w6irjwm

A user-friendly interactive framework for unsteady fluid flow segmentation and visualization

Danilo Motta, Wallace Casaca, Paulo Pagliosa, Afonso Paiva
2018 Journal of Visualization  
Keywords Flow segmentation Á Time-varying visualization Á Vector field Á Interactive tools Á Machine learning Introduction Segmenting vector fields is of key importance in the context of scientific illustration  ...  While vector fields are essential to simulate a large amount of natural phenomena, the difficulty to identify patterns and predict behaviors makes the visual segmentation in simulations an attractive and  ...  Acknowledgements We would like to thank Harsh Bhatia to kindly provide the results with Edge Maps (Bhatia et al. 2012 ).  ... 
doi:10.1007/s12650-018-0474-6 fatcat:z5gt6qs2nrbwbhkcz6jkmspazu

Visualization of Tensor Fields in Mechanics

Chiara Hergl, Christian Blecha, Vanessa Kretzschmar, Felix Raith, Fabian Günther, Markus Stommel, Jochen Jankowai, Ingrid Hotz, Thomas Nagel, Gerik Scheuermann
2021 Computer graphics forum (Print)  
Given the limitations of traditional methods, and the extra cognitive effort of simple methods, more advanced tensor field visualization approaches have been the focus of this work.  ...  Its utility is twofold: (i) It serves as basis for the visualization community to get an overview of recent visualization techniques.  ...  [PMC*16, PRK*17] presented an interactive three-dimensional tensor field design system that allows to locally edit the topology of the three-dimensional tensor field. Roy et al.  ... 
doi:10.1111/cgf.14209 fatcat:m6grkhl5pndpbbq7zxxgzj3snq

Topology, Computation and Data Analysis (Dagstuhl Seminar 19212)

Michael Kerber, Vijay Natarajan, Bei Wang, Michael Wagner
2019 Dagstuhl Reports  
This report documents the program and the outcomes of Dagstuhl Seminar 19212 "Topology, Computation and Data Analysis".  ...  The seminar brought together researchers with mathematical and computational backgrounds in addressing emerging directions within computational topology for data analysis in practice.  ...  Weber (Lawrence Berkeley National Laboratory, US) Persistence Meets Tensor Fields  ... 
doi:10.4230/dagrep.9.5.110 dblp:journals/dagstuhl-reports/KerberNW19 fatcat:cjmvdnglxvhfzjp6i4se2w6p6u

Exploring the human body space: A geographical information system based anatomical atlas

Antonio Barbeito, Marco Painho, Pedro Cabral, João Goyri O'Neill
2016 Journal of Spatial Information Science  
The new prototype emulates a 3D GIS with a topological model of the human body, which has the ability to replicate the information provided by the conventional anatomical atlases, and provides a higher  ...  The development of anatomical atlases in geographic information systems (GIS) environments allows the development of platforms with a high degree of interactivity and with tools that explore and analyse  ...  Acknowledgements The authors acknowledge the contribution of the U.S. National Library of Medicine for making available the datasets used in this work.  ... 
doi:10.5311/josis.2016.12.261 fatcat:ilgw77nbcngynngh4y7nc473be

Beyond Topology: A Lagrangian Metaphor to Visualize the Structure of 3D Tensor Fields [chapter]

Xavier Tricoche, Mario Hlawitschka, Samer Barakat, Christoph Garth
2012 Mathematics and Visualization  
Indeed, one can view eigenvector fields as the local superimposition of two vector fields, from which a bidirectional flow field can be defined.  ...  Topology was introduced in the visualization literature some 15 years ago as a mathematical language to describe and capture the salient structures of symmetric second-order tensor fields.  ...  Acknowledgements This work was supported in part by a gift from Intel Visual Computing initiative.  ... 
doi:10.1007/978-3-642-27343-8_5 fatcat:pfqgqkeyfrgkfpsddeai66oazi

Biomedical Visualization [chapter]

Chris R. Johnson, Xavier Tricoche
2009 Advances in Biomedical Engineering  
The usability of three-dimensional topology for the characterization of salient patterns of the bioelectric current remains limited. The explanation comes from the structure of a bioelectric field.  ...  Vector field methods in scientific visualization Visualizing vector field data is challenging because no existing natural representation can visually convey large amounts of three-dimensional directional  ... 
doi:10.1016/b978-0-444-53075-2.00006-x fatcat:ewd3kgeki5fthj55kfoce6bkcm

Visual Analysis of Bioelectric Fields [chapter]

Xavier Tricoche, Rob MacLeod, Chris R. Johnson
2008 Mathematics and Visualization  
This work was supported by the Center for Integrative Biomedical Computing, NIH NCRR Project 2-P41-RR12553-07.  ...  Acknowledgments The authors are greatly indebted to Drs. Bruno Taccardi and Frank Sachse from CVRTI at the University of Utah, as well as to Dr.  ...  Topological methods Topological methods apply to the visualization of vector fields a mathematical framework developed for the qualitative study of dynamical systems [11] .  ... 
doi:10.1007/978-3-540-72630-2_12 fatcat:mpzg6ewpqra2tlcj3lzjcp7iqi

Improving Topological Segmentation of Three-dimensional Vector Fields [article]

Karim M. Mahrous, Janine C. Bennett, Bernd Hamann, Kenneth I. Joy
2003 EUROVIS 2005: Eurographics / IEEE VGTC Symposium on Visualization  
We present three enhancements to accelerate the extraction of separatrices of three-dimensional vector fields, using intelligently selected "sample" streamlines.  ...  These enhancements enable us to perform separatrix construction for three-dimensional vector field data requiring less overall computation.  ...  We thank the members of the Visualization and Graphics Research Group at the Center for Image Processing and Integrated Computing (CIPIC) at the University of California, Davis.  ... 
doi:10.2312/vissym/vissym03/203-212 fatcat:4lxq2xmrmjbfpjfob4jwcz76ti

Appendix C: Perspectives in Topology [chapter]

2011 Topology and Its Applications  
It is the purest form of topology and provides a basic language for the rest of mathematics, relying on the basic definitions of open sets and topological spaces.  ...  The real line, the plane, and every subset of R n are topological spaces, and much of mathematics relies on continuous functions between these sets. Chapters 1 and 2 focus on point set topology.  ...  As an application of the integral of a vector filed around a loop, it is a result of differential topology that if the integral of a vector field around a loop is not zero then there must be a point (a  ... 
doi:10.1002/9780470067949.app3 fatcat:clarjrz4qfechnzmwyxnbdwsy4

Topological Features in 2D Symmetric Higher-Order Tensor Fields

T. Schultz
2011 Computer graphics forum (Print)  
The topological structure of scalar, vector, and second-order tensor fields provides an important mathematical basis for data analysis and visualization.  ...  This allows us to define and visualize topological structures in symmetric tensor fields of orders three and four.  ...  This work was supported by a fellowship within the Postdoc Program of the German Academic Exchange Service (DAAD).  ... 
doi:10.1111/j.1467-8659.2011.01933.x fatcat:fqxd7gxphzetrgyjs5ayjoumei
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