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Path Line Oriented Topology for Periodic 2D Time-Dependent Vector Fields [article]

K. Shi, H. Theisel, T. Weinkauf, H. Hauser, H.-C. Hege, H.-P. Seidel
2006 EUROVIS 2005: Eurographics / IEEE VGTC Symposium on Visualization  
This paper presents an approach to extracting a path line oriented topological segmentation for periodic 2D timedependent vector fields.  ...  For the data class of periodic vector fields, this restriction does not apply any more.  ...  Noack for the fruitful discussions and the supply of the cavity data set which was kindly provided by Mo Samimy and Edgar Caraballo.  ... 
doi:10.2312/vissym/eurovis06/139-146 fatcat:lcufnmtmnfcj3gikvm4iafna5u

Topological Methods for 2D Time-Dependent Vector Fields Based on Stream Lines and Path Lines

H. Theisel, T. Weinkauf, H.C. Hege, H.-P. Seidel
2005 IEEE Transactions on Visualization and Computer Graphics  
This paper describes approaches to topologically segmenting 2D time-dependent vector fields. For this class of vector fields, two important classes of lines exist: stream lines and path lines.  ...  To get the path line oriented topology we segment the vector field into areas of attracting, repelling and saddle-like behavior of the path lines.  ...  All visualizations in this paper have been created using AMIRA -a system for advanced 3D visualization and volume modeling [31] (see http://amira.zib.de/).  ... 
doi:10.1109/tvcg.2005.68 pmid:16138549 fatcat:gamfqp2p5bdudnla2uh4n2ahxq

Topological Representations of Vector Fields [chapter]

Holger Theisel, Christian Rössl, Tino Weinkauf
2008 Mathematics and Visualization  
After introducing topological features for 2D and 3D vector fields, we discuss how to extract and use them as visualization tools for complex flow phenomena.  ...  This chapter gives an overview on topological methods for vector field processing.  ...  Fig. 18 . 18 2D time-dependent flow at a cavity: (a) stream line oriented topology of the first 100 time steps; (b) path line oriented topology of the first 100 time steps (from [38]).  ... 
doi:10.1007/978-3-540-33265-7_7 fatcat:ozpa4e4xibfytiqaxhz4jrfmui

Topological Flow Structures in a Mathematical Model for Rotation-Mediated Cell Aggregation [chapter]

Alexander Wiebel, Raymond Chan, Christina Wolf, Andrea Robitzki, Angela Stevens, Gerik Scheuermann
2010 Mathematics and Visualization  
We find that traditional two-dimensional visualization techniques like path lines, streak lines and current time-dependent topology approaches are not able to answer the posed questions, for example they  ...  In this paper we apply vector field topology methods to a mathematical model for the fluid dynamics of reaggregation processes in tissue engineering.  ...  [14] restrict themselves to periodic fields and present a path line oriented topology for periodic 2D time-dependent vector fields.  ... 
doi:10.1007/978-3-642-15014-2_16 fatcat:4pcksaosvrannlvyrjryaihscm

Local Extraction of 3D Time‐Dependent Vector Field Topology

Lutz Hofmann, Filip Sadlo
2021 Computer graphics forum (Print)  
Figure 1: Time-dependent vector field topology of the von Kármán Vortex Street dataset at t=0.5 s, defined by attracting/repelling Lagrangian coherent structures (LCS, blue/red surfaces), obtained as streak  ...  manifolds seeded along hyperbolic path surfaces (time slice by green lines).  ...  structures for our extraction of the time-dependent 3D vector field topology.  ... 
doi:10.1111/cgf.14293 fatcat:snnz4ptrkzh6fevt5kmdbtoaaa

Topological Methods for Visualizing Vortical Flows [chapter]

Xavier Tricoche, Christoph Garth
2009 Mathematics and Visualization  
In both cases the mathematical framework is derived from the notion of parametric topology.  ...  The paper describes the application of topological methods to the visualization of vortical flow patterns that arise in simulations from Computational Fluid Dynamics.  ...  The method was originally designed for time-dependent 2D vector fields [18] and has been recently extended to the 3D case [5] .  ... 
doi:10.1007/b106657_5 fatcat:jzivpwki5vbgbh4tefwcubv4lu

The State of the Art [chapter]

David Levy, Monroe Newborn
1982 All About Chess and Computers  
Vector fields are a common concept for the representation of many different kinds of flow phenomena in science and engineering.Methods based on vector field topology have shown their convenience for visualizing  ...  relation to each other, taking classical (i.e. steady) vector field topology as our starting point.  ...  Acknowledgements The project SemSeg acknowledges the financial support of the Future and Emerging Technologies (FET) programme within the Seventh Framework Programme for Research of the European Commission  ... 
doi:10.1007/978-3-642-85538-2_9 fatcat:pebbowchanh6nnfq6ihq5cu5si

On the Way Towards Topology-Based Visualization of Unsteady Flow [article]

A. Pobitzer, R. Peikert, R. Fuchs, B. Schindler, A. Kuhn, H. Theisel, K. Matkovic, H. Hauser
2010 Eurographics State of the Art Reports  
Vector fields are a common concept for the representation of many different kinds of flow phenomena in science and engineering.Methods based on vector field topology have shown their convenience for visualizing  ...  relation to each other, taking classical (i.e. steady) vector field topology as our starting point.  ...  Acknowledgements The project SemSeg acknowledges the financial support of the Future and Emerging Technologies (FET) programme within the Seventh Framework Programme for Research of the European Commission  ... 
doi:10.2312/egst.20101065 fatcat:gwallqep5be5hgfk4pjei2yut4

The State of the Art in Topology-Based Visualization of Unsteady Flow

Armin Pobitzer, Ronald Peikert, Raphael Fuchs, Benjamin Schindler, Alexander Kuhn, Holger Theisel, Krešimir Matković, Helwig Hauser
2011 Computer graphics forum (Print)  
Methods based on vector field topology are known for their convenience for visualizing and analyzing steady flows, but a counterpart for unsteady flows is still missing.  ...  their relation to each other, taking classical (i.e., steady) vector field topology as our starting point.  ...  We also thank the anonymous reviewers of our survey for their constructive input and Matthew Geoffrey Parker (Univ. of Bergen) for proofreading.  ... 
doi:10.1111/j.1467-8659.2011.01901.x fatcat:vfbmhlwdpbfuplhuyix5ko43uu

Feature Flow Fields in Out-of-Core Settings [chapter]

Tino Weinkauf, Holger Theisel, Hans-Christian Hege, Hans-Peter Seidel
2007 Mathematics and Visualization  
We apply the approach to tracking of critical points in 2D and 3D time-dependent vector fields.  ...  Especially for 3D vector fields this may be a serious restriction, since the size of time-dependent vector fields can exceed the main memory of even high-end workstations.  ...  Considering a stream line oriented topology of time-dependent vector fields, critical points smoothly change their location and orientation over time.  ... 
doi:10.1007/978-3-540-70823-0_4 fatcat:lug3geuxarc6dpvdwqnvybe6cq

Topological defects in two-dimensional orientation-field models for grain growth

Bálint Korbuly, Mathis Plapp, Hervé Henry, James A. Warren, László Gránásy, Tamás Pusztai
2017 Physical review. E  
Standard two-dimensional orientation-field based phase-field models rely on a continuous scalar field to represent crystallographic orientation.  ...  The first is based on a 3-component unit vector field, while in the second we utilise a 2-component vector field with an additional potential.  ...  Due to the 2π periodicity of the orientation field θ, there exist two continuous paths connecting the orientations θA = 0.9π and θB = 1.6π (a).  ... 
doi:10.1103/physreve.96.052802 pmid:29347746 fatcat:vnd5fiw4hfexjjap7n6bsr77li

Time-Dependent 2-D Vector Field Topology: An Approach Inspired by Lagrangian Coherent Structures

F. Sadlo, D. Weiskopf
2010 Computer graphics forum (Print)  
This paper presents an approach to a time-dependent variant of the concept of vector field topology for 2-D vector fields.  ...  The presented approach represents a generalization for saddle-type critical points and their separatrices to unsteady vector fields based on generalized streak lines, with the classical vector field topology  ...  for time-dependent vector fields.  ... 
doi:10.1111/j.1467-8659.2009.01546.x fatcat:czscfueftnb2xc3rtnsn67k6hi

How superfluid vortex knots untie

Dustin Kleckner, Louis H. Kauffman, William T. M. Irvine
2016 Nature Physics  
Knotted and tangled structures frequently appear in physical fields, but so do mechanisms for untying them.  ...  Moreover, we find that the topological pathways of untying knots have simple descriptions in terms of minimal 2D knot diagrams, and tend to concentrate in states along specific maximally chiral pathways  ...  Proment for useful discussions.  ... 
doi:10.1038/nphys3679 fatcat:x6xta7t2jbe3fhfzs7lymwcdg4

Design of 2D Time-Varying Vector Fields

Guoning Chen, Vivek Kwatra, Li-Yi Wei, Charles D. Hansen, Eugene Zhang
2012 IEEE Transactions on Visualization and Computer Graphics  
In this paper, we present a framework for the design of time-varying vector fields, both for planar domains as well as manifold surfaces.  ...  In these applications, the time-varying vector fields have been applied as either orientation fields or advection fields to control the instantaneous appearance or evolving trajectories of the dynamic  ...  Konstantin Mischaikow for the valuable discussion on the topology and dynamics of vector fields, which initiated this work. We also thank Dr.  ... 
doi:10.1109/tvcg.2011.290 pmid:22201068 fatcat:glq3tiv3pjg2dohni54xbr37ta

Topologically relevant stream surfaces for flow visualization

Ronald Peikert, Filip Sadlo
2009 Proceedings of the 2009 Spring Conference on Computer Graphics - SCCG '09  
Abstract When vector field topology is used for the visualization of a 3D vector field, various types of topological features have uniquely defined stream surfaces associated with them.  ...  We discuss error bounds and we give application examples for the range of topological features under consideration.  ...  Acknowledgment We wish to thank Roger Bugmann for implementing the algorithm in his master's thesis, VA Tech Hydro for the Pelton turbine dataset, and the anonymous reviewers for their valuable comments  ... 
doi:10.1145/1980462.1980472 dblp:conf/sccg/PeikertS09 fatcat:nql3ogc3wreolafa64fs3wvh3u
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