Analysis of 2D/2.5D Vector Fields
IEEE Transactions on Visualization
and Computer Graphics
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Abstract |
Scientific simulation has become an integral part of many
engineering and scientific applications for the study of various aero- and
hydro-dynamical systems. These dynamical systems describe the behaviors of
gas and fluid under different conditions, which dominate a wide range of
natural and physical phenomena.
The data stemming from the simulations of these dynamical systems are
represented as vector fields. Analysis of these vector fields
provides critical insight of the simulated phenomena which cannot be observed
otherwise. This project demonstrates an effort to achieve efficient analysis
of the vector fields from various simulations that defined on 2-dimenional
triangular meshes (e.g., 2D plan or curved surfaces embedded in 3D).
Specifically, the computation of the topological structures of the vector
fields is studied for their analysis. An Entity Connection Graph (ECG) is
proposed to incorporate periodic orbits, an important flow recurrent dynamics
that describe the invariant property of the dynamical system, into the
topological skeleton. To address the instability issue in the computation of
the differential topology including ECG, a discrete topology is introduced to
the visualization community based on the computation of the Morse
decompositions of the vector fields. The obtained topology is called a Morse
Connection Graph (MCG) that has been shown more stable than ECG. The
computation of Morse decomposition is improved later by a hierarchical refinement
framework, which achieves not only faster computation but also consistent
decompositions of the vector field structure. |
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Papers |
This work has
been published in the following three papers ·
Guoning
Chen, Konstantin Mischaikow, Robert S. Laramee, Pawel Pilarczyk, and Eugene Zhang. Vector Field Editing and
Periodic Orbit Extraction Using Morse Decomposition. IEEE Transactions on
Visualization and Comptuer Graphics, Vol. 13,
No. 4, pp. 769-785 [pdf]. ·
Guoning
Chen, Konstantin Mischaikow, Robert S. Laramee, and
Eugene Zhang. Efficient Morse Decompositions of Vector Fields. IEEE
Transactions on Visualization and Computer Graphics, Vol. 14, No. 4, 2008,
pp. 848-862 [pdf]. ·
Guoning
Chen, Qingqing Deng, Andrzej
Szymczak, Robert S. Laramee, and Eugene Zhang.
Morse Set Classification and Hierarchical Refinement using Conley Index. IEEE
Transactions on Visualization and Computer Graphics, to appear, 2011 [pdf]. |
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Bibtex entry |
@ARTICLE{Chen:ECG:2007, page = {769-785 }, @ARTICLE{Chen:MCG:2008, page = {848-862 }, @ARTICLE{Chen:hierMCG:2011, note = { prePrint }, |
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Source code |
A version of the tool can be downloaded here, which can be compiled using Visual Studio Community 2019 on Windows 10. Unzip the downloaded file and put the glut32.dll under the same directory as the executable file. NOTE that the source code is for the use of the research purpose only. This sample contains a number of vector field data files (in 2D plane or on curved surfaces). Currently, the system supports only .ply format as the input. To obtain the suitable data file format for this program, one may also need to orient the mesh!
An old version of the code can be found here, which was developed and compiled using Visual Studio 2005. |
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Results |
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Talks |
NAFEM 2007, Vancouver, Canada KAV07 workshop (in associate with IEEE Vis 2007), Sacramento, CA Invited talk at SCI, University of Utah 2009 IEEE Conference of Visualization 2011 Invited talk at the University of Houston 2012 Invited talk at the University of Notre Dame 2012 |
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Acknowledgment |
Greg Turk Zhongzang Lin Charles Hansen
NSF CCF-0546881 NSF IIS-0830808
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Research Projects Related
to NSF Grant CCF-0546881 Any opinions, findings and conclusions or
recommendations expressed in this material are those of the author(s) and do
not necessarily reflect the views of the National Science Foundation (NSF). |