Analysis of 2D/2.5D Vector Fields

IEEE Transactions on Visualization and Computer Graphics

 

 

 

 

 

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.

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].

Bibtex

entry

@ARTICLE{Chen:ECG:2007,
    author    =  {Guoning Chen and Konstantin Mischaikow and Robert S. Laramee and Pawel Pilarczyk and Eugene Zhang},
    title         =  {
Vector Field Editing and Periodic Orbit Extraction Using Morse Decomposition },
    journal    =  {IEEE Trans. Visualization and Computer Graphics},
    year        =  {2007},
    volume   =  {13},
    number  =  {4},

 page = {769-785 },
}

@ARTICLE{Chen:MCG:2008,
    author    =  {Guoning Chen and Konstantin Mischaikow and Robert S. Laramee and Eugene Zhang},
    title         =  {
Efficient Morse Decompositions of Vector Fields },
    journal    =  {IEEE Trans. Visualization and Computer Graphics},
    year        =  {2008},
    volume   =  {14},
    number  =  {4},

 page = {848-862 },
}

@ARTICLE{Chen:hierMCG:2011,
    author    =  {Guoning Chen and Andrzej and Robert S. Laramee and Pawel Pilarczyk and Eugene Zhang},
    title         =  {
Morse Set Classification and Hierarchical Refinement using Conley Index },
    journal    =  {IEEE Trans. Visualization and Computer Graphics},
    year        =  {2011},
    volume   =  {},
    number  =  {},

 note = { prePrint },
}

Source code

  The source code (and a short manual) of this project is available [here]. It was written using C++ and compiled under Visual Studio 2005 and later. NOTE that the source code is for the use of the research purpose only.

An old version of the tool can be downloaded here. Unzip the downloaded file and put the glut32.dll under the same directory as the executable file.

Some example models with designed vector fields can be found here. 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!

Results

   

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

Acknowledgment

  • People

Greg Turk

Zhongzang Lin

Charles Hansen

 

  • Funding

NSF CCF-0546881

NSF IIS-0830808

       

 

 

Research Projects Related to NSF Grant CCF-0546881

This material is based upon work supported by the National Science Foundation under Grant No. 0546881 and No. 0830808.

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).

 

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