Lagrangian Visualization Methods for Very Large Time-Dependent Vector Fields

IIS-0916289

Principal Investigator: Kenneth I. Joy (kijoy@ucdavis.edu)
Co-Principal Investigator: Christoph Garth (cgarth@ucdavis.edu)

Award Period, 2009-2012, with extension through 2015

Last Updated: October 1, 2015

 

Proposal Abstract:

Lagrangian methods assume a central role in the analysis and visualization of vector fields resulting from simulation and measurement across many application domains. These methods provide key insight into vector field structures and dynamics, but are based on the expensive computation of integral curves. Applied to large-scale problems and data sets, they are burdened heavily by enormous computational cost. To improve this situation, we replace the on-demand and problem-specific computation of integral curves typically employed in vector field visualization techniques by a two-stage process consisting of an adaptive pre-computation of integral curve sets and methods for interpolation within these sets, effectively transferring the vector field representation to the Lagrangian domain. Hence, we isolate the computational burden into a pre-computation stage, and transfer the obtained Lagrangian representation of a vector field into efficient out-of-core data structures. Integration-based visualization algorithms can leverage fast interpolation of integral curves, whose approximative characteristics we examine in detail, from this pre-computed data. Based on this generic framework, we enhance existing integration-based visualization methods to become interactive, and provide a basis for research into fast and efficient and interactive vector field visualization for very large vector fields. We take advantage of the expected performance and efficiency of the proposed methods to develop novel visualization tools based on Lagrangian analysis of transport processes in vector fields. In order to increase the impact of our research, we integrate our results with an open-source visualization package to distribute our work to a large community of scientists and engineers.


Results from this Grant:

As is normal with one of these projects, our investigations have led us in several directions. It was our objective to focus on the Lagrangian representation of flow fields, and investigate and analyze flow maps as a new paradigm for flow visualization algorithms. In this regard, we were extemely successful, as were were able to modify flow visualization methods to enhance the understanding of 3d flow, and show that a Lagrangian representation is a viable data representation scheme for flow visualization algorithms. Specifically, this project has enabled us to

  • develop a new method for representation large-scale flow that is based upon flow maps, maps with short curves emantating from each data point. We have developed an interpolation scheme that enables us to interpolate these curves, and have shown that these methods can be used as a base for all flow visualization algorithms, and are faster, can take less memory, and are more accurate than previous algorithms.
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  • establish stream surfaces as a viable visualization method for three-dimensional flow -- establishing a method of coordinatizing these surfaces so that computer graphics techniques can be used to make the surfaces semi-transparent and map features onto the surfaces.

  • change the focus of visualization from streamlines to pathlines -- from a steady problem to a dynamic problem -- from stream surfaces to path surfaces, streak surfaces, and time surfaces, dramatically increasing the number of visualization techniques available to the scientist.
  • generated parallel methods for flow visualization. Here we have investigated several methods -- some taylored specifically to different computer systems -- but there is much more work to do, especially in Lagrangian Methods. .

  • developed new methods for flow representation in ensembles. This was an extension of our basic work, but has been very successful.

  • developed new methods for illustrative visualization of vector fields, working on stream, path, streak and time surfaces, and developed methods to map local flow onto these surfaces.

  • We were the first to develop algorithms for visualization of blood flow using PC-MRI images.

These efforts resulted in 38 publications directly related to this project, including two that won "Best Paper" awards. It supported several students, researchers and postdocs that have taken positions in academics and professional fields related to visualization.




 

Students/Collaborators on this Project:

Roxana Bujack
Postdoc, UC Davis

Roxana worked on the mathematical aspects of visualization that arise in this project. She has taken a postdoc position at the University of Kaiserslautern as of January 2016.
Harald Obermaier,
Postdoc, UC Davis through 2014.
Harald worked on flow visualization and was leading the effort to develop new methods for representation of flow. He is now working for Apple.
Alex Agranovsky,
Graduate Student, UC Davis
Alex worked on the computation aspects of Lagrangian representation for flow. He efforts focused on interpolation methods for curve segments in flow maps.

David Camp,
Graduate Student, UC Davis
Ph.D. Awarded, September 2012,
Now employed by Lawrence Berkeley National Laboratory

David has been working on the design and implementation of parallel flow visualization methods. He is currently a staff scientist at Lawrence Berkeley National Laboratory
Jennifer Chandler,
Graduate Student, UC Davis
Jennifer has been working on particle-based flow visualization, using the position of few particles to determine the flow characteristics of general particles. She will complete her Ph.D. in July of 2016.
Hank Childs,
Lawrence Berkeley National Laboratory and University of Oregon
Hank was a professional research at UC Davis and the architect of VisIt, a visualization software system for scientific applications. We utilize VisIt for our technology transfer in this project. As of April 2013, he has taken a faculty position at the University of Oregon
Christoph Garth,
University of Kaiserslautern, Germany
Professor Garth, an award-winning postdoc on this project has taken a faculty position at the University of Kaiserslautern. He continued as a collaborator on this project, especially working with stream surface methods.
DoE Scalable Data Management, Analysis and Visualization (SDAV) Institute The SDAV Institute is the successor to the DoE VACET Center. This collaboration enabled us to obtain complex data sets and use large-scale parallel systems to test our algorithms.

DoE SciDAC II VACET (Visualization and Analytics Center for Enabling Technologies)

The VACET Center was an excellent collaboration that enables us to obtain complex data sets for this project. They have also enabled us to test our parallel algorithms on large-scale processing systems.
Siemens Corporation Siemens has shared data from their PC-MRI systems on which we based our blood-flow visualization work.
International Research Training Group, Kaiserslautern Germany Our Institute at UC Davis collaborates with International Research Training Group 1131in Kaiserslautern Germany. Typically three to five students visit us yearly and many collaborated on projects related to this proposal.

 


 

Publications to date:

Jennifer Chandler, Harald Obermaier, and Kenneth I. Joy, “WebGL-Enabled Remote Visualization of Smoothed Particle Hydrodynamics Simulations,” In Eurographics Conference on Visualization (EuroVis 2015) - Short Papers.  
Roxana Bujack, Jens Kasten, Vijay Natarajan, Gerik Scheuermann, Kenneth I. Joy, “Clustering Moment Invariants to Identify Similarity within 2D Flow Fields,” In Eurographics Conference on Visualization (EuroVis 2015) - Short Papers.  
Alexy Agranovsky, Harald Obermaier, Christoph Garth and Kenneth I. Joy, “A Multi-resolution Interpolation Scheme for Pathline-based Lagrangian Flow Representations,” Proceedings of SPIE, Visual Data Analysis Conference, San Francisco CA, February 2015.  
Alexy Agranovsky, David Camp Kenneth I. Joy, and Hank Chids, “Subsampling-based Compression and Flow Visualizaiton,”  Proceedings of SPIE, Visual Data Analysis Conference, San Francisco CA, February 2015.  
Alexy Agranovsky, David Camp, Christoph Garth, E. Wes Bethel, Kenneth I. Joy and Hank Childs, "Improved Post hoc Flow Analysis vis Lagrangian Representations," IEEE Symposium on Large Data Analysis and Visualization (LDAV), Paris, France, November 2014, 67-75 [Best Paper].  
Mikhail M. Shashkov, Connie S. Hguyen, Mario Yepez, Mauricio Hess-Flores, and Kenneth I. Joy, "Semi-Autonomous Digitization of Real-World Environments," in Proceedings of the 19th International Conference on Computer Games: AI, Animation, Interactive Multimedia, Virtual Worlds and Serious Games (C-GAMES USA 2014) .  
Sohail Shafii, Harald Obermaier, Bernd Hamann, and Kenneth I. Joy, "Topological Features in Glyph-Based Corotation Visualization," Topological Methods in Data Analysis and Visualization III - Theory, Algorithms, and Applications, Springer, 2014, pp. 263-276.  
Harald Obermaier and Kenneth I. Joy. "Future Challenges for Ensemble Visualization", IEEE Computer Graphics and Applications, Vol. 34, No. 3, pp. 8-11, May/June 2014.  
Jennifer Chandler, Harald Obermaier, and Kenneth I. Joy, "Interpolation-based Pathline Tracing in Particle-Based Flow Visualization, IEEE Transactions on Visualization and Computer Graphics, Vol 20, (accepted for publication).  
Jennifer Chandler, Harald Obermaier, and Kenneth I. Joy, "Illustrative Rendering of Particle Systems," Proceedings of Vision, Modeling, and Visualization (VMV 2013), 177-185.  
Sohail Shafii, Harald Obermaier, Rodman Linn, Eunmo Koo, Mario Hlawitschka, Christoph Garth, Bernd Hamann, and Kenneth I. Joy, “Visualization and Analysis of Vortex-Turbine Intersections in Wind Farms, IEEE Transactions on Visualization and Computer Graphics, Vol 19, No. 9, September 2013, 1581-1594  
Alexy Agranovsky, Harald Obermaier, and Kenneth I. Joy. A Framework for the Visualization of Finite-Time Continuum Mechanics Effects in Time-Varying Flow, 9th International Symposium on Visual Computing (ISVC), LCNS Volume 8034, 349-360..  
Mathias Hummel, Harald Obermaier, Christoph Garth, and Kenneth I. Joy, "Comparative Visual Analysis of Lagrangian Transport in CFD Ensembles," IEEE Transactions on Visualization and Computer Graphics, (Proceedings of IEEE Visualization Conference),Vol 19, No. 12, 2743-2752  
Sohail Shafii, Harald Obermaier, Vaclav Kolar, Mario Hlawitschka, Christoph Garth, Bernd Hamann and Kenneth I. Joy, "Illustrative Rendering of Vortex Cores," in Proceedings of EuroVis Short Papers 2013, Leipzig Germany, June 2013.  
David Camp, Hari Krishnan, Dave Pugmire, Christoph Garth, Ian Johnson, E. Wes Bethel, Kenneth I. Joy and Hank Childs, "GPU Acceleration of Particle Advection Workloads in a Parallel, Distributed Memory Setting," in Proceedings of the Eurographics Symposium on Parallel Graphics and Visualization, Girona, Spain, April 2013.  
S. Shafii, H. Obermaier, R. Linn, E. Koo, M. Hlawitschka, C. Garth, B. Hamann, K. I. Joy. Visualization and Analysis of Vortex-Turbine Intersections in Wind Farms, IEEE Transactions on Visualization and Computer Graphics, vol. 19, no. 9, pp. 1579-1591, 2013.  
E. Wes Bethel, David Camp, Hank Childs, Christoph Garth, Mark Howison, Kenneth I. Joy and David Pugmire, “Hybrid Parallelism” in High Performance Visualization---Enabling Extreme-Scale Scientific Insight, E.W. Bethel, H. Childs, and C. Hansen, eds., 2012, 261-290  
Harald Obermaier, Magali I. Billen, Kenneth I. Joy, Hans Hagen and Martin Hering-Bertram, “Visualization and Multivariate Clustering of Scattered Moment Tensors,”  Information Visualization, Vol. 11, No. 1, January 2012, 43-59.  
Harald Obermaier, Fang Chen, Hans Hagen and Kenneth I. Joy, “Visualization of Material Interface Stability,”  Proceedings of Pacific Visualization Conference, Songdo, Korea, 2012, 225-232  
David Camp, Hank Childs, Christoph Garth, Dave Pugmire and Kenneth I. Joy, “Parallel Stream Surface Computation for Large Data Sets,” Proceedings of the IEEE Symposium on Large-Scale Data Analysis and Visualization, Seattle WA, USA, 2012 ,October 2012, 39-47  
Alexy Agranovsky, Christoph Garth and Kenneth I. Joy, “Extracting Flow Structures Using Sparse Particles,” Proceedings of the Vision, Modeling and Visualization Workshop, 2011, Berlin Germany, 153-160.  
Harald Obermaier and Kenneth I. Joy, “Derived Metric Tensors for Flow Surface Visualization,” IEEE Transactions on Visualization and Computer Graphics, Proceedings of IEEE Visualization 2012, December 2012, Vol. 18, No. 12, 2149-2158.  
Simon Schroeder, John A. Peterson, Harald Obermaier, Louise H. Kellogg, Kenneth I. Joy and Hans Hagen, “Visualization of Flow Behavior in Earth Mantle Convection,” IEEE Transactions on Visualization and Computer Graphics, Proceedings of IEEE Visualization 2012, December 2012,Vol. 18, No. 12, 2198-2207.  
Harald Obermaier and Kenneth I. Joy, "Function Field Analysis for the Visualization of Flow Similarity in Time-Varying Vector Fields, Proceedings of the 8th International Symposium on Visual Computing (ISVC), Rethymnon, Crete, Greece, 2012.  
David Camp, Hank Childs, Amit Chourasia, Christoph Garth, and Kenneth I. Joy, "Evaluating the Benefits of An Extended Memory Hierarchy for Parallel Streamline Algorithms," Proceedings of the IEEE Symposium on Large-Scale Data Analysis and Visualization, Providence RI, October 201, 57-64.  
Xavier Tricoche, Christoph Garth and Alan Sanderson, "Visualization of Topological Structures in Area-Preserving Maps," IEEE Transactions on Visualization and Computer Graphics, Vol. 17, No. 6, Vol. 17, No. 12, 1765-1774  
Hari Krishnan, Christoph Garth, Jens Guhring, M. Akif Gulsun, Andreas Greiser, and Kenneth I. Joy, “Analysis of Time-Dependent Flow-Sensitive PC-MRI Data,” IEEE Transactions on Visualization and Computer Graphics, Vol. 18, No. 6,1-13.  
David Camp, Christoph Garth, Hank Childs, David Pugmire, and Kenneth I. Joy, "Streamline Integration using MPI-Hybrid Parallelism on Large Multi-Core Architectures," IEEE Transactions on Visualization and Computer Graphics, Vol. 17, No. 11, November 2011, 1702-1713  
Christoph Garth and Kenneth I. Joy, “Fast, Memory-Efficient Cell Location in Unstructured Grids for Visualization,” IEEE Transactions on Visualization and Computer Graphics (Proceedings of IEEE Visualization 2010), Vol. 16, No. 6, October 2010, 1541-1550.  
Mattias Hummel, Christoph Garth, Bernd Hamann, Hans Hagen, and Kenneth I. Joy, “IRIS: Illustrative Rendering of Integral Surfaces”, IEEE Transactions on Visualization and Computer Graphics, (Proceedings of IEEE Visualization 2010), Vol 16, No. 6, October 2010, 1319 - 1328  
John Anderson, Christoph Garth, Mark A. Duchaineau, and Kenneth I. Joy, “Interactive Visualization of Function Fields by Range-Space Segmentation,” Proceedings of EuroVis 2009, Computer Graphics Forum, Vol. 28, No. 3, 727-734.  
E. Deines, G. H. Weber, C. Garth, B. Van Straalen, S. Borovikov, D. F. Martin, and K. I. Joy," On the Computation of Integral Curves in Adaptive Mesh Refinement Vector Fields," In Scientific Visualization: Advanced Concepts, Dagstuhl Follow-Ups, Schloss Dagstuhl--Leibniz Center for Informatics, 2010.  
 
Christoph Garth, Eduard Deines, Kenneth Joy, Hank Childs, Gunther H. Weber, E. Wes Bethel, Sean Ahern, David Pugmire, Chris Johnson, "Vector Field Visual Data Analysis for Petascale", in "SciDAC Review", Number 15, pp 10--21, 2009.  
David Pugmire, Hank Childs, Christoph Garth, Sean Ahern, Gunther H. Weber, "Scalable Computation of Streamlines on Very Large Datasets", in "SC '09: Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis", pp 1--12, 2009  
Mario Hlawitschka, Christoph Garth, Xavier Tricoche, Gordon Kindlmann, Gerik Scheuermann, Kenneth I. Joy, Bernd Hamann, “Direct Visualization of Fiber Information by Coherence,” Journal of Computer Assisted Radiology and Surgery, Vol. 5, No. 2, (2010), pp125.  
Luke Gosink, Christoph Garth, John Anderson, E. Wes Bethel, and Kenneth I. Joy, “An Application of Multivariate Statistical Analysis for Query-Driven Visualization,” IEEE Transactions on Visualization and Computer Graphics, Vol. 17, No. 3, 2011, 264--275.  
John Anderson, Christoph Garth, Mark A. Duchaineau, and Kenneth I. Joy, “Smooth, Volume-Accurate Material Interface Reconstruction,” IEEE Transactions on Visualization and Computer Graphics, Vol. 16, No. 5, 2010, 802-814.  

 

Presentations:

Jennifer Chandler's presentation of “WebGL-Enabled Remote Visualization of Smoothed Particle Hydrodynamics Simulations,” given at EuroVis 2015.  
Ken Joy's Acceptance Speech for the IEEE 2014 VGTC Career Award  
Alexy Agranovsky's presentation of “A Multi-resolution Interpolation Scheme for Pathline-based Lagrangian Flow Representations,” given at the Visual Data Analysis Conference, San Francisco CA, February 2015.  
Alexy Agranovsky's presentation of “Subsampling-based Compression and Flow Visualizaiton,”  given at the Visual Data Analysis Conference, San Francisco CA, February 2015.  
Alexy Agranovsky's presentation of, "Improved Post hoc Flow Analysis vis Lagrangian Representations," given as the best paper of the IEEE Symposium on Large Data Analysis and Visualization (LDAV), Paris, France, November 2014.  
Jennifer Chandler's presentation of "Illustrative Rendering of Particle Systems," Given at the Conference on Vision, Modeling, and Visualization (VMV 2013), Lugano Switzerland  
Alex Agranovsky's presentation of "A Framework for the Visualization of Finite-Time Continuum Mechanics Effects in Time-Varying Flow" given at the 2013 International Symposium on Visual Computing, July 29-31, 2013 Rethymnon, Crete, Greece  
Sohail Shafii's presentation of "Illustrative Rendering of Vortex Cores," given at the EuroVis 2013 Conference, Leipzig Germany  
Mathias Hummel presentation of the paper "Comparative Visual Analysis of Lagrangian Transport in CFD Ensembles." Given at the IEEE Visualization Conference 2013, Atlanta GA.  
David Camp's Presentation of "GPU Acceleration of Particle Advection Workloads in a Parallel, Distributed Memory Setting,", given at the Eurographics Symposium on Parallel Graphics and Visualization, Girona Spain, April 2013  
Harald Obermaier's presentation of "Visualization of Material Interface Stability", given at the Pacific Visualization Conference, 2012.  
Harald Obermaier's presentation of "Function Field Analysis for the Visualization of Flow Similarity in Time-­‐Varying Vector Fields" at the International Symposium of Visualization Computing in Rethymnon, Crete, Greece. 2012  
Material Interface Reconstruction, by Ken Joy, Talk given at the University of Kaiserslautern Germany, Summer 2012  
David Camp's presentation of the paper, "Evaluating the Benefits of An Extended Memory Hierarchy for Parallel Streamline Algorithms," Proceedings of the IEEE Symposium on Large-Scale Data Analysis and Visualization, Providence RI, October 2011.  
David Camp's presentation of the paper, "Streamline Integration using MPI-Hybrid Parallelism on Large Multi-Core Architectures," Invited talk of the best IEEE TVCG Papers of 2011. IEEE Visualization Conference, Providence RI, October 2011  
The Impact of Data Complexity on Scientific Visualization Methods, Ken Joy, invited talk given at the SciDAC 2011 Conference.  
Integrated Multi-Field Visualization, by Ken Joy, given at the Dagstuhl Visualization Seminar, Leibnitz Center for Informatics, Dagstuhl Germany, June 2011  
Hari Krishnan's presentation of the paper, “Time and Streak Surfaces for Flow Visualization in Large Time-Varying Data Sets,” IEEE Transactions on Visualization and Computer Graphics, (Proceedings of IEEE Visualization 2009), Vol. 15, No. 6, October, 2009, 1267-1274.  
Christoph Garth's presentation of the paper, “Fast Memory-Efficient Cell Location in Unstructured Grids for Visualization”, in IEEE Transactions on Visualization and Computer Graphics (Proceedings of IEEE Visualization 2010), Vol. 16, No. 6, October 2010, 1541-1550.  

 

Videos:

A companion video illustrating the multiresolution scheme from the paper "A Multi-Resolution Interpolation Scheme for Path-Line Based Lagrangian Flow Representations"
Video of an internally simulated exhaust, illustrating FTLE.
The IRIS Video, initially presented at the IEEE Visualization 2010 Conference, Salt Lake City Utah
The SciDAC 2010 Award Winning Video describing stream, path, streak, and time surfaces. Also the first to show dynamic flow on the stream surfaces.
The "fish-tank" video, illustrating 250,000 points traced through an unstructured data set. The video was shot in real-time, with computations largely on the GPU.

 

Outreach Activities:

Interactive Flythrough of the Known Universe. We sponsored this project through the UC Davis Computer Science Department's Senior Project Course. The students took a catalog of templates from the Sloan Digital Sky Survey, and wrote an octree-based sprite rendering system. They also utilize a LeapFrog system for navigation, and had 1.7M images rendering in real-time [60fps] off a MacBook Pro.  
Automatic image classification of the Miami skyline. We sponsored this project through the UC Davis Computer Science Department's Senior Project Course. A team of three students were able to develop a system that could process video from a camera system developed by Lawrence Berkeley Lab researchers and deployed in Miami. They read a bunch of literature from climate sciences and computer vision, and put together matlab code that automatically segment out, and classify cloud types with 95% accuracy. We expect to submit a poster to AGU this fall, with the students as co-authors.  

Online Course on Geometric Modeling, designed by Ken Joy, offered Fall 2012 at UC Davis

This course has been expanded into a set of geometric modeling lectures with the purpose that any student worldwide can access these lectures and learn the basic material behind geometric modeling. Find the enhanced lectures here.

 
Images from the UC Davis Visualization and Graphics Art Show  
Why go to Graduate School Presentation, by Ken Joy -- various times, UC Davis  
How to Give a Professional Talk -- given several times -- UC Davis.  

Awards:

Ken Joy won the IEEE TCVG Visualization Career award in October of 2014. This award was given in recognition of Ken's foundational research in the mathematical representation of data for visualization and for service to the community. The announcement of the award can be found here.
Alexy Agranovsky, David Camp, Christoph Garth, E. Wes Bethel, and Kenneth I. Joy have been awarded the Best Paper at the IEEE Symposium on Large Data Analysis and Visualization (LDAV for the paper "Improved Post hoc Flow Analysis vis Lagrangian Representations,").
Harald Obermaier was named Honorable Mention in the UC Davis Award for Postdoctoral Research. This was a significant honor, as there are over 1000 postdocs at UC Davis eligible for the award.
The paper "Comparative Visual Analysis of Lagrangian Transport in CFD Ensembles," by Mathias Hummel, Harald Obermaier, Christoph Garth, and Kenneth I. Joy, was selected best scientific visualization paper at the 2013 IEEE Visualization Conference.
Alexy Agranovsky was awarded a one-year fellowship at Lawrence Berkeley National Laboratory, where he is completing his dissertation work. He is currently working on a parallel version of the interpolation of short streamlines.
Hank Childs has accepted a faculty position at the University of Oregon. He received a positive tenure evaluation in July 2015.
Jennifer Chandler was awarded a 2012 NSF Graduate Fellowship
Christoph Garth has accepted a position of Junior Professor for Computational Topology at the University of Kaiserslautern in Kaiserslautern Germany.
Christoph Garth, co-PI of this project, was awarded the UC Davis Award for Excellence in Postdoctoral Research. This award is given yearly to two recipients, drawn from the nearly 1000 post docs at UC Davis.
The paper by Christoph Garth and Kenneth I. Joy, entitled “Fast, Memory-Efficient Cell Location in Unstructured Grids for Visualization,” published in the IEEE Transactions on Visualization and Computer Graphics (Proceedings of IEEE Visualization 2010), Vol. 16, No. 6, was awarded the "Imp of the Year Award" for 2010 from the IEEE Visualization Conference. This award is given to the result that is most likely to be implemented by vote of the conference participants.
The Vortex Breakdown Bubble Image, from the paper by Mattias Hummel, Christoph Garth, Bernd Hamann, Hans Hagen, and Kenneth I. Joy, entitled “IRIS: Illustrative Rendering of Integral Surfaces”,and published in the IEEE Transactions on Visualization and Computer Graphics, (Proceedings of IEEE Visualization 2010), Vol 16, No. 6, was has won the Computer Graphics Forum 2011 cover image contest. This yearly competition is hosted by the Computer Graphics Forum, the preeminent journal of the Eurographics Society. The image shows a stream surface in a vortex breakdown bubble, and was created using IRIS, a system for illustrative surface rendering produced in IDAV. The image will appear on the Journal Cover throughout 2011
The video "Visualization of a Convective Flow with Integral Surfaces" won an "OASCR" (Note the spelling) at the DoE SciDAC 2010 Conference. This video illustrates the various methods for stream, path, streak and time surface generation pioneered through this grant. Find the video here.

Other Things:

An image from this project appeared on the Cover of SciDAC Review in 2009

The "Vortex Breakdown Bubble" image appears as the cover image for the new book High Performance Visualization: Enabling Extreme-Scale Scientific Insight by E. Wes Bethel, Hank Childs, and Charles Hansen, published by Chapman & Hall in the CRC Computational Science Series, November 2012. Two other images from this project appear on the back cover of the book.

Find the full cover image here.