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GPU-Based Interactive Cut-Surface Extraction From High-Order Finite Element Fields
Dec. 2011 (vol. 17 no. 12)
pp. 1803-1811
ASCII Text
x 
 
Blake Nelson, Robert M. Kirby, Robert Haimes, "GPU-Based Interactive Cut-Surface Extraction From High-Order Finite Element Fields," IEEE Transactions on Visualization and Computer Graphics, vol. 17, no. 12, pp. 1803-1811, Dec., 2011.
 
 
BibTex
x
 
@article{ 10.1109/TVCG.2011.206,
author = {Blake Nelson and Robert M. Kirby and Robert Haimes},
title = {GPU-Based Interactive Cut-Surface Extraction From High-Order Finite Element Fields},
journal ={IEEE Transactions on Visualization and Computer Graphics},
volume = {17},
number = {12},
issn = {1077-2626},
year = {2011},
pages = {1803-1811},
doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2011.206},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Visualization and Computer Graphics
TI - GPU-Based Interactive Cut-Surface Extraction From High-Order Finite Element Fields
IS - 12
SN - 1077-2626
SP1803
EP1811
EPD - 1803-1811
A1 - Blake Nelson,
A1 - Robert M. Kirby,
A1 - Robert Haimes,
PY - 2011
KW - High-order finite elements
KW - spectral/hp elements
KW - cut-plane extraction
KW - GPU-based root-finding
KW - GPU ray-tracing
KW - cutsurface extraction.
VL - 17
JA - IEEE Transactions on Visualization and Computer Graphics
ER -
 
Blake Nelson, University of Utah
Robert M. Kirby, University of Utah
We present a GPU-based ray-tracing system for the accurate and interactive visualization of cut-surfaces through 3D simulations of physical processes created from spectral/hp high-order finite element methods. When used by the numerical analyst to debug the solver, the ability for the imagery to precisely reflect the data is critical. In practice, the investigator interactively selects from a palette of visualization tools to construct a scene that can answer a query of the data. This is effective as long as the implicit contract of image quality between the individual and the visualization system is upheld. OpenGL rendering of scientific visualizations has worked remarkably well for exploratory visualization for most solver results. This is due to the consistency between the use of first-order representations in the simulation and the linear assumptions inherent in OpenGL (planar fragments and color-space interpolation). Unfortunately, the contract is broken when the solver discretization is of higher-order. There have been attempts to mitigate this through the use of spatial adaptation and/or texture mapping. These methods do a better job of approximating what the imagery should be but are not exact and tend to be view-dependent. This paper introduces new rendering mechanisms that specifically deal with the kinds of native data generated by high-order finite element solvers. The exploratory visualization tools are reassessed and cast in this system with the focus on image accuracy. This is accomplished in a GPU setting to ensure interactivity.

[1] J. Akin, W. Gray, and Q. Zhang, Colouring isoparametric contours. Engineering Computations, 1: 36—41, 1984.
[2] M. Brasher and R. Haimes, Rendering planar cuts through quadratic and cubic finite elements. In Proceedings of the conference on Visualization '04, VIS '04, pages 409–416, Washington, DC, USA, 2004. IEEE Computer Society.
[3] G. Coppola, S. J. Sherwin, and J. Peiro, Nonlinear particle tracking for high-order elements. J. Comput Phys., 172: 356-386, September 2001.
[4] B. Haasdonk, M. Ohlberger, M. Rumpf, A. Schmidt, and K. G. Siebert, Multiresolution visualization of higher order adaptive finite element simulations. Computing, 70: 181-204, July 2003.
[5] A. Knoll, Y. Hijazi, I. Wald, C. Hansen, and H. Hagen, Interactive ray tracing of arbitrary implicits with simd interval arithmetic. In Proceedings of the 2nd IEEE/EG Symposium on Interactive Ray Tracing, pages 11-18,2007.
[6] G. D. Kontopidis and D. E. Limbert, A predictor-corrector contouring algorithm for isoparametric 3d elements. International Journal for Numerical Methods in Engineering, 19 (7): 995-1004, 1983.
[7] A. O. Leone, R. Scateni, S. Pedinotti, L. Marzano, P. Marzano, E. Gob-betti, E. Gobbetti, and S. S. Pedinotti, Discontinuous finite element visualization. In 8th International Symposium on Flow Visualisation, 1998.
[8] J. L. Meek and G. Beer, Contour plotting of data using isoparametric element representation. International Journal for Numerical Methods in Engineering, 10 (4): 954-957, 1976.
[9] M. Meyer, B. Nelson, R. Kirby, and R. Whitaker, Particle systems for efficient and accurate high-order finite element visualization. IEEE Transactions on Visualization and Computer Graphics, 13: 1015-1026, 2007.
[10] R. E. Moore, R. B. Kearfott, and M. J. Cloud, Introduction to Interval Analysis. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2009.
[11] B. Nelson and R. M. Kirby, Ray-tracing polymorphic multidomain spec-tral/hp elements for isosurface rendering. IEEE Transactions on Visualization and Computer Graphics, 12: 114-125, January 2006.
[12] NVIDIA. NVIDIA OptiX Ray Tracing Engine Programming Guide, version 2.1 edition, 03 2011.
[13] S. G. Parker, J. Bigler, A. Dietrich, H. Friedrich, J. Hoberock, D. Luebke, D. McAllister, M. McGuire, K. Morley, A. Robison, and M. Stich, Optix: A general purpose ray tracing engine. ACM Transactions on Graphics, August 2010.
[14] J.-F. Remacle, N. Chevaugeon, E. Marchandise, and C. Geuzaine, Efficient visualization of high-order finite elements. International Journal for Numerical Methods in Engineering, 69 (4): 750-771, 2007.
[15] W. Schroeder, F. Bertel, M. Malaterre, D. Thompson, P. Pebay, R. O'Barall, and S. Tendulkar, Framework for visualizing higher-order basis functions. In Visualization, 2005. VIS 05. IEEE, pages 43 - 50, 2005.
[16] W. Schroeder, K. M. Martin, and W. E. Lorensen, The visualization toolkit (2nd ed.): an object-oriented approach to 3D graphics. Prentice-Hall, Inc., Upper Saddle River, NJ, USA, 1998.
[17] C. Singh and D. Sarkar, A simple and fast algorithm for the plotting of contours using quadrilateral meshes. Finite Elem. Anal. Des., 7: 217-228, December 1990.
[18] C. Singh and J. Singh, Accurate contour plotting using 6-node triangular elements in 2d. Finite Elem. Anal. Des., 45: 81-93, January 2009.
[19] J. M. Snyder, Interval analysis for computer graphics. SIGGRAPH Comput. Graph., 26: 121-130, July 1992.
[20] M. Uffinger, S. Frey, and T. Ertl, Interactive high-quality visualization of higher-order finite elements. Computer Graphics Forum, 29 (2): 337–346, 2010.
[21] D. F Wiley, H. Childs, B. Hamann, and K. Joy, Ray casting curved-quadratic elements. In O. Deussen, C. D. Hansen, D. Keim, and D. Saupe editors, Data Visualization 2004, pages 201-209. Eurographics/IEEE TCVG, ACM Siggraph, 2004.
[22] D. F Wiley, H. R. Childs, B. F Gregorski, B. Hamann, and K. I. Joy, Contouring curved quadratic elements. In Proceedings of the symposium on Data visualisation 2003, VISSYM '03, pages 167–176, Aire-la-Ville, Switzerland, Switzerland, 2003. Eurographics Association.
[23] P. L. Williams, N. L. Max, and C. M. Stein, A high accuracy volume Tenderer for unstructured data. IEEE Transactions on Visualization and Computer Graphics, 4: 37-54, January 1998.
[24] Y. Zhou and M. Garland, Interactive point-based rendering of higher-order tetrahedral data. IEEE Transactions on Visualization and Computer Graphics, 12 (5): 2006, 2006.

Index Terms:
High-order finite elements, spectral/hp elements, cut-plane extraction, GPU-based root-finding, GPU ray-tracing, cutsurface extraction.
Citation:
Blake Nelson, Robert M. Kirby, Robert Haimes, "GPU-Based Interactive Cut-Surface Extraction From High-Order Finite Element Fields," IEEE Transactions on Visualization and Computer Graphics, vol. 17, no. 12, pp. 1803-1811, Dec. 2011, doi:10.1109/TVCG.2011.206
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