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Issue No.12 - Dec. (2012 vol.18)
pp: 2315-2324
A. Bock , Sci. Visualization Group, Linkoping Univ., Linkoping, Sweden
E. Sunden , Sci. Visualization Group, Linkoping Univ., Linkoping, Sweden
Bingchen Liu , Comput. Sci. Dept., Univ. of Auckland, Auckland, New Zealand
B. Wunsche , Comput. Sci. Dept., Univ. of Auckland, Auckland, New Zealand
T. Ropinski , Sci. Visualization Group, Linkoping Univ., Linkoping, Sweden
ABSTRACT
Finite element (FE) models are frequently used in engineering and life sciences within time-consuming simulations. In contrast with the regular grid structure facilitated by volumetric data sets, as used in medicine or geosciences, FE models are defined over a non-uniform grid. Elements can have curved faces and their interior can be defined through high-order basis functions, which pose additional challenges when visualizing these models. During ray-casting, the uniformly distributed sample points along each viewing ray must be transformed into the material space defined within each element. The computational complexity of this transformation makes a straightforward approach inadequate for interactive data exploration. In this paper, we introduce a novel coherency-based method which supports the interactive exploration of FE models by decoupling the expensive world-to-material space transformation from the rendering stage, thereby allowing it to be performed within a precomputation stage. Therefore, our approach computes view-independent proxy rays in material space, which are clustered to facilitate data reduction. During rendering, these proxy rays are accessed, and it becomes possible to visually analyze high-order FE models at interactive frame rates, even when they are time-varying or consist of multiple modalities. Within this paper, we provide the necessary background about the FE data, describe our decoupling method, and introduce our interactive rendering algorithm. Furthermore, we provide visual results and analyze the error introduced by the presented approach.
INDEX TERMS
rendering (computer graphics), data compression, data reduction, data visualisation, finite element analysis, ray tracing, interactive rendering, coherency-based curve compression, high-order finite element model visualization, engineering, life sciences, time-consuming simulations, regular grid structure, volumetric data sets, medicine, geosciences, nonuniform grid, high-order basis functions, ray casting, uniformly distributed sample points, viewing ray, computational complexity, interactive data exploration, interactive exploration, world-to-material space transformation, rendering stage, computes view-independent proxy rays, data reduction, decoupling method, Rendering (computer graphics), Computational modeling, Finite element methods, Splines (mathematics), GPU-based ray-casting, Finite element visualization
CITATION
A. Bock, E. Sunden, Bingchen Liu, B. Wunsche, T. Ropinski, "Coherency-Based Curve Compression for High-Order Finite Element Model Visualization", IEEE Transactions on Visualization & Computer Graphics, vol.18, no. 12, pp. 2315-2324, Dec. 2012, doi:10.1109/TVCG.2012.206
REFERENCES
[1] C. Abraham, P. Cornillion, E. Matzner-L⊘er,, and N. Molinari., Unsuper-vised curve clustering using b-splines. Scandinavian lournal of Statistics, 30: 581-595, 2003.
[2] C. Bradley, A. Pullan, and P. Hunter, Geometric modeling of the human torso using cubic hermite elements Annals of Biomedical Engineering, 25(1): 96-111, 1997.
[3] M. Brasher and R. Haimes., Rendering planar cuts through quadratic and cubic finite elements. In IEEE Visualization, pages 409-416, 2004.
[4] E. Catmull and R. Rom, A class of local interpolating splines Computer Aided Geometric Design, 1974.
[5] R. Farias,J. S. B. Mitchell,, and C. T. Silva., Zsweep: an efficient and exact projection algorithm for unstructured volume rendering. In IEEE Volume Visualization, pages 91-99, 2000.
[6] M. P. Garrity., Ray tracing irregular volume data SIGGRAPH Comput. Graph., 24(5): 35-40, Nov. 1990.
[7] J. Georgii and R. Westermann, A generic and scalable pipeline for gpu tetrahedral grid rendering IEEE Transactions on Visualization and Computer Graphics, 12: 1345-1352, 2006.
[8] S. Grimm, M. Meissner, A. Kanitsar,, and M. E., Groller, Parallel peeling of curvilinear grids. Technical Report TR-186–2-04–07, Institute of Computer Graphics and Algorithms, Vienna University of Technology, 2004.
[9] B. Guenter and R. Parent, Computing the arc length of parametric curves IEEE Computer Graphics & Applications, 1990.
[10] J. Hartigan., Clustering Algorithms. New York: Wiley, 1975.
[11] L. Hong and A. Kaufman., Accelerated ray-casting for curvilinear volumes. In Proceedings of the conference on Visualization ‘98, pages 247253, 1998.
[12] L. Hong and A. E. Kaufman., Fast projection-based ray-casting algorithm for rendering curvilinear volumes IEEE Transactions on Visualization and Computer Graphics, 5: 322-332, October 1999.
[13] G. E. Karniadakis and S. J., Sherwin Spectral/hp Element Methods for CFD. Oxford University Press, 1999.
[14] P. M. Knupp., Remarks on mesh quality American Institute of Aeronautics and Astronautics, 2007.
[15] A. W. C. Lee,J. A. Schnabel, V. Rajagopal, P. M. F. Nielsen,, and M. P. N. ash., Breast image registration by combining finite elements and free-form deformations. In Proceedings of the 10th International Workshop on Digital Mammography (IWDM 2010), pages 736-743, 2010.
[16] A. Mammen, Transparency and antialiasing algorithms implemented with the virtual pixel maps technique IEEE Comput. Graph. Appl., 9(4): 43-55, July 1989.
[17] G. Marmitt, H. Friedrich, and P. Slusallek., Recent advancements in ray-tracing based volume rendering techniques. In Proceedings of 10th International Fall Workshop - Vision, Modeling, and Visualization (VMV) 2005, pages 131-138, 2005.
[18] S. Martin, H.-W. Shen, and R. Samtaney., Efficient rendering of extrud-able curvilinear volumes. In Visualization Symposium, 2008. Pacific VIS ‘08. IEEE Pacific, 2008.
[19] C. Meß and T. Ropinski., Efficient Acquisition and Clustering of Local Histograms for Representing Voxel Neighborhoods. In IEEE/EG Volume Graphics, pages 117-124, 2010.
[20] 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, 2007.
[21] K. Moreland and E. Angel., A fast high accuracy volume renderer for unstructured data. In IEEE Symposium on Volume Visualization and Graphics, 2004.
[22] B. Nelson, R. Haimes, and R. Kirby, Gpu-based interactive cut-surface extraction from high-order finite element fields IEEE Transactions on Visualization and Computer Graphics, 2011.
[23] B. Nelson and R. Kirby, Ray-tracing polymorphic multidomain spec-tral/hp elements for isosurface rendering IEEE Transactions on Visualization and Computer Graphics, 2006.
[24] w. H. Press,W. T. Vetterling,S. A. Teukolsky,, and B. P. Flannery, Numerical Recipes in C - The Art of Scientific Computing. Cambridge University Press, 1992.
[25] D. M. Reed, R. Yagel, A. Law., P.-W. Shin, and N. Shareef., Hardware assisted volume rendering of unstructured grids by incremental slicing. In Proceedings of the 1996 symposium on Volume visualization, VVS ‘96, pages 55–ff., Piscataway, NJ, USA, 1996. IEEE Press.
[26] D. Rose and T. Ertl., Interactive visualization of large finite element models. In Proceedings of the Workshop on Vision, Modelling, and Visualization VMV ‘03, pages 585-592, 2003.
[27] W. Schroeder, F. Bertel, M. Malaterre., D. Thompson, P. Pebay,R. O’Bara,, and S. Tendulkar., Methods and framework for visualizing higher-order finite elements. IEEE Transactions on Visualization and Computer Graphics, 12(4): 446-460, 2006.
[28] C. Schwab., p- and hp-Finite Element Methods. Oxford University Press, 1999.
[29] B. Szab ó and 1. Babuska. Finite Element Analysis. Wiley-Interscience, 1991.
[30] M. Uffinger, S. Frey, and T. Ertl, Interactive high-quality visualization of higher-order finite elements Computer Graphics Forum, 29(2): 337-346, 2010.
[31] J. Wihelms, J. Challinger, N. Alper., S. Ramamoorthy, and A. Vaziri, Direct volume rendering of curvilinear volumes SIGGRA PH, 24: 41-47, 1990.
[32] D. Wiley, H. Childs, B. Hamann,, and K. Joy., Ray casting curved-quadratic elements. IEEE Transactions on Visualization and Computer Graphics, 2004.
[33] B. Wiinsche., A toolkit for visualizing biomedical data sets. In GRAPHITE ‘03, pages 167-175, 2003.
[34] B. C. Wiinsche and A. A. Young., The visualization and measurement of left ventricular deformation using finite element models JVLC - Biomedical Visualization for Biointormatics. 14(4): 299-326. 2003.
[35] A. A. Young,B. R. Cowan,S. F. Thrupp,W. J. Hedley,, and L. J. Dell'Italia., Left ventricular mass and volume: Fast calculation with guide-point modeling on MR images Radiology, 216: 597-602, Aug. 2000.
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