CPU-GPU Algorithms for Triangular Surface Mesh Simplification

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16 Suzanne M. Shontz and Dragos M. Nistor(a) Armadillo (b) Bunny (c) Gargoyle(d) Hand (e) Horse (f) KittenFig. 9. The resulting meshes after 10 iterations of the CPU-GPU inverse reductionalgorithm.version of an original mesh. They may also be useful for real-time visualizationof triangular surface meshes used in scientific computing applications.The simplification rate and running time of the CPU-GPU algorithmsdepended on multiple factors, including the GPU algorithm selected. BothCPU-GPU algorithms used the same amount of GPU memory for any specificCPU-GPU split, as they both needed to keep track of the same numbers ofvertices and elements on the GPU. As the GPU workload was increased, theamount of GPU memory used increased as well. For both algorithms, as thesize of a mesh increased, the decrease in simplification time increased, asthe GPU workload was increased. The simplification rate of approximately68% that the CPU-GPU marking algorithm achieved was higher than thesimplification rate of approximately 59% that was achieved by the inversereduction algorithm, over ten iterations. This slight increase in simplificationrate provided by the marking algorithm was counterbalanced by an increaseof 5.55% to 11.48% in the running time when the GPU was given the fullworkload. Further simplification is possible if the simplification algorithm wererun for a larger number of iterations. This suggests that the GPU markingalgorithm should be used when a larger simplification rate per iteration isneeded and running time is not a limiting factor. However, the GPU inversereduction algorithm should be used when time is a limiting factor or when alesser simplification rate per iteration is required, such as for smaller meshes.Our results show that certain areas of the surface mesh were repeatedlysimplified over multiple iterations, causing the meshes to look excessively simplifiedin these areas, since element ordering determines the simplification
CPU-GPU Algorithms for Triangular Surface Mesh Simplification 17order. Reordering the mesh elements as a preprocessing step would likelyminimize the repeated simplification of mesh elements in a given area. Meshoptimization may also be useful for improving the quality of the surface meshelements.It would also be interesting to implement a hybrid mesh simplificationalgorithm that takes advantage of the speed of the GPU inverse reductionalgorithm and the simplification rate of the GPU marking algorithm. Thiscould potentially increase the simplification rate as well as decrease the runningtime of the simplification algorithm. Further algorithmic speed may beaccomplished through the utilization of additional CPU cores or additionalGPUs, which could take full advantage of parallelism. This may prove to be especiallyuseful for real-time graphics and scientific visualization applications.5 AcknowledgementsThe work of the first author is supported in part by NSF grants CNS-0720749and NSF CAREER Award OCI-1054459.References1. Y. Afek, E. Gafni, J. Tromp, and P. Vitany. Wait-free test-and-set. In AdrianSegall and Shmuel Zaks, editors, Distributed Algorithms, volume 647 of LectureNotes in Computer Science, pages 85–94. Springer Berlin / Heidelberg, 1992.2. AIM@SHAPE. Aim@shape shape repository 4.0, February 2012.http://shapes.aimatshape.net/.3. M.-E. Algorri and F. Schmitt. Mesh simplification. Computer Graphics Forum,15(3):77–86, 1996.4. C.L. Bajaj, V. Pascucci, and G. Zhuang. Progressive compression and transmissionof arbitrary triangular meshes. In Proc. Visualization ’99, Visualization’99, pages 307–537, 1999.5. D. Brodsky and J.B. Pedersen. A parallel framework for simplification of massivemeshes. In Proc. of the 2003 IEEE Symposium on Parallel and Large-DataVisualization and Graphics, PVG ’03, pages 17–24, Washington, DC, USA, 2003.IEEE Computer Society.6. P. Cignoni, C. Montani, and R. Scopigno. A comparison of mesh simplificationalgorithms. Computers & Graphics, 22:37–54, 1997.7. NVIDIA Corporation. CUDA Toolkit, January 2012.http://developer.nvidia.com/cuda-toolkit-41.8. C. DeCoro and N. Tatarchuk. Real-time mesh simplification using the GPU. InProc. of the 2007 Symposium on Interactive 3D Graphics and Games, I3D ’07,pages 161–166, New York, NY, USA, 2007. ACM.9. F. Dehne, C. Langis, and G. Roth. Mesh simplification in parallel. In ICA3PP’00, pages 281–290, 2000.10. C. Dick, J. Schneider, and R. Westermann. Efficient geometry compression forGPU-based decoding in realtime terrain rendering. Computer Graphics Forum,28(1):67–83, 2009.
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CPU-GPU Algorithms for Triangular Surface Mesh Simplification

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