Korean Journal of Computational Design and Engineering (한국CDE학회논문집)

Society for Computational Design and Engineering (한국CDE학회)
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GPU Algorithm for Outer Boundaries of a Triangle Set

GPU를 이용한 삼각형 집합의 외경계 계산 알고리즘

  • 경민호 (아주대학교 미디어학과)
  • Received : 2012.01.30
  • Accepted : 2012.06.18
  • Published : 2012.08.01
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Abstract

We present a novel GPU algorithm to compute outer cell boundaries of 3D arrangement subdivided by a given set of triangles. An outer cell boundary is defined as a 2-manifold surface consisting of subdivided polygons facing outward. Many geometric problems, such as Minkowski sum, sweep volume, lower/upper envelop, Bool operations, can be reduced to finding outer cell boundaries with specific properties. Computing outer cell boundaries, however, is a very time-consuming job and also is susceptible to numerical errors. To address these problems, we develop an algorithm based on GPU with a robust scheme combining interval arithmetic and multi-level precisions. The proposed algorithm is tested on Minkowski sum of several polygonal models, and shows 5-20 times speedup over an existing algorithm running on CPU.

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References

  1. Sacks, E., Milenkovic, V. and Kyung, M.-H., 2011, Controlled Linear Perturbation, Computer-Aided Design, 43(10), pp. 1250-1257. https://doi.org/10.1016/j.cad.2011.06.015
  2. Abrams, S. and Allen, P., 2000, Computing Swept Volums, Journal of Visualization and Computer Animation, 11, pp. 69-82. https://doi.org/10.1002/1099-1778(200005)11:2<69::AID-VIS219>3.0.CO;2-7
  3. Tilove, R.B. and Requicha, A., 1980, Closure of Boolean Operations on Geometric Entities, Computer-Aided Design, 12(5), pp. 219-220. https://doi.org/10.1016/0010-4485(80)90025-1
  4. Requicha, A., 1985, Boolean Operations in Solid Modeling: Boundary Evaluation and Merging Algorithms, Proc. IEEE, pp. 30-44.
  5. Pach, J. and Sharir, M., 1989, The Upper Envelope of Piecewise Linear Functions and the Boundary of a Region Enclosed by Convex Plates: Combinatorial Analysis, Discrete & Computational Geometry, 4, pp. 291-309. https://doi.org/10.1007/BF02187732
  6. Arnovo, B. and Sharir, M., 1990, Triangles in Space or Building (and analyzing) Castles in the Air, Combinatorica, 10(2), pp. 137-173. https://doi.org/10.1007/BF02123007
  7. Halperin, D., 2002, Robust Geometric Computing in Motion", The Journal of Robotics Research, 21(3), pp. 219-232. https://doi.org/10.1177/027836402320556412
  8. Pach, J. and Sharir, M., 2009, Combinatorial Geometry and Its Algorithmic Applications: The Alcala Lectures, AMS.
  9. de Berg, M., Guibas, L.J. and Halperin, D., 1994, Vertical Decomposition for Triangles in 3-space, Proc. the 10th Annu. ACM Symposium on Computational Geometry.
  10. de Berg, M., Dobrindt, K. and Schwarzkopf, O., 1994, On Lazy Randomized Incremental Construction, Discrete & Computational Geometry, 14(1), pp 261-286.
  11. Agarwal, P. and Sharir, M., 1998, Arrangements and Their Applications, Handbook of Computational Geometry, Elsevier Sience Publishers, pp. 49-119.
  12. Sharir, M., 2007, Arrangements in Geometry: Recent Advances and Challenges, Proc. the 15th annual European conference on Algorithms, Eilat, Isarael, pp. 12-16.
  13. Krishnamurthy, Sara McMains, S. and Haller, K., 2009, Accelerating Geometric Queries using the GPU, Proc. 2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling, pp. 199-210.
  14. Li, W. and McMains, S., 2011, Voxelized Minkowski Sum Computation on the GPU with Robust Culling, Computer-Aided Design, 43(10), pp 1270-1283. https://doi.org/10.1016/j.cad.2011.06.022
  15. Halperin, D. and Shelton, C., 1998, A Perturbation Scheme for Spherical Arrangements with Application to Molecular Modeling, Computational Geometry: Theory and Applications, 10(4), pp. 273-288. https://doi.org/10.1016/S0925-7721(98)00014-5
  16. Halperin, D. and Leiserowitz, E., 2004, Controlled Perturbation for Arrangements of Circles, International Journal of Computational Geometry and Applications, 14(4), pp. 277-310. https://doi.org/10.1142/S0218195904001482
  17. Halperin, D. and Raab, S., 1999, Controlled Perturbation for Arrangements of Polyhedral Surfaces with Application to Swept Volumes, Proc. 15th Annual ACM Symposium on Computational Geometry, pp 163-172.
  18. Milenkovic, V. and Sacks, E., 2012, Adaptive-Precision Controlled Perturbation, submitted to Symposium on Computational Geometry.
  19. Kyung, M.-H., Keun, K.-J. and Choi, J.-J., 2011, Robust GPU-based Intersection Algorithm for a Large Triangle Set, Journal of Korea Computer Graphics, 17(3), pp. 9-20.
  20. Lozano-Perez, T., 1983, Spatial Planning: A Configuration Space Approach, IEEE Transactions on Computers, C-32(2), pp. 108-120. https://doi.org/10.1109/TC.1983.1676196
  21. Guibas, L.J., Ramshaw, L. and Stolfi, J., 1983, A Kinetic Framework for Computational Geometry, Proc. 24th Annu. IEEE Symposium on Foundation of Computer Science, pp. 100-111.
  22. Kaul, A. and O'Connor, M.A., 1993, Computing Minkowski Sums of Regular Polyhedra, Technical Report RC 18891(82557), IBM T. J. Watson Research Center, Yorktown Heights, N. Y..
  23. Laurent Fousse, Guillaume Hanrot, Vincent Lefevre, Patrick Pelissier, Paul Zimmermann, 2007, MPFR: A Multiple-Precision Binary Floating-Point Library With Correct Rounding, ACM Transactions on Mathematical Software, 33(2).