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Industrial application of exact Boolean operations for meshes

Published:13 May 2010Publication History

ABSTRACT

We present an algorithm for robust Boolean operations of triangulated solids, which is suitable for real-word industrial applications involving meshes with large numbers of triangles. In order to avoid potential robustness problems, which may be caused by (almost) degenerate triangles or by intersections of nearly co-planar triangles, we use filtered exact arithmetic, based on the libraries CGAL and GNU Multi Precision Arithmetic Library. The method consists of two major steps: First we compute the exact intersection of the meshes using a sweep plane algorithm. Second we apply mesh cleaning methods which allow us to generate output which can safely be represented using floating point numbers. The performance of the method is demonstrated by several examples which are taken from applications at ECS Magna Powertrain.

References

  1. Ayala, D., Brunet, P., R. Juan, and I. Navazzo. 1985. Object representation by means of nonminimal division quadtrees and octrees. ACM Trans Graph. 4, 41--59. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. Bernstein, G., and Fussel, D. 2009. Fast, exact, linear Booleans. Comput. Graph. Forum 28 5, 1269--1278.Google ScholarGoogle ScholarCross RefCross Ref
  3. Brönnimann, H., Burnikel, C., and Pion, S. 2001. Interval arithmetic yields efficient dynamic filters for computational geometry. Discrete Appl. Math. 109, 1--2, 25--47. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. Campen, M., and Kobbelt, L. 2010. Exact and robust (Self-) intersections for polygonal meshes. In Proc. Eurographics, Eurographics Assoc. to appear.Google ScholarGoogle Scholar
  5. CGAL, 2009. Computational Geometry Algorithms Library. http://www.cgal.org/, last accessed: Oct 27, 2009.Google ScholarGoogle Scholar
  6. Chang, J.-W., Wang, W., and Kim, M.-S. 2010. Efficient collision detection using a dual OBB-sphere bounding volume hierarchy. Comp. -Aided Design 42, 50--57. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. Dokken, T. 2008. The GAIA project on intersection and implicitization. In Geometric modeling and algebraic geometry, B. Jüttler and R. Piene, Eds. Springer, Berlin, 5--29.Google ScholarGoogle Scholar
  8. Fabri, A., and S. Pion. 2006. A generic lazy evaluation scheme for exact geometric computations. In Proc. 2nd Library-Centric Software Design, 75--84.Google ScholarGoogle Scholar
  9. Fortune, S. 1998. Vertex-rounding a three-dimensional polyhedral subdivision. In Proc. ACM Symp. Comp. Geom., 116--125. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. GNU Multiple Precision Arithmetic Library. http://gmplib.org/, last accessed: Nov 12, 2009.Google ScholarGoogle Scholar
  11. Guttman, A. 1984. R-trees: A dynamic index structure for spatial searching. In ACM SIGMOD International Conference on Management of Data, 47--57. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. Hachenberger, P., and Kettner, L. 2005. Boolean operations on 3d selective Nef complexes: Optimized implementation and experiments. In ACM Symposium on Solid and Physical Modeling (SPM 2005), 163--174. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. Hoffmann, C. M. 2005. Geometric and Solid Modeling: an Introduction. Springer.Google ScholarGoogle Scholar
  14. Hubbard, P. 1996. Approximating polyhedra with spheres for time-critical collision detection. ACM Transactions on Graphics 15, 179--210. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. Jimenez, P., Thomas, F., and Torras, C. 2001. 3D collision detection: a survey. Comput. Graphics 25, 269--285.Google ScholarGoogle ScholarCross RefCross Ref
  16. Laidlaw, D. H., Trumbore, W., and Hughes, J. 1986. Constructive solid geometry for polyhedral objects. SIGGRAPH Computational Graph. 20, 161--170. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. Lo, S., and Wang, W. 2003. An algorithm for the intersection of quadrilateral surfaces by tracing of neighbours. Comput. Methods Appl. Mech. Eng. 192, 2319--2338.Google ScholarGoogle ScholarCross RefCross Ref
  18. Manolopoulos, Y., Nanopoulos, A., Papadopoulos, A., and Theodoridis, Y. 1989. R-Trees: Theory and Applications. Morgan Kaufmann.Google ScholarGoogle Scholar
  19. Park, S. C. 2004. Triangular mesh intersection. The Visual Computer 20, 448--456. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. Pavic, D., Campen, M., and Kobbelt, L. 2010. Hybrid Booleans. Computer Graphics Forum. to appear.Google ScholarGoogle Scholar
  21. Sugihara, K., and Ira, M. 1989. A solid modelling system free from topological inconsisteny. J. Inf. Process. 12, 380--393. Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. Teschner, M., Heidelberger, B., Müller, M., Pomeranets, D., and Gross, M. 2003. Optimized spatial hashing for collision detection of deformable objects. In Proceedings of VMV'03, 47--54.Google ScholarGoogle Scholar
  23. Thibault, W. C., and Naylor, B. 1987. Set operations on polyhedra using binary space partitioning trees. SIGGRAPH Comput. Graph 21, 153--162. Google ScholarGoogle ScholarDigital LibraryDigital Library
  24. Thibault, W. C. 1987. Application of binary space partitioning trees to geometric modeling and ray-tracing. PhD thesis, Georgia Institute of Technology. Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. Thomas, M., and Prosolvia, C. 1997. A fast triangle-triangle intersection test. J. Graphics Tools 22, 25--30. Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. Tropp, O., Tal, A., and Shimshoni, I. 2006. A fast triangle to triangle intersection test for collision detection. Computer Animation and Virtual Worlds 17, 527--535. Google ScholarGoogle ScholarDigital LibraryDigital Library

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        cover image ACM Other conferences
        SCCG '10: Proceedings of the 26th Spring Conference on Computer Graphics
        May 2010
        180 pages
        ISBN:9781450305587
        DOI:10.1145/1925059

        Copyright © 2010 ACM

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        Publication History

        • Published: 13 May 2010

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