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On the Reliability of Triangle Intersection in 3D

  • Conference paper
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Computational Science and Its Applications — ICCSA 2003 (ICCSA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2669))

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Abstract

Implementors of triangle/triangle intersection tests often opt to forego exact calculations for speed reasons. It is widely known that such code will fail for certain inputs, but it is not evident from the literature that published intersection tests implemented using floating-point arithmetic are not stable. We show how such a test can fail on a triangle pair that is widely separated in space. We find that an exact intersection test can be implemented with a modest speed penalty.

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References

  1. M.J. Aftosmis, M.J. Berger, and J.E. Melton. Robust and efficient cartesian mesh generation for component-based geometry. In 35th AIAA Aerospace Sciences Meeting, Reno NV, USA, January 1997. AIAA97-0196.

    Google Scholar 

  2. Hervé Brönnimann, Christoph Burnikel, and Sylvain Pion. Interval arithmetic yields efficient dynamic filters for computational geometry. In Proc. 14th Annu. ACM Sympos. Comput. Geom., pages 165–174, 1998.

    Google Scholar 

  3. Christoph Burnikel, Stefan Funke, and Michael Seel. Exact geometric predicates using cascaded computation. In Proc. 14th Annu. ACM Sympos. Comput. Geom., pages 175–183, 1998.

    Google Scholar 

  4. Christoph Burnikel, Kurt Mehlhorn, and Stefan Schirra. The LEDA class real number. Technical Report MPI-I-96-1-001, Max-Planck-Institut fur Informatik, January 1996.

    Google Scholar 

  5. CORE. The core library, v1.5. Web Page, 2002. http://www.cs.nyu.edu/exact/core/.

  6. Marina Gavrilova and Jon Rokne. Reliable line segment intersection testing. Computer-Aided Design, 32:737–745, 2000.

    Article  Google Scholar 

  7. S. Gottschalk, Ming C. Lin, and D. Manocha. OBBTree: A hierarchical structure for rapid interference detection. In ACM Siggraph, 1996.

    Google Scholar 

  8. Martin Held. ERIT: A collection of efficient and reliable intersection tests. Journal of Graphics Tools, 2(4):25–44, 1997.

    MATH  MathSciNet  Google Scholar 

  9. V. Karamcheti, C. Li, I. Pechtchanski, and C. Yap. A core library for robust numeric and geometric computation. In Proc. 15th Annual ACM Symp. Comput. Geom., pages 351–359, 1999.

    Google Scholar 

  10. Michael Karasick, Derek Lieber, and Lee R. Nackman. Efficient delaunay triangulation using rational arithmetic. ACM Transactions on Graphics, 10(1):71–91, January 1991.

    Article  Google Scholar 

  11. Chen Li and Chee Yap. Recent progress in exact geometric computation. http://cs.nyu.edu/exact/doc/dimacs.ps.gz, June 2001.

  12. K. Mehlhorn and S. Naher. The LEDA Platform of Combinatorial and Geometric Computing. Cambridge University Press, 1999.

    Google Scholar 

  13. Tomas Möller. A fast triangle-triangle intersection test. Journal of Graphics Tools, 2(2): 25–30, 1997.

    Google Scholar 

  14. Joseph O’Rourke. Computational Geometry in C. Cambridge University Press, second edition, 1998.

    Google Scholar 

  15. T. Ottmann, G. Theimt, and C. Ullrich. Numerical stability of geometric algorithms. In Proceedings of the third annual symposium on Computational geometry, pages 119–125. ACM Press, 1987.

    Google Scholar 

  16. Jonathan Richard Shewchuk. Adaptive precision floating-point arithmetic and fast robust geometric predicates. Discrete and Computational Geometry, 18(3):305–363, October 1997. Source code available at http://www.cs.cmu.edu/~quake/robust.html.

    Article  MATH  MathSciNet  Google Scholar 

  17. Chee Yap and Thomas Dubé. The exact computation paradigm. In Ding-Zhu Du and Frank Hwang, editors, Computing in Euclidean Geometry. World Scientific, second edition, 1995.

    Google Scholar 

  18. Chee K. Yap. Robust geometric computation. In Jacob E. Goodman and Joseph O’Rourke, editors, Handbook of Discrete and Computational Geometry. CRC Press, 1997.

    Google Scholar 

  19. Afra Zomorodian and Herbert Edelsbrunner. Fast software for box intersections. International Journal of Computational Geometry and Applications, 12:143–172, 2002.

    Article  MATH  Google Scholar 

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© 2003 Springer-Verlag Berlin Heidelberg

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Robbins, S., Whitesides, S. (2003). On the Reliability of Triangle Intersection in 3D. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44842-X_94

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  • DOI: https://doi.org/10.1007/3-540-44842-X_94

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40156-8

  • Online ISBN: 978-3-540-44842-6

  • eBook Packages: Springer Book Archive

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