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Exact, robust and efficient full visibility computation in Plücker space

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Abstract

We present a set of new techniques to compute an exact polygon-to-polygon visibility in Plücker space. The contributions are based on the definition of the minimal representation of lines stabbing two convex polygons. The new algorithms are designed to indicate useless computations, which results in more compact visibility data, faster to exploit, and in a reduced computation time. We also define a simple robust and exact solution to handle degeneracies, where previous methods proposed aggressive solutions.

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References

  1. Bittner, J.: Hierarchical Techniques for Visibility Computations. Dissertation, Czech Technical University in Prague (2002)

  2. Boissonnat, J.D., Yvinec, M.: Algorithmic Geometry (translated by Hervé Brönnimann). Cambridge University Press, Cambridge UK (1998)

    MATH  Google Scholar 

  3. Charneau, S., Aveneau, L., Fuchs, L.: Plücker space and polygon to polygon visibility computation with geometric algebra. Tech. rep., Laboratoire SIC, University of Poitiers, http://www.sic.sp2mi.univ-poitiers.fr/charneau (2006)

  4. Haumont, D., Mäkinen, O., Nirenstein, S.: A low dimensional framework for exact polygon-to-polygon occlusion queries. In: Proceedings of the Eurographics Symposium on Rendering, pp. 211–222 (2005)

  5. Laine, S., Aila, T., Assarsson, U., Lehtinen, J., Akenine-Möller, T.: Soft shadow volumes for ray tracing. ACM Trans. Graph. 24(3), 1156–1165 (2005)

    Article  Google Scholar 

  6. Mora, F., Aveneau, L.: Fast and exact direct illumination. In: Proceedings of CGI’2005, pp. 191–197. IEEE Computer Society, Stony Brooks University, New York, USA (2005)

    Google Scholar 

  7. Mora, F., Aveneau, L., Mériaux, M.: Coherent and exact polygon-to-polygon visibility. In: Proceedings of WSCG’05, pp. 87–94. UNION Agency – Science Press, University of West Bohemia, Plzen, Czech Republic (2005)

    Google Scholar 

  8. Naylor, B., Amanatides, J., Thibault, W.: Merging BSP trees yields polyhedral set operations. In: Proceedings of the 17th Annual Conference on Computer Graphics and Interactive Techniques, pp. 115–124. ACM, New York (1990)

  9. Nirenstein, S.: Fast and Accurate Visibility Preprocessing. Dissertation, University of Cape Town (2003)

  10. Nirenstein, S., Blake, E., Gain, J.: Exact from-region visibility culling. In: Proceedings of the 13th Eurographics Workshop on Rendering, pp. 191–202. Eurographics Association, Aire-la-Ville, Switzerland, Switzerland (2002)

  11. Plücker, J.: On a new geometry of space. Phil. Trans. R. Soc. London 155, 725–791 (1865)

    Article  Google Scholar 

  12. Pu, F.-T., Mount, D.M.: Binary space partitions in Plücker space. In: Selected Papers from the International Workshop on Algorithm Engineering and Experimentation, vol. 32, pp. 94–113. ALENEX’99, Springer, Berlin Heidelberg New York (1999)

  13. Sommerville, D.M.L.Y.: Analytical Geometry of Three Dimensions. Cambridge University Press, Cambridge, UK (1959)

    Google Scholar 

  14. The Free Software Foundation: GMP: The GNU Multiple Precision Arithmetic Library. http://www.swox.com/gmp (Cited 2006)

  15. Wald, I.: Realtime Ray Tracing and Interactive Global Illumination. Dissertation, Saarland University (2004)

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Correspondence to Sylvain Charneau.

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Charneau, S., Aveneau, L. & Fuchs, L. Exact, robust and efficient full visibility computation in Plücker space. Visual Comput 23, 773–782 (2007). https://doi.org/10.1007/s00371-007-0129-4

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