Abstract
We experimentally study the reliability of geometric software for point location in simple polygons. As expected, the code we tested works very well for random query points. However, our experiments reveal that the tested code often fails for more challenging degenerate and also nearly degenerate queries.
Partially supported by DFG grant SCHI 858/1-1.
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References
Akenine-Möller, T., Haines, E.: Real-Time Rendering, 2nd edn. AK Peters, Ltd. (2002)
Auer, T., Held, M.: Heuristics for the generation of random polygons. In: Proc. of CCCG 1996, pp. 38–44 (1996)
CGAL, Computational Geometry Algorithms Library, http://www.cgal.org
Forrest, A.R.: Computational geometry in practice. In: Earnshaw, R.A. (ed.) Fundamental Algorithms for Computer Graphics. NATO ASI, vol. F17, pp. 707–724. Springer, Heidelberg (1985)
Franklin, W.R.: PNPOLY–point inclusion in polygon test, http://www.ecse.rpi.edu/Homepages/wrf/Research/Short_Notes/pnpoly.html
Hacker, R.: Certification of algorithm 112: position of point relative to polygon. Commun. ACMÂ 5, 606 (1962)
Haines, E.: Point in polygon strategies. In: Heckbert, P. (ed.) Graphics Gems IV, pp. 24–46. Academic Press, Boston (1994), http://tog.acm.org/editors/erich/ptinpoly/
Haran, I., Halperin, D.: An experimental study of point location in general planar arrangements. In: Proc. of ALENEX 2006, pp. 16–25 (2006)
Kettner, L., Mehlhorn, K., Pion, S., Schirra, S., Yap, C.: Classroom examples of robustness problems in geometric computations. Comput. Geom. Theory Appl. 40(1), 61–78 (2008)
Mehlhorn, K., Näher, S.: LEDA: A Platform for Combinatorial and Geometric Computing. Cambridge University Press, Cambridge (2000)
Nassar, A., Walden, P., Haines, E., Dickens, T., Capelli, R., Narasimhan, S., Jam, C., MacMartin, S.: Fastest point in polygon test. Ray Tracing News 5(3) (1992)
Schirra, S.: Companion pages to How reliable are practical point in polygon strategies? http://wwwisg.cs.uni-magdeburg.de/ag/pointInPolygonReliability/
Shewchuk, J.R.: Adaptive precision floating-point arithmetic and fast robust geometric predicates. Discrete & Computational Geometry 18(3), 305–368 (1997)
Shimrat, M.: Algorithm 112: position of point relative to polygon. Commun. ACMÂ 5, 434 (1962)
Snoeyink, J.: Point location. In: Goodman, J.E., O’Rourke, J. (eds.) Handbook of Discrete and Computational Geometry, ch. 34, 2nd edn., pp. 767–786. CRC Press LLC, Boca Raton (2004)
Walker, R., Snoeyink, J.: Practical point-in-polygon tests using CSG representations of polygons. In: Goodrich, M.T., McGeoch, C.C. (eds.) ALENEX 1999. LNCS, vol. 1619, pp. 114–123. Springer, Heidelberg (1999)
Weiler, K.: An incremental angle point in polygon test. In: Heckbert, P. (ed.) Graphics Gems IV, pp. 16–23. Academic Press, Boston (1994)
Yap, C.-K.: Towards exact geometric computation. Comput. Geom.–Theory and Appl. 7, 3–23 (1997)
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Schirra, S. (2008). How Reliable Are Practical Point-in-Polygon Strategies?. In: Halperin, D., Mehlhorn, K. (eds) Algorithms - ESA 2008. ESA 2008. Lecture Notes in Computer Science, vol 5193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87744-8_62
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DOI: https://doi.org/10.1007/978-3-540-87744-8_62
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