A point-in-polygon method based on a quasi-closest point (original) (raw)

Abstract

This paper presents a numerically stable solution to a point-in-polygon problem by combining the orientation method and the uniform subdivision technique. We define first a quasi-closest point that can be locally found through the uniform subdivision cells, and then we provide the criteria for determining whether a point lies inside a polygon according to the quasi-closest point. For a large number of points to be tested against the same polygon, the criteria are employed to determine the inclusion property of an empty cell as well as a test point. The experimental tests show that the new method resolves the singularity of a test point on an edge without loss of efficiency. The GIS case study also demonstrates the capability of the method to identify which region contains a test point in a map.

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References (21)

  1. Bresenham, J.E., 1965. Algorithm for computer control of a digital plotter. IBM Systems Journal 4 (1), 25-30.
  2. Cleary, J.G., Wyvill, G., 1988. Analysis of an algorithm for fast ray tracing using uniform space subdivision. The Visual Computer 4 (2), 65-83.
  3. Ellis, F., 2001. Vector Overlay Processing-Specific Theory. GIS Self Learning Tool-University of Melbourne, Department of Geomatics, Melbourne, Australia. /http://www.sli.unimelb.edu.au/gisweb/VOModule/VO\_Theory.pdfS [last access: 22 Oct, 2009].
  4. Etzion, M., Rappoport, A., 1997. On compatible star decomposition of simple polygons. IEEE Transactions on Visualization and Computer Graphics 3 (1), 87-95.
  5. Feito, F.R., Torres, J.C., Urena, A., 1995. Orientation, simplicity, and inclusion test for planar polygons. Computers & Graphics 19 (4), 595-600.
  6. Fujimoto, A., Iwata, K., 1983. Jag-free images on raster displays. IEEE Computer Graphics and Applications 3 (9), 26-34.
  7. Fujimoto, A., Tanaka, T., Iwata, K., 1986. ARTS: accelerated ray-tracing system. IEEE Computer Graphics and Applications 6 (4), 16-26.
  8. Gombosi, M., Zalik, B., 2005. Point-in-polygon tests for geometric buffers. Computers & Geosciences 31 (10), 1201-1212.
  9. Hormann, K., Agathos, A., 2001. The point in polygon problem for arbitrary polygons. Computational Geometry 20 (3), 131-144.
  10. Huang, C.W., Shih, T.Y., 1997. On the complexity of point-in-polygon algorithms. Computers & Geosciences 23 (1), 109-118.
  11. Jime ´nez, J.J., Feito, F.R., Segura, R.J., 2009. A new hierarchical triangle-based point-in-polygon data structure. Computers & Geosciences 35 (9), 1843-1853, doi:10.1016/j.cageo.2008.09.013.
  12. Li, J., Wang, W.C., Wu, E.H., 2007. Point-in-polygon tests by convex decomposition. Computers & Graphics 31 (4), 636-648.
  13. Martinez, F., Rueda, A.J., Feito, F.R., 2006. The multi-L-REP decomposition and its application to a point-in-polygon inclusion test. Computers & Graphics 30 (6), 947-958.
  14. Nordbeck, S., Rystedt, B., 1967. Computer cartography point-in-polygon programs. BIT Numerical Mathematics 7 (1), 39-64.
  15. Preparata, F.P., Shamos, M.I., 1991. In: Computational Geometry: An Introduction. Springer, New York 390 pp.
  16. O'Rourke, J., 2000. In: Computational Geometry in C. Cambridge University Press, Cambridge 376 pp.
  17. Salomon, K.B., 1978. An efficient point-in-polygon algorithm. Computers & Geosciences 4 (2), 173-178.
  18. Taylor, G., 1994. Point in polygon test. Survey Review 32 (254), 479-484.
  19. Wang, W.C., Li, J., Wu, E.H., 2005. 2D point-in-polygon test by classifying edges into layers. Computers & Graphics 29 (3), 427-439.
  20. Zalik, B., Clapworthy, G., Oblonsek, C., 1997. An efficient code-based voxel- traversing algorithm. Computer Graphics Forum 16 (2), 119-128.
  21. Zalik, B., Kolingerova, I., 2001. A cell-based point-in-polygon algorithm suitable for large sets of points. Computers & Geosciences 27 (10), 1135-1145.