공차를 고려한 다각형 영역의 내외부 판별 알고리즘

Tolerance-based Point Classification Algorithm for a Polygonal Region

  • 정연찬 (큐빅테크 큐빅기술연구소) ;
  • 박준철 (큐빅테크 큐빅기술연구소)
  • 발행 : 2002.06.01

초록

This paper details a robust and efficient algorithm for point classification with respect to a polygon in 2D real number domain. The concept of tolerance makes this algorithm robust and consistent. It enables to define‘on-boundary’ , which can be interpreted as either‘in-’or‘out-’side region, and to manage rounding errors in floating point computation. Also the tolerance is used as a measure of reliability of point classifications. The proposed algorithm is based on a ray-intersection technique known as the most efficient, in which intersections between a ray originating from a given test point and the boundary of a region are counted. An odd number of intersections indicates that the point is inside region. For practical examples the algorithm is most efficient because most edges of the polygon region are processed by simple bit operations.

키워드

참고문헌

  1. Geometric Modeling Mortenson, M. E.
  2. Computational Geometry in C($2^{nd}$ ed.) O'Rourke, Joseph.
  3. Computational Geometry-An Introduction Preparata, F. P;Shamos, M. I.
  4. The Computer Journal v.27 no.4 Consistency in point-in-polygon tests Burton, F. W.;Kollias, V. J.;Kollias, J. G. https://doi.org/10.1093/comjnl/27.4.375
  5. Computer and Graphics v.19 no.4 Orientation, simplicity and inclusion test for planar polygons Feito, F.;Torres, J. C.;Urena, A. https://doi.org/10.1016/0097-8493(95)00037-D
  6. Graphic Gems Point in Polygon Strategies Haines, E.
  7. Computers and Geosciences v.23 no.1 On the compluxity of point-in-polygon algorithms Huang, C-. W.;Shih, T. -Y. https://doi.org/10.1016/S0098-3004(96)00071-4
  8. Computer-Aided Design v.29 no.11 A robust point inclusion algorithm for regions bounded by parametric curve segments Hui, K. C. https://doi.org/10.1016/S0010-4485(97)00023-7
  9. Survey Review 1994 v.32 no.254 Point in polygon test Taloy, G.
  10. Graphic Gems An Incremental Angle Point in Polygon Test Weiler, K.
  11. Computers & Graphics v.24 An algebraic algorithm for point inclusion query Wu, H.;Gong, J.;Li, D.;Shi, W. https://doi.org/10.1016/S0097-8493(00)00054-6
  12. Proceedings of ASME Design Technical Conference, 16-th Design Automation Conference Two robust point-in-polygon tests based on the 4×4 determinant method Yamaguchi, F.;Niizeki, M.;Fukunaga, H.
  13. Computer-Aided Design v.25 no.9 Robustness in Solid Modeling: a tolerance-based intuitionistic approach Fing, S.;Bruderlin, B.;Zhu, X. https://doi.org/10.1016/0010-4485(93)90072-V
  14. Sculptured Surface Machining - Theory and Applications Choi, B. K.;Robert, B.;Jerard
  15. The Initial Graphics Exchange Specification (IGES)(Version 5.2) IGES/PDES Organization
  16. Computer Graphics: Principles and Practice($2^{nd}$ ed.) Foley, J.;Vam, D. A.;Feiner, S.;Hughes, J.