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An algorithm for winding numbers for closed polygonal paths


Author: Kenneth O. Leland
Journal: Math. Comp. 29 (1975), 554-558
MSC: Primary 65E05
DOI: https://doi.org/10.1090/S0025-5718-1975-0373246-2
MathSciNet review: 0373246
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Abstract: A winding number algorithm for closed polygonal paths (not necessarily simple) based on the notion of counting the number of oriented "signed cuts" of the negative x axis by the path is given. The algorithm is justified by a theory of integer-valued analogues of the complex log function. The algorithm is much simpler than those of J. V. Petty [this journal, v. 27, 1973, pp. 333-337] and H. R. P. Ferguson [Notices Amer. Math. Soc., v. 20, 1973, p. A-211] and leads to faster computation.


References [Enhancements On Off] (What's this?)

  • [1] H. R. P. FERGUSON, Point in Polygon Algorithms: A Critical Element in Urban Data Systems, Urban Data Center, Univ. of Washington, NTIS PB219-671; Notices Amer. Math. Soc., v. 20, 1973. Abstract #701-68-2.
  • [2] K. O. LELAND, "Computer generated winding numbers and integer valued analogues of the log function" (Preliminary Report), Notices Amer. Math. Soc., v. 20, 1973. Abstract #73T-B177.
  • [3] J. V. PETTY, "A winding number algorithm for closed polygonal paths," Math. Comp., v. 27, 1973, pp. 333-337. MR 0329216 (48:7558)
  • [4] G. T. WHYBURN, Topological Analysis, 2nd. rev. ed., Princeton Math. Series, no. 23, Princeton Univ. Press, Princeton, N. J., 1964. MR 29 #2758. MR 0165476 (29:2758)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1975-0373246-2
Keywords: Computation of winding numbers, closed polygonal paths, turning point string, computer program, integer-valued log function analogues, topological analysis, signed cut
Article copyright: © Copyright 1975 American Mathematical Society

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