An algorithm for winding numbers for closed polygonal paths
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- by Kenneth O. Leland PDF
- Math. Comp. 29 (1975), 554-558 Request permission
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
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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.
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.
- J. V. Petty, A winding number algorithm for closed polygonal paths, Math. Comp. 27 (1973), 333–337. MR 329216, DOI 10.1090/S0025-5718-1973-0329216-1
- Gordon Thomas Whyburn, Topological analysis, Second, revised edition, Princeton Mathematical Series, No. 23, Princeton University Press, Princeton, N.J., 1964. MR 0165476
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Math. Comp. 29 (1975), 554-558
- MSC: Primary 65E05
- DOI: https://doi.org/10.1090/S0025-5718-1975-0373246-2
- MathSciNet review: 0373246