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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

An algorithm for winding numbers for closed polygonal paths


Author: Kenneth O. Leland
Journal: Math. Comp. 29 (1975), 554-558
MSC: Primary 65E05
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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1975-0373246-2
PII: S 0025-5718(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