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.

**[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