Computing the writhing number of a polygonal knot

P. Agarwal, H. Edelsbrunner, Y. Wang, Discrete & Computational Geometry 32 (2004) 37–53.

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Journal Article | Published
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Abstract
The writhing number measures the global geometry of a closed space curve or knot. We show that this measure is related to the average winding number of its Gauss map. Using this relationship, we give an algorithm for computing the writhing number for a polygonal knot with n edges in time roughly proportional to n(1.6). We also implement a different, simple algorithm and provide experimental evidence for its practical efficiency.
Publishing Year
Date Published
2004-05-01
Journal Title
Discrete & Computational Geometry
Acknowledgement
Partially supported by NSF under grants CCR-00-86013, EIA-9972879 and NSF under grant CCR-97-12088.
Volume
32
Issue
1
Page
37 - 53
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Agarwal P, Edelsbrunner H, Wang Y. Computing the writhing number of a polygonal knot. Discrete & Computational Geometry. 2004;32(1):37-53. doi:10.1007/s00454-004-2864-x
Agarwal, P., Edelsbrunner, H., & Wang, Y. (2004). Computing the writhing number of a polygonal knot. Discrete & Computational Geometry, 32(1), 37–53. https://doi.org/10.1007/s00454-004-2864-x
Agarwal, Pankaj, Herbert Edelsbrunner, and Yusu Wang. “Computing the Writhing Number of a Polygonal Knot.” Discrete & Computational Geometry 32, no. 1 (2004): 37–53. https://doi.org/10.1007/s00454-004-2864-x.
P. Agarwal, H. Edelsbrunner, and Y. Wang, “Computing the writhing number of a polygonal knot,” Discrete & Computational Geometry, vol. 32, no. 1, pp. 37–53, 2004.
Agarwal P, Edelsbrunner H, Wang Y. 2004. Computing the writhing number of a polygonal knot. Discrete & Computational Geometry. 32(1), 37–53.
Agarwal, Pankaj, et al. “Computing the Writhing Number of a Polygonal Knot.” Discrete & Computational Geometry, vol. 32, no. 1, Springer, 2004, pp. 37–53, doi:10.1007/s00454-004-2864-x.

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