Computing the writhing number of a polygonal knot

article Computing the writhing number of a polygonal knot published Pankaj Agarwal author Herbert Edelsbrunner author 3FB178DA-F248-11E8-B48F-1D18A9856A870000-0002-9823-6833 Yusu Wang author 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. Springer Nature2004 eng Discrete & Computational Geometry 0179537610.1007/s00454-004-2864-x 32137 - 53 yes P. Agarwal, H. Edelsbrunner, Y. Wang, Discrete & Computational Geometry 32 (2004) 37–53. Agarwal, Pankaj, Herbert Edelsbrunner, and Yusu Wang. “Computing the Writhing Number of a Polygonal Knot.” Discrete & Computational Geometry. Springer Nature, 2004. <a href="https://doi.org/10.1007/s00454-004-2864-x">https://doi.org/10.1007/s00454-004-2864-x</a>. Agarwal P, Edelsbrunner H, Wang Y. 2004. Computing the writhing number of a polygonal knot. Discrete & Computational Geometry. 32(1), 37–53. Agarwal, P., Edelsbrunner, H., & Wang, Y. (2004). Computing the writhing number of a polygonal knot. Discrete & Computational Geometry. Springer Nature. <a href="https://doi.org/10.1007/s00454-004-2864-x">https://doi.org/10.1007/s00454-004-2864-x</a> Agarwal P, Edelsbrunner H, Wang Y. Computing the writhing number of a polygonal knot. Discrete & Computational Geometry. 2004;32(1):37-53. doi:<a href="https://doi.org/10.1007/s00454-004-2864-x">10.1007/s00454-004-2864-x</a> Agarwal, Pankaj, et al. “Computing the Writhing Number of a Polygonal Knot.” Discrete & Computational Geometry, vol. 32, no. 1, Springer Nature, 2004, pp. 37–53, doi:<a href="https://doi.org/10.1007/s00454-004-2864-x">10.1007/s00454-004-2864-x</a>. P. Agarwal, H. Edelsbrunner, and Y. Wang, “Computing the writhing number of a polygonal knot,” Discrete & Computational Geometry, vol. 32, no. 1. Springer Nature, pp. 37–53, 2004. 39902018-12-11T12:06:18Z2026-06-25T13:00:36Z