---
_id: '3990'
abstract:
- lang: eng
  text: 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.
acknowledgement: Partially supported by NSF under grants CCR-00-86013, EIA-9972879
  and NSF under grant CCR-97-12088.
author:
- first_name: Pankaj
  full_name: Agarwal, Pankaj K
  last_name: Agarwal
- first_name: Herbert
  full_name: Herbert Edelsbrunner
  id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
  last_name: Edelsbrunner
  orcid: 0000-0002-9823-6833
- first_name: Yusu
  full_name: Wang, Yusu
  last_name: Wang
citation:
  ama: Agarwal P, Edelsbrunner H, Wang Y. Computing the writhing number of a polygonal
    knot. <i>Discrete &#38; Computational Geometry</i>. 2004;32(1):37-53. doi:<a href="https://doi.org/10.1007/s00454-004-2864-x">10.1007/s00454-004-2864-x</a>
  apa: Agarwal, P., Edelsbrunner, H., &#38; Wang, Y. (2004). Computing the writhing
    number of a polygonal knot. <i>Discrete &#38; Computational Geometry</i>. Springer.
    <a href="https://doi.org/10.1007/s00454-004-2864-x">https://doi.org/10.1007/s00454-004-2864-x</a>
  chicago: Agarwal, Pankaj, Herbert Edelsbrunner, and Yusu Wang. “Computing the Writhing
    Number of a Polygonal Knot.” <i>Discrete &#38; Computational Geometry</i>. Springer,
    2004. <a href="https://doi.org/10.1007/s00454-004-2864-x">https://doi.org/10.1007/s00454-004-2864-x</a>.
  ieee: P. Agarwal, H. Edelsbrunner, and Y. Wang, “Computing the writhing number of
    a polygonal knot,” <i>Discrete &#38; Computational Geometry</i>, vol. 32, no.
    1. Springer, pp. 37–53, 2004.
  ista: Agarwal P, Edelsbrunner H, Wang Y. 2004. Computing the writhing number of
    a polygonal knot. Discrete &#38; Computational Geometry. 32(1), 37–53.
  mla: Agarwal, Pankaj, et al. “Computing the Writhing Number of a Polygonal Knot.”
    <i>Discrete &#38; Computational Geometry</i>, vol. 32, no. 1, Springer, 2004,
    pp. 37–53, doi:<a href="https://doi.org/10.1007/s00454-004-2864-x">10.1007/s00454-004-2864-x</a>.
  short: P. Agarwal, H. Edelsbrunner, Y. Wang, Discrete &#38; Computational Geometry
    32 (2004) 37–53.
date_created: 2018-12-11T12:06:18Z
date_published: 2004-05-01T00:00:00Z
date_updated: 2021-01-12T07:53:42Z
day: '01'
doi: 10.1007/s00454-004-2864-x
extern: 1
intvolume: '        32'
issue: '1'
month: '05'
page: 37 - 53
publication: Discrete & Computational Geometry
publication_status: published
publisher: Springer
publist_id: '2138'
quality_controlled: 0
status: public
title: Computing the writhing number of a polygonal knot
type: journal_article
volume: 32
year: '2004'
...