# Computing the writhing number of a polygonal knot

Agarwal P, Edelsbrunner H, Wang Y. 2002. Computing the writhing number of a polygonal knot. Proceedings of the 13th annual ACM-SIAM symposium on Discrete algorithms. SODA: Symposium on Discrete Algorithms, 791–799.

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Author

Agarwal, Pankaj;
Edelsbrunner, Herbert

^{ISTA}^{}; Wang, YusuAbstract

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

2002-01-01

Proceedings Title

Proceedings of the 13th annual ACM-SIAM symposium on Discrete algorithms

Acknowledgement

NSF under grants CCR-00-86013 and EIA-9972879, NSF under grant CCR-97-12088.

Page

791 - 799

Conference

SODA: Symposium on Discrete Algorithms

Conference Location

San Francisco, CA, USA

Conference Date

2002-01-06 – 2002-01-08

ISBN

IST-REx-ID

### Cite this

Agarwal P, Edelsbrunner H, Wang Y. Computing the writhing number of a polygonal knot. In:

*Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms*. SIAM; 2002:791-799.Agarwal, P., Edelsbrunner, H., & Wang, Y. (2002). Computing the writhing number of a polygonal knot. In

*Proceedings of the 13th annual ACM-SIAM symposium on Discrete algorithms*(pp. 791–799). San Francisco, CA, USA: SIAM.Agarwal, Pankaj, Herbert Edelsbrunner, and Yusu Wang. “Computing the Writhing Number of a Polygonal Knot.” In

*Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms*, 791–99. SIAM, 2002.P. Agarwal, H. Edelsbrunner, and Y. Wang, “Computing the writhing number of a polygonal knot,” in

*Proceedings of the 13th annual ACM-SIAM symposium on Discrete algorithms*, San Francisco, CA, USA, 2002, pp. 791–799.Agarwal, Pankaj, et al. “Computing the Writhing Number of a Polygonal Knot.”

*Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms*, SIAM, 2002, pp. 791–99.