Discrete & Computational Geometry

, Volume 32, Issue 1, pp 37–53 | Cite as

Computing the Writhing Number of a Polygonal Knot

  • Pankaj K. AgarwalEmail author
  • Herbert EdelsbrunnerEmail author
  • Yusu WangEmail 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 n1.6. We also implement a different, simple algorithm and provide experimental evidence for its practical efficiency.


Experimental Evidence Simple Algorithm Space Curve Closed Space Global Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Department of Computer Science, Duke University, Durham, NC 27708USA
  2. 2.Raindrop Geomagic, Research Triangle Park, NC 27709USA

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