Computing the Writhing Number of a Polygonal Knot |
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| Authors: | Pankaj K Agarwal Herbert Edelsbrunner and Yusu Wang |
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| Institution: | (1) Department of Computer Science, Duke University, Durham, NC 27708, USA;(2) Raindrop Geomagic, Research Triangle Park, NC 27709, USA |
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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 n1.6.
We also implement a different, simple algorithm and provide
experimental evidence for its practical efficiency. |
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