Computing the writhing number of a polygonal knot

Authors:
Pankaj K. Agarwal;Herbert Edelsbrunner;Yusu Wang
Affiliations:
Duke University, Durham, North Carolina;Duke University, Durham and Raindrop Geomagic, Research Triangle Park, North Carolina;Duke University, Durham, North Carolina
Venue:
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Year:
2002

Citing 2
Cited 2

Cutting hyperplanes for divide-and-conquer

Discrete & Computational Geometry
Computational geometry: algorithms and applications

Computational geometry: algorithms and applications

Protein similarity from knot theory and geometric convolution

RECOMB '04 Proceedings of the eighth annual international conference on Resaerch in computational molecular biology
Modeling time and topology for animation and visualization with examples on parametric geometry

Theoretical Computer Science

Quantified Score

Hi-index	0.00

Visualization

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.