Computing the writhing number of a polygonal knot

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.