2008•Journal of Knot Theory and Its RamificationsRequires access

THE WRITHE OF ORIENTED POLYGONAL GRAPHS

Christian Laing, D. W. Sumners

Abstract

Given an edge-oriented polygonal graph in ℝ3, we describe a method for computing the writhe as the average of weighted directional writhe numbers of the graph in a few directions. These directions are determined by the graph and the weights are determined by areas of path-connected open regions on the unit sphere. Within each open region, the directional writhe is constant. We obtain a closed formula which extends the formula for the writhe of a polygon in ℝ3, including the important special case of writhe of embedded open arcs.

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Key concepts: Writhe, Mathematics, Polygon (computer graphics), Polygonal chain, Graph, Combinatorics, Twist, Enumeration