linkingNumber: Compute the linking number of a polygonal link

In FedericoComoglio/Rknots: Topological Analysis of Knotted Proteins, Biopolymers and 3D Structures

Description

Compute the linking number of a polygonal link

Usage

linkingNumber(points3D, ends, M = c())

Arguments

points3D	an N x 3 matrix of the x, y, z coordinates of a polygonal link
ends	a vector of positive integers defining the separators of the polygonal link
M	the intersection matrix of the polygonal link. If no matrix is provided, the function will compute it (default)

Details

The linking number is defined for a two-component oriented link as the sum of +1 crossings and -1 crossing over all crossings between the two links divided by 2. For components α and β,

lk(α, β) = \frac{1}{2} ∑_{c \in α \cap β} ε(c)

where α \cap β is the set of crossings of α with β, and ε(c) is the sign of the crossing.

Value

lk	the linking number of the polygonal link

Note

This is a low-level function.

Author(s)

Federico Comoglio, [e-mail]

References

Weisstein, Eric W. "Linking Number." From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/LinkingNumber.html

Kauffman, L. Knots and Physics. Teaneck, NJ: World Scientific, p. 19, 1991.

See Also

intersectionMatrix

Examples

link <- makeExampleKnot(k = FALSE)
linkingNumber(points3D = link$points3D, ends = link$ends)

FedericoComoglio/Rknots documentation built on May 6, 2019, 4:35 p.m.