AlexanderBriggs: Alexander-Briggs reduction of a polygonal knot or link
In FedericoComoglio/Rknots: Topological Analysis of Knotted Proteins, Biopolymers and 3D Structures

Description Usage Arguments Value Note Author(s) References See Also Examples

Apply the Alexander-Briggs reduction to a polygonal knot or link. This method is based on the concept of elementary deformation, which consists in the replacement of two sides of a triangle with the third provided that the triangle is empty. From version 1.1 a fast implementation for links is provided.

1	AlexanderBriggs(points3D, ends = c())

`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

A list of two slots:

`points3D`	an M x 3 matrix of the x, y, z coordinates of the reduced structure, M≤q N
`ends`	if a non empty `ends` has been provided as an input, a vector of positive integers defining the separators of the reduced structure

This is a low-level function.

Federico Comoglio, federico.comoglio@bsse.ethz.ch

Maurizio Rinaldi, maurizio.rinaldi@pharm.unipmn.it

Reidemeister K (1926), Abh Math Sem Univ Hamburg 5: 24-32.

Alexander JW, Briggs GB (1926) On types of knotted curves. Ann of Math 28: 562-586.

msr

#reducing a knot
k <- makeExampleKnot(k = TRUE)
AlexanderBriggs(points3D = k)

#reducing a link
k <- makeExampleKnot(k = FALSE)
AlexanderBriggs(points3D = k$points3D, ends = k$ends)