AlexanderBriggs: Alexander-Briggs reduction of a polygonal knot or link

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

View source: R/AlexanderBriggs.R

Description

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.

Usage

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AlexanderBriggs(points3D, ends = 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

Value

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

Note

This is a low-level function.

Author(s)

Federico Comoglio, [email protected]

Maurizio Rinaldi, maurizio.ri[email protected]

References

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.

See Also

msr

Examples

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

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

Rknots documentation built on May 29, 2017, 1:38 p.m.