Rknots (version 1.3.0)

msr: Minimal Structure Reduction

Description

Reduce a polygonal link to its minimal structure by applying Generalized Reidemeister Moves.

Usage

msr(points3D, ends = c(), n = 100)

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

n

the number of iterations

Value

• Returns a list of three elements
• points3D
  an $M$ x 3 matrix of the $x$, $y$, $z$ coordinates of the reduced structure
• ends
  a vector of positive integers (if a non empty ends has been provided as an argument defining the separators of the reduced structure
• M
  the intersection matrix of the reduced structure

Details

A minimal structure for a polygonal link $L$ is a nested sequence of subsets of $L$: $$L \supset L_1 \supset \ldots \supset L_N$$ that cannot be extended. Each inclusion corresponds to a Generalized Reidemeister Move.

References

Comoglio F. and Rinaldi M. A Topological Framework for the Computation of the HOMFLY Polynomial and Its Application to Proteins (2011) PLoS ONE 6(4): e18693, doi:10.1371/journal.pone.0018693 ArXiv:1104.3405

Examples

knot <- makeExampleKnot()
reduced <- msr(points3D = knot)

## 3D plot of both the trefoil and its reduced structure
plotKnot3D(knot, ends = c(), radius = 0.01, lwd = 2.5)
plotKnot3D(reduced$points3D, reduced$ends, colors = 'red', radius = 0.1, lwd = 2.5)