intersectionMatrix: Compute the intersection matrix of a polygonal link

Description Usage Arguments Details Value Note Note Author(s) References Examples

Description

Compute the intersection matrix of a polygonal link. See details.

Usage

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intersectionMatrix(points3D, ends = c())

Arguments

points3D

an N x 3 matrix of the x, y, z coordinates of a three-dimensional structure

ends

a vector of positive integers defining the separators of the polygonal link

Details

The entries of the intersection matrix are defined as follows. Given two sets of edges A and B we can compute the intersection matrix I=I(A,B) by setting

(I(A,B))_{i,j} = 0

if A_i and B_j do not intersect transversally.

(I(A,B))_{i,j} = +1

if A_i lays over B_j.

(I(A,B))_{i,j} = -1

if A_i lays under B_j. Finally, if A=B we get the skew symmetric square matrix I(A)

Value

An N-1 x N-1 matrix

Note

This is a low-level function.

Note

If ends is not null, the corresponding rows and columns of the intersection matrix are set to zero.

Author(s)

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

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

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##Compute the intersection matrix of a random structure of 20 points
points <- matrix(runif(60,-1,1), ncol = 3)

intersectionMatrix(points)

##Compute the intersection matrix of the trefoil knot
data(Rolfsen.table, package = "Rknots")
trefoil <- Rolfsen.table$"3.1"

intersectionMatrix(trefoil)

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