intersectionMatrix: Compute the intersection matrix of a polygonal link
In FedericoComoglio/Rknots: Topological Analysis of Knotted Proteins, Biopolymers and 3D Structures

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

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

1	intersectionMatrix(points3D, ends = c())

`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

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)

An N-1 x N-1 matrix

This is a low-level function.

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

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

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

##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)