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 |

`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

1 2 3 4 5 6 7 8 9 10 | ```
##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)
``` |

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