contract: Edge contraction

In simplextree: Provides Tools for Working with General Simplicial Complexes

Description

Performs an edge contraction.

Usage

contract(st, edge)

Arguments

st	a simplex tree.
edge	an edge to contract, as a 2-length vector.

Details

This function performs an edge contraction in the sense described by (1), which is summarized here. Given an edge {va, vb}, vb is contracted to va if vb is removed from the complex and the link of va is augmented with the link of vb. This may be thought as applying the mapping:

f(u) = va

if u = vb and identity otherwise, to all simplices in the complex.
edge is not sorted prior to contraction: the second vertex of the edge is always contracted to the first. Note that edge contraction is not symmetric.

References

1. Boissonnat, Jean-Daniel, and Clement Maria. "The simplex tree: An efficient data structure for general simplicial complexes." Algorithmica 70.3 (2014): 406-427.

Examples

st <- simplex_tree(1:3) 
st %>% print_simplices()
# 1, 2, 3, 1 2, 1 3, 2 3, 1 2 3
st %>% contract(c(1, 3)) %>% print_simplices()
# 1, 2, 1 2

simplextree documentation built on Sept. 13, 2020, 5:06 p.m.