boundarypgramdata {zonohedra}

compute data about specific parallelograms in the boundary of a zonohedron

Description

The boundary of a zonohedron is the union of parallelograms, where some of them may be facets, and some may be tiles in the standard tiling of more complex facets. The edges of each parallelogram are given by a pair of distinct simplified generators. If a zonohedron has n of these generators, then there are n(n{-}1)/2 such pairs. For each pair of generators, there are 2 parallelograms which are antipodal to each other. This function computes data about one parallelogram from this antipodal pair. The total number of parallelograms is n(n{-}1).

Usage

boundarypgramdata( x, gndpair, cube=FALSE )

Arguments

x

a zonohedron object as returned by the constructor zonohedron()

gndpair

an Mx2 integer matrix. Each row of gndpair must contain a pair of points in the ground set of the simplified matroid of the zonohedron x. The 1st point must be less that the 2nd point.
gndpair can also be a numeric vector that can be converted to such a matrix, by row.

cube

if TRUE, then a point of the cube that maps to the center of the given parallelogram is returned, see Value.

Value

boundarypgramdata() returns a data.frame with M rows and these columns:

gndpair

the given gndpair

hyperplaneidx

the index of the hyperplane in the simplified matroid of x that contains gndpair

center

the center of the parallelogram relative to the center of the zonohedron. For the antipodal parallelogram, multiply this by -1.

transitions

the number of transitions in pcube - a point in the n-cube that maps to center. This is a non-negative even integer.

And if cube is TRUE, then this column is added:

pcube

a point in the n-cube that maps to center. For the antipodal parallelogram, subtract this from 1; the number of transitions is the same.

If a row of gndpair has an invalid pair, the other columns are filled with NAs.

In case of global error, the function returns NULL.

WARNING

In this version of the package, when the parallelogram is a tile in a more complex facet, the function may return incorrect results. This will be fixed in a future version.

See Also

zonohedron()