R: the support function for a zonotope

support {zonohedra}

R Documentation

the support function for a zonotope

Description

Compute the classical support function for a zonotope. It also computes a point on the boundary where the linear functional is maximized, and the dimension of the face where the supporting hyperplane intersects the zonotope.

Usage

## S3 method for class 'zonotope'
support( x, direction, tol=5.e-15 )

Arguments

`x`	a zonotope object - a zonohedron, a zonogon, or a zonoseg
`direction`	an NxM matrix with N directions in the rows. If `x` is a zonohedron, M must be 3. If `x` is a zonogon, M must be 2. If `x` is a zonoseg, M must be 1. `direction` can also be a vector that can be converted to such a matrix, by row. The direction is normal to the supporting hyperplane
`tol`	the tolerance for determining whether the supporting hyperplane intersects a face with positive dimension. This does not affect the value of the support function. For a zonoseg, `tol` is ignored.

Value

The function returns a data.frame with N rows and these columns:

`direction`	the given direction
`value`	the value of the support function of `x`, in the given direction
`argmax`	a point on the boundary of `x` where the functional max is taken. This point is the center of the face where the supporting hyperplane intersects the zonotope.
`dimension`	of the face where the supporting hyperplane intersects the zonotope. 0 means a vertex, 1 means an edge, and 2 means a 2-face.

If direction is 0, the other columns are NA. If the rownames of direction are unique, they are copied to the row names of the output.
In case of error, the function returns NULL.

References