support: the support function for a zonotope

In zonohedra: Compute and Plot Zonohedra from Vector Generators

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

Wikipedia - Support function
https://en.wikipedia.org/wiki/Support_function

See Also

zonoseg()

zonohedra documentation built on Sept. 1, 2025, 9:08 a.m.