inside: test points for being inside a zonotope

Description

Test points for being inside a zonotope. The boundary points are considered to be inside.

Usage

# S3 method for zonotope
inside( x, p )

Value

inside.zonotope() returns a data.frame with N rows and these columns:

p: the given point
inside: whether the point is inside the zonotope. For boundary points, inside is TRUE.
distance: the distance from the point to the zonotope. For boundary points, distance is 0. When distance > 0, it may be larger than the true mathematical distance, so distance is really a pseudo-distance.
idxhyper: the index of the critical hyperplane in the simplified matroid. This is the index of the slab where the maximum slab distance was taken. For a zonoseg there is only 1 hyperplane (the empty set) so this is always 1.

If the row names of p are unique, they are copied to the row names of the output.

In case of error, the function returns NULL.

Arguments

x: a zonotope object - a zonohedron, zonogon, or zonoseg
p: an NxM numeric matrix, where M is the dimension of the zonotope. The points to be tested are in the rows. p can also be a numeric vector that can be converted to such a matrix, by row.

Details

The given zonotope is viewed as the intersection of slabs; there is a slab for each hyperplane in the simplified matroid. For each slab a signed distance to boundary of the slab is computed. For points outside the slab the distance is positive, for points on the boundary, the distance is 0, and for points in the interior of the slab the distance is negative. The distance to the zonotope is computed as the maximum over all these slab distances, and the critical hyperplane index is recorded. A point is inside iff the zonotope distance \(\le\) 0.

Examples

Run this code

zono1 = zonoseg( c(1,-2,3,0,-3,-4) )

getsegment(zono1)
# [1] -9 4

p = c( 0, -3*pi, pi, 2*pi, getsegment(zono1) )

inside( zono1, p )
#           p inside   distance idxhyper
# 1  0.000000   TRUE -4.0000000        1
# 2 -9.424778  FALSE  0.4247780        1
# 3  3.141593   TRUE -0.8584073        1
# 4  6.283185  FALSE  2.2831853        1
# 5 -9.000000   TRUE  0.0000000        1
# 6  4.000000   TRUE  0.0000000        1