isFullDim

Purpose

Test if a polyhedron has a non-empty interior.

Syntax

tf = P.isFullDim
tf = isFullDim(P)

Description

Return true if the polyhedron ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isfulldim1.png has a non-empty interior and false otherwise. A polyhedron has a non-empty interior if and only if its dimension is the same as its dimension of representation. i.e. rank affhull P = size(P.A,2), or equivalently if there exists a non-empty ball of dimension size(P.A,2) that is contained within it.

Input Arguments

P

Polyhedron in any format

Class: Polyhedron

Output Arguments

tf

true if the polyhedron ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/isfulldim2.png has a non-empty interior and false otherwise.

Class: logical

Allowed values:

  • true
  • false

Example(s)

Example 1

Full-dimensional polyhedra:
Polyhedron('V', randn(30,5)).isFullDim
ans =

     1

Polyhedron('V', randn(30,5), 'R', randn(2,5)).isFullDim
ans =

     1

Lower-dimensional polyhedra:
Polyhedron('V', [randn(10,2) zeros(10,1)]).isFullDim
ans =

     0

Polyhedron('H', [rand(30,5) ones(30,1)], 'He', [randn(1,5) 0]).isFullDim
ans =

     0

See Also

isemptyset, isbounded


© 2010-2013 Colin Neil Jones: EPF Lausanne, colin.jones@epfl.ch