homogenize

Purpose

Compute the homogenization of the given Polyhedron.

Syntax

H = P.homogenize(type)
H = homogenize(P, type)

Description

Compute the homogenization of the given Polyhedron. Parametrize the right hand side of the inequalities/equalities that describe the polyhedron to get homogenized system of equations ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/homogenize1.png and ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/homogenize2.png. Given Polyhedron

../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/homogenize7.png

the homogenization is

../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/homogenize8.png

where the ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/homogenize3.png is the lifting parameter. The dimension of the polyhedron ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/homogenize4.png is by one greater than the dimension of ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/homogenize5.png. If type = 'Hrep' or type = 'Vrep' is specified, then the homogenization is returned in this form, otherwise the returned type is equal to the type of ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/homogenize6.png.

Input Arguments

P

Polyhedron in any format

Class: Polyhedron

type

Desired type of the returned polyhedron

Class: char

Allowed values:

  • Hrep

    Hyperplane representation.
  • Vrep

    Vertex representation.

Output Arguments

H

Homogenization of P polyhedron

Class: Polyhedron

Example(s)

Example 1

Create random polyhedron and homogenize:
P = ExamplePoly.randHrep;

H = P.homogenize;
Plot the result:
plot([P, H]);

../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/homogenize_img_1.png


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