minHRep

Purpose

Compute an irredundant H-representation of a polyhedron.

Syntax

P.minHRep()
[P, sol] = P.minHRep()

Description

Computes an irredundant H-representation of the polyhedron:

../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minhrep4.png

Notes:

Input Arguments

P

Polyhedron in any format

Class: Polyhedron

Output Arguments

sol

Irredundant H-representation of ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minhrep3.png

Class: struct

sol.H

Matrix of inequalities

../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minhrep5.png

Class: double matrix

sol.He

Matrix of equalities

../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minhrep6.png

Class: double matrix

Example(s)

Example 1

Create redundant description of a polyhedron:
P = Polyhedron('H', [randn(20,3) ones(20,1)], 'He', [randn(1,3) 0])
Polyhedron in R^3 with representations:
    H-rep (redundant)   : Inequalities  20 | Equalities   1
    V-rep               : Unknown (call computeVRep() to compute)
Functions : none
Remove redundancies:
P.minHRep()
Polyhedron in R^3 with representations:
    H-rep (irredundant) : Inequalities   6 | Equalities   1
    V-rep               : Unknown (call computeVRep() to compute)
Functions : none
Plot the result
plot(P);

../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minhrep_img_1.png

The polyhedron P has been permanently changed:
disp(P)
  <a href="matlab:help Polyhedron">Polyhedron</a> <a href="matlab:help handle">handle</a>

  Properties:
    irredundantVRep: 1
    irredundantHRep: 1
            hasHRep: 1
            hasVRep: 1
                  A: [6x3 double]
                  b: [6x1 double]
                 Ae: [1.054537042432 0.942364915344315 -0.463781292098188]
                 be: 0
                  H: [6x4 double]
                 He: [1.054537042432 0.942364915344315 -0.463781292098188 0]
                  R: [0x3 double]
                  V: [6x3 double]
                Dim: 3
               Data: []

  <a href="matlab:methods('Polyhedron')">Methods</a>, <a href="matlab:events('Polyhedron')">Events</a>, <a href="matlab:superclasses('Polyhedron')">Superclasses</a>

Example 2

Create vertex representation of a polyhedron:
P = Polyhedron('V', randn(20,3), 'R', -[1 0 0])
Polyhedron in R^3 with representations:
    H-rep               : Unknown (call computeHRep() to compute)
    V-rep (redundant)   : Vertices  20 | Rays   1
Functions : none
Compute inequality representation:
P.minHRep()
Polyhedron in R^3 with representations:
    H-rep (irredundant) : Inequalities  18 | Equalities   0
    V-rep (irredundant) : Vertices  10 | Rays   1
Functions : none
Plot the result
plot(P);

../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minhrep_img_2.png

References

[1] Fukuda: PolyFaq

See Also

minvrep


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

© 2010-2013 Martin Herceg: ETH Zurich, herceg@control.ee.ethz.ch

© 2003-2013 Michal Kvasnica: STU Bratislava, michal.kvasnica@stuba.sk