Polyhedron

Purpose

Create a Polyhedron object.

Syntax

P = Polyhedron(param, value, ...)
P = Polyhedron(dat)
P = Polyhedron(con, var)
P = Polyhedron(Q)

Description

Creates a Polyhedron:

../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/polyhedron17.png

or

../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/polyhedron18.png

  1. Polyhedral data specified as param, value pairs (detailed below).
  2. Polyhedral data given in a structure. The same data as described below for param/value pair, but given as a structure.
  3. Yalmip description con[straints] var[iables] specified
  4. Polyhedron ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/polyhedron1.png specified. The polyhedron object is a handle object. This means that executing ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/polyhedron2.png does NOT create a copy of ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/polyhedron3.png, both only another object by the same name. If you want to copy ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/polyhedron4.png, then call ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/polyhedron5.png.
This class repreents the following polyhedra:

Input Arguments

P

Polyhedron in any format

Class: Polyhedron

H

Inequality description (must be full-dimensional) ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/polyhedron11.png

Class: double

He

Affine set ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/polyhedron12.png

Class: double

V

Points defining the set ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/polyhedron13.png.

Class: double

R

Rays defining the set ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/polyhedron14.png.

Class: double

irredundantVRep

If true, then the given V-representation is assumed irredundant.

Class: logical

Allowed values:

  • true
  • false

irredundantHRep

If true, then the given H-representation is assumed irredundant.

Class: logical

Allowed values:

  • true
  • false

lb

Add a constraint of the form ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/polyhedron15.png.

Class: double

ub

Add a constraint of the form ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/polyhedron16.png.

Class: double

Output Arguments

P

Object of the Polyhedron class.

Example(s)

Example 1

Create V-Polyhedron
P = Polyhedron([2 2;-5 -2; -5 3])
Polyhedron in R^2 with representations:
    H-rep               : Unknown (call computeHRep() to compute)
    V-rep (redundant)   : Vertices   3 | Rays   0
Functions : none
Create H-Polyhedron
Q = Polyhedron([1 -1;0.5 -2;-1 0.4; -1 -2],[1;2;3;4])
Polyhedron in R^2 with representations:
    H-rep (redundant)   : Inequalities   4 | Equalities   0
    V-rep               : Unknown (call computeVRep() to compute)
Functions : none
Plot the polyhedra
 plot([P,Q]); 

../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/polyhedron_img_1.png

Example 2

Import polyhedron from YALMIPDefine yalmip variables and the set
 x = sdpvar(3,1); 

 S = set([-1;-2;-3]<= x <= [1;2;3]); 
 Construct polyhedron 
 P = Polyhedron(S,x) 
Polyhedron in R^3 with representations:
    H-rep (redundant)   : Inequalities   6 | Equalities   0
    V-rep               : Unknown (call computeVRep() to compute)
Functions : none
Plot the polyhedron
 plot(P); 

../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/polyhedron_img_2.png

See Also

yset


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