# Representing Polyhedral Convex Hulls by Vertices or (In)Equalities (Scripts) 1.0

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• Last update: 5 years ago
• Operating system: Linux, Mac OS X, Win All, BSD, Solaris
• Publisher: Matt J (15 other programs)
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## Representing Polyhedral Convex Hulls by Vertices or (In)Equalities (Scripts) Publisher's description

### This submission contains VERT2LCON and LCON2VERT

This submission contains VERT2LCON and LCON2VERT, which will find the linear constraints defining a bounded polyhedron in R^n, given its vertices, or vice versa. They are extensions of Michael Kleder's VERT2CON and CON2VERT functions that can handle cases where the polyhedron is not solid in R^n, i.e., where the polyhedron is defined by both equality and inequality constraints. Some other refinements to the original VERT2CON and CON2VERT subroutines, meant to improve speed and reliability, have also been made.

SYNTAX:

[A,b,Aeq,beq]=VERT2LCON(V,TOL)

[V,nr,nre]=LCON2VERT(A,b,Aeq,beq,TOL)

The rows of the N x n matrix V are a series of N vertices of the polyhedron
in R^n, defined by the linear constraints

A*x <= b
Aeq*x = beq

For LCON2VERT, Aeq=beq=[] are the default inputs, implying no equality constraints. The output "nr" lists non-redundant inequality constraints, and "nre" lists non-redundant equality constraints.

The optional TOL argument is a tolerance used for rank-estimation purposes and to handle finite precision issues. Default=1e-10.

EXAMPLE:

Consider V=eye(3) corresponding to the 3D region defined by x+y+z=1, x>=0, y>=0, z>=0.

>> [A,b,Aeq,beq]=vert2lcon(eye(3))

A =

0.4082 -0.8165 0.4082
0.4082 0.4082 -0.8165
-0.8165 0.4082 0.4082

b =

0.4082
0.4082
0.4082

Aeq =

0.5774 0.5774 0.5774

beq =

0.5774

And the reverse conversion is,

>> V=lcon2vert(A,b,Aeq,beq)

V =

1.0000 0.0000 0.0000
-0.0000 1.0000 0
0 0.0000 1.0000

#### System Requirements:

MATLAB 7.11 (2010b)
Program Release Status: New Release
Program Install Support: Install and Uninstall

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