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# VERT2CON - vertices to constraints

### Michael Kleder (view profile)

22 Jun 2005 (Updated )

Create inequality constraints to bound the convex hull of the given points.

File Information
Description

VERT2CON - convert a set of points to the set of inequality constraints which most tightly contain the points; i.e., create constraints to bound the convex hull of the given points

[A,b] = vert2con(V)

V = a set of points, each ROW of which is one point
A,b = a set of constraints such that A*x <= b defines the region of space enclosing the convex hull of the given points

For n dimensions:
V = p x n matrix (p vertices, n dimensions)
A = m x n matrix (m constraints, n dimensions)
b = m x 1 vector (m constraints)

NOTES:
NOTES:
(1) In higher dimensions, redundant constraints can appear. This program detects redundancy at 6 digits of precision (per dimension), then returns the unique constraints.
(2) See companion function CON2VERT.
(3) ver 1.0: initial version, June 2005.
(4) ver 1.1: enhanced redundancy checks, July 2005
(5) Written by Michael Kleder

Acknowledgements

This file inspired Representing Polyhedral Convex Hulls By Vertices Or (In)Equalities.

MATLAB release MATLAB 7.0.1 (R14SP1)
17 Apr 2011 Jay Berger

### Jay Berger (view profile)

Nice program. How do I enforce constraints for points to lie only on the boundary of the convex hull?

Comment only
11 Feb 2011 Chris Z.

### Chris Z. (view profile)

04 Feb 2011 Sean de

### Sean de (view profile)

Excellent program!
Very useful for calculating 3-dimensional convex masks.

A few speedups for newer versions replacing REPMAT with BSXFUN:
V = bsxfun(@minus,V,c);

and in the example:
p = bsxfun(@le,A*p,b);

10 Jul 2008 Vishal Narula

nice work..keep it up!

20 Jun 2008 GagoX GagoX

Thanx Michael,

great program! and very elegantly coded as well.