affineHull

Purpose

Computes affine hull of a convex set.

Syntax

He = affineHull(Set)
He = Set.affineHull

Description

Compute an implicitly-defined affine hull of the convex Set. The output is a real matrix He that defines the affine set

../../../../../../fig/mpt/modules/geometry/sets/@ConvexSet/affinehull1.png

If He is empty, then the affine hull is empty. The affine hull function for general convex sets will only function for bounded sets. If you want the affine hull of an unbounded set, then intersect your set with a large full-dimensional box.

Input Arguments

Set

Any object derived from the ConvexSet class, e.g. Polyhedron, YSet, ...

Class: ConvexSet

Output Arguments

H

The real matrix that defines the affine hull.

Class: double

Example(s)

Example 1

Construct a set by intersecting a circle, linear equality and inequality constraints using YALMIP. Define variable first
 x = sdpvar(2,1); 
 Define a set S using YSet class  
 opts = sdpsettings('solver','sedumi','verbose',0); 

 S = YSet(x, [norm(x)<=1; x(1)-x(2)==0.2; [1 -0.5; 0.3, 0.8]*x<=[0.5;0.6]], opts); 
 We can plot the set
 S.plot 
Plotting...
34 of 40

../../../../../../fig/mpt/modules/geometry/sets/@ConvexSet/affinehull_img_1.png

Compute the affine hull
 S.affineHull 
ans =

         -0.70710678116385         0.707106781209245        -0.141421356213361

See Also

innerapprox, outerapprox, isemptyset


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

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