outerApprox

Purpose

Computes outer bounding box for the union of polyhedra

Syntax

B = outerApprox(U)
B = U.outerApprox

Description

Compute the smallest axis-aligned hypercube that contains all polyhedra in this union. The lower and upper bounds of the hypercube are stored under Internal property, i.e. Internal.lb for lower bound and Internal.ub for upper bound.

Input Arguments

U

Union of polyhedra in the same dimension

Class: PolyUnion

Output Arguments

B

Bounding box ../../../../../../fig/mpt/modules/geometry/unions/@PolyUnion/outerapprox1.png described as Polyhedron in H-representation.

Class: Polyhedron

Example(s)

Example 1

We have union of two polyhedra.
 P(1) = Polyhedron('A',randn(9,2),'b',2*ones(9,1));

 P(2) = Polyhedron('V',randn(9,2));
 Create the union without specifying the properties 
 U = PolyUnion(P); 
 Compute the bounding box
 B = U.outerApprox; 
 Plot the sets such that the outer approximation is wired. 
 U.plot; hold on; B.plot('wire',true,'LineWidth',2) 

../../../../../../fig/mpt/modules/geometry/unions/@PolyUnion/outerapprox_img_1.png

See Also

convexhull


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

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