minus

Purpose

Subtract a Polyhedron or a vector from a Polyhedron.

Syntax

Q = P - S
Q = minus(P,S)
Q = P - x
Q = minus(P, x)

Description

Compute the Pontryagin difference of ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minus1.png and ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minus2.png, or ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minus3.png and ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minus4.png.

../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minus5.png

or

../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minus6.png

Input Arguments

P

Polyhedron in any format

Class: Polyhedron

S

Polyhedron in any format

Class: Polyhedron

x

Column vector of length P.Dim

Class: Polyhedron

Output Arguments

Q

Polyhedron Q = P-S or Q = P-x.

Class: Polyhedron

Example(s)

Example 1

Subtract one polytope from another
P = Polyhedron('H',[sin([0:0.5:2*pi])' cos([0:0.5:2*pi])' ones(13,1)]);

S = Polyhedron('lb',[-1;-1]*0.1,'ub',[1;1]*0.1);

Q = P-S;

P.plot('color','b'); hold on;
	Q.plot('color','g');
	S.plot('color','r');

../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minus_img_1.png

Example 2

Subtract a line segment from a polytope
P = Polyhedron('H',[sin([0:0.5:2*pi])' cos([0:0.5:2*pi])' ones(13,1)]);

S = Polyhedron('V', 0.1*[-1 1;1 -1]);

Q = P-S;

P.plot('color','b'); hold on;
	 Q.plot('color','r');
	 S.plot('color','g','linewidth',2);

../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minus_img_2.png

Example 3

Unbounded polyhedron minus lower-dimensional polytope
P = Polyhedron('lb',-[1;1;1]*0.5,'ub',[1;1;1]*0.5,'He',[randn(1,3) 0.1]); 

S = Polyhedron('V',randn(10,3),'R',[1 1 1])+[1;1;1]; 

Q = S-P; 

P.plot('color', 'g'); hold on;
	 S.plot('color', 'b');
	 Q.plot('color','r');
    

../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minus_img_3.png

See Also

plus


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