invAffineMap

Purpose

Compute the inverse affine map of the Polyhedron.

Syntax

Q = P.invAffineMap(T)
Q = P.invAffineMap(T, t)

Description

Computes an inverse affine map Q of polyhedron P based on the transformation matrix ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/invaffinemap1.png and vector ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/invaffinemap2.png. The polyhedron Q is given by

../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/invaffinemap3.png

The matrix T must be a square real matrix. The vector t, if omitted, defaults to a zero vector of corresponding dimension.

Input Arguments

P

Polyhedron in any format.

Class: Polyhedron

T

Transformation matrix.

Class: double

t

Transformation vector.

Class: double

Output Arguments

Q

Polyhedron representing the affine map in H-representation.

Class: Polyhedron

Example(s)

Example 1

Inverse affine map of a unit box.
P = Polyhedron('lb', [-1; -1], 'ub', [1; 1]);
Inverse affine map with the matrix [1 1; 0 1] 
Q = P.invAffineMap([1 1; 0 1]) 
Polyhedron in R^2 with representations:
    H-rep (redundant)   : Inequalities   4 | Equalities   0
    V-rep               : Unknown (call computeVRep() to compute)
Functions : none
Plot P and Q.
plot([P, Q]);

../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/invaffinemap_img_1.png

See Also

affinehull


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