incidenceMap

Purpose

Compute the incidence map of this polyhedron.

Syntax

iMap = P.incidenceMap
iMap = incidenceMap(P)

Description

Computes map describing containment of vertices in facets. Note: This function computes both irredundant V and H-representations of the polyhedron and can be time consuming.

Input Arguments

P

Polyhedron in any format

Class: Polyhedron

Output Arguments

iMap

Incidence map or [] is ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/incidencemap1.png is empty.

Class: struct

iMap.V

Vertices of ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/incidencemap2.png
iMap.R

Rays of ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/incidencemap3.png
iMap.H

Inequalities of ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/incidencemap4.png
iMap.He

Equalities of ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/incidencemap5.png
iMap.incVH

Incidence of ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/incidencemap6.png in H. incVH(i,j) = 1 if [V(i,:);-1]*H(j,:)' = 0

Class: sparse logical

iMap.incRH

Incidence of ../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/incidencemap7.png in H. incRH(i,j) = 1 if [R(i,:);0]*H(j,:)' = 0

Class: sparse logical

Example(s)

Example 1

Create a polytope:
P = ExamplePoly.poly3d_sin
Polyhedron in R^2 with representations:
    H-rep (redundant)   : Inequalities  13 | Equalities   0
    V-rep               : Unknown (call computeVRep() to compute)
Functions : none
Compute the incidence map
iMap = P.incidenceMap;
	 full(iMap.incVH)
    
ans =

     0     0     0     0     0     0     0     0     1     1     0     0     0
     0     0     0     0     0     0     0     1     1     0     0     0     0
     0     0     0     0     0     0     1     1     0     0     0     0     0
     1     1     0     0     0     0     0     0     0     0     0     0     0
     0     1     1     0     0     0     0     0     0     0     0     0     0
     0     0     0     1     1     0     0     0     0     0     0     0     0
     0     0     1     1     0     0     0     0     0     0     0     0     0
     0     0     0     0     1     1     0     0     0     0     0     0     0
     0     0     0     0     0     1     1     0     0     0     0     0     0
     1     0     0     0     0     0     0     0     0     0     0     0     1
     0     0     0     0     0     0     0     0     0     0     0     1     1
     0     0     0     0     0     0     0     0     0     0     1     1     0
     0     0     0     0     0     0     0     0     0     1     1     0     0

See Also

minvrep, minhrep


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