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PolyhedralSets

  

InteriorPoint

  

get an interior point of a polyhedral set

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

InteriorPoint(polyset)

Parameters

polyset

-

PolyhedralSet

Description

• 

This command computes an interior point of the highest dimensional face for the given polyhedral set polyset.  If polyset is of lower dimension than its ambient space, then the point lies on the boundary of polyset, but the point is not an extreme point of the set.

• 

The command returns NULL if there are no interior points in polyset. In other words, if polyset is a vertex or an empty set.  Otherwise, the command returns a list of rationals representing a point in polyset's coordinate space.

Examples

withPolyhedralSets:

Get a point inside the cube

cExampleSets:-Cube:pInteriorPointc

p0,0,0

(1)

For a 2-D triangular set in 3-D space, the command returns a point which is interior to the triangle, but lies on the boundary of the set strictly speaking.

trianglePolyhedralSetz=1,1y,1x,xy+1,x,y,z

triangle{Coordinates:x,y,zRelations:z=1,y1,x1,x+y1

(2)

pInteriorPointtriangle

p0,0,1

(3)

The point lies on a 2 dimensional set, while the set is in a 3 dimensional space.

face_with_pLocatePointp,triangle

face_with_p{Coordinates:x,y,zRelations:z=1,y1,x1,x+y1

(4)

Dimensionface_with_p

2

(5)

nopsCoordinatesface_with_p

3

(6)

Compatibility

• 

The PolyhedralSets[InteriorPoint] command was introduced in Maple 2015.

• 

For more information on Maple 2015 changes, see Updates in Maple 2015.

See Also

PolyhedralSets[LocatePoint]

PolyhedralSets[Dimension]

PolyhedralSets[Coordinates]

PolyhedralSets[PolyhedralSet]

PolyhedralSets