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PolyhedralSets

  

ConvexHull

  

convex hull of polyhedral sets

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

ConvexHull(ps1, ps2, ..., psn)

ConvexHull(ps1, ps2, ..., psn, method = m)

Parameters

ps1, ps2, ..., psn

-

sequence of n polyhedral sets

m

-

(optional) one of hrepresentation (default) or vrepresentation

Description

• 

This command computes the convex hull of a sequence of polyhedral sets, returning the result as a new PolyhedralSet.

• 

The method = hrepresentation option computes the convex hull using the H-Representation of the polyhedral sets, forming their convex hull by accumulating the sets of relations.

• 

The method = vrepresentation option constructs a convex hull using the V-Representation of the polyhedral sets, computing their vertices and rays and combining the results to form a new set.

• 

There is also a ConvexHulls command in the ComputationalGeometry package. The Convex Hulls Example Worksheet discusses both commands and the usefulness of each.

Examples

withPolyhedralSets:

A dodecahedron can be formed as the convex hull of a tetrahedron and a cube.

tetrahedronPolyhedralSet321,1,1,1,1,1,1,1,1,1,1,1:cubeExampleSets:-Cube:Plottetrahedron,cube,faceoptions=transparency=0.25,0.

convhullConvexHulltetrahedron,cube:Plotconvhull

The tetrahedron and cube are then subsets of this convex hull.

tetrahedronsubsetconvhull

true

(1)

cubesubsetconvhull

true

(2)

The convex hull of a triangle with a point gives a tetrahedron.

trianglePolyhedralSet0x,0y,x+y1,z=0:pntPolyhedralSet0,0,1,x,y,z:Plottriangle,pnt,orientation=30,70,0

tetraConvexHullpnt,triangle;Plottetra,orientation=30,70,0

tetra{Coordinates:x,y,zRelations:z0,y0,x0,x+y+z1

Compatibility

• 

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

• 

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

See Also

PolyhedralSets[SplitIntoSimplices]

PolyhedralSets[`intersect`]

PolyhedralSets[`subset`]

PolyhedralSets[`in`]

PolyhedralSets[VerticesAndRays]

PolyhedralSets[PolyhedralSet]

PolyhedralSets

simplex[convexhull]

geometry[convexhull]