convex hull of polyhedral sets
ConvexHull(ps1, ps2, ..., psn)
ConvexHull(ps1, ps2, ..., psn, method = m)
ps1, ps2, ..., psn
sequence of n polyhedral sets
(optional) one of hrepresentation (default) or vrepresentation
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.
A dodecahedron can be formed as the convex hull of a tetrahedron and a cube.
tetrahedron ≔ PolyhedralSet⁡3⁢1,1,1,1,−1,−1,−1,1,−1,−1,−1,12:cube ≔ ExampleSets:-Cube⁡:Plot⁡tetrahedron,cube,faceoptions=transparency=0.25,0.0
convhull ≔ ConvexHull⁡tetrahedron,cube:Plot⁡convhull
The tetrahedron and cube are then subsets of this convex hull.
The convex hull of a triangle with a point gives a tetrahedron.
triangle ≔ PolyhedralSet⁡0≤x,0≤y,x+y≤1,z=0:pnt ≔ PolyhedralSet⁡0,0,1,x,y,z:Plot⁡triangle,pnt,orientation=−30,70,0
tetra ≔ ConvexHull⁡pnt,triangle;Plot⁡tetra,orientation=−30,70,0
The PolyhedralSets[ConvexHull] command was introduced in Maple 2015.
For more information on Maple 2015 changes, see Updates in Maple 2015.
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