PolyhedralSets
SplitIntoSimplices
split a polyhedral set into simplices
Calling Sequence
Parameters
Description
Examples
Compatibility
SplitIntoSimplices(polyset)
SplitIntoSimplices(polyset, point)
polyset
-
polyhedral set
point
polyhedral set representing a vertex, list of rationals, Vector or list/set of equations of the form coordinate = value; point where polyset will be split
This command splits the polyhedral set polyset into simplices, returning a list of polyhedral sets whose union is polyset. Only bounded polyhedral sets, that is to say polytopes, can be divided into simplices.
If point is provided, it will be a vertex of all the simplices when polyset is split. If point is omitted, an arbitrary vertex of polyset is chosen for the splitting point.
withPolyhedralSets:
Splitting the cube into simplices gives a list of tetrahedrons.
c≔ExampleSets:-Cube:
c_pieces≔SplitIntoSimplicesc
c_pieces≔{Coordinates:x1,x2,x3Relations:−x3≤1,−x2+x3≤0,−x1+x2≤0,x1≤1,{Coordinates:x1,x2,x3Relations:−x2≤1,x2−x3≤0,−x1+x3≤0,x1≤1,{Coordinates:x1,x2,x3Relations:−x3≤1,x2≤1,−x1+x3≤0,x1−x2≤0,{Coordinates:x1,x2,x3Relations:−x2+x3≤0,x2≤1,−x1≤1,x1−x3≤0,{Coordinates:x1,x2,x3Relations:x3≤1,−x2≤1,−x1+x2≤0,x1−x3≤0,{Coordinates:x1,x2,x3Relations:x3≤1,x2−x3≤0,−x1≤1,x1−x2≤0
The volume of the cube is equal to the sum of the volume of the simplices.
Volumec
8
volumes≔mapVolume,c_pieces
volumes≔43,43,43,43,43,43
`+`volumes
Plot the simplices with transparency to see the internal structure of the sets.
Plotc_pieces,transparency=0.5,orientation=23,62,0
The PolyhedralSets[SplitIntoSimplices] command was introduced in Maple 2015.
For more information on Maple 2015 changes, see Updates in Maple 2015.
See Also
PolyhedralSets[PolyhedralSet]
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