split a polyhedral set into simplices
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.
Splitting the cube into simplices gives a list of tetrahedrons.
c ≔ ExampleSets:-Cube⁡:
c_pieces ≔ SplitIntoSimplices⁡c
The volume of the cube is equal to the sum of the volume of the simplices.
volumes ≔ map⁡Volume,c_pieces
Plot the simplices with transparency to see the internal structure of the sets.
The PolyhedralSets[SplitIntoSimplices] command was introduced in Maple 2015.
For more information on Maple 2015 changes, see Updates in Maple 2015.
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