polyhedral intersection operator
polyhedral subset operator
polyhedral membership operator
s1 intersect s2
`intersect`(s1, s2, s3, ...)
s1 subset s2
s1 in s2
pnt in s1
s1, s2, s3, ...
point specified as list of rationals, or list or set of equations of the form coordinate = rational
The PolyhedralSets package provides definitions for the intersect, subset and in set operators. The intersection operators returns a new polyhedral set, while the subset and in operators return either true or false.
The definition of the set operators can be loaded using with(PolyhedralSets).
Four of the corners of a cube can be cut off by taking its intersection with a tetrahedron
tetra ≔ PolyhedralSet⁡2⁢1,1,1,1,−1,−1,−1,1,−1,−1,−1,1,x,y,z:cube ≔ ExampleSets:-Cube⁡x,y,z:t_c_intersect ≔ tetra∩cube
Construct a tetrahedron and a cube
tetra ≔ ExampleSets:-Tetrahedron⁡
cube ≔ ExampleSets:-Cube⁡
The tetrahedron tetra is a subset of the cube cube
But cube isn't a subset of tetra
Any point in a set will return true when tested with in
c ≔ ExampleSets:-Cube⁡
To find the face on which the point resides, see PolyhedralSets[LocatePoint]
The PolyhedralSets[`intersect`], PolyhedralSets[`subset`] and PolyhedralSets[`in`] commands were introduced in Maple 2015.
For more information on Maple 2015 changes, see Updates in Maple 2015.
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