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Intersection of a Cube with two planes and resulting polyhedron

asked 2013-02-19 00:21:51 +0200

assadabbasi gravatar image

updated 2013-02-19 05:31:10 +0200

ppurka gravatar image


I am new to sage and trying to solve a problem where I have two planes cutting a cube. How can I find the resulting polytope/polyhedron as a result of this cut.

cube = polytopes.n_cube(3)

plane1 = Polyhedron(eqns=[(0,1,0,0)])
plane2 = Polyhedron(eqns=[(1,0,0,-1)])

Please also tell me that what is meant by eqns=[(0,1,0,0)] in sage? what equality it represent? similarly eqns=[(1,0,0,-1)] ?


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The last example in the documentation might be useful to understand what `eqns` means.

fidbc gravatar imagefidbc ( 2013-02-19 09:49:11 +0200 )edit

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answered 2013-02-19 17:03:01 +0200

twch gravatar image

For an answer of the interpretation of eqns see your first post.

in order to calculate the intersection of your two planes and the cube, you can simply put all conditions in a new Polyhedron

cube = polytopes.n_cube(3)
plane1 = Polyhedron(eqns=[(0,1,0,0)])
plane2 = Polyhedron(eqns=[(1,0,0,-1)])
intersec=Polyhedron(eqns=plane1.equations()+plane2.equations(), ieqs=cube.inequalities())
print intersec.Hrepresentation()
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In a more recent version you can do:

sage: cube = polytopes.cube()
sage: plane1 = Polyhedron(eqns=[(0,1,0,0)])
sage: plane2 = Polyhedron(eqns=[(1,0,0,-1)])
sage: intersec = cube & plane1 & plane2
jipilab gravatar imagejipilab ( 2020-02-07 19:08:19 +0200 )edit

answered 2013-02-20 18:01:10 +0200

assadabbasi gravatar image

Thank you very much. Your explanation was very useful in solving my problem.

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Asked: 2013-02-19 00:21:51 +0200

Seen: 832 times

Last updated: Feb 20 '13