Intersection of a Cube with two planes and resulting polyhedron

intersection

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

assadabbasi
43 ●4 ●6 ●12

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

ppurka
2111 ●17 ●38

Hi,

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)
cube.Hrepresentation()

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)] ?

Thanks

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Comments

The last example in the documentation might be useful to understand what `eqns` means. http://x0.no/apde

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

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

twch
368 ●3 ●13 ●21

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()
intersec.show()

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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