Intersection of a Cube with two planes and resulting polyhedron

intersection

asked 12 years ago

assadabbasi
43 ●5 ●6 ●12

updated 12 years ago

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

Comments

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

fidbc ( 12 years ago )

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answered 12 years ago

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()

link

Comments

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