# Cutting a cuboid with a plane

Posted 11 months ago
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 Dear Community,I'm cutting (cliping away) a cuboid with an Infinity plane. How can I obtain i.e. separate the two resulting objects behind and in front of the plane? How can I visualize each of them? How I can extract the x, y, z coordinates of the corners of the obtained objects? How can I get the intersection polygon on the cutting plane? Notebook attached. Tx for the kind helpin advance, best regards, Andras Attachments:
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Posted 11 months ago
 Well, this would be certainly an overkill.Best regards, Andras
Posted 11 months ago
 You can discretize the region, but then you get a fine mesh, almost 2000 vertices.
Posted 11 months ago
 Dear Christopher,Tx for the kind help, I'm a newbie in Region computing. I'll test it immediately.Best regards,Andras
Posted 11 months ago
 In your first example, the intersection is being represented symbolically. You can get a mesh back using BoundaryDiscretizeRegion: cubd = Cuboid[{-2, -2, -2}, {4, 4, 4}]; hlfsp = HalfSpace[{-1, -1, 1}, {0, 0, 0}]; BoundaryDiscretizeRegion[RegionIntersection[cubd, hlfsp]] 
Posted 11 months ago
 Dear Gianluca,Thanks for your kind help, maybe Wolfram improves it in the upcoming versions. For me it was a great help anyway.Thanks and best regards Andras
Posted 11 months ago
 I find Region computation very frustrating, because there are glaring holes in functionality. For example, this gives useless output: cubd = Cuboid[{-2, -2, -2}, {4, 4, 4}]; hlfsp = HalfSpace[{-1, -1, 1}, {0, 0, 0}]; RegionIntersection[cubd, hlfsp] However, if I replace the HalfSpace with a large enough Simplex I get the intersection as a real Polyhedron: smpl = Simplex[{{24, -10, 14}, {-8, 22, 14}, {-24, -4, -28}, {20, 20, -20}}]; RegionWithin[smpl, RegionIntersection[cubd, hlfsp]] RegionIntersection[cubd, smpl] // Rationalize // Chop // InputForm It is irritating that I need to Rationalize and Chop the result.
Posted 11 months ago
 Dear Gianluca,Awsome, tx very much. Just one more tiny help:how I can extract the x, y, z coordinates of the corperpoints of the obtained objects?Tx for the kind help in advance, best regards Andras
Posted 11 months ago
 Here is a way: RegionIntersection[Cuboid[{ -2 , -2 , -2 } , { 4 , 4 , 4 } ], InfinitePlane[{{0, 0, 0}, {0, 1, 1}, {1, 0, 1}}]] // InputForm 
 One way is with Region computation: RegionPlot3D[ RegionIntersection[Cuboid[{ -2. , -2. , -2. } , { 4. , 4. , 4. } ], HalfSpace[Cross[{0, 1, 1}, {1, 0, 1}], {0, 0, 0}]]] RegionPlot3D[ RegionDifference[Cuboid[{ -2. , -2. , -2. } , { 4. , 4. , 4. } ], HalfSpace[Cross[{0, 1, 1}, {1, 0, 1}], {0, 0, 0}]]]