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How to make a hole in a Graphics3D object?

yang l

yang l, lanzhou jiaotong university.

Posted 10 years ago

My question is that: how to make a hole in a Graphics3D object? For example, there are two objects ,cub1 and cub2: cub1=Cuboid[{0,0,0},{20,2,20}]; cub2=Cuboid[{12,0,8},{17,2,17}]; Graphics3D[{cub1,cub2}] I want to make a window at the positon of the cub2, like under. DiscretizeRegion[RegionDifference[cub1,cub2]] But this object is obtained by use DiscretizeRegion, it is not a Graphics3D object, it is a MeshRegion object, and it make system too slow. Then, how to get a Graphics3D object?

POSTED BY: yang l

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Vitaliy Kaurov

Vitaliy Kaurov, WOLFRAM Research

Posted 10 years ago

Let's start from your code: cub1 = Cuboid[{0, 0, 0}, {20, 2, 20}]; cub2 = Cuboid[{12, 0, 8}, {17, 2, 17}]; Graphics3D[{cub1, cub2}]; reg = DiscretizeRegion[RegionDifference[cub1, cub2]] You have a lot of tetrahedrons: MeshCells[reg, 3] // Length 10093 And a lot of polygons: MeshCells[reg, 2] // Length 22096 You do not need all that for visual, - so get the surface (boundary): surface = BoundaryDiscretizeRegion[reg]; polygons = MeshCells[surface, 2]; polygons // Length 3820 Now so few polygons! Get the coordinates of the mesh too: points = MeshCoordinates[surface]; points // Length > 1910 And here you go: Graphics3D[{EdgeForm[Gray], GraphicsComplex[points, Polygon[polygons /. Polygon[x_] -> x]]}, Boxed -> False, Lighting -> "Neutral"]

Let's start from your code:

cub1 = Cuboid[{0, 0, 0}, {20, 2, 20}];
cub2 = Cuboid[{12, 0, 8}, {17, 2, 17}];
Graphics3D[{cub1, cub2}];
reg = DiscretizeRegion[RegionDifference[cub1, cub2]]

You have a lot of tetrahedrons:

MeshCells[reg, 3] // Length

10093

And a lot of polygons:

MeshCells[reg, 2] // Length

22096

You do not need all that for visual, - so get the surface (boundary):

surface = BoundaryDiscretizeRegion[reg];
polygons = MeshCells[surface, 2];
polygons // Length

3820

Now so few polygons! Get the coordinates of the mesh too:

points = MeshCoordinates[surface];
points // Length
> 1910

And here you go:

Graphics3D[{EdgeForm[Gray], 
  GraphicsComplex[points, Polygon[polygons /. Polygon[x_] -> x]]}, 
 Boxed -> False, Lighting -> "Neutral"]

enter image description here

POSTED BY: Vitaliy Kaurov

Nasser M. Abbasi

Nasser M. Abbasi, student

Posted 10 years ago

another option (made the cube little thicker to make it more clear ) there are many more options in the RegionPlot3D you can adjust also. cub1 = Cuboid[{0, 0, 0}, {20, 6, 20}]; cub2 = Cuboid[{12, 0, 8}, {17, 6, 17}]; r2 = RegionDifference[cub1, cub2]; RegionPlot3D[r2, PlotPoints -> 60, Mesh -> 10]