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If a region which is drawn by Region function is a 2D area, we can see the region. However, if a region is a 3D region, we sometimes cannot see the region when the region is inside of something because there seems to be no option to make it transparent for Region function. I use Mathematica 11.1.1.0 on Windows7.

For example, If the region I want to draw is a 2D area, Region show us what we want:

region = Disk[{0, 0}, 1];
complement = BooleanRegion[Not, {region}];
Region[complement]

2D case

However, if the region is a 3D region, Region does not give us a relevant draw:

region2 = Ball[{0, 0, 0}, 1];
complement2 = BooleanRegion[Not, {region2}];
Region[complement2]

3D case

Then, do you know any good workaround for this frustrating matter? I know if I convert the region into a set of inequality equations, I can use RegionPlot function and the function has an opacity option but I want to know other solutions.

Any advise is appreciated.

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1 Answer 1

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You could cheat and convert into a (Boundary)MeshRegion, and then use MeshCellStyle.

I'll use a more interesting example:

region2 = Ball[{0, 0, 0}, 1];
complement2 = BooleanRegion[Not, {region2}];
reg = Region[complement2];

BoundaryDiscretizeRegion[reg, MeshCellStyle -> {{2, All} -> Opacity[1/2]}]

discretized region

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  • $\begingroup$ Oh, I also misunderstood about Sphere, it doesn't contain the balk region. $\endgroup$
    – Taiki Bessho
    Commented Mar 20, 2018 at 6:04
  • $\begingroup$ This does not appear to work anymore in Mathematica 12.1 $\endgroup$
    – alessandro
    Commented Dec 10, 2020 at 23:49
  • $\begingroup$ BoundaryDiscretizeRegion[reg, MeshCellStyle -> {{All} -> Opacity[0.5]}] will make the box transparent (though the mesh is visible), but rather than a sphere, a tiny triangle appears inside of it... $\endgroup$
    – alessandro
    Commented Dec 10, 2020 at 23:55
  • $\begingroup$ It's slightly easier to see the tiny tetrahedron(?) with Show[reg, PlotRange -> {All, 0}]. $\endgroup$
    – alessandro
    Commented Dec 10, 2020 at 23:59
  • $\begingroup$ @alessandro, indeed, a lot seems to have changed in intervening versions... o well. $\endgroup$
    – J. M.'s missing motivation ♦
    Commented Dec 23, 2020 at 10:43

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