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I usually look at my regions by plugging them into graphics:

Graphics[{Disk[{0, 0}, 2], Disk[{3, 0}, 2]}]

That works. But when I try to create the union of the regions, I can no longer visualize it (this fails):

Graphics[RegionUnion[Disk[{0, 0}, 2], Disk[{3, 0}, 2]]]

Why? And how can I visualize a region constructed through unions?

Incidentally, the documentation for RegionMember suggests that Region[RegionUnion[Disk[{0, 0}, 2], Disk[{3, 0}, 2]]] should generate an image. But it doesn't for me.

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    $\begingroup$ What version are you using? Region was introduced in V11.1. $\endgroup$
    – Greg Hurst
    Commented Jul 13, 2017 at 2:10
  • $\begingroup$ @ChipHurst Ahh, I see. I'm using V11.0, naturally. There's a good reason to update! $\endgroup$
    – Shane
    Commented Jul 13, 2017 at 14:39

4 Answers 4

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Amplifying on the answer by e.doroskevic

The Head of RegionUnion is RegionUnion which is not a Graphics primitive.

Head@RegionUnion[Disk[{0, 0}, 2], Disk[{3, 0}, 2]]

(*  RegionUnion  *)

RegionQ@RegionUnion[Disk[{0, 0}, 2], Disk[{3, 0}, 2]]

(*  True  *)

Use RegionPlot

RegionPlot[
 RegionUnion[Disk[{0, 0}, 2], Disk[{3, 0}, 2]], AspectRatio -> 4/7]

enter image description here

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    $\begingroup$ You could use AspectRatio -> All instead. $\endgroup$
    – Carl Woll
    Commented Jul 12, 2017 at 16:15
  • $\begingroup$ @CarlWoll - Thanks. $\endgroup$
    – Bob Hanlon
    Commented Jul 12, 2017 at 16:23
  • $\begingroup$ @CarlWoll AspectRatio -> All produces an error in 10.1. Did you mean AspectRatio -> Automatic or is this something new? If the latter how is it different from Automatic? $\endgroup$
    – Mr.Wizard
    Commented Jul 13, 2017 at 2:02
  • $\begingroup$ All was just the first I thing I tried, and in M11 I think All and Automatic are equivalent. $\endgroup$
    – Carl Woll
    Commented Jul 13, 2017 at 5:27
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Another possibility is BoundaryDiscretizeRegion:

BoundaryDiscretizeRegion[
    RegionUnion[{Disk[{0,0},2],Disk[{3,0},2]}]
]

enter image description here

If you want a better discretization, you can use PrecisionGoal/AccuracyGoal:

BoundaryDiscretizeRegion[
    RegionUnion[{Disk[{0,0},2],Disk[{3,0},2]}],
    PrecisionGoal->6
]

enter image description here

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Input

RegionPlot @ RegionUnion[{Disk[{0, 0}, 2], Disk[{3, 0}, 2]}]

Output

region plot output

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In V11.1.1 a new function Region was introduced, which among other usages, makes viewing compound regions dirt simple.

Region @ RegionUnion[Disk[{0, 0}, 2], Disk[{3, 0}, 2]]

region

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