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I noticed DiscretizeGraphics does not work correctly with transformed Graphics such as 

Graphics[Rotate[Rectangle[], 30°]]

graphics1

Both using Rotate and GeometricTransformation together with RotationTransform yield EmptyRegion[2] when DiscretizeGraphics is used. 

Graphics[Rotate[Rectangle[], 30°]] // DiscretizeGraphics   
(* EmptyRegion[2] *)

GeometricTransformation[Rectangle[], 
RotationTransform[30°]]] // Graphics // DiscretizeGraphics
(* EmptyRegion[2] *)

Is this a bug? Is there a workaround?

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2 Answers 2

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Here are a four possibilities. Two of them are due to @JM's comments. (Thanks!) All of them are based on the fact that Rectangle[] can be used as a geometric region as well as a graphics primitive, and they all use TransformedRegion to get the rotation rather than GeometricTransformation, RotationTransform or Rotate.

Define the rotated rectangle as a region:

reg = TransformedRegion[Rectangle[], RotationTransform[π/6]]

(* Parallelogram[{0, 0}, {{-(1/2), Sqrt[3]/2}, {Sqrt[3]/2, 1/2}}] *)

Then we can do

GraphicsRow[
 Through[{DiscretizeRegion, DiscretizeGraphics, 
          BoundaryDiscretizeRegion, BoundaryDiscretizeGraphics}@reg]
 ]

enter image description here

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    $\begingroup$ BoundaryDiscretizeRegion[] and BoundaryDiscretizeGraphics[] can be used here too, of course. $\endgroup$
    – J. M.'s eventual burnout ♦
    Nov 1, 2017 at 14:52
  • $\begingroup$ @J.M. Thanks for that. I've updated the answer. $\endgroup$
    – aardvark2012
    Nov 1, 2017 at 23:31
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For the time being a workaround is using first DiscretizeGraphics and then transforming the region e.g.

Rectangle[] // DiscretizeGraphics //TransformedRegion[#, RotationTransform[30°]]&
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