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I want to transform a BoundaryMeshRegion but cannot find a way that conforms with the syntax. As given below, it doesn't work if I generate the BoundaryMeshRegion first and then perform a GeometricTransformation or vice versa. I have also tried BoundaryDiscretizeGraphics in this fashion, which also doesn't work.

reg1 = GeometricTransformation[
   BoundaryDiscretizeRegion[Cone[{{0, 0, 1/2}, {0, 0, 0}}, 1/4]], 
   ShearingTransform[ArcTan[1/2], {1, 0, 0}, {0, 0, 1}]];

reg2 = BoundaryDiscretizeRegion[
   GeometricTransformation[
   Cone[{{0, 0, 1/2}, {0, 0, 0}}, 1/4], 
   ShearingTransform[ArcTan[1/2], {1, 0, 0}, {0, 0, 1}]];
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1 Answer 1

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Use TransformedRegion instead of GeometricTransformation:

TransformedRegion[
    BoundaryDiscretizeRegion[Cone[{{0,0,1/2}, {0,0,0}}, 1/4]],
    ShearingTransform[ArcTan[1/2], {1,0,0}, {0,0,1}]
]

enter image description here

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