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I have this 2D graphics

a1 = {-1, Sqrt[3]}; a2 = {1, Sqrt[3]}; unitCell[x_, y_] := {Black, Disk[{x, y}, 0.1], Black, Disk[({x, y} + a1/2), 0.1], Black, Disk[({x, y} + a2/2), 0.1], Blue, Thickness[0.001], Line[{{x, y}, {x, y} + a1/2}], Line[{{x, y}, {x, y} + a2/2}], Line[{{x, y} + a2/2, {x, y} + a2/2 - (a2 - a1)/2}], Line[{{x, y} + a2/2, {x, y} + a2}], Line[{{x, y} + a1/2, {x, y} + a1}], Line[{{x, y} + a1/2, {x, y} + a1/2 - (a2 - a1)/2}]}; ff2=Graphics[{Table[ unitCell @@ (a1 j + a2 k), {j, -5, 5}, {k, -5, 5}]}, ImageSize -> 300, PlotRange -> {{-6, 6}, {-6, 6}}]

I would like to exclude points outside a disk of radius r (i.e. show only points inside the red or green circle as below.

enter image description here

This is how I did it be not working

r=2 desirdReg= RegionDifference[ff2, Disk[{0, 0}, r]]; Region[desirdReg]

it gives:

RegionDifference::reg: is not a correctly specified region.

I would like to get something like this

enter image description here

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  • $\begingroup$ What are the definitions of unitVectA and unitVectB? $\endgroup$ Commented Jan 3, 2022 at 11:32
  • $\begingroup$ @demm they are a1 and a2, code modified. $\endgroup$ Commented Jan 3, 2022 at 11:35

2 Answers 2

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I suggest using patterns and deleting the unwanted Disk and Line objects.

reg = Disk[{3/4, 0}, 2]; ff2 = {Table[unitCell @@ (a1 j + a2 k), {j, -5, 5}, {k, -5, 5}]}; Graphics[DeleteCases[ ff2, (Disk[{x_, y_}, r_] /; {x, y} \[NotElement] reg) | (Line[{{x1_, y1_}, {x2_, y2_}}] /; ({x1, y1} \[NotElement] reg || {x2, y2} \[NotElement] reg)), All]]

Mathematica graphics

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dsk = Disk[{0, Sqrt[3]}, Sqrt[3]]; reg = RegionIntersection[DiscretizeRegion@dsk, DiscretizeGraphics[ff2]]; cropped = MeshPrimitives[reg, All]; Graphics[{AbsoluteThickness[1], AbsolutePointSize[10], cropped}]

enter image description here

Graphics[{First@ff2, AbsoluteThickness[3], AbsolutePointSize[7], MapThread[{##} &, {{ Blue, Red}, Reverse@cropped}], Opacity[.5], Green, Circle @@ dsk}, PlotRange -> 4]

enter image description here

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