Combine RegionDifference with Graphics

Question

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.

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

Answer 1

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]]

Answer 2

dsk = Disk[{0, Sqrt[3]}, Sqrt[3]];

reg = RegionIntersection[DiscretizeRegion@dsk, DiscretizeGraphics[ff2]];

cropped = MeshPrimitives[reg, All];

Graphics[{AbsoluteThickness[1], AbsolutePointSize[10], cropped}]

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