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graphics - How to draw cylinders inside a cylinder


It can be considered as a sequel to 98724


I adopt the code of ybeltukov (thanks again) and I slightly modify it.


findPoints = 

  Compile[{{n, _Integer}, {low, _Real}, {high, _Real}, {minD, _Real}},
    Block[{data = RandomReal[{low, high}, {1, 2}], k = 1, rv, temp}, 
    While[k < n, rv = RandomReal[{low, high}, 2];
     temp = Transpose[Transpose[data] - rv];
     If[Min[Sqrt[(#.#)] & /@ temp] > minD, data = Join[data, {rv}];
      k++;];];
    data]];

npts = 150;
r = 0.03;

minD = 2.2 r;
low = 0;
high = 1;

SeedRandom[159]
pts = findPoints[npts, low, high, minD];
g2d = Graphics[{FaceForm@Lighter[Blue, 0.8], 
   EdgeForm@Directive[Thickness[0.004], Black], Disk[#, r] & /@ pts}, 
  PlotRange -> All, Background -> Lighter@Blue]


enter image description here


mask = BoundaryDiscretizeRegion[#, {{-1, 1}, {-1, 1}}, 
     MaxCellMeasure -> {1 -> .02}] &@
   BoundaryDiscretizeRegion[Disk[{0.5, 0.5}, {0.4, 0.5}]];
r2d = DiscretizeGraphics[g2d, MaxCellMeasure -> {1 -> .01}, 
   PlotRange -> All];
inside = RegionIntersection[r2d, mask]

enter image description here


edge = DiscretizeRegion@*Line@*Intersection @@ 

   Round[{Sort /@ 
      MeshPrimitives[RegionIntersection[r2d, mask], 1][[;; , 1]], 
     Sort /@ MeshPrimitives[RegionDifference[r2d, mask], 1][[;; , 
        1]]}, .0001];
points = DiscretizeRegion@*Point@*Intersection @@ 
   Round[{MeshPrimitives[RegionDifference[r2d, mask], 0][[;; , 1]], 
     MeshPrimitives[RegionDifference[mask, r2d], 0][[;; , 1]]}, .0001];

regionProduct[reg_, join_: True, y1_: 0, y2_: 1] := 
  Module[{n = MeshCellCount[reg, 0]}, 

   MeshRegion[
    Join @@ (ArrayFlatten@{{#[[;; , ;; 1]], #2, #[[;; , 2 ;;]]}} &[
         MeshCoordinates@reg, #] & /@ {y1, y2}), {MeshCells[reg, _], 
     MeshCells[reg, _] /. p : {__Integer} :> p + n, 
     If[join, 
      MeshCells[
        reg, _] /. {(Polygon | Line)[
          p_] :> (Polygon@Join[#, Reverse[#, 2] + n, 2] &@
           Partition[p, 2, 1, 1]), 
        Point[p_] :> Line@{p, p + n}}, ## &[]]}]];

mask3d = regionProduct@mask;
inside3d = regionProduct[inside, False];
edge3d = regionProduct@edge;
points3d = regionProduct@points;

toGC[reg_, dim_] := 
  GraphicsComplex[MeshCoordinates@reg, MeshCells[reg, dim]];

Graphics3D[{FaceForm@Lighter[Blue, 0.7], toGC[inside3d, 2], 
  EdgeForm[], toGC[edge3d, 2], toGC[points3d, 1], Lighter@Blue, 

  GeometricTransformation[toGC[mask3d, 2], 
   ScalingTransform[0.999 {1, 1, 1}, RegionCentroid@mask3d]]}, 
 Lighting -> "Neutral", Boxed -> False]

enter image description here


Graphics3D[{FaceForm@Lighter[Blue, 0.7], 
  toGC[regionProduct[RegionBoundary@inside, False], 1], EdgeForm[], 
  toGC[regionProduct@inside, 2], toGC[edge3d, 2], toGC[points3d, 1], 
  Blue, Opacity[0.11], 
  GeometricTransformation[toGC[mask3d, 2], 

   ScalingTransform[0.999 {1, 1, 1} #, RegionCentroid@mask3d] & /@ 
    Range[0, 1, 0.01]]}, Lighting -> "Neutral", Boxed -> False, 
 BaseStyle -> {RenderingOptions -> {"DepthPeelingLayers" -> 100}}]

enter image description here


My question is how I can get rid of the disks appeared "cut" and as the result the cylinders appeared also "cut"


enter image description here



Answer



The required modification is not too hard to do:


SeedRandom[159];

pts = Select[findPoints[npts, low, high, minD], 
             EuclideanDistance[#, {1, 1} (low + high)/2] < (low + high)/2 - r &];
g2d = Graphics[{FaceForm @ Lighter[Blue, 0.8],
                EdgeForm @ Directive[Thickness[0.004], Black],
                Disk[#, r] & /@ pts, Circle[{1/2, 1/2}, 1/2]},
               PlotRange -> All, Background -> Lighter @ Blue]

everything within the circle



The case where the confining region is an ellipse is a bit more complicated, since the parallel curve of an ellipse is complicated in general. Nevertheless,



ep = With[{a = 2/5, b = 1/2}, BoundaryDiscretizeRegion @
          ParametricRegion[(low + high) {1, 1}/2 + c ({a Cos[t], b Sin[t]} +
                           r Normalize[Cross[D[{a Cos[t], b Sin[t]}, t]]]),
                           {{c, 0, 1}, {t, 0, 2 π}}]];

SeedRandom[159];
pts = Select[findPoints[npts, low, high, minD], RegionMember[ep, #] &];
g2d = Graphics[{FaceForm @ Lighter[Blue, 0.8], 
                EdgeForm @ Directive[Thickness[0.004], Black],
                Disk[#, r] & /@ pts, Circle[{1/2, 1/2}, {2/5, 1/2}]},

               PlotRange -> All, Background -> Lighter @ Blue]

disks within an ellipse


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