Randomly distributed circles inside an annulus












5












$begingroup$


With the following code:



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, 0.4], 

    EdgeForm@Directive[Thickness[0.004], Black], Disk[#, r] & /@ pts},

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



d1 = Disk[{0.5, 0.5}, 0.5];

d2 = Disk[{0.5, 0.5}, 0.3];

annulus = RegionDifference[d1, d2];



mask2 = BoundaryDiscretizeRegion[#, {{-1, 1}, {-1, 1}}, 

     MaxCellMeasure -> {1 -> .02}] &@BoundaryDiscretizeRegion[annulus];

r2d2 = DiscretizeGraphics[g2d, MaxCellMeasure -> {1 -> .01}, 

   PlotRange -> All];

inside2 = RegionIntersection[r2d2, mask2]


I can produce (pseudo)randomly distributed circles inside an annulus.
enter image description here



I have two questions. The first is a ridiculous one: How can we modify the color (e.g. Red) of the DiscretizeGraphics output.



The second one is not a tricky one. I want the circles to have random radius. Any ideas of how can I achieve that?



For References about above codes see the question:



find the maximum number of not intersecting circles inside an ellipse



and references therein.






plotting graphics discretization







share|improve this question









$endgroup$












  • $begingroup$
    Do they all have to fit inside the annulus?
    $endgroup$
    – user5601
    2 hours ago










  • $begingroup$
    Yes, they should.
    $endgroup$
    – dimitris
    2 hours ago
















5












$begingroup$


With the following code:



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, 0.4], 

    EdgeForm@Directive[Thickness[0.004], Black], Disk[#, r] & /@ pts},

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



d1 = Disk[{0.5, 0.5}, 0.5];

d2 = Disk[{0.5, 0.5}, 0.3];

annulus = RegionDifference[d1, d2];



mask2 = BoundaryDiscretizeRegion[#, {{-1, 1}, {-1, 1}}, 

     MaxCellMeasure -> {1 -> .02}] &@BoundaryDiscretizeRegion[annulus];

r2d2 = DiscretizeGraphics[g2d, MaxCellMeasure -> {1 -> .01}, 

   PlotRange -> All];

inside2 = RegionIntersection[r2d2, mask2]


I can produce (pseudo)randomly distributed circles inside an annulus.
enter image description here



I have two questions. The first is a ridiculous one: How can we modify the color (e.g. Red) of the DiscretizeGraphics output.



The second one is not a tricky one. I want the circles to have random radius. Any ideas of how can I achieve that?



For References about above codes see the question:



find the maximum number of not intersecting circles inside an ellipse



and references therein.






plotting graphics discretization







share|improve this question









$endgroup$












  • $begingroup$
    Do they all have to fit inside the annulus?
    $endgroup$
    – user5601
    2 hours ago










  • $begingroup$
    Yes, they should.
    $endgroup$
    – dimitris
    2 hours ago














5












5








5





$begingroup$


With the following code:



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, 0.4], 

    EdgeForm@Directive[Thickness[0.004], Black], Disk[#, r] & /@ pts},

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



d1 = Disk[{0.5, 0.5}, 0.5];

d2 = Disk[{0.5, 0.5}, 0.3];

annulus = RegionDifference[d1, d2];



mask2 = BoundaryDiscretizeRegion[#, {{-1, 1}, {-1, 1}}, 

     MaxCellMeasure -> {1 -> .02}] &@BoundaryDiscretizeRegion[annulus];

r2d2 = DiscretizeGraphics[g2d, MaxCellMeasure -> {1 -> .01}, 

   PlotRange -> All];

inside2 = RegionIntersection[r2d2, mask2]


I can produce (pseudo)randomly distributed circles inside an annulus.
enter image description here



I have two questions. The first is a ridiculous one: How can we modify the color (e.g. Red) of the DiscretizeGraphics output.



The second one is not a tricky one. I want the circles to have random radius. Any ideas of how can I achieve that?



For References about above codes see the question:



find the maximum number of not intersecting circles inside an ellipse



and references therein.






plotting graphics discretization







share|improve this question









$endgroup$




With the following code:



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, 0.4], 

    EdgeForm@Directive[Thickness[0.004], Black], Disk[#, r] & /@ pts},

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



d1 = Disk[{0.5, 0.5}, 0.5];

d2 = Disk[{0.5, 0.5}, 0.3];

annulus = RegionDifference[d1, d2];



mask2 = BoundaryDiscretizeRegion[#, {{-1, 1}, {-1, 1}}, 

     MaxCellMeasure -> {1 -> .02}] &@BoundaryDiscretizeRegion[annulus];

r2d2 = DiscretizeGraphics[g2d, MaxCellMeasure -> {1 -> .01}, 

   PlotRange -> All];

inside2 = RegionIntersection[r2d2, mask2]


I can produce (pseudo)randomly distributed circles inside an annulus.
enter image description here



I have two questions. The first is a ridiculous one: How can we modify the color (e.g. Red) of the DiscretizeGraphics output.



The second one is not a tricky one. I want the circles to have random radius. Any ideas of how can I achieve that?



For References about above codes see the question:



find the maximum number of not intersecting circles inside an ellipse



and references therein.






plotting graphics discretization




plotting graphics discretization






share|improve this question













share|improve this question











share|improve this question




share|improve this question










asked 2 hours ago









dimitrisdimitris

2,1431331




2,1431331












  • $begingroup$
    Do they all have to fit inside the annulus?
    $endgroup$
    – user5601
    2 hours ago










  • $begingroup$
    Yes, they should.
    $endgroup$
    – dimitris
    2 hours ago


















  • $begingroup$
    Do they all have to fit inside the annulus?
    $endgroup$
    – user5601
    2 hours ago










  • $begingroup$
    Yes, they should.
    $endgroup$
    – dimitris
    2 hours ago
















$begingroup$
Do they all have to fit inside the annulus?
$endgroup$
– user5601
2 hours ago




$begingroup$
Do they all have to fit inside the annulus?
$endgroup$
– user5601
2 hours ago












$begingroup$
Yes, they should.
$endgroup$
– dimitris
2 hours ago




$begingroup$
Yes, they should.
$endgroup$
– dimitris
2 hours ago










1 Answer
1






active

oldest

votes


















4












$begingroup$

Far from efficient, but we can adapt the Neat Example from the RegionDisjoint ref page. Note that a non-uniform distribution of radii would probably speed things up.



outerReg = Annulus;



randomBall[dim_, reg_] := (

  While[

    !RegionWithin[reg, ball = Ball[RandomPoint[reg], RandomReal[{1/15, 1/6}]]],

    (* spin *)

  ];

  ball

)



appendDisjointBall[dim_][reg : Ball[pts_, rs_]] :=

  Block[{ball = randomBall[dim, outerReg]}, 

    While[! RegionDisjoint[ball, reg],

      ball = randomBall[dim, outerReg]

    ];

    Ball[Append[pts, #1], Append[rs, #2]] & @@ ball

  ]



disjointBalls[n_, dim_] := 

 Nest[appendDisjointBall[dim], List /@ randomBall[dim, outerReg], n - 1]



n = 40;

scene2D = disjointBalls[n, 2];



Graphics[{

  {EdgeForm[Black], GrayLevel[.9], Annulus}, 

  {EdgeForm[Black], Thread[{RandomColor[Hue[_], n], Thread[scene2D]}]}

}]







share|improve this answer









$endgroup$













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    oldest

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    4












    $begingroup$

    Far from efficient, but we can adapt the Neat Example from the RegionDisjoint ref page. Note that a non-uniform distribution of radii would probably speed things up.



    outerReg = Annulus;
    

    
randomBall[dim_, reg_] := (
    
  While[
    
    !RegionWithin[reg, ball = Ball[RandomPoint[reg], RandomReal[{1/15, 1/6}]]],
    
    (* spin *)
    
  ];
    
  ball
    
)
    

    
appendDisjointBall[dim_][reg : Ball[pts_, rs_]] :=
    
  Block[{ball = randomBall[dim, outerReg]}, 
    
    While[! RegionDisjoint[ball, reg],
    
      ball = randomBall[dim, outerReg]
    
    ];
    
    Ball[Append[pts, #1], Append[rs, #2]] & @@ ball
    
  ]
    

    
disjointBalls[n_, dim_] := 
    
 Nest[appendDisjointBall[dim], List /@ randomBall[dim, outerReg], n - 1]
    

    
n = 40;
    
scene2D = disjointBalls[n, 2];
    

    
Graphics[{
    
  {EdgeForm[Black], GrayLevel[.9], Annulus}, 
    
  {EdgeForm[Black], Thread[{RandomColor[Hue[_], n], Thread[scene2D]}]}
    
}]







    share|improve this answer









    $endgroup$


















      4












      $begingroup$

      Far from efficient, but we can adapt the Neat Example from the RegionDisjoint ref page. Note that a non-uniform distribution of radii would probably speed things up.



      outerReg = Annulus;
      

      
randomBall[dim_, reg_] := (
      
  While[
      
    !RegionWithin[reg, ball = Ball[RandomPoint[reg], RandomReal[{1/15, 1/6}]]],
      
    (* spin *)
      
  ];
      
  ball
      
)
      

      
appendDisjointBall[dim_][reg : Ball[pts_, rs_]] :=
      
  Block[{ball = randomBall[dim, outerReg]}, 
      
    While[! RegionDisjoint[ball, reg],
      
      ball = randomBall[dim, outerReg]
      
    ];
      
    Ball[Append[pts, #1], Append[rs, #2]] & @@ ball
      
  ]
      

      
disjointBalls[n_, dim_] := 
      
 Nest[appendDisjointBall[dim], List /@ randomBall[dim, outerReg], n - 1]
      

      
n = 40;
      
scene2D = disjointBalls[n, 2];
      

      
Graphics[{
      
  {EdgeForm[Black], GrayLevel[.9], Annulus}, 
      
  {EdgeForm[Black], Thread[{RandomColor[Hue[_], n], Thread[scene2D]}]}
      
}]







      share|improve this answer









      $endgroup$
















        4












        4








        4





        $begingroup$

        Far from efficient, but we can adapt the Neat Example from the RegionDisjoint ref page. Note that a non-uniform distribution of radii would probably speed things up.



        outerReg = Annulus;
        

        
randomBall[dim_, reg_] := (
        
  While[
        
    !RegionWithin[reg, ball = Ball[RandomPoint[reg], RandomReal[{1/15, 1/6}]]],
        
    (* spin *)
        
  ];
        
  ball
        
)
        

        
appendDisjointBall[dim_][reg : Ball[pts_, rs_]] :=
        
  Block[{ball = randomBall[dim, outerReg]}, 
        
    While[! RegionDisjoint[ball, reg],
        
      ball = randomBall[dim, outerReg]
        
    ];
        
    Ball[Append[pts, #1], Append[rs, #2]] & @@ ball
        
  ]
        

        
disjointBalls[n_, dim_] := 
        
 Nest[appendDisjointBall[dim], List /@ randomBall[dim, outerReg], n - 1]
        

        
n = 40;
        
scene2D = disjointBalls[n, 2];
        

        
Graphics[{
        
  {EdgeForm[Black], GrayLevel[.9], Annulus}, 
        
  {EdgeForm[Black], Thread[{RandomColor[Hue[_], n], Thread[scene2D]}]}
        
}]







        share|improve this answer









        $endgroup$



        Far from efficient, but we can adapt the Neat Example from the RegionDisjoint ref page. Note that a non-uniform distribution of radii would probably speed things up.



        outerReg = Annulus;
        

        
randomBall[dim_, reg_] := (
        
  While[
        
    !RegionWithin[reg, ball = Ball[RandomPoint[reg], RandomReal[{1/15, 1/6}]]],
        
    (* spin *)
        
  ];
        
  ball
        
)
        

        
appendDisjointBall[dim_][reg : Ball[pts_, rs_]] :=
        
  Block[{ball = randomBall[dim, outerReg]}, 
        
    While[! RegionDisjoint[ball, reg],
        
      ball = randomBall[dim, outerReg]
        
    ];
        
    Ball[Append[pts, #1], Append[rs, #2]] & @@ ball
        
  ]
        

        
disjointBalls[n_, dim_] := 
        
 Nest[appendDisjointBall[dim], List /@ randomBall[dim, outerReg], n - 1]
        

        
n = 40;
        
scene2D = disjointBalls[n, 2];
        

        
Graphics[{
        
  {EdgeForm[Black], GrayLevel[.9], Annulus}, 
        
  {EdgeForm[Black], Thread[{RandomColor[Hue[_], n], Thread[scene2D]}]}
        
}]








        share|improve this answer












        share|improve this answer



        share|improve this answer










        answered 1 hour ago









        Chip HurstChip Hurst

        20.8k15789




        20.8k15789






























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