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.










share|improve this question









$endgroup$












  • $begingroup$
    Do they all have to fit inside the annulus?
    $endgroup$
    – user5601
    3 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.










share|improve this question









$endgroup$












  • $begingroup$
    Do they all have to fit inside the annulus?
    $endgroup$
    – user5601
    3 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.










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






share|improve this question













share|improve this question











share|improve this question




share|improve this question










asked 3 hours ago









dimitrisdimitris

2,1431331




2,1431331












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










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


















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










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
















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




$begingroup$
Do they all have to fit inside the annulus?
$endgroup$
– user5601
3 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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    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 2 hours ago









        Chip HurstChip Hurst

        20.8k15789




        20.8k15789






























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