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









$endgroup$













    Your Answer





    StackExchange.ifUsing("editor", function () {
    return StackExchange.using("mathjaxEditing", function () {
    StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
    StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
    });
    });
    }, "mathjax-editing");

    StackExchange.ready(function() {
    var channelOptions = {
    tags: "".split(" "),
    id: "387"
    };
    initTagRenderer("".split(" "), "".split(" "), channelOptions);

    StackExchange.using("externalEditor", function() {
    // Have to fire editor after snippets, if snippets enabled
    if (StackExchange.settings.snippets.snippetsEnabled) {
    StackExchange.using("snippets", function() {
    createEditor();
    });
    }
    else {
    createEditor();
    }
    });

    function createEditor() {
    StackExchange.prepareEditor({
    heartbeatType: 'answer',
    autoActivateHeartbeat: false,
    convertImagesToLinks: false,
    noModals: true,
    showLowRepImageUploadWarning: true,
    reputationToPostImages: null,
    bindNavPrevention: true,
    postfix: "",
    imageUploader: {
    brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
    contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
    allowUrls: true
    },
    onDemand: true,
    discardSelector: ".discard-answer"
    ,immediatelyShowMarkdownHelp:true
    });


    }
    });














    draft saved

    draft discarded


















    StackExchange.ready(
    function () {
    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f190891%2frandomly-distributed-circles-inside-an-annulus%23new-answer', 'question_page');
    }
    );

    Post as a guest















    Required, but never shown

























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    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









    $endgroup$


















      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






























            draft saved

            draft discarded




















































            Thanks for contributing an answer to Mathematica Stack Exchange!


            • Please be sure to answer the question. Provide details and share your research!

            But avoid …



            • Asking for help, clarification, or responding to other answers.

            • Making statements based on opinion; back them up with references or personal experience.


            Use MathJax to format equations. MathJax reference.


            To learn more, see our tips on writing great answers.




            draft saved


            draft discarded














            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f190891%2frandomly-distributed-circles-inside-an-annulus%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown





















































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown

































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown







            -

            Popular posts from this blog

            Bundesstraße 106

            Image
            Dieser Artikel beschreibt die Bundesstraße 106 in Deutschland. Zur gleichnamigen Straße in Österreich siehe Mölltal Straße. Vorlage:Infobox hochrangige Straße/Wartung/DE-B Bundesstraße 106 in Deutschland Karte Basisdaten Betreiber: Deutschland  Bundesrepublik Deutschland Straßenbeginn: Wismar ( 53° 54′  N , 11° 24′  O 53.900536 11.396875 ) Straßenende: Schwerin ( 53° 36′  N , 11° 24′  O 53.592785 11.404892 ) Gesamtlänge: 40,7 km Bundesland: Mecklenburg-Vorpommern Ausbauzustand: zweistreifig [1] Bundesstraße 106 in Schwerin (Umgehungsstraße) Straßenverlauf Land Mecklenburg-Vorpommern Landkreis Nordwestmecklenburg Ortsumgehung Wismar Wallensteingraben über   Dorf Mecklenburg Wallensteingraben Groß Stieten Bad Kleinen OT Niendorf Bahnstrecke Lübeck–Bad Kleinen Zickhusen Lübstorf Klein Trebbow OT Kirch Stück
            Read more

            Verónica Boquete

            Image
            Verónica Boquete im Trikot der Nationalmannschaft (2013) Personalia Name Verónica Boquete Giadans Geburtstag 9. April 1987 Geburtsort Santiago de Compostela, Spanien Größe 159 cm Position Mittelfeld / Sturm Juniorinnen Jahre Station 2001–2005 Xuventú Aguiño Frauen Jahre Station Spiele (Tore) 1 2005–2008 Prainsa Zaragoza 83 (40) 2008–2010 Espanyol Barcelona 53 (30) 2010 Buffalo Flash 9 0 (9) 2010 Chicago Red Stars 3 0 (1) 2010–2011 Espanyol Barcelona 26 (41) 2011 Philadelphia Independence 13 0 (5) 2011 Energija Woronesch 5 0 (1) 2012–2014 Tyresö FF 39 (14) 2014 Portland Thorns FC 15 0 (4) 2014–2015 1. FFC Frankfurt 23 0 (7) 2015–2016 FC Bayern München 9 0 (0) 2016–2018 Paris Saint-Germain 31 0 (8) 2018 Peking BG Phoenix 2019– Utah Royals FC 0 0 (0) Nationalmannschaft Jahre Auswahl
            Read more

            Ida-Boy-Ed-Garten

            Image
            Die Lage des Ida-Boy-Ed-Gartens, rot markiert Der Ida-Boy-Ed-Garten Der Ida-Boy-Ed-Garten, Blick von der Wakenitzmauer durch das Tor in der Stadtmauer Der Ida-Boy-Ed-Garten ist eine Straße der Lübecker Altstadt. Inhaltsverzeichnis 1 Lage 2 Geschichte 3 Literatur 4 Weblinks Lage | Der etwa 90 Meter lange Ida-Boy-Ed-Garten befindet sich an der nördlichen Spitze der Altstadtinsel, vor dem Burgtor. Die in einem Bogen durch eine Grünanlage hangaufwärts führende Straße verbindet die Wakenitzmauer mit der Burgtorbrücke. Geschichte | Der heutige Ida-Boy-Ed-Garten wurde ursprünglich als Verlängerung der Wakenitzmauer angelegt. 1903 wurde in den erhaltenen Teil der mittelalterlichen Stadtmauer, an dem die Wakenitzmauer bei der Einmündung der Kaiserstraße begann, ein Tor mit einem großen Bogen für die Durchführung der Straße und zwei kleineren seitlichen Öffnungen für Fußgänger gebrochen, um für die neu errichteten Wohnhäuser in diesem Bereich
            Read more