Randomly distributed circles inside an annulus
$begingroup$
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.
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
asked 2 hours ago
dimitrisdimitris
2,1431331
$endgroup$
add a comment |
$begingroup$
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.
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
asked 2 hours ago
dimitrisdimitris
2,1431331
$endgroup$
$begingroup$
Do they all have to fit inside the annulus?
$endgroup$
– user5601
2 hours ago
$begingroup$
Yes, they should.
$endgroup$
– dimitris
1 hour ago
add a comment |
$begingroup$
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.
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
asked 2 hours ago
dimitrisdimitris
2,1431331
$endgroup$
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.
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
asked 2 hours ago
dimitrisdimitris
2,1431331
asked 2 hours ago
dimitrisdimitris
2,1431331
asked 2 hours ago
dimitrisdimitris
2,1431331
asked 2 hours ago
dimitrisdimitris
2,1431331
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
1 hour ago
add a comment |
$begingroup$
Do they all have to fit inside the annulus?
$endgroup$
– user5601
2 hours ago
$begingroup$
Yes, they should.
$endgroup$
– dimitris
1 hour 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
1 hour ago
$begingroup$
Yes, they should.
$endgroup$
– dimitris
1 hour ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
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]}]}
}]
answered 53 mins ago
Chip HurstChip Hurst
20.8k15789
$endgroup$
add a comment |
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
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
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
$begingroup$
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]}]}
}]
answered 53 mins ago
Chip HurstChip Hurst
20.8k15789
$endgroup$
add a comment |
$begingroup$
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]}]}
}]
answered 53 mins ago
Chip HurstChip Hurst
20.8k15789
$endgroup$
add a comment |
$begingroup$
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]}]}
}]
answered 53 mins ago
Chip HurstChip Hurst
20.8k15789
$endgroup$
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]}]}
}]
answered 53 mins ago
Chip HurstChip Hurst
20.8k15789
answered 53 mins ago
Chip HurstChip Hurst
20.8k15789
answered 53 mins ago
Chip HurstChip Hurst
20.8k15789
answered 53 mins ago
Chip HurstChip Hurst
20.8k15789
20.8k15789
add a comment |
add a comment |
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.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
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
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
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
$begingroup$
Do they all have to fit inside the annulus?
$endgroup$
– user5601
2 hours ago
$begingroup$
Yes, they should.
$endgroup$
– dimitris
1 hour ago