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 3 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 3 hours ago
dimitrisdimitris
2,1431331
$endgroup$
$begingroup$
Do they all have to fit inside the annulus?
$endgroup$
– user5601
3 hours ago
$begingroup$
Yes, they should.
$endgroup$
– dimitris
3 hours 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 3 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 3 hours ago
dimitrisdimitris
2,1431331
asked 3 hours ago
dimitrisdimitris
2,1431331
asked 3 hours ago
dimitrisdimitris
2,1431331
asked 3 hours ago
dimitrisdimitris
2,1431331
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
3 hours ago
add a comment |
$begingroup$
Do they all have to fit inside the annulus?
$endgroup$
– user5601
3 hours ago
$begingroup$
Yes, they should.
$endgroup$
– dimitris
3 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
3 hours ago
$begingroup$
Yes, they should.
$endgroup$
– dimitris
3 hours 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 2 hours ago
Chip HurstChip Hurst
20.8k15789
$endgroup$
add a comment |
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1 Answer
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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 2 hours 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 2 hours 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 2 hours 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 2 hours ago
Chip HurstChip Hurst
20.8k15789
answered 2 hours ago
Chip HurstChip Hurst
20.8k15789
answered 2 hours ago
Chip HurstChip Hurst
20.8k15789
answered 2 hours ago
Chip HurstChip Hurst
20.8k15789
20.8k15789
add a comment |
add a comment |
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$begingroup$
Do they all have to fit inside the annulus?
$endgroup$
– user5601
3 hours ago
$begingroup$
Yes, they should.
$endgroup$
– dimitris
3 hours ago