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 57 mins ago
Chip HurstChip Hurst
20.8k15789
$endgroup$
add a comment |
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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 57 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 57 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 57 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 57 mins ago
Chip HurstChip Hurst
20.8k15789
answered 57 mins ago
Chip HurstChip Hurst
20.8k15789
answered 57 mins ago
Chip HurstChip Hurst
20.8k15789
answered 57 mins 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
2 hours ago
$begingroup$
Yes, they should.
$endgroup$
– dimitris
1 hour ago