Mathematica Asked on May 12, 2021
I would like to draw a figure in 3D where I have a large cylinder inside which there are:
a) smaller cylinders parallel to the larger cylinder that contains them, like in the image below (taken from: How to draw cylinders inside a cylinder)
b) randomly distributed spheres that "break" the small cylinders. Occasionally these sphere may appear also on the surface of the main cylinder. I am also ok to place the sphere manually (rather than randomly)
I am looking for suggestion on how to proceed.
Something like the following?
Graphics3D[{
{Opacity[0.3], Cylinder[{{0, 0, -1}, {0, 0, 1}}, 1]},
{Opacity[0.4],
Table[If[x^2 + y^2 <= .9^2,
Cylinder[{{x, y, -1}, {x, y, 1}}, 0.1]], {x, -1, 1, .2}, {y, -1,
1, .2}]}
, Table[pos = RandomReal[{-.9, .9}, 3];
If[pos[[1 ;; 2]].pos[[1 ;; 2]] <= .9^2, Sphere[pos, 0.1]], 100]
}]
Correct answer by Daniel Huber on May 12, 2021
outerradius = 1.0;
seeds = RandomPoint[Disk[{0, 0}, outerradius], 3000];
radius = .05;
results = Reap[
While[Length[seeds] > 2,
(* pick a point and remove all others within radius *)
{{point}, seeds} = TakeDrop[seeds, 1];
seeds = Select[seeds, EuclideanDistance[#, point] > 2 radius &];
Sow[point];
]
][[2, 1]];
height = 1.0;
cylinders =
Cylinder[{Append[#, 0], Append[#, height]}, radius] & /@ results;
Graphics3D[{Blue, Opacity[.5],
Cylinder[{{0, 0, 0.001}, {0, 0, height - 0.001}},
outerradius + radius], Gray, Opacity[1], cylinders},
Lighting -> "Neutral", Boxed -> False]
Unfortunately I can't get the clipping of the cylinders at the edges. It is very slow to do a RegionUnion
of all the cylinders and then RegionIntersection
this bundle with the outer cylinder to chop the edges off. You'd be better off doing this in more optimized 3D software capable of boolean CSG operations.
Answered by flinty on May 12, 2021
Here is how you create non overlapping random circles inside a unit circles. Take care not to create too many circles, because if the unit circle is filled, the function will search forever:
oldpos = {};
newpos[] := (While[(t = RandomReal[{-.9, .9}, 2]; t.t > 0.9^2) || (
Min[Norm[# - t] & /@ oldpos] < 0.2)]; AppendTo[oldpos, t]; t)
Graphics[Table[Circle[newpos[], 0.1], {40}]]
Answered by Daniel Huber on May 12, 2021
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