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I'm using th following way to produce solid spheres for random microstructures. I'm trying to find a way to produce solid ellipsoids with the same way. Does anyone have any idea?

I have already a code for ellipsoids producing the centers and the 3 radius (rλ1,rλ2,rλ3) in each direction, but if I plot Ellipsoid ... then I will take hollow spheres. That's the reason I am trying using this way.

Centers ,X, have produced by an algorithm and they have an array structure.enter image description here

    centers = X;
unitball[c_, x_] := EuclideanDistance[c, x] <= r;
regs = Show[
  RegionPlot3D[
     unitball[#, {x, y, z}], {x, 0, 1}, {y, 0, 1}, {z, 0, 1}, 
     Mesh -> False, Boxed -> False, Axes -> False, 
     PlotPoints -> 100] & /@ centers]
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  • $\begingroup$ Please provide a minimal working example of your code. That will increase your chance to get helpful answers. $\endgroup$ Apr 16, 2021 at 13:36

2 Answers 2

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Try ( r: list of semiaxes)

unitelli[c_, r_, x_ ] := Total[ (x - c)^2/r^2] < 1 

RegionPlot3D[
 unitelli[{2, 1, 3}, {1, 1/2, 2}, {x, y, z}], {x, 0, 5}, {y, 0, 
  4}, {z, 0, 4}, Mesh -> False , PlotPoints -> 50, 
 AxesLabel -> {x, y, z}, Axes -> False]

enter image description here

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n = 10;
centers = RandomReal[1, {n, 3}];
radius = RandomReal[{.1, .2}, {n, 3}]; 
Table[RegionPlot3D[
   RegionIntersection[
    BoundaryDiscretizeRegion[Ellipsoid[centers[[i]], radius[[i]]]], 
    BoundaryDiscretizeRegion@Cuboid[]]], {i, n}] // Show

enter image description here

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