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I'd like to connect many spheres, by adding a new sphere at some point that's sitting on the surface of a previous sphere. How could we do this?

Suppose I have a unit sphere and a point on it:

myShpere1=Sphere[];
myPoint1=SpherePoints[1];
Graphics3D[{myShpere1, Point[myPoint1]}]

enter image description here

How can we add a second sphere who's surface is touching the previous one at the random point, then a third sphere on a random point of the second sphere, and so on? (for any number of spheres, always choosing a new random point). On a related issue, do spheres have an orientation in MMA, as ellipsoids do? If so, how do we get the "vector/axis" of orientation?

Thanks!

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2 Answers 2

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spheres = Sphere[#, 1] & /@ NestList[
  With[{rp = RandomPoint[Sphere[#, 1]]}, 2 rp - #] &, {0, 0, 0}, 5];

chained spheres

If you need the spheres to be self avoiding, then you could look into this question.

All spheres are oriented upward.

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    $\begingroup$ You don't need to map Sphere[], since it can support multiple centers if the radius is fixed: Graphics3D[Sphere[NestList[With[{rp = RandomPoint[Sphere[#, 1]]}, 2 rp - #] &, {0, 0, 0}, 5], 1]] $\endgroup$
    – J. M.'s eventual burnout ♦
    Aug 5, 2020 at 14:55
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NestList as in flinty's answer is a bit overkill. You can simply use Accumulate like this:

Graphics3D@Sphere@Accumulate[2 RandomPoint[Sphere[], 5]]

Output

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  • $\begingroup$ Very cool! From @flinty answer I was able to get the coordinates of the points of sphere-sphere contact from the NestList. How could I get this info from your answer? $\endgroup$
    – TumbiSapichu
    Jul 12, 2020 at 0:00
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    $\begingroup$ @TumbiSapichu That's a great question for you to figure out, I think, to make sure that you truly understand the solution. It's not difficult. $\endgroup$
    – C. E.
    Jul 12, 2020 at 0:01
  • $\begingroup$ Ah, I see everything to the right of the accumulate is the points, the rest is just the plotting. I've just never used Accumulate so I though it'd do something weird. Thanks! $\endgroup$
    – TumbiSapichu
    Jul 12, 2020 at 0:03

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