I have been trying to generate random $(x,y,z)$ coordinates (i.e. for 15 ellipsoids) so that they obey following constraints:

  • ellipsoid's length is constant,
  • ellipsoids do not intersect (fulfilled even when they are tilted),
  • $z$ can be adjustable, means that random coordinates can be generated 2D $(x,y)$ or 3D $(x,y,z)$,

however, it appeared as a tough task. I know how to generate 15 random ellipsoids but I do not know how to impose the constraints.

  • $\begingroup$ Similar problem, but not equal: mathematica.stackexchange.com/q/159484. $\endgroup$ Commented Aug 23, 2018 at 14:20
  • $\begingroup$ Also related: stackoverflow.com/q/6300640. $\endgroup$ Commented Aug 23, 2018 at 15:26
  • $\begingroup$ Are the ellipsoids at arbitrary angles? If so, you may need to simply define a sphere having radius the maximum radius of each ellipsoid, then use traditional sphere-packing algorithms. $\endgroup$ Commented Aug 23, 2018 at 16:42
  • $\begingroup$ I think you should probably consider acceptance/rejection methods. E.g. 1) generate a random set of ellipsoids 2) If they meet your constraints, accept them, otherwise reject them and try again $\endgroup$
    – mikado
    Commented Aug 23, 2018 at 18:19
  • $\begingroup$ Do the ellipsoids happen to be rotationally symmetric? $\endgroup$ Commented Aug 23, 2018 at 20:28


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