Your problem is to vague to propose a specific solution. The basic approach
that occurs to me is to set this up as an optimization problem to maximize
the intersection volume subject to a constraint on the ellipsoid volume. If
you have a simple way to compute the intersection volume then you can
probably apply standard optimization methods.
On the other hand, if you don't have a way to compute the intersection
volume I suppose you could represent your object in a 3d grid and then
estimate intersection volume numerically. This would be a fairly slow
calculation and it wouldn't have well behaved derivatives unless you did a
good job at the boundaries---but if you did that you might still be able to
apply an optimization method (e.g. steepest descent or a Newton method).
If you don't do a good job at the boundaries then you have a
nondifferentiable optimization problem. You could attack it by brute force:
evaluate for many ellipsoids and pick the best one.
Ekinoks wrote
> Hello,
>
> I would like to approximate a 3D object by an ellipsoid.
> By approximate I mean to get an ellipsoid of equivalent volume in such a
> way
> that it maximizes the intersection with the object to be approximated.
>
> Does anyone have an idea how to do this with a simple method?
>
> Do not hesitate to answer if you have any idea.
> Thank you :)
>
>
>
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