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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