CGAL users discussion list

[Bernd Gaertner <>]

Audette, Michel wrote:
> Dear All, 
>
> subsequent to the message below, as well as a fruitful discussion with Bernd Gaertner, I would like to tweak the algorithm for ellipsoid fitting, so that each rounded jaw of a surgical tool sits as a hat over the fitted ellipsoid. Currently, the results that we obtain indicates that the algorithm tries to center each jaw within an ellipsoidal hull. Is there a simple parameter or flag for telling the algorith to perform the fitting in a hat-like manner? 

If the jaw happens to have (almost) the shape of an ellipsoidal cap,
you can do the following: simply sample nine points from the jaw's
surface and compute the unique ellipsoid through these nine points
(this can be done by a system of linear equations). The resulting
ellipsoid should have the jaw as a "hat". If you want to make sure
that the jaw is really inside the ellipsoid, some care is order if
the jaw is not exactly ellipsoidal. But sampling the nine points
slightly off the surface might do the trick in this case.

Best,
        Bernd.