The sum of two ellipsoids as approximated by the intersectionof 30 optimal covering ellipsoids	The ellipsoid of smallest volume containing the sum of two ellipsoids

 

The sum of two ellipsoids approximated by the union of 30 optimal ellipsoids contained in the sum	The Minkowski sum: 15 optimal covering and 15 optimal internal ellipsoids

 

The largest volume ellipsoid inside the sum	The difference of two ellipsoids as approximated by the intersection of 30 optimal covering ellipsoids

 

Smallest volume ellipsoid around the difference of two ellipsoids	The difference of two ellipsoids approximated by the union of 30 optimal internal ellipsoids

 

The geometrical difference: 15 optimal covering and 15 optimal internal ellipsoids	Largest volume ellipsoid inside the difference of two ellipsoids