# Quality of Show with two Graphics3D: intersection quality

I plot following two shapes with Graphics 3D:

Show[Graphics3D[{Yellow, Ellipsoid[{1/E^(1/5), 1/E^(1/10), 1/E^(1/10)}, {1/E^(1/5), 1/E^(1/10), 1/E^(1/10)}]}, AxesOrigin -> {0, 0, 0}], Graphics3D[{Black, Sphere[{1/E^(2/5), 1/E^(1/5), 1/E^(1/5)}, 1]}]]

with the output

As one can see the quality of the intersection is very bad. How can I make it more smooth?

Use Method -> {"SpherePoints" -> {HorizontalPoints, VerticalPoints}}

Show[
Graphics3D[{Yellow,
Ellipsoid[{1/E^(1/5), 1/E^(1/10), 1/E^(1/10)}, {1/E^(1/5), 1/E^(1/10),
1/E^(1/10)}]},
AxesOrigin -> {0, 0, 0},
Method -> {"SpherePoints" -> {100, 100}}],
Graphics3D[{Black, Sphere[{1/E^(2/5), 1/E^(1/5), 1/E^(1/5)}, 1]},
Method -> {"SpherePoints" -> {100, 100}}]]

However, note that you can use a single Graphics3D

Graphics3D[{Yellow,
Ellipsoid[{1/E^(1/5), 1/E^(1/10), 1/E^(1/10)}, {1/E^(1/5), 1/E^(1/10),
1/E^(1/10)}],
Black, Sphere[{1/E^(2/5), 1/E^(1/5), 1/E^(1/5)}, 1]},
AxesOrigin -> {0, 0, 0},
Method -> {"SpherePoints" -> {100, 100}}]