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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

enter image description here

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

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1 Answer 1

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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}}]]

enter image description here

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}}]

enter image description here

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