How to include 2 dimensional disks in a Graphics3D object (Ellipsoid)

Question

I hope I am not doing something wrong.

Compare the following figures.

1) Ellipsoid

Graphics3D[{{Specularity[White, 40], Opacity[0.5], 
   Ellipsoid[{0, 0, 0}, {10, 3, 2}]}, {Opacity[1], 
   Ellipsoid[{0, 0, 0}, {0, 3, 2}], Ellipsoid[{0, 0, 0}, {10, 0, 2}], 
   Ellipsoid[{0, 0, 0}, {10, 3, 0}]}}, ImageSize -> Large]

2) The same goal but in a more "user-defined" way

 Graphics3D[{Specularity[White, 40], Opacity[0.5], 
        Scale[#, {10, 3, 2}], {Opacity[1], Scale[#, {.001, 3, 2}], 
         Scale[#, {10, 0.001, 2}], Scale[#, {10, 3, 0.001}]}} &@Sphere[], 
     ImageSize -> Large]

Why the quality of the first Graphics3D is so bad?

$Version

(*"10.3.0 for Linux x86 (64-bit) (October 9, 2015)"*)

Check out @Taiki's answer to this question for the ellipse3D function that draws 2D ellipses in 3D space. — shrx, Nov 20 '15 at 11:02
I upvoted Jasons answer, but the correct way would be to implement a 2d ellipse for 3d space using e.g. polygon. If you do such things like scaling one dimension of a 3d object to a very thin plate, is never a good idea and can still lead to artifacts. On the long run, you should follow shrx's suggestion above. — halirutan, Nov 20 '15 at 11:20

score 6 · Accepted Answer · edited Apr 13 '17 at 12:56

The problem with the first graphic is that you are trying to create a 3D object with exactly zero width in one dimension. In the second graphic, you make the width in that dimension equal to a small value. This same workaround can be applied to the Ellipsoid call,

Graphics3D[{{Specularity[White, 40], Opacity[0.5],
   Ellipsoid[{0, 0, 0}, {10, 3, 2}]},
  {Opacity[1],
   Ellipsoid[{0, 0, 0}, {0.001, 3, 2}],
   Ellipsoid[{0, 0, 0}, {10, 0.001, 2}],
   Ellipsoid[{0, 0, 0}, {10, 3, 0.001}]}}, ImageSize -> Large]

Thanks to shrx for pointing out a better way to do this, as shown in in this post by Taiki. Using the function ellipse3D[center,{r1,r2},normal], which takes as argument the center position, the two semiaxes, and the normal vector to the plane, we get

Graphics3D[{{Specularity[White, 40], Opacity[0.5], 
   Ellipsoid[{0, 0, 0}, {10, 3, 2}]},
  {Opacity[1], EdgeForm[None], 
   ellipse3D[{0, 0, 0}, {2, 3}, {1, 0, 0}], 
   ellipse3D[{0, 0, 0}, {10, 2}, {0, 1, 0}], 
   ellipse3D[{0, 0, 0}, {10, 3}, {0, 0, 1}]}}, ImageSize -> Large]

giving an identical looking result which, as halirutan says, will behave better in the long run.

Thanks. I thought I can create directly a disk with Ellipsoid. Should I change the title of the question since the error belongs to me and to Mathematica? — Dimitris, Nov 20 '15 at 11:02
Or change the title to reflect that the problem is how to include 2 dimensional disks in a Graphics3D object, which is something others may search for. This is one workaround, giving it a really small width — Jason B., Nov 20 '15 at 11:04

How to include 2 dimensional disks in a Graphics3D object (Ellipsoid)

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