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


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]

enter image description here


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]


enter image description here


Why the quality of the first Graphics3D is so bad?


$Version

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

Answer



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]

enter image description here


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]

enter image description here


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


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