modifying graphics3D objects after their creation

Question

Suppose I want to demnstrate two ellispoids; one with the center at the origin and the other translated.

After the advice I got in the last question I use

ellipse3D[centre_: {0, 0, 0}, radii_: {1, 1}, normal_: {0, 0, 1}] := 
 Polygon[RotationTransform[{{0, 0, 1}, normal}, centre][
   Map[Append[#, Last@centre] &][
    SortBy[#, N[ArcTan @@ (# - Most@centre)] &] &[
     MeshCoordinates[
      BoundaryDiscretizeRegion[Ellipsoid[Most@centre, radii]]]]]]]

arrowAxesXYZ[{a_, b_, c_}] := 
 Map[Arrow[Tube[{{0, 0, 0}, #}]] &, {a + 2, b + 2, 
    c + 2} IdentityMatrix[3]]
AxesXYZ[{a_, b_, c_}] := {Text[
   Style["X", 20, Italic], {a + 2.2, 0, 0}], 
  Text[Style["Y", 20, Italic], {0, b + 2.2, 0}], 
  Text[Style["Z", 20, Italic], {0, 0, c + 2.2}]}

EllipsoidXYZ[{a_, b_, c_}] := {{Specularity[White, 40], Opacity[0.5], 
   Ellipsoid[{0, 0, 0}, {a, b, c}]}, {Gray, Opacity[1], 
   EdgeForm[None], ellipse3D[{0, 0, 0}, {c, b}, {1, 0, 0}], 
   ellipse3D[{0, 0, 0}, {a, c}, {0, 1, 0}], 
   ellipse3D[{0, 0, 0}, {a, b}, {0, 0, 1}]}}

translatedEllipsoidXYZ[{a_, b_, c_}, {d_, e_, f_}] := 
 Translate[EllipsoidXYZ[{a, b, c}], {d, e, f}]
translateAxesXYZ[{a_, b_, c_}, {d_, e_, f_}] := 
 Translate[arrowAxesXYZ[{a, b, c}], {d, e, f}]
vectorofTranslation[{d_, e_, f_}] := {Gray, 
  Arrow[Tube[{{0, 0, 0}, {d, e, f}}, 0.05]]}

Show[Graphics3D[{EllipsoidXYZ[{10, 3, 2}], arrowAxesXYZ[{10, 3, 2}], 
   AxesXYZ[{10, 3, 2}], 
   translatedEllipsoidXYZ[{10, 3, 2}, {15, 7, 4}], 
   translateAxesXYZ[{10, 3, 2}, {15, 7, 4}], 
   vectorofTranslation[{15, 7, 4}]}], ImageSize -> 600]

taking

My question is how can someone modify this output? Saying for instance that we want
a) Get rid of the cross sections of the translated ellipsoid. b) Modify the opacity of the translated ellipsoid. c) Modify the apppearance of the translated axis.

I could add arguments in the definitions but I am wondering how in general we can modify a complex graphics3D after its creation.

If you are lost in the various definitions, it suffices to me a minimal example of "how-to-approach".

Answer 1

The basic answer to "how in general we can modify a complex graphics3D after its creation?" is to define each subelement of the 3D graphic as a separate entity, then combine them together with Show. Next you choose which ones to show by setting boolean variables, which you either define beforehand or manipulating them.

Too many different questions in there, but this should give a general idea on how to have people modify the graphics,

Manipulate[Module[
  {ellps, xdisk, ydisk, zdisk},
  ellps = {Specularity[White, 40], Opacity[opac], 
    Ellipsoid[{0, 0, 0}, {10, 3, 2}]};
  xdisk = {Opacity[1], EdgeForm[None], 
    ellipse3D[{0, 0, 0}, {2, 3}, {1, 0, 0}]};
  ydisk =  {Opacity[1], EdgeForm[None], 
    ellipse3D[{0, 0, 0}, {10, 2}, {0, 1, 0}]};
  zdisk =  {Opacity[1], EdgeForm[None], 
    ellipse3D[{0, 0, 0}, {10, 3}, {0, 0, 1}]};
  Graphics3D[Join[
    {ellps},
    {If[xtrue, xdisk]},
    {If[ytrue, ydisk]},
    {If[ztrue, zdisk]}
    ]
   ]
  ], {{xtrue, True, "X plane"}, {True, False}},
 {{ytrue, True, "Y plane"}, {True, False}},
 {{ztrue, True, "Z plane"}, {True, False}},
 {{opac, 0.5, "Ellipsoid Opacity"}, 0, 1}]