Ellipsoid in GraphicsComplex

Question

I am trying to use Ellipsoid in a GraphicsComplex and I am stuck. My understanding of GraphicsComplex is that explicit point coordinate assignments are replaced with integer values pointing to a list of coordinates instead.
So instead of
 Graphics3D[Sphere[{0, 0, 0}, 1]]

I can use
 Graphics3D[GraphicsComplex[{{0, 0, 0}}, Sphere[1, 1]]]

instead. Note, that the first argument of Sphere is replaced with the first point from the list, i.e. {0,0,0} while the second argument is correctly identified as radius (not coordinate) and not replaced with {0,0,0}.
If I use Ellipsoid instead, so instead of
Graphics3D[Ellipsoid[{0, 0, 0}, {2, 3, 4}]]

I use
Graphics3D[GraphicsComplex[{{0, 0, 0}}, Ellipsoid[1, {2, 3, 4}]]]

I get an error:
Affine transform 1 should be one of the forms {{{xx, yx, zx}, {xy, yy, zy}, {xz, yz, zz}}, {tx, ty, tz}}; {{xx, yx, zx}, {xy, yy, zy}, {xz, yz, zz}}; or {tx, ty, tz}.

and
Coordinate index 0 is out of range for the enclosing GraphicsComplex.

Two questions: do I use GraphicsComplex incorrectly? and is there a simple workaround to feed Ellipsoids to a GraphicsComplex?

Carl Woll · Answer

Note that Ellipsoid is rendered by using GeometricTransformation under the hood:
ToBoxes @ Graphics3D[Ellipsoid[{1,1,1}, {2,3,4}]]

Graphics3DBox[
InterpretationBox[
GeometricTransformation3DBox[
SphereBox[{0, 0, 0}], {{{2, 0, 0}, {0, 3, 0}, {0, 0, 4}}, {1, 1, 1}}],
Ellipsoid[{1, 1, 1}, {2, 3, 4}]]]

Basically, a sphere at the origin is translated and transformed by the GeometricTransformation3DBox so that it looks like the desired Ellipsoid. Now, notice that the center of the Ellipsoid is part of the transformation argument. Unfortunately, GraphicsComplex can only handle coordinate indices when they are inside of a normal graphics primitive, in this case inside of SphereBox. This is why GraphicsComplex of Ellipsoid doesn't work. Consider the corresponding GraphicsComplex version:
ToBoxes @ Graphics3D[GraphicsComplex[{{1,1,1}}, Ellipsoid[1, {2, 3, 4}]]]

Graphics3DBox[
GraphicsComplex3DBox[{{1, 1, 1}},
InterpretationBox[
GeometricTransformation3DBox[
SphereBox[{0, 0, 0}], {{{2, 0, 0}, {0, 3, 0}, {0, 0, 4}}, 1}],
Ellipsoid[1, {2, 3, 4}]]]]

If GraphicsComplex3DBox could understand that the 1 inside the GeometricTransformation3DBox represented the point {1, 1, 1} then it would render properly. However, it is tricky figuring out what parts of a such a list correspond to a point, and so GraphicsComplex3DBox gives up.

Ellipsoid in GraphicsComplex

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