Nice writeup, looks really cool. A further step might be to 3D scan the installation location you're placing it in to generate a completely custom mesh that takes into account the unique geometry of the room - you could even include the furniture if you wanted to!
Interesting idea! Maybe you could do it 'live' using a transparent curved display as the shade and a Kinect or equivalent...
One thing that also bugged me is the fact that an isotropic light source forms an unevenly-lit image, so maybe you'd want an anisotropic emitter too.
At this stage you've basically invented Illumiroom and you may as well just use a wide angle projector. You don't have full 360 coverage though so you'd need several projectors.
In normal 3D modelling for animation this is called 'creating a reflection map'. A normal 3D package will just do it and in the environment you can have more than the one 2D flat shape (e.g. the floor/ceiling here). Plus you can accommodate a change in position of the light fixture.
In another discipline - maps - we are talking projections. Personally I would like a globe of the illuminated variety with a paper cylinder around it getting a Mercator projection on it.
Either way, the maths and software for this has been on the desktop for at least 25 years (render times were a while back then).
You won't get a proper global Mercator map through light projection (a so called geometric projection) from a sphere, the relation is purely mathematical.
A central cylindrical projection is what you get when you put a light in the center of a sphere and project that on a cylinder
Ha! Dyslexics untie. After I re-read the title correctly I half wished this would be about projecting random dot stereograms on the ceiling / wall.
Dot stereograms might be hard as it would be difficult to get fine dots. But in principle it should be possible to project stereograms. That would be one perverse pun on 3D.
You could go full circle by mapping a tessellated tile-able projection like
Peirce quincuncial back onto the spherical lampshade via the inverse stereographic projection.
