Hi Alex,
The Camera Projection has no shadow option. To get this done, a light source must be employed.
This is a little bit more tricky than the camera mapping, but having a camera mapping set up is certainly a needed guide.
I have set up two scenes, “…_01.c4d” and “…_11.c4d”:
https://www.amazon.com/clouddrive/share/5r4KWdst32UkUR4oEj2l45UIetuOJlc8NvQCxOwsodW
Have as well a look at the screen-shot.
Please start with the …_01.c4d file to get an idea about the set up. Since the flat projection will not come anywhere close to camera projection, file …_11.c4d is set up with a Spherical Projection.
Please note the set up of the shadow and the Light> Details to get an evenly lit projection.
Additionally, one can rebuild just a projector:
Scene file “…_21.c4d”
https://www.amazon.com/clouddrive/share/KoEcpOhVArBatqhPYCxKlH1bDqckn8xnaivAH4k8Njv
Brainstorming: An Alternative would be to use the camera mapping, but have a light source first recreate the Frustum of the camera, and cast so the shadow, this needs to be backed on the object. The additional information of the camera projection should result then in the wanted appearance.
I have done this for a music video, kind of, to introduce the shadows of a billboard on the walls.
https://www.youtube.com/watch?v=fYNJd9QGHGo
You will find on my YouTube channel as well a little making of, for this clip.
https://www.youtube.com/watch?v=mSWrLLlGyJo&list=PLOLI4wu7NPsijH80qg6XvNZdUhlf2Ic5d
A screen-shot of the camera mapping with the “painted” shadow from the billboard is here:
https://www.amazon.com/clouddrive/share/GUXZgpg1V1dKRthgT0hqYNx7jlI5BrOb16LdvwVyVqr
All the best