Is there an easy way to position and rotate an object so that it fits a region (say, the left half) on my camera view and faces it? What I am after is somewhat similar to camera-controls FitToBox, except that I’d want the object to be moving instead of the camera. Thanks in advance!
A very gentle bump - please let me know if the question does not make sense 
The solution would depend on what object you have in mind as well as facing the camera - which part of the object needs to face it?
Or do you want, say, an object in a particular orientation and distance from the camera to be scaled so its size is half the cross-section of the frustum?
There is a lot of room for interpretation here, unless you have a concrete example.
See this thread, and this comment, for how to calculate distance from camera to fit an object in the camera viewport:
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