For a project we need 3d animations to start unfolding whilst a person is walking. The video camera will be moving. Using After effects, achieve such a thing?
Also what is this called? So I can also continue my search on google.
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You will need motion tracking at a minimum if the camera is moving during the shot and you want to composite a 3d animation. It will need to be able to do 3d motion tracking, which is the hardest to do. I believe that Mocha (which comes with recent versions of After Effects) can handle this passably enough for a simple project. I'm not entirely sure what you are trying to do with the animation though based on how you phrased the question.
The technique you're looking for is called 3D match moving, and AE is definitely capable of pulling this off for simple/short shots, but you'll need to use it in conjunction with a 3d package like blender, maya, max, c4d, etc. Basically, you use AE's Effect->Perspective->3d Camera Tracker to extract 3d information about your physical camera's spatial orientation, and use this data to animate a camera in your 3d package. Render your 3D animations (with separate passes for whatever info you'll need to recomp, shadows, lights, AO, reflections, alphas, etc), and then composite them with the original footage back in After Effects. Keep in mind, this is a VERY simplistic overview of a VERY difficult process. For more advanced tracking, you might want to look into programs like Boujou, PFTrack, or Autodesk MatchMover.
After Effects CC comes with Cinema 4D Lite, so if you're on the Adobe cloud, you're in luck. (CC is the successor to CS6 and was released this week)
There are many other programs that can accomplish this, (see other answers), but you'll need particular expertise in 3D and compositing (match moving) to accomplish it. There are tutorials floating around the net, but they are program specific...
You could also build something in After Effects 3D layers, but I wouldn't recommend it unless it is really simple boxes/planes.
If you're new to 3D, I'd suggest getting into Cinema 4D Lite as it looks like there is a lot of effort by the Maxon and Adobe teams making the match-moving and import processes really easy.