I think what you're looking for is called "photogrammetry" and is produced by taking several images (or an image sequence from a video) and comparing the perspective, scale, and overall shape of the captured image and how it changes.
Using this method, you can both create quite realistic 3D-models of things you just filmed and furthermore, you can thus create animations using these models. Alternatively, you could just use an image-sequence, in which the object is captured from all sides or just rotated and let the viewer go back and forth between frames and / or perspectives.
- only really works on stills, meaning that your subject won't move
- gives you the opportunity to really zoom in and out, create parallaxe (moving the subject seperately from the background)
- Skipping between different sequences
- is comparable to how the famous bullet-dodge effect in the matrix works, only that the viewer can direct the movement of the camera himself (which is pretty cool indeed).
- Needs a lot of cameras however, set up in a ring around the subject. So you need to erase the cameras filming themselves in post, which is quite tedious. (a setup of such rig can be seen here and here. This brings with it a big spike in production-cost.
- also, if your subject is moving and you want your camera to follow it, you need to move the entire rig which, if you've seen the pictures of it, is quite a pain in the rear.
So while capturing a sequence with dozens of cameras to allow different perspectives of a subject in motion can be a very very cool and impressive effect, there is a reason why not a lot of movies use it. It's expensive, difficult to work with on set and takes a lot of time to stitch together the sequences in post.
Photogrammetry on the other hand side offers a completely free perspective for the viewer, enabling him/her to look at the subject from any angle imaginable (which the multi-cam setup doesn't offer - you can only view from the perspectives that the cameras were set up on, especially concerning the y-axis)
The downside however is, that the subject won't be moving, unless you use stop motion in which case you can "photogrammetice" the subject in different states of momentum (which again, is very tedious).
I hope you found out what is what you want and my answer was helpful to your question :)