I'll make a guess...
i expect what the software does is use a 2D vector definition of an image. Lots of these things will be drawn for different characters. Each from a different angle.
The software can use these as keyframes, and then interpolate them, and can handle them in no particular order, so any view in between those pre drawn keyframes can be shown on screen.
eg, imagine you have three similar points of view A, B, C. Now can rotate the camera between any points within that triangle, not just in a straight line, but with two degrees of freedom.
So with enough of these keyframes you can completely wrap around the object and have free rotation.
To move the camera in and out would not be supported though, because there is no concept of depth to the images. But you can create new keyframes for those nostril shots, and interpolate your way into them as before.