Generate profile face from front face image

How can I generate profile face image, based on an input of a front face image?

specifically, I'm more interested in doing it for illustrated characters.

For example, given the input of the front face (left) of Homer Simpson, we'll generate his profile face (right):

(source)

I'm sure that that the technology exists, as evident by many 2D to 3D Avatar results (here's one for example), so I figure what I'm looking for should be possible (and maybe easier, since I'm not looking for a whole head generation).

However, I couldn't find online resources on how to achieve that, whether with realistic or non-realiatic (i.e. illustarated) images.

So, how can this be done?