I'm using an angle *range*, not 16 angles.
To get the correct angles to make something like this work, you have to know all the angles "in between" the standard 8 directional angles (The standard 8 directional angles IE; 0, 45, 90, 135, 180, 225, 270, 315)
You need to find the point that's half way between each of those angles, to create an angle "range".
See attached (badly drawn) diagram. Hopefully this will clear things up;
https://www.dropbox.com/s/fvns8tk4pvdk6im/angles.png?dl=0
So you only use 8 directions of actual animation/graphics but you change the frame or animation sequence based on a range of angle.
As I mentioned originally, this effect looks better with objects like cars/vehicles and not-so-much for a character sprite.... but that totally depends on how you've drawn your artwork as well. You will need to experiment to see if something like this will do what you're looking for.
~Sol