I couldn't find a good reference for Boo-style "freeze when you look at it" enemies in a top-down game, so I had to work it out from first principles. The solution I came to that felt good was:
- Divide the screen in half through the avatar. Anything on the front side of the line is considered visible.
- Use 8-way facing instead of 4-way. So it's a horizontal/vertical split if facing horizontally/vertically, diagonal split if facing diagonally.
- Shift the dividing point to the tile *behind* the avatar. This gives the avatar slightly more than 180 degree FOV.
- Delay a bit before the unseen guy unfreezes. I'm using about 8 frames of delay here.