I have an edge of a polygon (convex or concave). I want to find out if, going straight from start to end point of that edge, I have to turn right or left to get inside or ou
Another approach:
Project a perpendicular line and count how many times it crosses other edges.
odd -> interior
zero or even -> exterior
Equivalently If you happen to have a well optimized point-in-polygon routine available you can project a point some epsilon off the line and throw it into the inside test.
Traverse the whole polygon in that direction. If you find that you went clockwise, then the interior is to the right; if you went counter-clockwise, it's to the left.