# Computational geometry relationship between 2 arcs

I'm writing a program which is making offsets for provided shapes. On the attached picture you can see example of my arc object and all known values. Let's assume that a direction is CW.

$$O$$ - center of circle for arc

$$P_s$$ - start point on circle for arc

$$P_e$$ - end point on circle for arc

s_ang - angle for $$P_s$$

e_ang - angle for $$P_e$$

ext - angle between $$P_s$$ and $$P_e$$

If you take a look on the picture how can I tell if they create orange(segment1 concave, segment2 convex), purple(both convex) or yellow(segment1 convex, segment2 concave) shape?