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?