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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.

enter image description here

$O$ - 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?

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