Given a convex polygon with $n$ edges sorted in cyclic order. How fast can we decide whether a line $\bar{pq}$ is fully inside the polygon?
My idea was to use a method for deciding whether a point is inside a polygon (e.g. ray casting algorithm) and do this twice. If both points are inside then the line between them is also inside the convex polygon.
Now my question is if there is any other faster method I didn't know of or if this is the usual way to go.
Any hint is appreciated!