"Sharp" is relative. There is always a zoom level, which let a curve look smooth.
If you do not have a curve defined by a function, but a piecewise defined line, you are looking for neighboring elements with and included angle above a certain limit. But when such a piece has a length of 1e-200, while the others have a length of 1.0, can this have a "sharp turn"?!
But let's imagine, that you can control this fundamental problem by inventing some meaningful thresholds. Then this determines the angle between two lines:
angle = atan2(norm(cross(N1, N2)), dot(N1, N2))