How to detect concave point?

Let me explain on the picture:

Let’s say that all the points are distributed on spline, just like it’s shown in the image.

My first idea is to calculate a convex shape for all these points and then check if point is inside. But I haven’t figured that out yet. Maybe there is a better solution.
I’ll appreciate any help.

It’s possible by using one of the convex hull algorithms like Gift Wrapping or Graham Scan. Here is one of the examples: Convex Hull | Set 1 (Jarvis's Algorithm or Wrapping) - GeeksforGeeks

By using an algorithm like that you can create a convex hull that consists of a set of points. All the other points will be concave.