For work I need to decide if a random point is at a "strong" curvature of a cubic-2D-bezier or not. I'm testing with the Bezier below. I got the 1st 2 derivatives from Wikipedia. In the first image I've marked the areas which I would like to detect as strong curved in green. But I'm not sure how should I do that.
I guess I will have to work with the 2nd derivative but it's kind of linear and I only know it says, there is no curvature where it is equals/near zero. But my test-bezier has weak curvature at "begin", "middle" and "end". I'm not a big mathematician.
How can I setup a rule for strong or weak curvature at a specific point?
I don't need formulas. Pseudo language is enough. I'm programming this, so I got all the data at my disposal.
Idea 1: The points in the first image are equally distributed B(t), t0=0.00, t1 = 0.01, t2 = 0.02, ... Rule: "If next point close by, curvature is strong."
Bézier:
1st derivative (slopes?):
2nd derivative (curves?):
