Here is an idea which may not work:
For each point, fit a circle to the point and two neighbor points. The curvature will be 1 divided by the radius of the fitted circle.

I like the circle idea. That’s related to the circle of curvature, where circle and curve share a common tangent

r = 1 / k,

so

k = 1 / r.

But to use this you need to know the radius of curvature. For an sphere/ellipse this would be a great way to go I think.

Another way to express curvature from calculus is

k = ||V x A|| / ||V||^3,

where V and A are the velocity and acceleration vectors along the curve at some instant in time. For a set of points along the curve, you could use the definition of the derivative

r’(t) = V
~ (r(t+h) - r(t)) / h
~ (Pi+1 - Pi) / h,