I need to use cubic splines to interpolate between data points (sets of x-y-coordinate pairs). The problem is that there is the well-known "overhooting" of the spline that occurs every now and then (for example at 0.4 in the following image).
This behaviour is not desired for further processing of the spline, so I am searching for a way to get rid of these overshots. However, I need to be sure that the adjusted/processed spline will still be continuous up to the second derivative because it will be used to calculate a machine-toolpath which has constraints for its maximum velocity, acceleration and jerk.
Has anyone used the above mentioned method to avoid overhooting of a spline? As far as I understand I have to manually readjust the slope for each data point. Do these adjustments somehow "break" the continuity of the cubic spline (or its derivatives)?
The linked article does not specifically cover this topic. Maybe because it is obvious and I do not understand it completely.