Interpolation method that does never overshoot for implementing a system that will control hardware, I need an interpolation between points on a graph that does never overshoot.
By overshooting I mean that between two points there may be no y-result that has a higher value than either of thew two points. 

First I thought that "monotone cubic interpolation" might be what I need, however after implementation I found that this isn't always the case. After researching, I found that this only reduces overshooting, doesn't prevent it entirely. That can also be seen here, I think: Implementation of Monotone Cubic Interpolation )

So what other algorithms/formulas could fulfill this requirement?

Huge thanks in advance!
One option is use a monotone cubic interpolation but always check the values of the points on both sides, and if the value exceeds one of the two y values, just go with that y value instead.
One option is use a monotone cubic interpolation but always check the values of the points on both sides, and if the value exceeds one of the two y values, just go with that y value instead.