https://en.wikipedia.org/wiki/Monotone_cubic_interpolation https://en.wikipedia.org/wiki/Monotone_cubic_interpolation has some reference for monotone cubic spli

https://en.wikipedia.org/wiki/Monotone_cubic_interpolation https://en.wikipedia.org/wiki/Monotone_cubic_interpolation has some reference for monotone cubic splines. In theory they should be useful when know that the underlying process should be monotone. I think in the past I found them more sensitive to noise and wondered if monotone approximation might not be better than monotone interpolation for that reason.