Smooth Operator (Stineman 1D Interpolation)

interp1_stineman - interpolates using the Stineman interploation. Demo shows performance against spline and pchip interpolations.

Purpose: to compute the stineman interpolation of a 1D curve stineman interpolation is warranted when the input sample data (x, v) require that:

1. The curve requires piecewise smoothness between sample data, e.g., the values of ordinates at specified points change monotonically and the slopes of the line segements joining the points change monotonically, then the interpolating curve and its slope will change monotonically.
2. No discontinuity in the slope of the interpolated curve: If the first derivative of segments of the sample data join monotonically, then the interpolated curve will also change monotonically through that point.
3. Stability: Small changes in the sample ordinate value will result in small changes of the interpolated curve.

References:

• Stineman R.W., 'A consistently well-behaved method of interpolation.' Creative Computing, vol. 6, no. 7, 54-57, 1980. https://archive.org/details/creativecomputing-1980-07/page/n55/mode/1up or https://pages.uoregon.edu/dgavin/software/stineman.pdf