I found c++ source calculating "Hermite polynomial interpolating function and derivative values". Source: https://people.sc.fsu.edu/~jburkardt/cpp_src/hermite/hermite.html
I have looked to given examples in that source and no of them applies my case.
My case is to calculate y values at some x position from data points such as:
X: 0.9, 1.7, 2.55, 3.39...
Y: 0.9, 0.8, 0.85, 0.84...
And get result with equal x spaces (x space 0.5):
X: 0.5, 1.00, 1.5, 2.00, 2.5, 3.0,...
Y: 0.8, 0.95, 0.8, 0.85, 0.9, 0.9,...
Is that source even applicable for my case?
To apply Hermite interpolation, one need to define derivative values in initial nodes.
Is layman's terms derivative values are slopes (direction) of the curve at the nodes. Hermite interpolation assumes the you know real or "good" derivative values.
For example, to make Hermite interpolation of Sin function quater of period, you can set initial X-value 0, end X-value Pi/2, initial and end Y-values 0 and 1, and derivative values 1 and 0.
If you have no a priori information about derivatives - it is worth to use another interpolation method, for example - cubic interpolation splines