In this Smath document, InterpSpline(s,X,Y,t) is equivalent to
Mathcad linterp(s,X,Y,t), pinterp(s,X,Y,t), cinterp(s,X,Y,t)
except that in Smath you have to pre-assign the 's' spline type.
1. It supports the scalar plot on canvas, in-situ interpolation.
2. It supports the scalar 'dspline' up to 3rd derivative.
3. It supports the discrete cumulative integral, from which you
can extract value(s) from "row(,,)"
4. Of great interest, observe the 2nd order discrete derivative
Deriv2=augment(X,s)

Enjoy, best use, comments appreciated ... thanks.

Jean

Spline l_p_c [dspline, fintegrate].sm (70 KiB) downloaded 54 time(s).

... refactored a bit to be more generalised.
The graet cruncher is the tridiagonal solver.
I have no idea if it could be accelerated.

Cheers, Jean

Spline l_p_c [dspline, fintegrate].sm (71 KiB) downloaded 61 time(s).