This Hermite cubic spline is the Draftsman spline.
It has nothing to do with the other Hermite you will
find in the web and math literature. This data set
is from a pure symmetric function. The infinitesimal
derivative allows inspection for the quality of fit.
More advanced techniques apply to add points but not
introduced in this "curiosity document".
Most interesting is the introduction of an index in
the argument H(j,u) and the scalar interpolation
module J(u,Xdata) and the nesting H(J(u,X),u).
Note the Smath ainterp(X,Y,x) is a good candidate.
The orange and violet cubic don't please me !

In some ways, Hermite is an ancestor to Bézier.
More profitable than Bézier in difficult modeling.

Jean



Spline Cubic Hermite REVISIT.sm (43 KiB) downloaded 143 time(s).

Hello Jean,


The last graph , doesn't show the curve of "deriv"

Best Regards

Carlos

Oh ! Carlos,

The deriv graph is disabled [observe the upper right black corner].
By same token => set h 0.000001 for better deriv that should be
0 @ x = 0.5. Dencreasing 'h' has no influence on the timing.

Here is a more "Edu style".

Jean

Spline Cubic Hermite REVISIT.sm (53 KiB) downloaded 131 time(s).

Carlos, collabs,

Please, read more in this latest attached version.

Jean

Spline Cubic Hermite REVISIT.sm (53 KiB) downloaded 141 time(s).