Hi
See attached.
two S curves and I need to draw a similar curve in keeping with their shape but starting from the one and ending at the other.
Start from A and progress to B, giving the sketched out shape in red but doing it using inbuilt coding, geometry, mathematical principles etc etc.

Firstly it needs to leave the light blue curve at ‘A’ tangential to it, therein lies the first problem, we have no curve tangent from curve option.
Then halfway towards B it should be I would think halfway between Lt Blue and Dk Blue.
a 1/4 way from A a 1/4 way between Lt Blue and Dk Blue maybe.

BlendCrv You select the desired degrees if continuity at either end and can alter the shape of the curve.

Alternative is Blend but BlendCrv provides more control of the shape of the curve.

BlendCrv and Blend generate transition curves between ends of curves. So you will need to create temporary copies of the the initial curves and trim them to the locations where the transition curve is to start and end. Then use BlendCrv or Blend.

Actually BlendCrv can start anywhere on a curve, not just at the ends. Once you have selected the input curves, you can slide the blend points along them to where you want.