What Type of Curve Uses Sequential Control Points from A0 to A6?

[mymachine]

If I construct a curve such start from point A0, A3, to point A6 where A1-A2 and A4-A5 are control points, is called a Bezier curve.

What is it called by and what its equation if I construct and fit a curve start from point A0 > A1 > A2 > A3 > A4 > A5 > A6 such as below image?

 

[dodo]

It is called a "spline",

http://en.wikipedia.org/wiki/Spline_(mathematics)

and fitting one usually involves solving a band-diagonal system of equations, and some notions of calculus. (Or you could google for a software library that does the work.)

P.S.: There are actually many kinds of splines; the ones I had in mind, "cubic splines", are described in a link on the Wiki page I mentioned,

http://en.wikipedia.org/wiki/Spline_interpolation

But again, it's reinventing the wheel as there are probably libraries to do so.

 

[jfgobin]

gnuplot will do that for you.