Forgive me if its too basic, but i am looking to read some materials about a subject in which i don't know its name/field.
So what we need to do, is to get a 3 axises curve, with unknown shape, that means its not something the math already knows -like e(2x), but a random non-linear curve.
Then, we need to get other curves, and check if they match this one.
1.What should i read to know more about it? is it machine learning? interpolation? auto-corellation functions ? or just simple Leaner Algebra ?
2.Is there a way, that requires minimum processing, describing a curve, then to rate any other curve with a strong correlation to it ? or is it better to put it in a matrix and manipulate it ?
There is no unique answer to your question.
E.g.
$C_1: x^2 + z^2 = 4$ is a circle in the $x$-$z$ plane with the origin as center and radius $2$.
$C_2: y = x^2$ is a parabola in the $x$-$y$ plane.
It seems you want some function of $C_1$ and $C_2$ which describes how similar those curves are. Well both are conic sections, so they are related in this sense.
This touches subjects like the representation of curves and similarity, for which there are many choices.