Setting a function using an array of points, possible solutions, literature?

Question

Mathematics

Good day! I am looking for a possible solution to the following problem in the C++ language: there is a finite set of points of the form (x, y), the distance between the X coordinates is constant - you need to use some algorithm or formula to find a function whose coordinates approach the points from the array, the degree any approximation. Actually, I know that there are methods for solving such problems in mathematics, only due to my smallness, until I got acquainted with them. Very much I ask to prompt the literature on the given subject or possible algorithm. Thanks in advance!

Answer 1

google interpolation polynomial

Answer 2

any degree of approximation

So why didn't you immediately write that your function is a direct one?! Then everything is very easy: build on two points according to the school formula.