How to draw a curve close to the original

I have a set of points, and I want to draw a curve that should be approximated by the original curve.
Say, in the hawk eye system (used in cricket), I have a set of coordinates of the ball during the whole flight of the ball, now how can I draw such a curve passing through the coordinates of the ball space and looks appromixately to the original curve
one method, I thought that he will receive a large number of points, so that each point is very close to each other, and then draw a direct light between them.