# How to interpolate sequential points to obtain functions and/or vectors?

I would like to know how I can interpolate a sequence (time) of points in order to obtain curves as some kind of mathematical functions.

Unfortunately math is not my area so I don't really know the name of what I'm looking for... so I mock-up a couple of pictures :)

Example of sequential points:

The information related to those points are:

• coordinates $(x, y)$
• creation time

What I can imagine as result might look like this:

A sequence of functions/point/vectors generated by matching the points

I would like to know if there is/are mathematical functions to perform this kind of operation. I guess, I'm looking for approximate interpolation, and to eventually compute a value that express the interpolation accuracy.

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So, you have (t,x,y) values? Spline interpolation would probably suit your needs, unless you already have slope values handy (as you seem to indicate in the second image)... – J. M. May 12 '11 at 14:55
well, what i need to do is be able to represent the path as a collection/sequence of functions. – Cesar May 12 '11 at 15:08
You can certainly construct a parametric spline from your data. I assumed that each point of your curve had a corresponding "time" value in addition to coordinates; is that correct? – J. M. May 12 '11 at 15:34
Well, the images are actually generated in reversed order, with photoshop :) – Cesar May 12 '11 at 22:27