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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

example sequential points

What I can imagine as result might look like this:

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

example final result

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)...2011-05-12
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    well, what i need to do is be able to represent the path as a collection/sequence of functions.2011-05-12
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    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?2011-05-12
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    Well, the images are actually generated in reversed order, with photoshop :)2011-05-12
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    Follow the links [here](http://en.wikipedia.org/wiki/Spline_interpolation).2011-05-13
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    @Emre: Hehehe, thanks for the resource. I found it yesterday, Is since that I'm trying to decrypt the algorithm in the 2nd paragraph :)2011-05-13
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    Possible duplicate of but definitely related to http://math.stackexchange.com/questions/36652/evenly-distribute-points-along-a-path2011-05-13
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    Did you figure it out, or should we post an algorithm or something?2011-06-01
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    Well, I been bit busy, but i looked around. Apparently the best approach is by using "Monotone Cubic Interpolation" @mixedmath: I'm and IT guy, not a mathematical guys, if you would like to post an algorithm I would be 3 times happy :)2011-06-07
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    possible duplicate of [Implementation of Monotone Cubic Interpolation](http://math.stackexchange.com/questions/45218/implementation-of-monotone-cubic-interpolation)2013-07-18

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