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Basically, I have a set of up to 100 co-ordinates and their orders, in a 2D plane, along with the desired tangents to the curve at the first and last point.

I have looked into various methods of curve-fitting, by which I mean an algorithm with takes the inputted data points and tangents, and outputs the equation of the cure, such as the gaussian method and interpolation, but I really struggled understanding them.

I am not asking for code (If you choose to give it, thats acceptable though :) ), I am simply looking for help into this algorithm. It will eventually be converted to Objective-C for an iPhone app, if that changes anything..

I need the equation of the curve, given these points. Obviously there isn't a single correct equation, but i want a smooth interpolated curve as the output.

Is it possible?

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    [Least Squares](http://en.wikipedia.org/wiki/Least_squares) would probably be a good place to start.2012-10-22

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I wrote a tutorial article on linear and non-linear least squares methods:

Linear and Non-Linear Least Squares with Math.NET

C# source code and demo app are included.