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Given a set of n points {(x1, y1), (x2, y2), ... (xn, yn)} I need to obtain a linear function f from the broken line which connects all these points, so that I can the value of f at any point.

I need to do this for two sets of points, i.e. obtain functions f and g, because I have an expression which involves both the values of f and g at specific points.

Thanks in advance for any help.