I may be thinking of this too simplistically, but could you not do something along the lines of:

For each type of proposed pattern,

• Specify functions Fx and Fy as the functions to apply to the x and y values, respectively.
• Given that for a straight line, (y2 - y1) = m(x2 - x1), use the equation of a line in the form ( Fy(y2) - Fy(y1) ) = m ( Fx(x2) - Fx(x1) )
• Use the first and last data values to compute a value m
• Compute the estimated values for the internal data points
• Compute the error of the estimated values
• Select proposed pattern based on the one providing the smallest error

Is this a realistic idea, or am I thinking too simply?

Hope that helps.

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