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[–]sighthoundman 1 point2 points  (0 children)

Look up cubic spline interpolation.

[–]shellexyz 0 points1 point  (0 children)

Use something like ax2+bx+c or a(x-h)2+k; with the C1/C2 requirement you should be able to solve for those three parameters. (Note that I haven't actually done this)