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    $\begingroup$ Can you post your points somewhere, so that we can use them to compare? $\endgroup$ Commented Sep 5, 2012 at 20:10
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    $\begingroup$ I might be understanding your question correctly, but if you want to ensure a continuous derivative you will need to use the following option: ListInterpolation[pts1, {0, 1}, InterpolationOrder -> 4,PeriodicInterpolation -> True, Method -> "Spline"]. By default ListInterpolation is using a Hermite interpolation which does not guarantee a continuous derivative. $\endgroup$ Commented Sep 5, 2012 at 20:22
  • $\begingroup$ Is the function with open ends or a closed loop? And as @rcollyer already said, we really need the points. $\endgroup$ Commented Sep 5, 2012 at 21:16