http://bugs.winehq.org/show_bug.cgi?id=14717
--- Comment #206 from Alexander E. Patrakov patrakov@gmail.com 2011-11-05 01:19:32 CDT --- Sorry, yesterday I referenced a cubic interpolation formula that is not good for our task. Namely, it produces a cubic curve that passes through all four given points. It is (when compared to the exact value) actually as noisy as the linear interpolation, just changes the sign of the error.
A different formula gives a cubic curve that passes through the middle two given points and also gives correct derivatives here, but doesn't pass through the two outer points: http://www.paulinternet.nl/?page=bicubic (just below the words "So our cubic interpolation formula becomes"). From the noise viewpoint, it is much better.