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The polynomials in the code aren't used as blending functions, it's a piecewise cubic interpolator ... they are used as a convolution kernel.
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Yes, i agree.
I have been looking at the code from Panorama_Tools in panosrc.zip (which i attached here). In particular at resample.c where the resampling is implemented. I still haven't figured it out how it is used there. Have you ever looked at that source code?