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I'm implementing an algorithm that uses a so called 6-point interpolation, which I never heard before. In the article I'm reading it's described like this:

$\phi(p\Delta x, q\Delta y)=[q(q-1)/2] \phi_{0,-1}+[p(p-1)/2]\phi _{-1,0}$ $+(1-pq-p^2-q^2)\phi_{0,0}+[p(p-2q+1)/2]\phi_{1,0}+[q(q-2p+1)/2]\phi_{0,1}$ $+pq\phi_{1,1}+O(max(\Delta x,\Delta y)^2\phi_{0,0})$

Also, this image should clarify who are $q$ and $p$. http://i.minus.com/ibogDgHRRWKAVc.jpg

My implementation is running into some problems and I would like to at least exclude this obscure interpolation algorithm as a source of problems. Does anyone know how to obtain it?

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    oh! It is for a larger grid! I think I see your point. For every point to be interpolated I find the 4 surrounding points and then the last two, according to the current quadrant.2011-10-13

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I noticed a small mistake: the third term on the right hand side should be

$+(1+pq-p^2-q^2)\phi_{0,0}$

Notice the sign of $pq$. (If you set $p=q=0$, this term should be $\phi_{0,0}$, for example.)

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    Yes, I figured that out eventually. The paper had a typo, confirmed by the author :)2014-02-16