> Being given E(ui, vj), with i in [1..N], j in [1..M} the grid value of the
> data in question, and with steps du in u and dv in v, the value of E in a
> point (u, v) is given by:
> 
>         N    M
>        ---- ----
>                       sin(PI*(u-u1)/du - i*PI) sin(PI*(v-v1)/dv - j*PI)
> E(u,v)=/    /   E(ui,vj)------------------------ ------------------------
>        ---  ---           PI*(u-u1)/du - i*PI     PI*(v-v1)/dv - j*PI
>          i=1  j=1
> 

Yes, I heard about this before. In fact, what this formula does is 
summing plenty of 2D sinc functions, one for each point of the grid. The 
scaling with PI is merely to ensure that each sinc is zero at all grid 
points, except the one it is centered on.

This interpolation is indeed good in signal processing, because if I 
remember correctly, it does not add frequencies higher than the sampling 
you already have from the grid.

But it seems prohibitive to compute, since you must consider every point 
of the grid each time you need a value. It can be sped up by considering 
a limited set of neighbours, but then it becomes tricky to ensure that 
the value and derivative(s) stay continuous.

-- 
Vincent

Post a reply to this message