There is an interpolation method, based on signal-processing techniques,
known as 'Whittaker interpolation' that can be extended at 2 dimensions,
and therefore applies to 2-D data (diagrams, images or whatsoever that can
be expressed as f(u, v)). This method makes good interpolations and gives
good results.

The formula (seen in a book!) is:

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

OK it is quite a complicated formula, and I apologize, but perhaps POV-team
members who have implemented math-related features in POV can understand
and give an opinion.

However, there must be somewhere well-known image-processing techniques to
perform interpolations. If some of you are fresh engineers ...


    Bruno

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