interpolation issue...

[Jérôme Kieffer]

Hi all,

This is my first post on this list, but I think I met most participant
at EuroScipy this summer.

I write code for scientists and it seams to be a common problem to do
"interpolation with given constrains" (in tomography, but also in other
fields like [1]). 
A common case is the polar transformation: x,y -> r,theta 
Usually one takes a destination space coordinate (r,theta),
look for input coordinates (x,y) and interpolate the neighbours with
bilinear or bicubic spline. It is a backwards interpolation and plenty
of implementations are available.

First constraint: all signal in input has to appear in output:
interpolation has to be done in "forwards" mode and can be done with 2D
histogramming. Thanks to cython it is even 10x faster than the numpy
implementation (0.5s for 4Mpix float64).

Second constraint is that I need to conserve the surface density in the
transformation. One idea is to cut pixels (4 corners) into triangles (2
minimum), the number of them varying with the spatial extension of the
pixel in destination space (4 triangle if 1 bin boundary, 6 if 2 bin
boundaries, ....) ... then do the histogramming as before but the cost
is likely to be huge. Beside this I am convinced to re-invent the
wheel ... even if I was unable to find anything in google but I am
probably lacking the good keyword.

Do you know this problem and what implementations already exists ??

Thanks for reading this "long email"

-- 
Jérôme Kieffer 
<jerome.kieffer at terre-adelie.org>
[1]: https://forge.epn-campus.eu/attachments/1459/20111010-PyFAI-Poster-A0.pdf