Add flux-preserving exact reproject for HEALPIX?

[cdeil]

This is a feature request to add a flux-conserving (and equivalently count-conserving) reprojection method to / from HEALPIX.

For HEALPIX <-> HEALPIX it would be trivial, just multiply / divide by 4 to the power of difference in HEALPIX order. E.g. if one gets a huge HEALPIX file but doesn't need the high resolution, one could downsample. Not sure if this should be in reproject or in healpy. @lpsinger Maybe this exists in healpy and I missed it?

For HEALPIX <-> normal WCS projection image I don't know how to do it. I thought HEALPIX pixel boundaries are great circles and the 4-corner polygon "exact" method from Montage could be used as well, but this page http://healpix.jpl.nasa.gov/html/intronode4.htm explains that pixel boundaries are not great circles on the sphere.
The use case I have for this count- and flux-preserving reprojection would be to be able to go back and forth between HEALPIX and normal projections and be able to do correct photometry of sources e.g. on FERMI data. @lpsinger Easy or hard to implement? Worth the effort?

[astrofrog]

Actually for HEALPIX <-> HEALPIX it's also not trivial if you change coordinate system since the pixels are no longer aligned.