Looks good. Couple minor questions/comments:
In MatchBackgroundsConfig there is a config parameter called "usePolynomial" which is used the same way that "useApprox" is being used in meas_algorithms. We'll want eventual consistency, but it is not necessary on this ticket. I'm not sure useApprox is all that transparent to Task users.
python/lsst/meas/algorithms/detection.py: Double check that the comment starting at line 579 is current.
Are we temporarily losing the ability to do spline interpolation on doubles? I'm not too worried though since we will get this back with a stand alone interpolate2D class.
include/lsst/afw/math/Approximate.h: line 59-68 getters have comments but setters don't. I don't necessarily think the setters need comments, but I'm realizing our styles in header files are diverging.
approximate.i: Copyleft in brand new files says 2008, 2009, 2010? (I see tests/background.py was updated on this ticket to use 2008-2015 AURA/LSST)
*I like that there is a section for backwards compatibility here. Will we be supporting these new property set keys when they change in the future?
- line 171/172. ApproxOrderX/Y defaults when not useApprox: Please add a comment as to why is one default is -1 and the other +1.
- 809/820 commented-out print statements
ip_diffim: look good; no comments.