[task #15128] TPV and SIP keywords when WCS distortions are necessary

[Sachin Kumar Singh]

Follow-up Comment #23, task #15128 (project gnuastro):

The forward coefficients were done, but problems arose during the
implementation of reverse coefficients. It was also not easy to emulate the
python implementation without equations(which were not given in the paper). So
I asked the maintainer of sip_tpv module, David Shupe, to give me inner
workings of different components to help me with the implementation. He
replied back:


"To compute the SIP reverse coefficients, what is done in sip_tpv is to create
a grid of points, use the forward coefficients to populate points, and then
fit polynomials from that grid of points. The reverse polynomials are an
approximation to the forward ones. Some people do not like that; for example,
for Hubble Space Telescope data, only the forward coefficients are provided,
and an iterative solver must be used for the sky-to-image pixel direction."


Now, WCSLIB does the actual analysis of the polynomials to compute sky <--->
pixel translations, and as I don't have the exact equations, I think it's best
to use just do the implementation as shown in the python implementation and
see how it goes(as now he has explained it, it becomes more understandable to
implement it as-is)? Any thoughts?

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