Yesterday I made a figure showing how we parameterize quadrangles of stars for the astrometry.net blind system. The parameterization is clever, because it is rotation- and scale-free, but if stars are uniformly (ie, Poisson) distributed on the sky, the parameters uniformly fill a compact, finite, simply shaped volume in four-dimensional parameter space. This is not a requirement for a good system, but it makes a few things much easier.
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