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King3D - this is the deprojected version of king2d
Other
Table models (see tablemodel in Sherpa or LinearInterpolatedModel or NearestInterpolatedModel in PymodelFit 1D and 2D table models in GammaLib) with a few interpolation options. This is very important but I think should be discussed in a separate issue, with the discussion here focusing on "analytical" or "functional" or "mathematical" models.