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# Zenithal

class astropy.modeling.projections.Zenithal(*args, **kwargs)

  Bases: `Projection`

  Base class for all Zenithal projections.

  Zenithal (or azimuthal) projections map the sphere directly onto a plane. All zenithal projections are specified by defining the radius as a function of native latitude, \(R_\theta\).

  The pixel-to-sky transformation is defined as:

  \[\begin{split}\phi &= \arg(-y, x) \\ R_\theta &= \sqrt{x^2 + y^2}\end{split}\]

  and the inverse (sky-to-pixel) is defined as:

  \[\begin{split}x &= R_\theta \sin \phi \\ y &= R_\theta \cos \phi\end{split}\]