# Zenithal¶

class astropy.modeling.projections.Zenithal(*args, meta=None, name=None, **kwargs)[source]

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:

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