Conic

class astropy.modeling.projections.Conic(*args, meta=None, name=None, **kwargs)

Bases: astropy.modeling.projections.Projection

Base class for conic projections.

In conic projections, the sphere is thought to be projected onto the surface of a cone which is then opened out.

In a general sense, the pixel-to-sky transformation is defined as:

\[\begin{split}\phi &= \arg\left(\frac{Y_0 - y}{R_\theta}, \frac{x}{R_\theta}\right) / C \\ R_\theta &= \mathrm{sign} \theta_a \sqrt{x^2 + (Y_0 - y)^2}\end{split}\]

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

\[\begin{split}x &= R_\theta \sin (C \phi) \\ y &= R_\theta \cos (C \phi) + Y_0\end{split}\]

where \(C\) is the “constant of the cone”:

\[C = \frac{180^\circ \cos \theta}{\pi R_\theta}\]

Attributes Summary

delta
param_names
sigma

Attributes Documentation

delta

param_names = ('sigma', 'delta')

sigma