# Conic¶

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

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

Attributes Documentation

delta = Parameter('delta', value=0.0)
param_names = ('sigma', 'delta')
sigma = Parameter('sigma', value=90.0)