Conic¶

class astropy.modeling.projections.Conic(*args, **kwargs)[source] [edit on github]¶

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:

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

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

$x &= R_\theta \sin (C \phi) \\ y &= R_\theta \cos (C \phi) + Y_0$

where $C$ is the “constant of the cone”:

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

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