%YAML 1.1
---
$schema: "http://stsci.edu/schemas/yaml-schema/draft-01"
id: "http://stsci.edu/schemas/asdf/transform/stereographic-1.3.0"
title: |
  The stereographic projection.

description: |
  Corresponds to the `STG` projection in the FITS WCS standard.

  See
  [zenithal](ref:schemas/zenithal-1.2.0)
  for the definition of the full transformation.

  The pixel-to-sky transformation is defined as:

  $$\theta = 90^{\circ} - 2 \tan^{-1}\left(\frac{\pi R_\theta}{360^{\circ}}\right)$$

  And the sky-to-pixel transformation is defined as:

  $$R_\theta = \frac{180^{\circ}}{\pi}\frac{2 \cos \theta}{1 + \sin \theta}$$

  Invertibility: All ASDF tools are required to provide the inverse of
  this transform.

allOf:
  - $ref: "zenithal-1.3.0"
...
