%YAML 1.1
---
$schema: "http://stsci.edu/schemas/yaml-schema/draft-01"
id: "http://stsci.edu/schemas/asdf/transform/parabolic-1.2.0"
title: |
  Parabolic projection.

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

  The pixel-to-sky transformation is defined as:

  $$\phi &= \frac{180^\circ}{\pi} \frac{x}{1 - 4(y / 180^\circ)^2} \\
    \theta &= 3 \sin^{-1}\left(\frac{y}{180^\circ}\right)$$

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

  $$x &= \phi \left(2\cos\frac{2\theta}{3} - 1\right) \\
    y &= 180^\circ \sin \frac{\theta}{3}$$

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

allOf:
  - $ref: "pseudocylindrical-1.2.0"
...
