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

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

  The pixel-to-sky transformation is defined as:

  $$\phi &= x \\
  \theta &= 2 \tan^{-1}\left(e^{y \pi / 180^{\circ}}\right)-90^{\circ}$$

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

  $$x &= \phi \\
  y &= \frac{180^{\circ}}{\pi}\ln \tan \left(\frac{90^{\circ} + \theta}{2}\right)$$

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

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