%YAML 1.1
---
$schema: "http://stsci.edu/schemas/yaml-schema/draft-01"
id: "http://stsci.edu/schemas/asdf/transform/conic_orthomorphic-1.5.0"
title: |
  Conic orthomorphic projection.

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

  See
  [conic](ref:schemas/conic-1.3.0)
  for the definition of the full transformation.

  The transformation is defined as:

  $$C &= \frac{\ln \left( \frac{\cos\theta_2}{\cos\theta_1} \right)}
              {\ln \left[ \frac{\tan\left(\frac{90^\circ-\theta_2}{2}\right)}
                               {\tan\left(\frac{90^\circ-\theta_1}{2}\right)} \right] } \\
    R_\theta &= \psi \left[ \tan \left( \frac{90^\circ - \theta}{2} \right) \right]^C \\
    Y_0 &= \psi \left[ \tan \left( \frac{90^\circ - \theta_a}{2} \right) \right]^C$$

  where:

  $$\psi = \frac{180^\circ}{\pi} \frac{\cos \theta}
           {C\left[\tan\left(\frac{90^\circ-\theta}{2}\right)\right]^C}$$

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

allOf:
  - $ref: "conic-1.5.0"
...
