hammer_aitoff-1.2.0

Hammer-Aitoff projection.

Description

Corresponds to the AIT projection in the FITS WCS standard.

The pixel-to-sky transformation is defined as:

\[\begin{split}\phi &= 2 \arg \left(2Z^2 - 1, \frac{\pi}{180^\circ} \frac{Z}{2}x\right) \\ \theta &= \sin^{-1}\left(\frac{\pi}{180^\circ}yZ\right)\end{split}\]

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

\[\begin{split}x &= 2 \gamma \cos \theta \sin \frac{\phi}{2} \\ y &= \gamma \sin \theta\end{split}\]

where:

\[\gamma = \frac{180^\circ}{\pi} \sqrt{\frac{2}{1 + \cos \theta \cos(\phi / 2)}}\]

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

Outline

• Schema Definitions
• Original Schema

Schema Definitions

This node must validate against all of the following:

• pseudocylindrical-1.2.0

Original Schema

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

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

  The pixel-to-sky transformation is defined as:

  $$\phi &= 2 \arg \left(2Z^2 - 1, \frac{\pi}{180^\circ} \frac{Z}{2}x\right) \\
    \theta &= \sin^{-1}\left(\frac{\pi}{180^\circ}yZ\right)$$

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

  $$x &= 2 \gamma \cos \theta \sin \frac{\phi}{2} \\
    y &= \gamma \sin \theta$$

  where:

  $$\gamma = \frac{180^\circ}{\pi} \sqrt{\frac{2}{1 + \cos \theta \cos(\phi / 2)}}$$

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

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