1%YAML 1.1
2---
3$schema: "http://stsci.edu/schemas/yaml-schema/draft-01"
4id: "http://stsci.edu/schemas/asdf/transform/hammer_aitoff-1.2.0"
5tag: "tag:stsci.edu:asdf/transform/hammer_aitoff-1.2.0"
6title: |
7  Hammer-Aitoff projection.
8
9description: |
10  Corresponds to the `AIT` projection in the FITS WCS standard.
11
12  The pixel-to-sky transformation is defined as:
13
14  $$\phi &= 2 \arg \left(2Z^2 - 1, \frac{\pi}{180^\circ} \frac{Z}{2}x\right) \\
15    \theta &= \sin^{-1}\left(\frac{\pi}{180^\circ}yZ\right)$$
16
17  And the sky-to-pixel transformation is defined as:
18
19  $$x &= 2 \gamma \cos \theta \sin \frac{\phi}{2} \\
20    y &= \gamma \sin \theta$$
21
22  where:
23
24  $$\gamma = \frac{180^\circ}{\pi} \sqrt{\frac{2}{1 + \cos \theta \cos(\phi / 2)}}$$
25
26  Invertibility: All ASDF tools are required to provide the inverse of
27  this transform.
28
29$ref: "pseudocylindrical-1.2.0"
30...
31