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