molleweide-1.0.0

Molleweide’s projection.

Description

Corresponds to the MOL projection in the FITS WCS standard.

The pixel-to-sky transformation is defined as:

\[\begin{split}\phi &= \frac{\pi x}{2 \sqrt{2 - \left(\frac{\pi}{180^\circ}y\right)^2}} \\ \theta &= \sin^{-1}\left(\frac{1}{90^\circ}\sin^{-1}\left(\frac{\pi}{180^\circ}\frac{y}{\sqrt{2}}\right) + \frac{y}{180^\circ}\sqrt{2 - \left(\frac{\pi}{180^\circ}y\right)^2}\right)\end{split}\]

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

\[\begin{split}x &= \frac{2 \sqrt{2}}{\pi} \phi \cos \gamma \\ y &= \sqrt{2} \frac{180^\circ}{\pi} \sin \gamma\end{split}\]

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-1.0.0

Original Schema

%YAML 1.1
---
$schema: "http://stsci.edu/schemas/yaml-schema/draft-01"
id: "http://stsci.edu/schemas/asdf/transform/molleweide-1.0.0"
title: |
  Molleweide's projection.

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

  The pixel-to-sky transformation is defined as:

  $$\phi &= \frac{\pi x}{2 \sqrt{2 - \left(\frac{\pi}{180^\circ}y\right)^2}} \\
    \theta &= \sin^{-1}\left(\frac{1}{90^\circ}\sin^{-1}\left(\frac{\pi}{180^\circ}\frac{y}{\sqrt{2}}\right) + \frac{y}{180^\circ}\sqrt{2 - \left(\frac{\pi}{180^\circ}y\right)^2}\right)$$

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

  $$x &= \frac{2 \sqrt{2}}{\pi} \phi \cos \gamma \\
    y &= \sqrt{2} \frac{180^\circ}{\pi} \sin \gamma$$

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

allOf:
  - $ref: "pseudocylindrical-1.0.0"
...