zenithal_equal_area-1.0.0

The zenithal equal area projection.

Description

Corresponds to the ZEA projection in the FITS WCS standard.

See zenithal for the definition of the full transformation.

The pixel-to-sky transformation is defined as:

\[\theta = 90^\circ - 2 \sin^{-1} \left(\frac{\pi R_\theta}{360^\circ}\right)\]

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

\[\begin{split}R_\theta &= \frac{180^\circ}{\pi} \sqrt{2(1 - \sin\theta)} \\ &= \frac{360^\circ}{\pi} \sin\left(\frac{90^\circ - \theta}{2}\right)\end{split}\]

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:

• zenithal-1.0.0

Original Schema

%YAML 1.1
---
$schema: "http://stsci.edu/schemas/yaml-schema/draft-01"
id: "http://stsci.edu/schemas/asdf/transform/zenithal_equal_area-1.0.0"
title: |
  The zenithal equal area projection.

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

  See
  [zenithal](ref:schemas/zenithal-1.0.0)
  for the definition of the full transformation.

  The pixel-to-sky transformation is defined as:

  $$\theta = 90^\circ - 2 \sin^{-1} \left(\frac{\pi R_\theta}{360^\circ}\right)$$

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

  $$R_\theta &= \frac{180^\circ}{\pi} \sqrt{2(1 - \sin\theta)} \\
             &= \frac{360^\circ}{\pi} \sin\left(\frac{90^\circ - \theta}{2}\right)$$

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

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