transform/zenithal-1.2.0

Base class of all zenithal (or azimuthal) projections.

Description

Zenithal projections are completely specified by defining the radius as a function of native latitude, \(R_\theta\).

The pixel-to-sky transformation is defined as:

\[\begin{split}\phi &= \arg(-y, x) \\ R_\theta &= \sqrt{x^2 + y^2}\end{split}\]

and the inverse (sky-to-pixel) is defined as:

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

Outline

Schema Definitions

This node must validate against all of the following:

  • This type is an object with the following properties:
    • direction
      object
      This node has no type definition (unrestricted)

Original Schema

%YAML 1.1
---
$schema: "http://stsci.edu/schemas/yaml-schema/draft-01"
id: "http://stsci.edu/schemas/asdf/transform/zenithal-1.2.0"
title: |
  Base class of all zenithal (or azimuthal) projections.

description: |
  Zenithal projections are completely specified by defining the radius
  as a function of native latitude, $R_\theta$.

  The pixel-to-sky transformation is defined as:

  $$\phi &= \arg(-y, x) \\
  R_\theta &= \sqrt{x^2 + y^2}$$

  and the inverse (sky-to-pixel) is defined as:

  $$x &= R_\theta \sin \phi \\
  y &= R_\theta \cos \phi$$

allOf:
  - $ref: "transform-1.2.0"
  - type: object
    properties:
      direction:
        enum: [pix2sky, sky2pix]
        default: pix2sky
...