# 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
...
```