# 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:

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

### 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
...