# azel2phitheta

Convert angles from azimuth-elevation form to phi-theta form

## Description

converts
the azimuth/elevation
angle pairs to their corresponding phi/theta angle pairs.`PhiTheta`

= azel2phitheta(`AzEl`

)

## Examples

### Convert Azimuth-Elevation Coordinates to Phi-Theta Coordinates

Find the phi-theta representation for 30° azimuth and 10° elevation for the convention where phi is defined from the *y*-axis to the *z*-axis, and theta is defined from the *x*-axis toward the *yz*-plane.

PhiTheta = azel2phitheta([30;10])

`PhiTheta = `*2×1*
19.4254
31.4749

### Azimuth-Elevation Coordinates to Alternative Phi-Theta Coordinates

Find the phi-theta representation for 30° azimuth and 10° elevation for the convention with phi defined from the *x*-axis to the *y*-axis, and theta defined from the *z*-axis toward the *xy*-plane.

PhiTheta = azel2phitheta([30;10],false)

`PhiTheta = `*2×1*
30
80

## Input Arguments

`AzEl`

— Azimuth-elevation angle pairs

two-row matrix

Azimuth and elevation angles, specified as a two-row matrix. Each column of the matrix represents an angle in degrees, in the form [azimuth; elevation].

**Data Types: **`double`

`RotAx`

— Phi-theta angle convention selection

`true`

(default) | `false`

Phi-theta angle convention selection, specified as `true`

or `false`

.

If

`RotAx`

is`true`

, the phi angle is defined from the*y*-axis to the*z*-axis and the theta angle is defined from the*x*-axis toward the*yz*-plane.If

`RotAx`

is`false`

, the phi angle is defined from the*x*-axis to the*y*-axis and the theta angle is defined from the*z*-axis toward the*xy*- plane. (see Alternative Definition of Phi and Theta).

**Data Types: **`double`

## Output Arguments

`PhiTheta`

— Phi-theta angle pairs

two-row matrix

Phi and theta angles, returned as a two-row matrix. Each column of the
matrix represents an angle in degrees, in the form [phi; theta]. The matrix
dimensions of `PhiTheta`

are the same as those of
`AzEl`

.

## More About

### Azimuth and Elevation Angles

The *azimuth angle* of a vector is the angle between
the *x*-axis and the orthogonal projection of the vector onto the
*xy* plane. The angle is positive in going from the
*x* axis toward the *y* axis. Azimuth angles lie
between –180 and 180 degrees. The *elevation angle* is the angle
between the vector and its orthogonal projection onto the *xy*-plane. The
angle is positive when going toward the positive *z*-axis from the
*xy* plane. By default, the boresight direction of an element or array
is aligned with the positive *x*-axis. The boresight direction is the
direction of the main lobe of an element or array.

**Note**

The elevation angle is sometimes defined in the literature as the angle a vector makes
with the positive *z*-axis. The MATLAB^{®} and Phased Array System Toolbox™ products do not use this definition.

This figure illustrates the azimuth angle and elevation angle for a vector shown as a green solid line.

### Phi and Theta Angles

The phi angle (*φ*) is the angle from the positive
*y*-axis to the vector’s orthogonal projection onto the
*yz* plane. The angle is positive toward the positive
*z*-axis. The phi angle is between 0 and 360 degrees. The theta angle
(*θ*) is the angle from the *x*-axis to the vector
itself. The angle is positive toward the *yz* plane. The theta angle is
between 0 and 180 degrees.

The figure illustrates phi and theta for a vector that appears as a green solid line.

The coordinate transformations between φ/θ and *az/el* are described by
the following equations

$$\begin{array}{l}\mathrm{sin}el=\mathrm{sin}\varphi \mathrm{sin}\theta \\ \mathrm{tan}az=\mathrm{cos}\varphi \mathrm{tan}\theta \\ \mathrm{cos}\theta =\mathrm{cos}el\mathrm{cos}az\\ \mathrm{tan}\varphi =\mathrm{tan}el/\mathrm{sin}az\end{array}$$

This transformation applies when `RotAx`

is
`true`

.

### Alternative Definition of Phi and Theta

The phi angle (*φ*) is the angle from the positive
*x*-axis to the vector’s orthogonal projection onto the
*xy* plane. The angle is positive toward the positive
*y*-axis. The phi angle is between 0 and 360 degrees. The theta angle
(*θ*) is the angle from the *z*-axis to the vector
itself. The angle is positive toward the *xy* plane. The theta angle is
between 0 and 180 degrees.

The figure illustrates *φ* and *θ* for a vector that appears as a green solid line.

$$\begin{array}{l}\varphi =az\\ \theta =90-el\\ az=\varphi \\ el=90-\theta \end{array}$$

## Extended Capabilities

### C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

Does not support variable-size inputs.

## Version History

**Introduced in R2012a**

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