phitheta2azel

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

Syntax

AzEl = phitheta2azel(PhiTheta)

Description

AzEl = phitheta2azel(PhiTheta) converts the phi/theta angle pairs to their corresponding azimuth/elevation angle pairs.

Examples

Convert Phi and Theta to Azimuth and Elevation

Find the azimuth and elevation representation for φ = 30° and θ = 0°.

azel = phitheta2azel([30;0]);

Input Arguments

PhiTheta — Phi/theta angle pairs

two-row matrix

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

Data Types: double

Output Arguments

AzEl — Azimuth/elevation angle pairs

two-row matrix

Azimuth and elevation angles, returned as a two-row matrix. Each column of the matrix represents an angle in degrees, in the form [azimuth; elevation]. The matrix dimensions of AzEl are the same as those of PhiTheta.

More About

Phi Angle, Theta Angle

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

The figure illustrates φ and θ for a vector that appears as a green solid line. The coordinate system is relative to the center of a uniform linear array, whose elements appear as blue circles.

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

$$\begin{array}{l}\sin (\text{el})=\sin \varphi \sin \theta \hfill \\ \tan (\text{az})=\cos \varphi \tan \theta \hfill \\ \hfill \\ \cos \theta =\cos (\text{el})\cos (\text{az})\hfill \\ \tan \varphi =\tan (\text{el})/\sin (\text{az})\hfill \end{array}$$

Azimuth Angle, Elevation Angle

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. These definitions assume the boresight direction is the positive x-axis.

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. The coordinate system is relative to the center of a uniform linear array, whose elements appear as blue disks.

Extended Capabilities

C/C++ Code Generation

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

Usage notes and limitations:

Does not support variable-size inputs.