Convert azimuth/elevation angles to u/v coordinates
Find the corresponding uv representation for 30° azimuth and 0° elevation.
uv = azel2uv([30;0])
uv = 2×1 0.5000 0
AzEl— Azimuth/elevation angle pairs
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].
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.
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 u/v coordinates for the positive hemisphere x ≥ 0 can be derived from the phi and theta angles.
The relation between these two coordinates systems is
In these expressions, φ and θ are the phi and theta angles, respectively.
In terms of azimuth and elevation, the u and v coordinates are
The values of u and v satisfy the inequalities
Conversely, the phi and theta angles can be written in terms of u and v using
The azimuth and elevation angles can also be written in terms of u and v
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
Usage notes and limitations:
Does not support variable-size inputs.