Convert u/v coordinates to azimuth/elevation angles
AzEl = uv2azel(UV)
Find the corresponding azimuth/elevation representation for u = 0.5 and v = 0.
azel = uv2azel([0.5; 0])
azel = 30.0000 0
UV— Angle in u/v space
Angle in u/v space, specified as a two-row matrix. Each column of the matrix represents a pair of coordinates in the form [u; v]. Each coordinate is between –1 and 1, inclusive. Also, each pair must satisfy u2 + v2≤ 1.
The u/v coordinates for the positive hemisphere x ≥ 0 can be derived from the phi and theta angles.
The relation between the two coordinates 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 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
The azimuth angle is the angle from the positive x-axis toward the positive y-axis, to the vector's orthogonal projection onto the xy plane. The azimuth angle is between –180 and 180 degrees. The elevation angle is the angle from the vector's orthogonal projection onto the xy plane toward the positive z-axis, to the vector. The elevation angle is between –90 and 90 degrees. 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 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.