azel2uv
Convert azimuth/elevation angles to u/v coordinates
Syntax
Description
converts
the azimuth/elevation
angle pairs to their corresponding coordinates in u/v space.UV
= azel2uv(AzEl
)
Examples
Conversion of Azimuth and Elevation to UV
Find the corresponding uv representation for 30° azimuth and 0° elevation.
uv = azel2uv([30;0])
uv = 2×1
0.5000
0
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 pair in the form [azimuth;elevation]
.
Azimuth angles must lie in the range [-90, 90]. Units are
in degrees.
Data Types: double
Output Arguments
UV
— Angle in u/v space
two-row matrix
Angle in u/v space, returned
as a two-row matrix. Each column of the matrix represents an angle
in the form [u; v]. The matrix
dimensions of UV
are the same as those of AzEl
.
More About
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. 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.
U/V Space
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.
To convert azimuth and elevation to u and v use the transformation
which is valid only in the range abs(az)≤=90.
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:
Phi Angle, Theta Angle
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
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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