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
30.0000
80.0000
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
istrue
, 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
isfalse
, 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
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.
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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