pat_phitheta = azel2phithetapat(pat_azel,az,el) expresses
the antenna radiation pattern pat_azel in φ/θ
angle coordinates instead of azimuth/elevation angle coordinates. pat_azel samples
the pattern at azimuth angles in az and elevation
angles in el. The pat_phitheta matrix
covers φ values from 0 to 180 degrees and θ values from
0 to 360 degrees. pat_phitheta is uniformly sampled
with a step size of 1 for φ and θ. The function interpolates
to estimate the response of the antenna at a given direction.

pat_phitheta = azel2phithetapat(pat_azel,az,el,phi,theta) uses
vectors phi and theta to
specify the grid at which to sample pat_phitheta.
To avoid interpolation errors, phi should cover
the range [0, 180], and theta should cover the
range [0, 360].

[pat_phitheta,phi,theta]
= azel2phithetapat(___) returns vectors containing
the φ and θ angles at which pat_phitheta samples
the pattern, using any of the input arguments in the previous syntaxes.

Antenna radiation pattern in azimuth/elevation form, specified
as a Q-by-P matrix. pat_azel samples the 3-D
magnitude pattern in decibels, in terms of azimuth and elevation angles.
P is the length of the az vector, and Q is the
length of the el vector.

Antenna radiation pattern in phi/theta form, returned as an
M-by-L matrix. pat_phitheta samples the 3-D magnitude
pattern in decibels, in terms of φ and θ angles. L is
the length of the phi vector, and M is the length
of the theta vector.

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.

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