Convert u/v coordinates to phi/theta angles
PhiTheta = uv2phitheta(UV)
Find the corresponding φ/θ representation for u = 0.5 and v = 0.
PhiTheta = uv2phitheta([0.5; 0])
PhiTheta = 0 30.0000
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