Convert phi/theta angles to u/v coordinates
Find the corresponding u-v representation for φ = 30° and φ = 0°.
uv = phitheta2uv([30; 0])
uv = 2×1 0 0
PhiTheta— Phi/theta angle pairs
Phi and theta angles, specified as a two-row matrix. Each column of the matrix represents an angle in degrees, in the form [phi; theta].
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
The u/v coordinates for the hemisphere x ≥ 0 are derived from the phi and theta angles.
The relations are
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:
Usage notes and limitations:
Does not support variable-size inputs.