Convert u/v coordinates to phi/theta angles
Conversion of U/V Coordinates
Find the corresponding φ/θ representation for u = 0.5 and v = 0.
PhiTheta = uv2phitheta([0.5; 0])
PhiTheta = 2×1 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.
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
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Usage notes and limitations:
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