Convert u/v coordinates to phi/theta angles



PhiTheta = uv2phitheta(UV) converts the u/v space coordinates to their corresponding phi/theta angle pairs.


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Find the corresponding φ/θ representation for u = 0.5 and v = 0.

PhiTheta = uv2phitheta([0.5; 0])
PhiTheta = 2×1


Input Arguments

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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.

Data Types: double

Output Arguments

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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 UV.

More About

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U/V Space

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


Phi Angle, Theta Angle

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


Extended Capabilities

Introduced in R2012a