uv2phitheta

Convert u/v coordinates to phi/theta angles

Syntax

Description

example

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

Examples

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Conversion of U/V Coordinates

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

PhiTheta = uv2phitheta([0.5; 0]);

Input Arguments

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UV — Angle in u/v spacetwo-row matrix

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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PhiTheta — Phi/theta angle pairstwo-row matrix

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 hemisphere x ≥ 0 are derived from the phi and theta angles, as follows:

u=sinθcosϕv=sinθsinϕ

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

u=coselsinazv=sinel

The values of u and v satisfy the inequalities

1u11v1u2+v21

Conversely, the phi and theta angles can be written in terms of u and v using

tanϕ=u/vsinθ=u2+v2

The azimuth and elevation angles can also be written in terms of u and v

sinel=vtanaz=u1u2v2

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

sin(el)=sinϕsinθtan(az)=cosϕtanθcosθ=cos(el)cos(az)tanϕ=tan(el)/sin(az)

See Also

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