azel2uv

Convert azimuth/elevation angles to u/v coordinates

Syntax

UV = azel2uv(AzEl)

Description

example

UV = azel2uv(AzEl) converts the azimuth/elevation angle pairs to their corresponding coordinates in u/v space.

Examples

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Find the corresponding uv representation for 30° azimuth and 0° elevation.

uv = azel2uv([30;0])
uv = 2×1

    0.5000
         0

Input Arguments

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Azimuth and elevation angles, specified as a two-row matrix. Each column of the matrix represents an angle in degrees, in the form [azimuth; elevation].

Data Types: double

Output Arguments

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Angle in u/v space, returned as a two-row matrix. Each column of the matrix represents an angle in the form [u; v]. The matrix dimensions of UV are the same as those of AzEl.

More About

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Azimuth Angle, Elevation Angle

The azimuth angle of a vector is the angle between the x-axis and the orthogonal projection of the vector onto the xy plane. The angle is positive in going from the x axis toward the y axis. Azimuth angles lie between –180 and 180 degrees. The elevation angle is the angle between the vector and its orthogonal projection onto the xy-plane. The angle is positive when going toward the positive z-axis from the xy plane. These definitions assume the boresight direction is the positive x-axis.

Note

The elevation angle is sometimes defined in the literature as the angle a vector makes with the positive z-axis. The MATLAB® and Phased Array System Toolbox™ products do not use this definition.

This figure illustrates the azimuth angle and elevation angle 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.

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 these two coordinates systems is

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)

Extended Capabilities

Introduced in R2012a