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sph2cart

Transform spherical coordinates to Cartesian

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Syntax

[x,y,z] = sph2cart(azimuth,elevation,r)

Description

[x,y,z] = sph2cart(azimuth,elevation,r) transforms corresponding elements of the spherical coordinate arrays azimuth, elevation, and r to Cartesian, or xyz, coordinates.

example

Examples

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Open Live Script

Convert the spherical coordinates defined by corresponding entries in the matrices az, el, and r to Cartesian coordinates x, y, and z. These points correspond to the eight vertices of a cube.

az = [0.7854 0.7854 -0.7854 -0.7854; 2.3562 2.3562 -2.3562 -2.3562]
az = 2×4

    0.7854    0.7854   -0.7854   -0.7854
    2.3562    2.3562   -2.3562   -2.3562


el = [0.6155 -0.6155 0.6155 -0.6155; 0.6155 -0.6155 0.6155 -0.6155]
el = 2×4

    0.6155   -0.6155    0.6155   -0.6155
    0.6155   -0.6155    0.6155   -0.6155


r = 1.7321*ones(2,4)
r = 2×4

    1.7321    1.7321    1.7321    1.7321
    1.7321    1.7321    1.7321    1.7321


[x,y,z] = sph2cart(az,el,r)
x = 2×4

    1.0000    1.0000    1.0000    1.0000
   -1.0000   -1.0000   -1.0000   -1.0000


y = 2×4

    1.0000    1.0000   -1.0000   -1.0000
    1.0000    1.0000   -1.0000   -1.0000


z = 2×4

    1.0001   -1.0001    1.0001   -1.0001
    1.0001   -1.0001    1.0001   -1.0001

Input Arguments

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Azimuth angle, specified as a scalar, vector, matrix, or multidimensional array. azimuth, elevation, and r must be the same size, or have sizes that are compatible (for example, azimuth is an M-by-N matrix, elevation is a scalar, and r is a scalar or 1-by-N row vector). For more information, see Compatible Array Sizes for Basic Operations.

azimuth is the counterclockwise angle in the x-y plane measured in radians from the positive x-axis.

Data Types: single | double
Complex Number Support: Yes

Elevation angle, specified as a scalar, vector, matrix, or multidimensional array. azimuth, elevation, and r must be the same size, or have sizes that are compatible.

elevation is the elevation angle in radians from the x-y plane.

Data Types: single | double
Complex Number Support: Yes

Radius, specified as a scalar, vector, matrix, or multidimensional array. azimuth, elevation, and r must be the same size, or have sizes that are compatible.

The length units of r can be arbitrary, and the output arrays x, y, and z use the same units.

Data Types: single | double
Complex Number Support: Yes

Output Arguments

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Cartesian coordinates, returned as arrays.

Algorithms

The mapping from spherical coordinates to three-dimensional Cartesian coordinates is

x = r .* cos(elevation) .* cos(azimuth)
y = r .* cos(elevation) .* sin(azimuth)
z = r .* sin(elevation)

Figure shows a point plotted in 3-D space with X and Y in the horizontal plane and Z along the vertical axis. The point has a radius measured from the origin, an azimuthal angle measured in relation to X in the horizontal plane, and an elevation angle measured as elevation above the XY plane.

Extended Capabilities

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Version History

Introduced before R2006a

See Also

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