sph2cart

Transform spherical coordinates to Cartesian

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.

Examples

Spherical to Cartesian Coordinates

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

azimuth — Azimuth angle

scalar | vector | matrix | multidimensional array

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 — Elevation angle

scalar | vector | matrix | multidimensional array

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

r — Radius

scalar | vector | matrix | multidimensional array

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

x,y,z — Cartesian coordinates

arrays

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)

Extended Capabilities

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

The sph2cart function fully supports tall arrays. For more information, see Tall Arrays.

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• If you use sph2cart with single type and double type operands, the generated code might not produce the same result as MATLAB^®. See Binary Element-Wise Operations with Single and Double Operands (MATLAB Coder).

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

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

The sph2cart function fully supports GPU arrays. To run the function on a GPU, specify the input data as a gpuArray (Parallel Computing Toolbox). For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Version History

Introduced before R2006a