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 must be real. azimuth, elevation, and r must either 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

elevation — Elevation angle

scalar | vector | matrix | multidimensional array

Elevation angle, specified as a scalar, vector, matrix, or multidimensional array. elevation must be real. azimuth, elevation, and r must either 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

r — Radius

scalar | vector | matrix | multidimensional array

Radius, specified as a scalar, vector, matrix, or multidimensional array. r must be real. azimuth, elevation, and r must either 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

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™.

Refer to the usage notes and limitations in the C/C++ Code Generation section. The same usage notes and limitations apply to GPU code generation.

Thread-Based Environment

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

The sph2cart 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™.

The sph2cart function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Version History

Introduced before R2006a

R2026a: Complex inputs are not accepted

The sph2cart function returns an error for complex inputs. This function no longer accepts complex inputs because its inverse function, cart2sph, does not accept complex inputs.

To preserve the behavior of previous releases for complex inputs, use the formulas that map spherical coordinates to Cartesian coordinates, as shown in this table.

Not Recommended (Errors)	Recommended
azimuth = 1i; elevation = 2i; r = 1; [x,y,z] = sph2cart(azimuth,elevation,r);	azimuth = 1i; elevation = 2i; r = 1; x = r*cos(elevation)*cos(azimuth); y = r*cos(elevation)*sin(azimuth); z = r*sin(elevation);