pol2cart

Transform polar or cylindrical coordinates to Cartesian

Syntax

[x,y] = pol2cart(theta,rho)

[x,y,z] = pol2cart(theta,rho,z)

Description

[x,y] = pol2cart(theta,rho) transforms corresponding elements of the polar coordinate arrays theta and rho to two-dimensional Cartesian, or xy, coordinates.

[x,y,z] = pol2cart(theta,rho,z) transforms corresponding elements of the cylindrical coordinate arrays theta, rho, and z to three-dimensional Cartesian, or xyz, coordinates.

Examples

Polar to Cartesian Coordinates

Convert the polar coordinates defined by corresponding entries in the matrices theta and rho to two-dimensional Cartesian coordinates x and y.

theta = [0 pi/4 pi/2 pi]

theta = 1×4

         0    0.7854    1.5708    3.1416

rho = [5 5 10 10]

rho = 1×4

     5     5    10    10

[x,y] = pol2cart(theta,rho)

x = 1×4

    5.0000    3.5355    0.0000  -10.0000

y = 1×4

         0    3.5355   10.0000    0.0000

Cylindrical to Cartesian Coordinates

Convert the cylindrical coordinates defined by corresponding entries in the matrices theta, rho, and z to three-dimensional Cartesian coordinates x, y, and z.

theta = [0 pi/4 pi/2 pi]'

theta = 4×1

         0
    0.7854
    1.5708
    3.1416

rho = [1 3 4 5]'

rho = 4×1

     1
     3
     4
     5

z = [7 8 9 10]'

z = 4×1

     7
     8
     9
    10

[x,y,z] = pol2cart(theta,rho,z)

x = 4×1

    1.0000
    2.1213
    0.0000
   -5.0000

y = 4×1

         0
    2.1213
    4.0000
    0.0000

z = 4×1

     7
     8
     9
    10

Input Arguments

theta — Angular coordinate

scalar | vector | matrix | multidimensional array

Angular coordinate, specified as a scalar, vector, matrix, or multidimensional array. theta must be real. theta, rho, and z must either be the same size or have sizes that are compatible (for example, theta is an M-by-N matrix, rho is a scalar, and z is a scalar or 1-by-N row vector). For more information, see Compatible Array Sizes for Basic Operations.

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

Data Types: single | double

rho — Radial coordinate

scalar | vector | matrix | multidimensional array

Radial coordinate, specified as a scalar, vector, matrix, or multidimensional array. rho must be real. theta, rho, and z must either be the same size or have sizes that are compatible.

rho is the distance from the origin to a point in the x-y plane.

Data Types: single | double

z — Elevation coordinate

scalar | vector | matrix | multidimensional array

Elevation coordinate, specified as a scalar, vector, matrix, or multidimensional array. z must be real. theta, rho, and z must either be the same size or have sizes that are compatible.

z is the height above the x-y plane.

Data Types: single | double

Output Arguments

x, y, z — Cartesian coordinates

arrays

Cartesian coordinates, returned as arrays.

Algorithms

The mapping from polar and cylindrical coordinates to Cartesian coordinates is:

Extended Capabilities

Tall Arrays

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

The pol2cart 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 pol2cart 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 pol2cart 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 pol2cart 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 pol2cart 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 pol2cart function returns an error for complex inputs. This function no longer accepts complex inputs because its inverse function, cart2pol, does not accept complex inputs.

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

Not Recommended (Errors)	Recommended
theta = 2i; rho = 1i; [x,y] = pol2cart(theta,rho);	theta = 2i; rho = 1i; x = rho*cos(theta); y = rho*sin(theta);