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, rho, and z must 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
Complex Number Support: Yes

rho — Radial coordinate

scalar | vector | matrix | multidimensional array

Radial coordinate, specified as a scalar, vector, matrix, or multidimensional array. theta, rho, and z must 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
Complex Number Support: Yes

z — Elevation coordinate

scalar | vector | matrix | multidimensional array

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

z is the height above the x-y plane.

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 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™.

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 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™.

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

Version History

Introduced before R2006a