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pol2cart

Transform polar or cylindrical coordinates to Cartesian

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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.

example

[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.

example

Examples

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Open Live Script

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
Open Live Script

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

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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

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

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

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Cartesian coordinates, returned as arrays.

Algorithms

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

Figure shows 2-D and 3-D mappings from polar to Cartesian coordinates. The 2-D mapping has X and Y axes, with rho equal to the radius of the point and theta its angle in relation to X. The 3-D mapping additionally has a value for Z that requires no conversion.

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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