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cart2pol

Transform Cartesian coordinates to polar or cylindrical

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Syntax

[theta,rho] = cart2pol(x,y)
[theta,rho,z] = cart2pol(x,y,z)

Description

[theta,rho] = cart2pol(x,y) transforms corresponding elements of the two-dimensional Cartesian coordinate arrays x and y into polar coordinates theta and rho.

example

[theta,rho,z] = cart2pol(x,y,z) transforms three-dimensional Cartesian coordinate arrays x, y, and z into cylindrical coordinates theta, rho, and z.

example

Examples

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Open Live Script

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

x = [5 3.5355 0 -10]
x = 1×4

    5.0000    3.5355         0  -10.0000


y = [0 3.5355 10 0]
y = 1×4

         0    3.5355   10.0000         0


[theta,rho] = cart2pol(x,y)
theta = 1×4

         0    0.7854    1.5708    3.1416


rho = 1×4

    5.0000    5.0000   10.0000   10.0000
Open Live Script

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

x = [1 2.1213 0 -5]'
x = 4×1

    1.0000
    2.1213
         0
   -5.0000


y = [0 2.1213 4 0]'
y = 4×1

         0
    2.1213
    4.0000
         0


z = [7 8 9 10]'
z = 4×1

     7
     8
     9
    10


[theta,rho,z] = cart2pol(x,y,z)
theta = 4×1

         0
    0.7854
    1.5708
    3.1416


rho = 4×1

    1.0000
    3.0000
    4.0000
    5.0000


z = 4×1

     7
     8
     9
    10

Input Arguments

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Cartesian coordinates, specified as scalars, vectors, matrices, or multidimensional arrays. x, y, and z must be the same size, or have sizes that are compatible (for example, x is an M-by-N matrix, y is a scalar, and z is a scalar or 1-by-N row vector). For more information, see Compatible Array Sizes for Basic Operations.

Data Types: single | double

Output Arguments

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Angular coordinate, returned as an array. theta is the counterclockwise angle in the x-y plane measured in radians from the positive x-axis. The value of the angle is in the range [-pi pi].

Radial coordinate, returned as an array. rho is the distance from the origin to a point in the x-y plane.

Elevation coordinate, returned as an array. z is the height above the x-y plane.

Algorithms

The mapping from two-dimensional Cartesian coordinates to polar coordinates, and from three-dimensional Cartesian coordinates to cylindrical coordinates is

Figure shows 2-D and 3-D mappings from Cartesian to polar 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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