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cart2pol

Transform Cartesian coordinates to polar or cylindrical

Syntax

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

Description

example

[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.

Examples

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Cartesian to Polar Coordinates

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 =

    5.0000    3.5355         0  -10.0000

y = [0 3.5355 10 0]
y =

         0    3.5355   10.0000         0

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

         0    0.7854    1.5708    3.1416


rho =

    5.0000    5.0000   10.0000   10.0000

Cartesian to Cylindrical Coordinates

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 =

    1.0000
    2.1213
         0
   -5.0000

y = [0 2.1213 4 0]'
y =

         0
    2.1213
    4.0000
         0

z = [7 8 9 10]'
z =

     7
     8
     9
    10

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

         0
    0.7854
    1.5708
    3.1416


rho =

    1.0000
    3.0000
    4.0000
    5.0000


z =

     7
     8
     9
    10

Input Arguments

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x, y, z — Cartesian coordinatesscalars | vectors | matrices | multidimensional arrays

Cartesian coordinates, specified as scalars, vectors, matrices, or multidimensional arrays. x, y, and z must be the same size, or any of them can be scalar.

Data Types: single | double

Output Arguments

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theta — Angular coordinatearray

Angular coordinate, returned as an array. theta is the counterclockwise angle in the x-y plane measured in radians from the positive x-axis.

rho — Radial coordinatearray

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

z — Elevation coordinatearray

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

More About

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Algorithms

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

See Also

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Introduced before R2006a

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