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pol2cart

Transform polar or cylindrical coordinates to Cartesian

Syntax

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

Description

example

[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.

Examples

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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 =

         0    0.7854    1.5708    3.1416

rho = [5 5 10 10]
rho =

     5     5    10    10

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

    5.0000    3.5355    0.0000  -10.0000


y =

         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 =

         0
    0.7854
    1.5708
    3.1416

rho = [1 3 4 5]'
rho =

     1
     3
     4
     5

z = [7 8 9 10]'
z =

     7
     8
     9
    10

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

    1.0000
    2.1213
    0.0000
   -5.0000


y =

         0
    2.1213
    4.0000
    0.0000


z =

     7
     8
     9
    10

Input Arguments

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theta — Angular coordinatescalar | 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 any of them can be scalar.

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 coordinatescalar | 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 any of them can be scalar.

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 coordinatescalar | 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 any of them can be scalar.

z is the height above the x-y plane.

Data Types: single | double
Complex Number Support: Yes

Output Arguments

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x, y, z — Cartesian coordinatesarrays

Cartesian coordinates, returned as arrays.

More About

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Algorithms

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

See Also

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Introduced before R2006a

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