pol2cart

Transform polar or cylindrical coordinates to Cartesian

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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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

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 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

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

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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Cartesian coordinates, returned as arrays.

Algorithms

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