geoana.spatial.cartesian_to_cylindrical

geoana.spatial.cartesian_to_cylindrical(grid, vec=None)

Transform gridded locations or a set of vectors from Cartesian coordinates \((x, y, z)\) to cylindrical coordinates \((r, \phi, z)\). Where the azimuthal angle \(\phi \in [-\pi , \pi ]\) will be given output in radians.

Parameters:

grid(…, 3) array_like

Gridded locations defined in Cartesian coordinates \((x, y z)\).

vec(…, 3) array_like, optional

Vectors defined in Cartesian coordinates \((v_x, v_y, v_z)\) at the gridded locations. Also accepts a flattened array with the same total elements in column major order.

Returns:

(…, 3) numpy.ndarray

If vec is None, this returns the transformed grid array, otherwise this is the transformed vec array.

Examples

Here, we convert a series of vectors in 3D space from Cartesian coordinates to cylindrical coordinates.

>>> from geoana.spatial import cartesian_to_cylindrical
>>> import numpy as np

Create set of vectors in Cartesian coordinates

>>> r = np.ones(9)
>>> phi = np.linspace(0, 2*np.pi, 9)
>>> z = np.linspace(-4., 4., 9)
>>> x = r*np.cos(phi)
>>> y = r*np.sin(phi)
>>> u = np.c_[x, y, z]
>>> u
array([[ 1.00000000e+00,  0.00000000e+00, -4.00000000e+00],
       [ 7.07106781e-01,  7.07106781e-01, -3.00000000e+00],
       [ 6.12323400e-17,  1.00000000e+00, -2.00000000e+00],
       [-7.07106781e-01,  7.07106781e-01, -1.00000000e+00],
       [-1.00000000e+00,  1.22464680e-16,  0.00000000e+00],
       [-7.07106781e-01, -7.07106781e-01,  1.00000000e+00],
       [-1.83697020e-16, -1.00000000e+00,  2.00000000e+00],
       [ 7.07106781e-01, -7.07106781e-01,  3.00000000e+00],
       [ 1.00000000e+00, -2.44929360e-16,  4.00000000e+00]])

Compute equivalent set of vectors in cylindrical coordinates

>>> v = cartesian_to_cylindrical(u)
>>> v
array([[ 1.00000000e+00,  0.00000000e+00, -4.00000000e+00],
       [ 1.00000000e+00,  7.85398163e-01, -3.00000000e+00],
       [ 1.00000000e+00,  1.57079633e+00, -2.00000000e+00],
       [ 1.00000000e+00,  2.35619449e+00, -1.00000000e+00],
       [ 1.00000000e+00,  3.14159265e+00,  0.00000000e+00],
       [ 1.00000000e+00, -2.35619449e+00,  1.00000000e+00],
       [ 1.00000000e+00, -1.57079633e+00,  2.00000000e+00],
       [ 1.00000000e+00, -7.85398163e-01,  3.00000000e+00],
       [ 1.00000000e+00, -2.44929360e-16,  4.00000000e+00]])