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(n, 3) array_like

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

vec(n, 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
(n, 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]])