geoana.spatial.cartesian_to_spherical#

geoana.spatial.cartesian_to_spherical(grid, vec=None)#

Transform gridded locations or a set of vectors from Cartesian coordinates \((x, y, z)\) to spherical coordinates \((r, \phi, \theta)\). \(\phi\) and \(\theta\) are the azimuthal and polar angle, respectively. \(\phi\) and \(\theta\) are given 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. Will also except a flattend array in column major order with the same number of elements.

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 spherical coordinates.

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

Construct original set of vectors in cartesian coordinates

>>> r = np.ones(9)
>>> phi = np.linspace(0, 2*np.pi, 9)
>>> theta = np.linspace(0., np.pi, 9)
>>> x = r*np.sin(theta)*np.cos(phi)
>>> y = r*np.sin(theta)*np.sin(phi)
>>> z = r*np.cos(theta)
>>> u = np.c_[x, y, z]
>>> u
array([[ 0.00000000e+00,  0.00000000e+00,  1.00000000e+00],
       [ 2.70598050e-01,  2.70598050e-01,  9.23879533e-01],
       [ 4.32978028e-17,  7.07106781e-01,  7.07106781e-01],
       [-6.53281482e-01,  6.53281482e-01,  3.82683432e-01],
       [-1.00000000e+00,  1.22464680e-16,  6.12323400e-17],
       [-6.53281482e-01, -6.53281482e-01, -3.82683432e-01],
       [-1.29893408e-16, -7.07106781e-01, -7.07106781e-01],
       [ 2.70598050e-01, -2.70598050e-01, -9.23879533e-01],
       [ 1.22464680e-16, -2.99951957e-32, -1.00000000e+00]])

Compute equivalent set of vectors in spherical coordinates

>>> v = cartesian_to_spherical(u)
>>> v
array([[ 1.00000000e+00,  0.00000000e+00,  0.00000000e+00],
       [ 1.00000000e+00,  7.85398163e-01,  3.92699082e-01],
       [ 1.00000000e+00,  1.57079633e+00,  7.85398163e-01],
       [ 1.00000000e+00,  2.35619449e+00,  1.17809725e+00],
       [ 1.00000000e+00,  3.14159265e+00,  1.57079633e+00],
       [ 1.00000000e+00, -2.35619449e+00,  1.96349541e+00],
       [ 1.00000000e+00, -1.57079633e+00,  2.35619449e+00],
       [ 1.00000000e+00, -7.85398163e-01,  2.74889357e+00],
       [ 1.00000000e+00, -2.44929360e-16,  3.14159265e+00]])

geoana.spatial.cartesian_to_spherical#

This Page