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]])