# Copyright (C) 2016 Christopher M. Biwer
#
#
# This program is free software; you can redistribute it and/or modify it
# under the terms of the GNU General Public License as published by the
# Free Software Foundation; either version 3 of the License, or (at your
# option) any later version.
#
# This program is distributed in the hope that it will be useful, but
# WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
# Public License for more details.
#
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
""" Coordinate transformations.
"""
import numpy
[docs]def cartesian_to_spherical_rho(x, y, z):
""" Calculates the magnitude in spherical coordinates from Cartesian
coordinates.
Parameters
----------
x : {numpy.array, float}
X-coordinate.
y : {numpy.array, float}
Y-coordinate.
z : {numpy.array, float}
Z-coordinate.
Returns
-------
rho : {numpy.array, float}
The radial amplitude.
"""
return numpy.sqrt(x**2 + y**2 + z**2)
[docs]def cartesian_to_spherical_azimuthal(x, y):
""" Calculates the azimuthal angle in spherical coordinates from Cartesian
coordinates. The azimuthal angle is in [0,2*pi].
Parameters
----------
x : {numpy.array, float}
X-coordinate.
y : {numpy.array, float}
Y-coordinate.
Returns
-------
phi : {numpy.array, float}
The azimuthal angle.
"""
y = float(y) if isinstance(y, int) else y
phi = numpy.arctan2(y, x)
return phi % (2 * numpy.pi)
[docs]def cartesian_to_spherical_polar(x, y, z):
""" Calculates the polar angle in spherical coordinates from Cartesian
coordinates. The polar angle is in [0,pi].
Parameters
----------
x : {numpy.array, float}
X-coordinate.
y : {numpy.array, float}
Y-coordinate.
z : {numpy.array, float}
Z-coordinate.
Returns
-------
theta : {numpy.array, float}
The polar angle.
"""
return numpy.arccos(z / cartesian_to_spherical_rho(x, y, z))
[docs]def cartesian_to_spherical(x, y, z):
""" Maps cartesian coordinates (x,y,z) to spherical coordinates
(rho,phi,theta) where phi is in [0,2*pi] and theta is in [0,pi].
Parameters
----------
x : {numpy.array, float}
X-coordinate.
y : {numpy.array, float}
Y-coordinate.
z : {numpy.array, float}
Z-coordinate.
Returns
-------
rho : {numpy.array, float}
The radial amplitude.
phi : {numpy.array, float}
The azimuthal angle.
theta : {numpy.array, float}
The polar angle.
"""
rho = cartesian_to_spherical_rho(x, y, z)
phi = cartesian_to_spherical_azimuthal(x, y)
theta = cartesian_to_spherical_polar(x, y, z)
return rho, phi, theta
[docs]def spherical_to_cartesian(rho, phi, theta):
""" Maps spherical coordinates (rho,phi,theta) to cartesian coordinates
(x,y,z) where phi is in [0,2*pi] and theta is in [0,pi].
Parameters
----------
rho : {numpy.array, float}
The radial amplitude.
phi : {numpy.array, float}
The azimuthal angle.
theta : {numpy.array, float}
The polar angle.
Returns
-------
x : {numpy.array, float}
X-coordinate.
y : {numpy.array, float}
Y-coordinate.
z : {numpy.array, float}
Z-coordinate.
"""
x = rho * numpy.cos(phi) * numpy.sin(theta)
y = rho * numpy.sin(phi) * numpy.sin(theta)
z = rho * numpy.cos(theta)
return x, y, z
__all__ = ['cartesian_to_spherical_rho', 'cartesian_to_spherical_azimuthal',
'cartesian_to_spherical_polar', 'cartesian_to_spherical',
'spherical_to_cartesian',
]