#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
Coordinates System Transformations
==================================
Defines objects to apply transformations on coordinates systems.
The following transformations are available:
- :func:`cartesian_to_spherical`: Cartesian to Spherical transformation.
- :func:`spherical_to_cartesian`: Spherical to Cartesian transformation.
- :func:`cartesian_to_cylindrical`: Cartesian to Cylindrical transformation.
- :func:`cylindrical_to_cartesian`: Cylindrical to Cartesian transformation.
References
----------
.. [1] Wikipedia. (n.d.). List of common coordinate transformations.
Retrieved from
http://en.wikipedia.org/wiki/List_of_common_coordinate_transformations
"""
from __future__ import division, unicode_literals
import numpy as np
from colour.utilities import tsplit, tstack
__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013-2016 - Colour Developers'
__license__ = 'New BSD License - http://opensource.org/licenses/BSD-3-Clause'
__maintainer__ = 'Colour Developers'
__email__ = 'colour-science@googlegroups.com'
__status__ = 'Production'
__all__ = ['cartesian_to_spherical',
'spherical_to_cartesian',
'cartesian_to_cylindrical',
'cylindrical_to_cartesian']
[docs]def cartesian_to_spherical(a):
"""
Transforms given Cartesian coordinates array to Spherical coordinates.
Parameters
----------
a : array_like
Cartesian coordinates array (x, y, z) to transform.
Returns
-------
ndarray
Spherical coordinates array (r, theta, phi).
See Also
--------
spherical_to_cartesian, cartesian_to_cylindrical, cylindrical_to_cartesian
Examples
--------
>>> a = np.array([3, 1, 6])
>>> cartesian_to_spherical(a) # doctest: +ELLIPSIS
array([ 6.7823299..., 1.0857465..., 0.3217505...])
"""
x, y, z = tsplit(a)
r = np.linalg.norm(a, axis=-1)
theta = np.arctan2(z, np.linalg.norm(tstack((x, y)), axis=-1))
phi = np.arctan2(y, x)
rtp = tstack((r, theta, phi))
return rtp
[docs]def spherical_to_cartesian(a):
"""
Transforms given Spherical coordinates array to Cartesian coordinates.
Parameters
----------
a : array_like
Spherical coordinates array (r, theta, phi) to transform.
Returns
-------
ndarray
Cartesian coordinates array (x, y, z).
See Also
--------
cartesian_to_spherical, cartesian_to_cylindrical, cylindrical_to_cartesian
Examples
--------
>>> a = np.array([6.78232998, 1.08574654, 0.32175055])
>>> spherical_to_cartesian(a) # doctest: +ELLIPSIS
array([ 3. , 0.9999999..., 6. ])
"""
r, theta, phi = tsplit(a)
x = r * np.cos(theta) * np.cos(phi)
y = r * np.cos(theta) * np.sin(phi)
z = r * np.sin(theta)
xyz = tstack((x, y, z))
return xyz
[docs]def cartesian_to_cylindrical(a):
"""
Transforms given Cartesian coordinates array to Cylindrical coordinates.
Parameters
----------
a : array_like
Cartesian coordinates array (x, y, z) to transform.
Returns
-------
ndarray
Cylindrical coordinates array (z, theta, rho).
See Also
--------
cartesian_to_spherical, spherical_to_cartesian, cylindrical_to_cartesian
Examples
--------
>>> a = np.array([3, 1, 6])
>>> cartesian_to_cylindrical(a) # doctest: +ELLIPSIS
array([ 6. , 0.3217505..., 3.1622776...])
"""
x, y, z = tsplit(a)
theta = np.arctan2(y, x)
rho = np.linalg.norm(tstack((x, y)), axis=-1)
return tstack((z, theta, rho))
[docs]def cylindrical_to_cartesian(a):
"""
Transforms given Cylindrical coordinates array to Cartesian coordinates.
Parameters
----------
a : array_like
Cylindrical coordinates array (z, theta, rho) to transform.
Returns
-------
ndarray
Cartesian coordinates array (x, y, z).
See Also
--------
cartesian_to_spherical, spherical_to_cartesian, cartesian_to_cylindrical
Examples
--------
>>> a = np.array([6.00000000, 0.32175055, 3.16227766])
>>> cylindrical_to_cartesian(a) # doctest: +ELLIPSIS
array([ 3. , 0.9999999..., 6. ])
"""
z, theta, rho = tsplit(a)
x = rho * np.cos(theta)
y = rho * np.sin(theta)
return tstack((x, y, z))