Source code for colour.algebra.coordinates.transformations

#!/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]  http://en.wikipedia.org/wiki/List_of_common_coordinate_transformations
"""

from __future__ import division, unicode_literals

import math
import numpy as np

__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013 - 2014 - Colour Developers'
__license__ = 'New BSD License - http://opensource.org/licenses/BSD-3-Clause'
__maintainer__ = 'Colour Developers'
__email__ = 'colou[email protected]'
__status__ = 'Production'

__all__ = ['cartesian_to_spherical',
           'spherical_to_cartesian',
           'cartesian_to_cylindrical',
           'cylindrical_to_cartesian']


[docs]def cartesian_to_spherical(vector): """ Transforms given Cartesian coordinates vector to Spherical coordinates. Parameters ---------- vector : array_like Cartesian coordinates vector (x, y, z) to transform. Returns ------- ndarray Spherical coordinates vector (r, theta, phi). See Also -------- spherical_to_cartesian, cartesian_to_cylindrical, cylindrical_to_cartesian Examples -------- >>> vector = np.array([3, 1, 6]) >>> cartesian_to_spherical(vector) # doctest: +ELLIPSIS array([ 6.7823299..., 1.0857465..., 0.3217505...]) """ r = np.linalg.norm(vector) x, y, z = np.ravel(vector) theta = math.atan2(z, np.linalg.norm((x, y))) phi = math.atan2(y, x) return np.array((r, theta, phi))
[docs]def spherical_to_cartesian(vector): """ Transforms given Spherical coordinates vector to Cartesian coordinates. Parameters ---------- vector : array_like Spherical coordinates vector (r, theta, phi) to transform. Returns ------- ndarray Cartesian coordinates vector (x, y, z). See Also -------- cartesian_to_spherical, cartesian_to_cylindrical, cylindrical_to_cartesian Examples -------- >>> vector = np.array([6.78232998, 1.08574654, 0.32175055]) >>> spherical_to_cartesian(vector) # doctest: +ELLIPSIS array([ 3. , 0.9999999..., 6. ]) """ r, theta, phi = np.ravel(vector) x = r * math.cos(theta) * math.cos(phi) y = r * math.cos(theta) * math.sin(phi) z = r * math.sin(theta) return np.array((x, y, z))
[docs]def cartesian_to_cylindrical(vector): """ Transforms given Cartesian coordinates vector to Cylindrical coordinates. Parameters ---------- vector : array_like Cartesian coordinates vector (x, y, z) to transform. Returns ------- ndarray Cylindrical coordinates vector (z, theta, rho). See Also -------- cartesian_to_spherical, spherical_to_cartesian, cylindrical_to_cartesian Examples -------- >>> vector = np.array([3, 1, 6]) >>> cartesian_to_cylindrical(vector) # doctest: +ELLIPSIS array([ 6. , 0.3217505..., 3.1622776...]) """ x, y, z = np.ravel(vector) theta = math.atan2(y, x) rho = np.linalg.norm((x, y)) return np.array((z, theta, rho))
[docs]def cylindrical_to_cartesian(vector): """ Transforms given Cylindrical coordinates vector to Cartesian coordinates. Parameters ---------- vector : array_like Cylindrical coordinates vector (z, theta, rho) to transform. Returns ------- ndarray Cartesian coordinates vector (x, y, z). See Also -------- cartesian_to_spherical, spherical_to_cartesian, cartesian_to_cylindrical Examples -------- >>> vector = np.array([6, 0.32175055, 3.16227766]) >>> cylindrical_to_cartesian(vector) # doctest: +ELLIPSIS array([ 3. , 0.9999999..., 6. ]) """ z, theta, rho = np.ravel(vector) x = rho * math.cos(theta) y = rho * math.sin(theta) return np.array((x, y, z))