Source Code for Module maths_fns.coord_transform

 1  ############################################################################### 
 2  #                                                                             # 
 3  # Copyright (C) 2010 Edward d'Auvergne                                        # 
 4  #                                                                             # 
 5  # This file is part of the program relax.                                     # 
 6  #                                                                             # 
 7  # relax is free software; you can redistribute it and/or modify               # 
 8  # it under the terms of the GNU General Public License as published by        # 
 9  # the Free Software Foundation; either version 2 of the License, or           # 
10  # (at your option) any later version.                                         # 
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12  # relax is distributed in the hope that it will be useful;                    # 
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14  # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the               # 
15  # GNU General Public License for more details.                                # 
16  #                                                                             # 
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19  # Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA   # 
20  #                                                                             # 
21  ############################################################################### 
22   
23  # Module docstring. 
24  """Module for transforming between different coordinate systems.""" 
25   
26  # Python module imports. 
27  from math import acos, atan2, cos, sin 
28  from numpy import array, float64, zeros 
29  from numpy.linalg import norm 
30   
31   
32 -def cartesian_to_spherical(vector): 
33      """Convert the Cartesian vector [x, y, z] to spherical coordinates [r, theta, phi]. 
34   
35      The parameter r is the radial distance, theta is the polar angle, and phi is the azimuth. 
36   
37   
38      @param vector:  The Cartesian vector [x, y, z]. 
39      @type vector:   numpy rank-1, 3D array 
40      @return:        The spherical coordinate vector [r, theta, phi]. 
41      @rtype:         numpy rank-1, 3D array 
42      """ 
43   
44      # The radial distance. 
45      r = norm(vector) 
46   
47      # Unit vector. 
48      unit = vector / r 
49   
50      # The polar angle. 
51      theta = acos(unit[2]) 
52   
53      # The azimuth. 
54      phi = atan2(unit[1], unit[0]) 
55   
56      # Return the spherical coordinate vector. 
57      return array([r, theta, phi], float64) 
58   
59   
60 -def spherical_to_cartesian(spherical_vect, cart_vect): 
61      """Convert the spherical coordinate vector [r, theta, phi] to the Cartesian vector [x, y, z]. 
62   
63      The parameter r is the radial distance, theta is the polar angle, and phi is the azimuth. 
64   
65   
66      @param spherical_vect:  The spherical coordinate vector [r, theta, phi]. 
67      @type spherical_vect:   3D array or list 
68      @param cart_vect:       The Cartesian vector [x, y, z]. 
69      @type cart_vect:        3D array or list 
70      """ 
71   
72      # Trig alias. 
73      sin_theta = sin(spherical_vect[1]) 
74   
75      # The vector. 
76      cart_vect[0] = spherical_vect[0] * cos(spherical_vect[2]) * sin_theta 
77      cart_vect[1] = spherical_vect[0] * sin(spherical_vect[2]) * sin_theta 
78      cart_vect[2] = spherical_vect[0] * cos(spherical_vect[1]) 
79