Source Code for Module lib.geometry.vectors

 1  ############################################################################### 
 2  #                                                                             # 
 3  # Copyright (C) 2004-2014 Edward d'Auvergne                                   # 
 4  #                                                                             # 
 5  # This file is part of the program relax (http://www.nmr-relax.com).          # 
 6  #                                                                             # 
 7  # This program 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 3 of the License, or           # 
10  # (at your option) any later version.                                         # 
11  #                                                                             # 
12  # This program is distributed in the hope that it will be useful,             # 
13  # but WITHOUT ANY WARRANTY; without even the implied warranty of              # 
14  # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the               # 
15  # GNU General Public License for more details.                                # 
16  #                                                                             # 
17  # You should have received a copy of the GNU General Public License           # 
18  # along with this program.  If not, see <http://www.gnu.org/licenses/>.       # 
19  #                                                                             # 
20  ############################################################################### 
21   
22  # Module docstring. 
23  """Collection of functions for vector operations.""" 
24   
25  # Python module imports. 
26  from math import acos, cos, pi, sin 
27  from numpy import array, float64 
28  from numpy.linalg import norm 
29  from random import uniform 
30   
31   
32 -def random_unit_vector(vector): 
33      """Generate a random rotation axis. 
34   
35      Uniform point sampling on a unit sphere is used to generate a random axis orientation. 
36   
37      @param vector:  The 3D rotation axis. 
38      @type vector:   numpy 3D, rank-1 array 
39      """ 
40   
41      # Random azimuthal angle. 
42      u = uniform(0, 1) 
43      theta = 2*pi*u 
44   
45      # Random polar angle. 
46      v = uniform(0, 1) 
47      phi = acos(2.0*v - 1) 
48   
49      # Random unit vector. 
50      vector[0] = cos(theta) * sin(phi) 
51      vector[1] = sin(theta) * sin(phi) 
52      vector[2] = cos(phi) 
53   
54   
55 -def unit_vector_from_2point(point1, point2): 
56      """Generate the unit vector connecting point 1 to point 2. 
57   
58      @param point1:  The first point. 
59      @type point1:   list of float or numpy array 
60      @param point2:  The second point. 
61      @type point2:   list of float or numpy array 
62      @return:        The unit vector. 
63      @rtype:         numpy float64 array 
64      """ 
65   
66      # Convert to numpy data structures. 
67      point1 = array(point1, float64) 
68      point2 = array(point2, float64) 
69   
70      # The vector. 
71      vect = point2 - point1 
72   
73      # Return the unit vector. 
74      return vect / norm(vect) 
75