Source Code for Module lib.geometry.lines

 1  ############################################################################### 
 2  #                                                                             # 
 3  # Copyright (C) 2013 Edward d'Auvergne                                        # 
 4  #                                                                             # 
 5  # This file is part of the program relax (http://www.nmr-relax.com).          # 
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20  ############################################################################### 
21   
22  # Module docstring. 
23  """Functions relating to line geometry.""" 
24   
25  # Python module imports. 
26  from numpy import dot 
27  from numpy.linalg import norm 
28   
29   
30 -def closest_point(line_pt1=None, line_pt2=None, point=None): 
31      """Determine the closest position on the line to the given point. 
32   
33      This function defines the line using any two points on the line. 
34   
35   
36      @keyword line_pt1:  The first point defining the line. 
37      @type line_pt1:     numpy rank-1 array 
38      @keyword line_pt2:  The second point defining the line. 
39      @type line_pt2:     numpy rank-1 array 
40      @keyword point:     The point. 
41      @type point:        numpy rank-1 array 
42      @return:            The position on the line closest to the point. 
43      @rtype:             numpy rank-1 array 
44      """ 
45   
46      # The vector along the line. 
47      vect = line_pt2 - line_pt1 
48   
49      # Forward. 
50      return closest_point_ax(line_pt=line_pt1, axis=vect, point=point) 
51   
52   
53 -def closest_point_ax(line_pt=None, axis=None, point=None): 
54      """Determine the closest position on the line to the given point. 
55   
56      This function defines the line using any point on the line and the axis. 
57   
58   
59      @keyword line_pt1:  The point defining the line. 
60      @type line_pt1:     numpy rank-1 array 
61      @keyword axis:      The axis defining the line. 
62      @type axis:         numpy rank-1 array 
63      @keyword point:     The point. 
64      @type point:        numpy rank-1 array 
65      @return:            The position on the line closest to the point. 
66      @rtype:             numpy rank-1 array 
67      """ 
68   
69      # Check if the two points are the same, returning the point to avoid NaNs. 
70      if norm(line_pt - point) < 1e-6: 
71          return point 
72   
73      # The hypotenuse. 
74      hypo = point - line_pt 
75      hypo_len = norm(hypo) 
76      unit_hypo = hypo / hypo_len 
77   
78      # Normalise the axis. 
79      axis = axis / norm(axis) 
80   
81      # The distance from the point defining the line to the closest point. 
82      d = hypo_len * dot(axis, unit_hypo) 
83   
84      # The closest point. 
85      return line_pt + d*axis 
86