r18671 - /trunk/lib/geometry/lines.py -- March 07, 2013 - 17:15

Author: bugman
Date: Thu Mar  7 17:15:53 2013
New Revision: 18671

URL: http://svn.gna.org/viewcvs/relax?rev=18671&view=rev
Log:
Implemented the closest_point() and closest_point_ax() functions of 
lib.geometry.lines.

These two functions do the same thing - find the closest point on a line to 
any given point - but
take different arguments to define the line.


Modified:
    trunk/lib/geometry/lines.py

Modified: trunk/lib/geometry/lines.py
URL: 
http://svn.gna.org/viewcvs/relax/trunk/lib/geometry/lines.py?rev=18671&r1=18670&r2=18671&view=diff
==============================================================================
--- trunk/lib/geometry/lines.py (original)
+++ trunk/lib/geometry/lines.py Thu Mar  7 17:15:53 2013
@@ -22,9 +22,16 @@
 # Module docstring.
 """Functions relating to line geometry."""
 
+# Python module imports.
+from numpy import dot
+from numpy.linalg import norm
+
 
 def closest_point(line_pt1=None, line_pt2=None, point=None):
     """Determine the closest position on the line to the given point.
+
+    This function defines the line using any two points on the line.
+
 
     @keyword line_pt1:  The first point defining the line.
     @type line_pt1:     numpy rank-1 array
@@ -36,3 +43,39 @@
     @rtype:             numpy rank-1 array
     """
 
+    # The vector along the line.
+    vect = line_pt2 - line_pt1
+
+    # Forward.
+    return closest_point_ax(line_pt=line_pt1, axis=vect, point=point)
+
+
+def closest_point_ax(line_pt=None, axis=None, point=None):
+    """Determine the closest position on the line to the given point.
+
+    This function defines the line using any point on the line and the axis.
+
+
+    @keyword line_pt1:  The point defining the line.
+    @type line_pt1:     numpy rank-1 array
+    @keyword axis:      The axis defining the line.
+    @type axis:         numpy rank-1 array
+    @keyword point:     The point.
+    @type point:        numpy rank-1 array
+    @return:            The position on the line closest to the point.
+    @rtype:             numpy rank-1 array
+    """
+
+    # The hypotenuse.
+    hypo = point - line_pt
+    hypo_len = norm(hypo)
+    unit_hypo = hypo / hypo_len
+
+    # Normalise the axis.
+    axis = axis / norm(axis)
+
+    # The distance from the point defining the line to the closest point.
+    d = hypo_len * dot(axis, unit_hypo)
+
+    # The closest point.
+    return line_pt + d*axis