r9485 - in /1.3: maths_fns/rotation_matrix.py test_suite/unit_tests/_maths_fns/test_rotation_matrix.py -- September 08, 2009 - 19:51

Author: bugman
Date: Tue Sep  8 19:51:14 2009
New Revision: 9485

URL: http://svn.gna.org/viewcvs/relax?rev=9485&view=rev
Log:
Created the maths_fns.rotation_matrix.quaternion_to_axis_angle() function.

This is accompanied by 2 unit tests.


Modified:
    1.3/maths_fns/rotation_matrix.py
    1.3/test_suite/unit_tests/_maths_fns/test_rotation_matrix.py

Modified: 1.3/maths_fns/rotation_matrix.py
URL: 
http://svn.gna.org/viewcvs/relax/1.3/maths_fns/rotation_matrix.py?rev=9485&r1=9484&r2=9485&view=diff
==============================================================================
--- 1.3/maths_fns/rotation_matrix.py (original)
+++ 1.3/maths_fns/rotation_matrix.py Tue Sep  8 19:51:14 2009
@@ -325,6 +325,41 @@
     axis[2] = cos(phi)
 
 
+def quaternion_to_axis_angle(quat):
+    """Convert a quaternion into the axis-angle notation.
+
+    Conversion equations
+    ====================
+
+    From Wolfram MathWorld (http://mathworld.wolfram.com/Quaternion.html), 
the conversion is given by::
+
+        q = (cos(angle/2), n * sin(angle/2)),
+
+    where q is the quaternion and n is the unit vector representing the 
rotation axis.  Therfore::
+
+        angle = 2*acos(w),
+
+        axis = 2*asin([x, y, z])
+
+    @param quat:    The quaternion.
+    @type quat:     numpy 4D, rank-1 array
+    @return:        The 3D rotation axis and angle.
+    @rtype:         numpy 3D rank-1 array, float
+    """
+
+    # The angle.
+    angle = 2 * acos(quat[0])
+
+    # The axis.
+    if angle:
+        axis = quat[1:] / sin(angle/2)
+    else:
+        axis = quat[1:] * 0.0
+
+    # Return
+    return axis, angle
+
+
 def quaternion_to_R(quat, R):
     """Convert a quaternion into rotation matrix form.
 

Modified: 1.3/test_suite/unit_tests/_maths_fns/test_rotation_matrix.py
URL: 
http://svn.gna.org/viewcvs/relax/1.3/test_suite/unit_tests/_maths_fns/test_rotation_matrix.py?rev=9485&r1=9484&r2=9485&view=diff
==============================================================================
--- 1.3/test_suite/unit_tests/_maths_fns/test_rotation_matrix.py (original)
+++ 1.3/test_suite/unit_tests/_maths_fns/test_rotation_matrix.py Tue Sep  8 
19:51:14 2009
@@ -353,6 +353,41 @@
         self.assertAlmostEqual(gamma, gamma_new)
 
 
+    def test_quaternion_to_axis_angle_no_rot(self):
+        """Test the quaternion to rotation matrix conversion for a zero 
angle rotation."""
+
+        # Quaternion of zero angle.
+        quat = array([1, 0, 0, 0], float64)
+
+        # The axis and angle.
+        axis, angle = quaternion_to_axis_angle(quat)
+        print("Axis:  %s" % axis)
+        print("Angle: %s" % angle)
+
+        # The correct result.
+        self.assertEqual(angle, 0.0)
+        for i in range(3):
+            self.assertEqual(axis[i], 0.0)
+
+
+    def test_quaternion_to_axis_angle_180_complex(self):
+        """Test the quaternion to axis-angle conversion for a 180 degree 
rotation about [1, 1, 1]."""
+
+        # The quaternion.
+        quat = array([0, 1, 1, 1], float64) / sqrt(3)
+
+        # The axis and angle.
+        axis, angle = quaternion_to_axis_angle(quat)
+        print("Axis:  %s" % axis)
+        print("Angle: %s" % angle)
+
+        # The correct result.
+        self.assertEqual(angle, pi)
+        for i in range(3):
+            self.assertEqual(axis[i], 1.0 / sqrt(3))
+
+
+
     def test_quaternion_to_R_no_rot(self):
         """Test the quaternion to rotation matrix conversion for a zero 
angle rotation."""