r9484 - in /1.3: maths_fns/rotation_matrix.py test_suite/unit_tests/_maths_fns/test_rotation_matrix.py -- September 08, 2009 - 19:17

Author: bugman
Date: Tue Sep  8 19:17:29 2009
New Revision: 9484

URL: http://svn.gna.org/viewcvs/relax?rev=9484&view=rev
Log:
Created the maths_fns.rotation_matrix.axis_angle_to_quaternion() 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=9484&r1=9483&r2=9484&view=diff
==============================================================================
--- 1.3/maths_fns/rotation_matrix.py (original)
+++ 1.3/maths_fns/rotation_matrix.py Tue Sep  8 19:17:29 2009
@@ -83,6 +83,40 @@
     R[2, 2] = z*zC + ca
 
 
+def axis_angle_to_quaternion(axis, angle, quat, norm_flag=True):
+    """Generate the quaternion from 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.
+
+
+    @param axis:        The 3D rotation axis.
+    @type axis:         numpy array, len 3
+    @param angle:       The rotation angle.
+    @type angle:        float
+    @param quat:        The quaternion structure.
+    @type quat:         numpy 4D, rank-1 array
+    @keyword norm_flag: A flag which if True forces the axis to be converted 
to a unit vector.
+    @type norm_flag:    bool
+    """
+
+    # Convert to unit vector.
+    if norm_flag:
+        axis = axis / norm(axis)
+
+    # The scalar component of q.
+    quat[0] = cos(angle/2)
+
+    # The vector component.
+    quat[1:] = axis * sin(angle/2)
+
+
 def euler_zyz_to_R(alpha, beta, gamma, R):
     """Function for calculating the z-y-z Euler angle convention rotation 
matrix.
 

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=9484&r1=9483&r2=9484&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 
19:17:29 2009
@@ -109,6 +109,46 @@
                 self.assertEqual(R[i, j], R_true[i, j])
 
 
+    def test_axis_angle_to_quaternion_no_rot(self):
+        """Test the axis-angle to quaternion conversion for a zero angle 
rotation."""
+
+        # Random axis and zero angle.
+        axis = array([-1, 1, 1], float64) / sqrt(3)
+        angle = 0.0
+
+        # The quaternion matrix.
+        quat = zeros(4, float64)
+        axis_angle_to_quaternion(axis, angle, quat)
+        print("Quaternion:\n%s" % quat)
+
+        # The correct result.
+        quat_true = array([1, 0, 0, 0], float64)
+
+        # Checks.
+        for i in range(4):
+            self.assertEqual(quat[i], quat_true[i])
+
+
+    def test_axis_angle_to_quaternion_180_complex(self):
+        """Test the axis-angle to quaternion conversion for a 180 degree 
rotation about [1, 1, 1]."""
+
+        # Random axis and zero angle.
+        axis = array([1, 1, 1], float64) / sqrt(3)
+        angle = pi
+
+        # The quaternion matrix.
+        quat = zeros(4, float64)
+        axis_angle_to_quaternion(axis, angle, quat)
+        print("Quaternion:\n%s" % quat)
+
+        # The correct result.
+        quat_true = array([0, 1, 1, 1], float64) / sqrt(3)
+
+        # Checks.
+        for i in range(4):
+            self.assertAlmostEqual(quat[i], quat_true[i])
+
+
     def test_axis_angle_to_R_z_30(self):
         """Test the quaternion to rotation matrix conversion for a 30 degree 
rotation about z."""