r10709 - /1.3/maths_fns/rotation_matrix.py -- February 18, 2010 - 10:59

Author: bugman
Date: Thu Feb 18 10:59:41 2010
New Revision: 10709

URL: http://svn.gna.org/viewcvs/relax?rev=10709&view=rev
Log:
Added the tilt and torsion angle convention conversions to and from rotation 
matrices.


Modified:
    1.3/maths_fns/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=10709&r1=10708&r2=10709&view=diff
==============================================================================
--- 1.3/maths_fns/rotation_matrix.py (original)
+++ 1.3/maths_fns/rotation_matrix.py Thu Feb 18 10:59:41 2010
@@ -1829,6 +1829,32 @@
     return R_to_euler(R, 'zyz')
 
 
+def R_to_tilt_torsion(R):
+    """Convert the rotation matrix to the tilt and torsion rotation angles.
+
+    This notation is taken from:
+
+        Bonev, I. A. and Gosselin, C. M. (2006)  Analytical determination of 
the workspace of symmetrical spherical parallel mechanisms.  IEEE 
Transactions on Robotics, 22(5), 1011-1017.
+
+
+    @param R:       The 3x3 rotation matrix to extract the tilt and torsion 
angles from.
+    @type R:        3D, rank-2 numpy array
+    @return:        The phi, theta, and sigma tilt and torsion angles.
+    @rtype:         tuple of float
+    """
+
+    # First obtain the zyz Euler angles.
+    alpha, beta, gamma = R_to_euler(R, 'zyz')
+
+    # The convert to tilt and torsion.
+    phi = gamma
+    theta = beta
+    sigma = alpha + gamma
+
+    # Return the angles.
+    return phi, theta, sigma
+
+
 def R_to_quaternion(R, quat):
     """Convert a rotation matrix into quaternion form.
 
@@ -2318,6 +2344,33 @@
     R[2, 1] = yz + xw
 
 
+def tilt_torsion_to_R(phi, theta, sigma, R):
+    """Generate a rotation matrix from the tilt and torsion rotation angles.
+
+    This notation is taken from:
+
+        Bonev, I. A. and Gosselin, C. M. (2006)  Analytical determination of 
the workspace of symmetrical spherical parallel mechanisms.  IEEE 
Transactions on Robotics, 22(5), 1011-1017.
+
+
+    @param phi:     The angle defining the x-y plane rotation axis.
+    @type phi:      float
+    @param theta:   The tilt angle - the angle of rotation about the x-y 
plane rotation axis.
+    @type theta:    float
+    @param sigma:   The torsion angle - the angle of rotation about the z' 
axis.
+    @type sigma:    float
+    @param R:       The 3x3 rotation matrix to update.
+    @type R:        3D, rank-2 numpy array
+    """
+
+    # Convert to zyz Euler angles.
+    alpha = sigma - phi
+    beta = theta
+    gamma = phi
+
+    # Update the rotation matrix using the zyz Euler angles.
+    euler_to_R_zyz(alpha, beta, gamma, R)
+
+
 def two_vect_to_R(vector_orig, vector_fin, R):
     """Calculate the rotation matrix required to rotate from one vector to 
another.