r9059 - /1.3/maths_fns/rotation_matrix.py -- May 15, 2009 - 10:48

Author: bugman
Date: Fri May 15 10:47:59 2009
New Revision: 9059

URL: http://svn.gna.org/viewcvs/relax?rev=9059&view=rev
Log:
Created the R_axis_angle() function to generate the rotation matrix from the 
axis-angle notation.


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=9059&r1=9058&r2=9059&view=diff
==============================================================================
--- 1.3/maths_fns/rotation_matrix.py (original)
+++ 1.3/maths_fns/rotation_matrix.py Fri May 15 10:47:59 2009
@@ -80,6 +80,62 @@
     R[2,2] = 1.0 + (1.0 - ca)*(z**2 - 1.0)
 
 
+def R_axis_angle(matrix, axis, angle):
+    """Generate the rotation matrix from the axis-angle notation.
+
+    Conversion equations
+    ====================
+
+    From Wikipedia (http://en.wikipedia.org/wiki/Rotation_matrix), the 
conversion is given by::
+
+        c = cos(angle); s = sin(angle); C = 1-c
+        xs = x*s;   ys = y*s;   zs = z*s
+        xC = x*C;   yC = y*C;   zC = z*C
+        xyC = x*yC; yzC = y*zC; zxC = z*xC
+        [ x*xC+c   xyC-zs   zxC+ys ]
+        [ xyC+zs   y*yC+c   yzC-xs ]
+        [ zxC-ys   yzC+xs   z*zC+c ]
+
+
+    @param matrix:  The 3x3 rotation matrix to update.
+    @type matrix:   3x3 numpy array
+    @param axis:    The 3D rotation axis.
+    @type axis:     numpy array, len 3
+    @param angle:   The rotation angle.
+    @type angle:    float
+    """
+
+    # Trig factors.
+    ca = cos(angle)
+    sa = sin(angle)
+    C = 1 - ca
+
+    # Depack the axis.
+    x, y, z = axis
+
+    # Multiplications (to remove duplicate calculations).
+    xs = x*sa
+    ys = y*sa
+    zs = z*sa
+    xC = x*C
+    yC = y*C
+    zC = z*C
+    xyC = x*yC
+    yzC = y*zC
+    zxC = z*xC
+
+    # Update the rotation matrix.
+    matrix[0, 0] = x*xC + ca
+    matrix[0, 1] = xyC - zs
+    matrix[0, 2] = zxC + ys
+    matrix[1, 0] = xyC + zs
+    matrix[1, 1] = y*yC + ca
+    matrix[1, 2] = yzC - xs
+    matrix[2, 0] = zxC - ys
+    matrix[2, 1] = yzC + xs
+    matrix[2, 2] = z*zC + ca
+
+
 def R_euler_zyz(matrix, alpha, beta, gamma):
     """Function for calculating the z-y-z Euler angle convention rotation 
matrix.