Author: bugman
Date: Thu Feb 21 09:07:46 2008
New Revision: 5061
URL: http://svn.gna.org/viewcvs/relax?rev=5061&view=rev
Log:
Merged revisions 5058-5060 via svnmerge from
svn+ssh://bugman@xxxxxxxxxxx/svn/relax/1.3
........
r5058 | bugman | 2008-02-20 18:23:52 +0100 (Wed, 20 Feb 2008) | 6 lines
Renamed rotation_matrix_zyz() to R_euler_zyz().
This name is more descriptive and is a better naming scheme for rotation
matrices constructed using
other inputs.
........
r5059 | bugman | 2008-02-20 18:53:03 +0100 (Wed, 20 Feb 2008) | 7 lines
Wrote a new function R_2vect() to generate a rotation matrix from 2 vectors.
This rotation matrix is not unique because of axially symmetry allowing the
rotation axis to be any
vector within the symmetry plane, so the cross product with the axis-angle
convention is used to
define this matrix.
........
r5060 | bugman | 2008-02-20 18:54:37 +0100 (Wed, 20 Feb 2008) | 6 lines
Started writing the generic_fns.structure.cone_edge() function.
This function generates a geometric shape constructed from atoms to be
embedded into a PDB file,
representing the outer edge of the cone.
........
Modified:
branches/N_state_model/ (props changed)
branches/N_state_model/generic_fns/structure.py
branches/N_state_model/maths_fns/rotation_matrix.py
Propchange: branches/N_state_model/
------------------------------------------------------------------------------
Binary property 'svnmerge-integrated' - no diff available.
Modified: branches/N_state_model/generic_fns/structure.py
URL:
http://svn.gna.org/viewcvs/relax/branches/N_state_model/generic_fns/structure.py?rev=5061&r1=5060&r2=5061&view=diff
==============================================================================
--- branches/N_state_model/generic_fns/structure.py (original)
+++ branches/N_state_model/generic_fns/structure.py Thu Feb 21 09:07:46 2008
@@ -301,6 +301,53 @@
return R,M
else:
return R
+
+
+def cone_edge(atomic_data=None, apex=None, axis=None, angle=None,
length=None, inc=None):
+ """Add a residue to the atomic data representing a cone of the given
angle.
+
+ A series of vectors totalling the number of increments and starting at
the origin are equally
+ spaced around the cone axis. The atoms representing neighbouring
vectors will be directly
+ bonded together. This will generate an object representing the outer
edge of a cone.
+
+
+ @param atomic_data: The dictionary to place the atomic data into.
+ @type atomic_data: dict
+ @param apex: The apex of the cone.
+ @type apex: numpy array, len 3
+ @param axis: The central axis of the cone.
+ @type axis: numpy array, len 3
+ @param angle: The cone angle in radians.
+ @type angle: float
+ @param length: The cone length in meters.
+ @type length: float
+ @param inc: The number of increments or number of vectors
used to generate the outer
+ edge of the cone.
+ @type inc: int
+ """
+
+ # Initialise the rotation matrix.
+ R = zeros((3,3), float64)
+
+ # Get the rotation matrix.
+ R_2vect(R, array([0,0,1], float64), axis)
+
+ # Loop over each vector.
+ for i in xrange(inc):
+ # The azimuthal angle theta.
+ theta = 2.0 * pi * float(i) / float(inc)
+
+ # X coordinate.
+ x = cos(theta) * sin(angle)
+
+ # Y coordinate.
+ y = sin(theta)* sin(angle)
+
+ # Z coordinate.
+ z = cos(angle)
+
+ # The vector in the unrotated frame.
+ vector = array([x, y, z], float64)
def create_diff_tensor_pdb(scale=1.8e-6, file=None, dir=None, force=False):
Modified: branches/N_state_model/maths_fns/rotation_matrix.py
URL:
http://svn.gna.org/viewcvs/relax/branches/N_state_model/maths_fns/rotation_matrix.py?rev=5061&r1=5060&r2=5061&view=diff
==============================================================================
--- branches/N_state_model/maths_fns/rotation_matrix.py (original)
+++ branches/N_state_model/maths_fns/rotation_matrix.py Thu Feb 21 09:07:46
2008
@@ -21,11 +21,64 @@
###############################################################################
# Python module imports.
-from numpy import dot
-from math import cos, sin
+from numpy import cross, dot
+from math import acos, cos, sin
-def rotation_matrix_zyz(matrix, alpha, beta, gamma):
+def R_2vect(R, vector_orig, vector_fin):
+ """Calculate the rotation matrix required to rotate from one vector to
another.
+
+ For the rotation of one vector to another, there are an infinit series
of rotation matrices
+ possible. Due to axially symmetry, the rotation axis can be any vector
lying in the symmetry
+ plane between the two vectors. Hence the axis-angle convention will be
used to construct the
+ matrix with the rotation axis defined as the cross product of the two
vectors. The rotation
+ angle is the arccosine of the dot product of the two unit vectors.
+
+ Given a unit vector parallel to the rotation axis, w = [x, y, z] and the
rotation angle a,
+ the rotation matrix R is:
+
+ | 1 + (1-cos(a))*(x*x-1) -z*sin(a)+(1-cos(a))*x*y
y*sin(a)+(1-cos(a))*x*z |
+ R = | z*sin(a)+(1-cos(a))*x*y 1 + (1-cos(a))*(y*y-1)
-x*sin(a)+(1-cos(a))*y*z |
+ | -y*sin(a)+(1-cos(a))*x*z x*sin(a)+(1-cos(a))*y*z 1 +
(1-cos(a))*(z*z-1) |
+
+ @param R: The 3x3 rotation matrix to update.
+ @type R: 3x3 numpy array
+ @param vector_orig: The unrotated vector defined in the reference frame.
+ @type vector_orig: numpy array, len 3
+ @param vector_fin: The rotated vector defined in the reference frame.
+ @type vector_fin: numpy array, len 3
+ """
+
+ # Convert the vectors to unit vectors.
+ vector_orig = vector_orig / norm(vector_orig)
+ vector_fin = vector_fin / norm(vector_fin)
+
+ # The rotation axis.
+ axis = cross(vector_orig, vector_fin)
+ x = axis[0]
+ y = axis[1]
+ z = axis[2]
+
+ # The rotation angle.
+ angle = acos(dot(vector_orig, vector_fin))
+
+ # Trig functions (only need to do this maths once!).
+ ca = cos(angle)
+ sa = sin(angle)
+
+ # Calculate the rotation matrix elements.
+ R[0,0] = 1.0 + (1.0 - ca)*(x**2 - 1.0)
+ R[0,1] = -z*sa + (1.0 - ca)*x*y
+ R[0,2] = y*sa + (1.0 - ca)*x*z
+ R[1,0] = z*sa+(1.0 - ca)*x*y
+ R[1,1] = 1.0 + (1.0 - ca)*(y**2 - 1.0)
+ R[1,2] = -x*sa+(1.0 - ca)*y*z
+ R[2,0] = -y*sa+(1.0 - ca)*x*z
+ R[2,1] = x*sa+(1.0 - ca)*y*z
+ R[2,2] = 1.0 + (1.0 - ca)*(z**2 - 1.0)
+
+
+def R_euler_zyz(matrix, alpha, beta, gamma):
"""Function for calculating the z-y-z Euler angle convention rotation
matrix.
Unit vectors
r5061 - in /branches/N_state_model: ./ generic_fns/structure.py maths_fns/rotation_matrix.py