def dcquat( dc0, dc1 ):
"""
Get the quaternions describing rotation from one double couple to
another. dc0 is the one we're rotating from.
"""
q0 = quat( A=dc0.pbt ) # make quaternions based on pbt as a rotation matrix
q1 = quat( A=dc1.pbt )
# quaternion for rotation from dc0 to dc1 is the same as inverse of dc0 then dc1
qdiff = q1*q0.conjugate() # equivelent to q1 then q0
# return the four different rotations
return qdiff, qdiff*quat([0,1,0,0]), qdiff*quat([0,0,1,0]), qdiff*quat([0,0,0,1])
def dcquat(dc0, dc1):
"""
Get the quaternions describing rotation from one double couple to
another. dc0 is the one we're rotating from.
"""
q0 = quat(A=dc0.pbt) # make quaternions based on pbt as a rotation matrix
q1 = quat(A=dc1.pbt)
# quaternion for rotation from dc0 to dc1 is the same as inverse of dc0 then dc1
qdiff = q1 * q0.conjugate() # equivelent to q1 then q0
# return the four different rotations
return qdiff, qdiff * quat([0, 1, 0, 0]), qdiff * quat(
[0, 0, 1, 0]), qdiff * quat([0, 0, 0, 1])
def quats( self ):
"""
Get the 4 quaternions describing rotation from the reference
orientation where p = (1,0,0), t=(0,0,1)
"""
# get direct mapping from rotation matrix
q0 = quat( A=self.pbt )
# get other four options by quaternion multiplication
q1, q2, q3 = q0*quat([0,1,0,0]), q0*quat([0,0,1,0]), q0*quat([0,0,0,1])
# force the scalar part to be positive
for q in ( q0, q1, q2, q3 ):
if q.w < 0: q*= -1
return q0, q1, q2, q3
def quats(self):
"""
Get the 4 quaternions describing rotation from the reference
orientation where p = (1,0,0), t=(0,0,1)
"""
# get direct mapping from rotation matrix
q0 = quat(A=self.pbt)
# get other four options by quaternion multiplication
q1, q2, q3 = q0 * quat([0, 1, 0, 0]), q0 * quat(
[0, 0, 1, 0]), q0 * quat([0, 0, 0, 1])
# force the scalar part to be positive
for q in (q0, q1, q2, q3):
if q.w < 0: q *= -1
return q0, q1, q2, q3
# get file to test
srcpath = os.path.join( os.getcwd(), '..' )
sys.path.append( srcpath )
from quaternions import quatn as quat
D2R = pi/180.0
R2D = 180/pi
# reference
A0 = np.array( [[ 1, 0, 0 ],
[ 0, 1, 0 ],
[ 0, 0, 1 ]], dtype=float )
print "reference rotation matrix"
print A0
q0 = quat( A=A0 )
print "q = ", q0
print ""
# make x1->-x3, x3->x1
A1 = dc1 = np.array( [[ 0, 0, 1 ],
[ 0, 1, 0 ],
[ -1, 0, 0 ]] , dtype=float)
print "posn 1"
print A1
q1 = quat( A=A1 )
print "q1 = ", q1
(a, u) = q1.toAngleAxis()
print "angle", a*R2D, "ACW around axis",u
print ""
from numpy import pi, cos, sin, arccos as acos # get file to test srcpath = os.path.join(os.getcwd(), '..') sys.path.append(srcpath) from quaternions import quatn as quat D2R = pi / 180.0 R2D = 180 / pi # reference A0 = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]], dtype=float) print "reference rotation matrix" print A0 q0 = quat(A=A0) print "q = ", q0 print "" # make x1->-x3, x3->x1 A1 = dc1 = np.array([[0, 0, 1], [0, 1, 0], [-1, 0, 0]], dtype=float) print "posn 1" print A1 q1 = quat(A=A1) print "q1 = ", q1 (a, u) = q1.toAngleAxis() print "angle", a * R2D, "ACW around axis", u print "" # make x1->-x3, x2->-x1, x3->x2