def euler2angle_axis(z=0, y=0, x=0):
''' Return angle, axis corresponding to these Euler angles
Uses the z, then y, then x convention above
Parameters
----------
z : scalar
Rotation angle in radians around z-axis (performed first)
y : scalar
Rotation angle in radians around y-axis
x : scalar
Rotation angle in radians around x-axis (performed last)
Returns
-------
theta : scalar
angle of rotation
vector : array shape (3,)
axis around which rotation occurs
Examples
--------
>>> theta, vec = euler2angle_axis(0, 1.5, 0)
>>> print(theta)
1.5
>>> np.allclose(vec, [0, 1, 0])
True
'''
# delayed import to avoid cyclic dependencies
import nibabel.quaternions as nq
return nq.quat2angle_axis(euler2quat(z, y, x))
def euler2angle_axis(z=0, y=0, x=0):
''' Return angle, axis corresponding to these Euler angles
Uses the z, then y, then x convention above
Parameters
----------
z : scalar
Rotation angle in radians around z-axis (performed first)
y : scalar
Rotation angle in radians around y-axis
x : scalar
Rotation angle in radians around x-axis (performed last)
Returns
-------
theta : scalar
angle of rotation
vector : array shape (3,)
axis around which rotation occurs
Examples
--------
>>> theta, vec = euler2angle_axis(0, 1.5, 0)
>>> print(theta)
1.5
>>> np.allclose(vec, [0, 1, 0])
True
'''
# delayed import to avoid cyclic dependencies
import nibabel.quaternions as nq
return nq.quat2angle_axis(euler2quat(z, y, x))
def infTwist(xyz):
pts = xyz.T
ors = normr(pts[1:] - pts[:-1])
start2end_rope = eye(3)
for (or1, or2) in zip(ors[:-1], ors[1:]):
start2end_rope = dot(minRot(or2, or1), start2end_rope)
assert almostEq(dot(start2end_rope, ors[0]), ors[-1])
end2start_min = minRot(ors[0], ors[-1])
twist_mat = dot(end2start_min, start2end_rope)
ang, _ = quat2angle_axis(mat2quat(twist_mat))
return ang
def infTwist(xyz):
pts = xyz.T
ors = normr(pts[1:] - pts[:-1])
start2end_rope = eye(3)
for (or1,or2) in zip(ors[:-1],ors[1:]):
start2end_rope = dot(minRot(or2,or1),start2end_rope)
assert almostEq(dot(start2end_rope,ors[0]),ors[-1])
end2start_min = minRot(ors[0],ors[-1])
twist_mat = dot(end2start_min,start2end_rope)
ang,_ = quat2angle_axis(mat2quat(twist_mat))
return ang
