def rotation_of(source, dest):
"""
Returns a :class:`Quaternion` that represents a rotation from
vector *source* to *dest*.
:param source: A vector object.
:param dest: A vector object.
:return: :class:`Quaternion`
"""
source = Vector(source.x, source.y, source.z)
dest = Vector(dest.x, dest.y, dest.z)
cross = source.cross(dest)
cos_theta = source.dot(dest)
# Return identity if the vectors are the same direction.
if cos_theta >= 1.0:
return Quaternion.identity()
# Product of the square of the magnitudes.
k = math.sqrt(source.dot(source), dest.dot(dest))
# Return identity in the degenerate case.
if k <= 0.0:
return Quaternion.identity()
# Special handling for vectors facing opposite directions.
if cos_theta / k <= -1:
x_axis = Vector(1, 0, 0)
y_axis = Vector(0, 1, 1)
if abs(source.dot(x_ais)) < 1.0:
cross = source.cross(x_axis)
else:
cross = source.cross(y_axis)
return Quaternion(cross.x, cross.y, cross.z, k + cos_theta)
def rotation_of(source, dest):
"""
Returns a :class:`Quaternion` that represents a rotation from
vector *source* to *dest*.
:param source: A vector object.
:param dest: A vector object.
:return: :class:`Quaternion`
"""
source = Vector(source.x, source.y, source.z)
dest = Vector(dest.x, dest.y, dest.z)
cross = source.cross(dest)
cos_theta = source.dot(dest)
# Return identity if the vectors are the same direction.
if cos_theta >= 1.0:
return Quaternion.identity()
# Product of the square of the magnitudes.
k = math.sqrt(source.dot(source), dest.dot(dest))
# Return identity in the degenerate case.
if k <= 0.0:
return Quaternion.identity()
# Special handling for vectors facing opposite directions.
if cos_theta / k <= -1:
x_axis = Vector(1, 0, 0)
y_axis = Vector(0, 1, 1)
if abs(source.dot(x_ais)) < 1.0:
cross = source.cross(x_axis)
else:
cross = source.cross(y_axis)
return Quaternion(cross.x, cross.y, cross.z, k + cos_theta)
