Module Expr Str ImportFrom alias alias alias Import alias identifier ImportFrom alias alias alias ImportFrom alias alias ClassDef bases body Assign NameStore Num Assign NameStore Num Assign NameStore Num Assign NameStore Num decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam defaults Num Num Num Num NameLoad body Return Call AttributeLoad NameLoad attr ListLoad NameLoad NameLoad NameLoad NameLoad keyword NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults NameLoad body Assign NameStore BinOpMult NameLoad Num Return Call AttributeLoad NameLoad attr ListLoad Call AttributeLoad NameLoad attr NameLoad Num Num Call AttributeLoad NameLoad attr NameLoad keyword NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults NameLoad body Assign NameStore BinOpMult NameLoad Num Return Call AttributeLoad NameLoad attr ListLoad Num Call AttributeLoad NameLoad attr NameLoad Num Call AttributeLoad NameLoad attr NameLoad keyword NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults NameLoad body Assign NameStore BinOpMult NameLoad Num Return Call AttributeLoad NameLoad attr ListLoad Num Num Call AttributeLoad NameLoad attr NameLoad Call AttributeLoad NameLoad attr NameLoad keyword NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults NameLoad body Assign NameStore BoolOpOr NameLoad AttributeLoad NameLoad attr If UnaryOpNot Call AttributeLoad NameLoad attr Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad Num body Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore BinOpMult NameLoad Num Assign NameStore Call AttributeLoad NameLoad attr NameLoad Return Call AttributeLoad NameLoad attr ListLoad BinOpMult NameLoad SubscriptLoad NameLoad Index Num BinOpMult NameLoad SubscriptLoad NameLoad Index Num BinOpMult NameLoad SubscriptLoad NameLoad Index Num Call AttributeLoad NameLoad attr NameLoad keyword NameLoad decorator_list Call NameLoad Str FunctionDef arguments args NameParam NameParam defaults NameLoad body Assign NameStore BoolOpOr NameLoad AttributeLoad NameLoad attr Assign NameStore Call AttributeLoad NameLoad attr ListLoad BinOpDiv Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr Num BinOpSub BinOpSub BinOpAdd Num SubscriptLoad SubscriptLoad NameLoad Index Num Index Num SubscriptLoad SubscriptLoad NameLoad Index Num Index Num SubscriptLoad SubscriptLoad NameLoad Index Num Index Num Num BinOpDiv Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr Num BinOpSub BinOpAdd BinOpSub Num SubscriptLoad SubscriptLoad NameLoad Index Num Index Num SubscriptLoad SubscriptLoad NameLoad Index Num Index Num SubscriptLoad SubscriptLoad NameLoad Index Num Index Num Num BinOpDiv Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr Num BinOpAdd BinOpSub BinOpSub Num SubscriptLoad SubscriptLoad NameLoad Index Num Index Num SubscriptLoad SubscriptLoad NameLoad Index Num Index Num SubscriptLoad SubscriptLoad NameLoad Index Num Index Num Num BinOpDiv Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr Num BinOpAdd BinOpAdd BinOpAdd Num SubscriptLoad SubscriptLoad NameLoad Index Num Index Num SubscriptLoad SubscriptLoad NameLoad Index Num Index Num SubscriptLoad SubscriptLoad NameLoad Index Num Index Num Num keyword NameLoad Return NameLoad decorator_list Call NameLoad Str FunctionDef arguments args NameParam NameParam defaults NameLoad body Expr Str Assign NameStore BoolOpOr NameLoad AttributeLoad NameLoad attr Assign TupleStore NameStore NameStore NameStore NameLoad Assign NameStore BinOpMult NameLoad Num Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore BinOpMult NameLoad Num Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore BinOpMult NameLoad Num Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad Return Call AttributeLoad NameLoad attr ListLoad BinOpSub BinOpMult BinOpMult UnaryOpUSub NameLoad NameLoad NameLoad BinOpMult BinOpMult NameLoad NameLoad NameLoad BinOpSub BinOpMult BinOpMult NameLoad NameLoad NameLoad BinOpMult BinOpMult NameLoad NameLoad NameLoad BinOpSub BinOpMult BinOpMult NameLoad NameLoad NameLoad BinOpMult BinOpMult NameLoad NameLoad NameLoad BinOpAdd BinOpMult BinOpMult NameLoad NameLoad NameLoad BinOpMult BinOpMult NameLoad NameLoad NameLoad keyword NameLoad decorator_list Call NameLoad Str FunctionDef arguments args NameParam NameParam defaults NameLoad body Expr Str Assign NameStore BoolOpOr NameLoad AttributeLoad NameLoad attr Assign TupleStore NameStore NameStore NameStore TupleLoad Call AttributeLoad NameLoad attr NameLoad Call AttributeLoad NameLoad attr NameLoad Call AttributeLoad NameLoad attr NameLoad Assign NameStore BinOpMult NameLoad Num Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore BinOpMult NameLoad Num Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore BinOpMult NameLoad Num Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call AttributeLoad NameLoad attr NameLoad Return Call AttributeLoad NameLoad attr ListLoad BinOpAdd BinOpMult BinOpMult NameLoad NameLoad NameLoad BinOpMult BinOpMult NameLoad NameLoad NameLoad BinOpAdd BinOpMult BinOpMult UnaryOpUSub NameLoad NameLoad NameLoad BinOpMult BinOpMult NameLoad NameLoad NameLoad BinOpAdd BinOpMult BinOpMult UnaryOpUSub NameLoad NameLoad NameLoad BinOpMult BinOpMult NameLoad NameLoad NameLoad BinOpAdd BinOpMult BinOpMult NameLoad NameLoad NameLoad BinOpMult BinOpMult NameLoad NameLoad NameLoad keyword NameLoad decorator_list Call NameLoad Str FunctionDef arguments args NameParam NameParam defaults body Expr Str Assign TupleStore NameStore NameStore NameStore NameStore NameLoad Assign TupleStore NameStore NameStore NameStore NameStore NameLoad Return Call AttributeLoad NameLoad attr ListLoad BinOpAdd BinOpSub BinOpAdd BinOpMult NameLoad NameLoad BinOpMult NameLoad NameLoad BinOpMult NameLoad NameLoad BinOpMult NameLoad NameLoad BinOpAdd BinOpAdd BinOpAdd BinOpMult UnaryOpUSub NameLoad NameLoad BinOpMult NameLoad NameLoad BinOpMult NameLoad NameLoad BinOpMult NameLoad NameLoad BinOpAdd BinOpAdd BinOpSub BinOpMult NameLoad NameLoad BinOpMult NameLoad NameLoad BinOpMult NameLoad NameLoad BinOpMult NameLoad NameLoad BinOpAdd BinOpSub BinOpSub BinOpMult UnaryOpUSub NameLoad NameLoad BinOpMult NameLoad NameLoad BinOpMult NameLoad NameLoad BinOpMult NameLoad NameLoad keyword AttributeLoad NameLoad attr decorator_list NameLoad FunctionDef arguments args NameParam defaults body Expr Str Return CompareEqEqEqEq SubscriptLoad NameLoad Index Num SubscriptLoad NameLoad Index Num SubscriptLoad NameLoad Index Num SubscriptLoad NameLoad Index Num Num decorator_list FunctionDef arguments args NameParam defaults body Expr Str Return UnaryOpNot Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults body Expr Str Return Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam defaults body Expr Str Return Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam defaults body Expr Str Return Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam defaults body Expr Str Assign NameStore Call AttributeLoad NameLoad attr SubscriptLoad NameLoad Index Num Return BinOpMult NameLoad Num decorator_list FunctionDef arguments args NameParam defaults body Expr Str Assign NameStore BinOpSub Num BinOpPow SubscriptLoad NameLoad Index Num Num If CompareLtE NameLoad Num body Return Call AttributeLoad NameLoad attr ListLoad Num Num Num keyword AttributeLoad NameLoad attr Assign NameStore BinOpDiv Num Call AttributeLoad NameLoad attr NameLoad Return Call AttributeLoad NameLoad attr ListLoad BinOpMult SubscriptLoad NameLoad Index Num NameLoad BinOpMult SubscriptLoad NameLoad Index Num NameLoad BinOpMult SubscriptLoad NameLoad Index Num NameLoad keyword AttributeLoad NameLoad attr decorator_list NameLoad FunctionDef arguments args NameParam NameParam defaults body Expr Str Return Call AttributeLoad NameLoad attr NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults body Expr Str Return Call AttributeLoad NameLoad attr ListLoad UnaryOpUSub SubscriptLoad NameLoad Index Num UnaryOpUSub SubscriptLoad NameLoad Index Num UnaryOpUSub SubscriptLoad NameLoad Index Num SubscriptLoad NameLoad Index Num keyword AttributeLoad NameLoad attr decorator_list NameLoad FunctionDef arguments args NameParam NameParam defaults body Expr Str If CompareGt Call AttributeLoad NameLoad attr SubscriptLoad NameLoad Index Num Num body Assert NameLoad Expr Call NameLoad Str Return NameLoad Assign NameStore Call AttributeLoad NameLoad attr SubscriptLoad NameLoad Index Num Assign NameStore BinOpMult NameLoad NameLoad Assign NameStore BinOpDiv Call AttributeLoad NameLoad attr NameLoad Call AttributeLoad NameLoad attr NameLoad Return Call AttributeLoad NameLoad attr ListLoad BinOpMult SubscriptLoad NameLoad Index Num NameLoad BinOpMult SubscriptLoad NameLoad Index Num NameLoad BinOpMult SubscriptLoad NameLoad Index Num NameLoad Call AttributeLoad NameLoad attr NameLoad keyword AttributeLoad NameLoad attr decorator_list Call NameLoad Str FunctionDef arguments args NameParam defaults body Expr Str Return BinOpDiv Call NameLoad NameLoad Call NameLoad NameLoad decorator_list FunctionDef arguments args NameParam defaults body Expr Str Return BinOpMult NameLoad Num decorator_list NameLoad FunctionDef arguments args NameParam defaults body Return Call AttributeLoad NameLoad attr NameLoad ListLoad Num Num Num Num decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str FunctionDef arguments args NameParam NameParam defaults body Expr Str Assign NameStore Call AttributeLoad NameLoad attr NameLoad Assign SubscriptStore NameLoad Slice Call AttributeLoad NameLoad attr NameLoad Assign NameStore Call NameLoad NameLoad Call NameLoad NameLoad Call NameLoad NameLoad AugAssignMult NameStore NameLoad Return NameLoad decorator_list If CompareEq AttributeLoad NameLoad attr Num body Assign NameStore Call AttributeLoad NameLoad attr ListLoad SubscriptLoad NameLoad Index Num SubscriptLoad NameLoad Index Num SubscriptLoad NameLoad Index Num Num keyword AttributeLoad NameLoad attr Assign NameStore Call NameLoad NameLoad NameLoad Assign NameStore SubscriptLoad NameLoad Slice Num Return NameLoad orelse If CompareEq AttributeLoad NameLoad attr Num body Assign NameStore Call NameLoad NameLoad NameLoad Return NameLoad orelse Raise Call NameLoad Str decorator_list NameLoad
N/A N/A Provide functions for the creation and manipulation of Quaternions.
 __future__ absolute_import division print_function N/A numpy np N/A vector vector3 vector4 utils all_parameters_as_numpy_arrays parameters_as_numpy_arrays index N/A N/A N/A x 0 N/A y 1 N/A z 2 N/A w 3 N/A create N/A N/A x y z w dtype N/A 0.0 0.0 0.0 1.0 None N/A N/A N/A N/A np array N/A x y z w dtype dtype N/A create_from_x_rotation N/A N/A theta dtype N/A None N/A N/A thetaOver2 N/A theta 0.5 N/A N/A N/A np array N/A N/A N/A np sin thetaOver2 0.0 0.0 N/A N/A np cos thetaOver2 dtype dtype N/A create_from_y_rotation N/A N/A theta dtype N/A None N/A N/A thetaOver2 N/A theta 0.5 N/A N/A N/A np array N/A 0.0 N/A N/A np sin thetaOver2 0.0 N/A N/A np cos thetaOver2 dtype dtype N/A create_from_z_rotation N/A N/A theta dtype N/A None N/A N/A thetaOver2 N/A theta 0.5 N/A N/A N/A np array N/A 0.0 0.0 N/A N/A np sin thetaOver2 N/A N/A np cos thetaOver2 dtype dtype N/A create_from_axis_rotation N/A N/A axis theta dtype N/A None N/A N/A dtype N/A dtype N/A axis dtype N/A N/A N/A N/A np isclose N/A N/A N/A np linalg norm axis 1.0 N/A N/A axis N/A N/A vector normalise axis N/A thetaOver2 N/A theta 0.5 N/A sinThetaOver2 N/A N/A np sin thetaOver2 N/A N/A N/A np array N/A N/A sinThetaOver2 N/A axis N/A 0 N/A sinThetaOver2 N/A axis N/A 1 N/A sinThetaOver2 N/A axis N/A 2 N/A N/A np cos thetaOver2 dtype dtype N/A N/A parameters_as_numpy_arrays axis create_from_matrix N/A N/A mat dtype N/A None N/A N/A dtype N/A dtype N/A mat dtype N/A quat N/A N/A np array N/A N/A N/A N/A np sqrt N/A N/A np maximum 0.0 N/A N/A N/A 1.0 N/A N/A mat N/A 0 N/A 0 N/A N/A mat N/A 1 N/A 1 N/A N/A mat N/A 2 N/A 2 2.0 N/A N/A N/A np sqrt N/A N/A np maximum 0.0 N/A N/A N/A 1.0 N/A N/A mat N/A 0 N/A 0 N/A N/A mat N/A 1 N/A 1 N/A N/A mat N/A 2 N/A 2 2.0 N/A N/A N/A np sqrt N/A N/A np maximum 0.0 N/A N/A N/A 1.0 N/A N/A mat N/A 0 N/A 0 N/A N/A mat N/A 1 N/A 1 N/A N/A mat N/A 2 N/A 2 2.0 N/A N/A N/A np sqrt N/A N/A np maximum 0.0 N/A N/A N/A 1.0 N/A N/A mat N/A 0 N/A 0 N/A N/A mat N/A 1 N/A 1 N/A N/A mat N/A 2 N/A 2 2.0 dtype dtype N/A quat N/A N/A parameters_as_numpy_arrays mat create_from_eulers N/A N/A eulers dtype N/A None N/A N/A Creates a quaternion from a set of Euler angles.

    Eulers are an array of length 3 in the following order::
        [yaw, pitch, roll]
     N/A dtype N/A dtype N/A eulers dtype N/A N/A pitch yaw roll eulers N/A halfPitch N/A pitch 0.5 N/A sP N/A N/A np sin halfPitch N/A cP N/A N/A np cos halfPitch N/A halfRoll N/A roll 0.5 N/A sR N/A N/A np sin halfRoll N/A cR N/A N/A np cos halfRoll N/A halfYaw N/A yaw 0.5 N/A sY N/A N/A np sin halfYaw N/A cY N/A N/A np cos halfYaw N/A N/A N/A np array N/A N/A N/A N/A N/A cY sP cR N/A N/A sY cP sR N/A N/A N/A cY sP sR N/A N/A sY cP cR N/A N/A N/A sY sP cR N/A N/A cY cP sR N/A N/A N/A cY cP cR N/A N/A sY sP sR dtype dtype N/A N/A parameters_as_numpy_arrays eulers create_from_inverse_of_eulers N/A N/A eulers dtype N/A None N/A N/A Creates a quaternion from the inverse of a set of Euler angles.

    Eulers are an array of length 3 in the following order::
        [yaw, pitch, roll]
     N/A dtype N/A dtype N/A eulers dtype N/A N/A pitch roll yaw N/A N/A N/A euler pitch eulers N/A N/A euler roll eulers N/A N/A euler yaw eulers N/A halfRoll N/A roll 0.5 N/A sinRoll N/A N/A np sin halfRoll N/A cosRoll N/A N/A np cos halfRoll N/A halfPitch N/A pitch 0.5 N/A sinPitch N/A N/A np sin halfPitch N/A cosPitch N/A N/A np cos halfPitch N/A halfYaw N/A yaw 0.5 N/A sinYaw N/A N/A np sin halfYaw N/A cosYaw N/A N/A np cos halfYaw N/A N/A N/A np array N/A N/A N/A N/A cosYaw sinPitch cosRoll N/A N/A sinYaw cosPitch sinRoll N/A N/A N/A N/A cosYaw sinPitch sinRoll N/A N/A sinYaw cosPitch cosRoll N/A N/A N/A N/A sinYaw sinPitch cosRoll N/A N/A cosYaw cosPitch sinRoll N/A N/A N/A cosYaw cosPitch cosRoll N/A N/A sinYaw sinPitch sinRoll dtype dtype N/A N/A parameters_as_numpy_arrays axis cross N/A N/A quat1 quat2 N/A N/A N/A Returns the cross-product of the two quaternions.

    Quaternions are **not** communicative. Therefore, order is important.

    This is NOT the same as a vector cross-product.
    Quaternion cross-product is the equivalent of matrix multiplication.
     N/A N/A q1x q1y q1z q1w quat1 N/A N/A q2x q2y q2z q2w quat2 N/A N/A N/A np array N/A N/A N/A N/A N/A q1x q2w N/A q1y q2z N/A q1z q2y N/A q1w q2x N/A N/A N/A N/A N/A q1x q2z N/A q1y q2w N/A q1z q2x N/A q1w q2y N/A N/A N/A N/A q1x q2y N/A q1y q2x N/A q1z q2w N/A q1w q2z N/A N/A N/A N/A N/A q1x q2x N/A q1y q2y N/A q1z q2z N/A q1w q2w dtype N/A quat1 dtype N/A all_parameters_as_numpy_arrays is_zero_length N/A N/A quat N/A N/A N/A Checks if a quaternion is zero length.

    :param numpy.array quat: The quaternion to check.
    :rtype: boolean.
    :return: True if the quaternion is zero length, otherwise False.
     N/A N/A N/A quat N/A 0 N/A quat N/A 1 N/A quat N/A 2 N/A quat N/A 3 0.0 N/A is_non_zero_length N/A N/A quat N/A N/A N/A Checks if a quaternion is not zero length.

    This is the opposite to 'is_zero_length'.
    This is provided for readability.

    :param numpy.array quat: The quaternion to check.
    :rtype: boolean
    :return: False if the quaternion is zero length, otherwise True.

    .. seealso:: is_zero_length
     N/A N/A N/A is_zero_length quat N/A squared_length N/A N/A quat N/A N/A N/A Calculates the squared length of a quaternion.

    Useful for avoiding the performanc penalty of
    the square root function.

    :param numpy.array quat: The quaternion to measure.
    :rtype: float, numpy.array
    :return: If a 1d array was passed, it will be a scalar.
        Otherwise the result will be an array of scalars with shape
        vec.ndim with the last dimension being size 1.
     N/A N/A N/A vector4 squared_length quat N/A length N/A N/A quat N/A N/A N/A Calculates the length of a quaternion.

    :param numpy.array quat: The quaternion to measure.
    :rtype: float, numpy.array
    :return: If a 1d array was passed, it will be a scalar.
        Otherwise the result will be an array of scalars with shape
        vec.ndim with the last dimension being size 1.
     N/A N/A N/A vector4 length quat N/A normalise N/A N/A quat N/A N/A N/A Ensure a quaternion is unit length (length ~= 1.0).

    The quaternion is **not** changed in place.

    :param numpy.array quat: The quaternion to normalise.
    :rtype: numpy.array
    :return: The normalised quaternion(s).
     N/A N/A N/A vector4 normalise quat N/A rotation_angle N/A N/A quat N/A N/A N/A Calculates the rotation around the quaternion's axis.

    :param numpy.array quat: The quaternion.
    :rtype: float.
    :return: The quaternion's rotation about the its axis in radians.
     N/A thetaOver2 N/A N/A np arccos N/A quat N/A 3 N/A N/A thetaOver2 2.0 N/A rotation_axis N/A N/A quat N/A N/A N/A Calculates the axis of the quaternion's rotation.

    :param numpy.array quat: The quaternion.
    :rtype: numpy.array.
    :return: The quaternion's rotation axis.
     N/A sinThetaOver2Sq N/A 1.0 N/A N/A quat N/A 3 2 N/A N/A sinThetaOver2Sq 0.0 N/A N/A N/A N/A np array N/A 0.0 0.0 -1.0 dtype N/A quat dtype N/A oneOverSinThetaOver2 N/A 1.0 N/A N/A np sqrt sinThetaOver2Sq N/A N/A N/A np array N/A N/A N/A quat N/A 0 oneOverSinThetaOver2 N/A N/A quat N/A 1 oneOverSinThetaOver2 N/A N/A quat N/A 2 oneOverSinThetaOver2 dtype N/A quat dtype N/A all_parameters_as_numpy_arrays dot N/A N/A quat1 quat2 N/A N/A N/A Calculate the dot product of quaternions.

    This is the same as a vector dot product.

    :param numpy.array quat1: The first quaternion(s).
    :param numpy.array quat2: The second quaternion(s).
    :rtype: float, numpy.array
    :return: If a 1d array was passed, it will be a scalar.
        Otherwise the result will be an array of scalars with shape
        vec.ndim with the last dimension being size 1.
     N/A N/A N/A vector4 dot quat1 quat2 N/A conjugate N/A N/A quat N/A N/A N/A Calculates a quaternion with the opposite rotation.

    :param numpy.array quat: The quaternion.
    :rtype: numpy.array.
    :return: A quaternion representing the conjugate.
     N/A N/A N/A np array N/A N/A N/A quat N/A 0 N/A N/A quat N/A 1 N/A N/A quat N/A 2 N/A quat N/A 3 dtype N/A quat dtype N/A all_parameters_as_numpy_arrays power N/A N/A quat exponent N/A N/A N/A Multiplies the quaternion by the exponent.

    The quaternion is **not** changed in place.

    :param numpy.array quat: The quaternion.
    :param float scalar: The exponent.
    :rtype: numpy.array.
    :return: A quaternion representing the original quaternion
        to the specified power.
     N/A N/A N/A N/A np fabs N/A quat N/A 3 0.9999 N/A N/A False N/A N/A print rotation axis was identity N/A quat N/A alpha N/A N/A np arccos N/A quat N/A 3 N/A newAlpha N/A alpha exponent N/A multi N/A N/A N/A np sin newAlpha N/A N/A np sin alpha N/A N/A N/A np array N/A N/A N/A quat N/A 0 multi N/A N/A quat N/A 1 multi N/A N/A quat N/A 2 multi N/A N/A np cos newAlpha dtype N/A quat dtype N/A N/A parameters_as_numpy_arrays quat inverse N/A N/A quat N/A N/A N/A Calculates the inverse quaternion.

    The inverse of a quaternion is defined as
    the conjugate of the quaternion divided
    by the magnitude of the original quaternion.

    :param numpy.array quat: The quaternion to invert.
    :rtype: numpy.array.
    :return: The inverse of the quaternion.
     N/A N/A N/A conjugate quat N/A length quat N/A negate N/A N/A quat N/A N/A N/A Calculates the negated quaternion.

    This is essentially the quaternion * -1.0.

    :param numpy.array quat: The quaternion.
    :rtype: numpy.array
    :return: The negated quaternion.
     N/A N/A quat -1.0 N/A all_parameters_as_numpy_arrays is_identity N/A N/A quat N/A N/A N/A N/A N/A np allclose quat N/A 0.0 0.0 0.0 1.0 N/A apply_to_vector N/A N/A quat vec N/A N/A N/A Rotates a vector by a quaternion.

    :param numpy.array quat: The quaternion.
    :param numpy.array vec: The vector.
    :rtype: numpy.array
    :return: The vector rotated by the quaternion.
    :raise ValueError: raised if the vector is an unsupported size

    .. seealso:: http://content.gpwiki.org/index.php/OpenGL:Tutorials:Using_Quaternions_to_represent_rotation
     apply N/A N/A quat vec4 N/A N/A N/A 
        v = numpy.array(vec)
        return v + 2.0 * vector.cross(
            quat[:-1],
            vector.cross(quat[:-1], v) + (quat[-1] * v)
           )
         N/A length N/A N/A vector length vec4 N/A N/A vec4 N/A N/A N/A vector normalise vec4 N/A result N/A cross quat N/A cross vec4 N/A conjugate quat N/A result length N/A result N/A N/A N/A N/A vec size 3 N/A N/A vec N/A N/A np array N/A N/A vec N/A 0 N/A vec N/A 1 N/A vec N/A 2 0.0 dtype N/A vec dtype N/A vec N/A apply quat vec N/A vec N/A vec N/A 3 N/A vec N/A N/A N/A N/A vec size 4 N/A N/A vec N/A apply quat vec N/A vec N/A N/A N/A ValueError Vector size unsupported N/A all_parameters_as_numpy_arrays