Package Scientific :: Package Geometry :: Module Quaternion :: Class Quaternion

Class Quaternion

Quaternion (hypercomplex number)

This implementation of quaternions is not complete; only the features needed for representing rotation matrices by quaternions are implemented.

Quaternions support addition, subtraction, and multiplication, as well as multiplication and division by scalars. Division by quaternions is not provided, because quaternion multiplication is not associative. Use multiplication by the inverse instead.

The four components can be extracted by indexing.

Instance Methods

__add__(self, other)

__div__(self, other)

__getitem__(self, item)

__init__(self, *data)
There are two calling patterns:

__mul__(self, other)

__rdiv__(self, other)

__repr__(self)

__rmul__(self, other)

__sub__(self, other)

Numeric.array

asMatrix(self)
Returns: a 4x4 matrix representation

Scientific.Geometry.Transformation.Rotation

asRotation(self)
Returns: the corresponding rotation matrix

dot(self, other)

Quaternion

inverse(self)
Returns: the inverse

float

norm(self)
Returns: the norm

Quaternion

normalized(self)
Returns: the quaternion scaled such that its norm is 1

Class Variables
	is_quaternion = `1`

Method Details

init(self, data)
(Constructor)*

There are two calling patterns:

Quaternion(q0, q1, q2, q3) (from four real components)
Quaternion(q) (from a sequence containing the four components)

asMatrix(self)

Returns: Numeric.array: a 4x4 matrix representation

asRotation(self)

Returns: Scientific.Geometry.Transformation.Rotation

the corresponding rotation matrix

Raises:

ValueError - if the quaternion is not normalized

inverse(self)

Returns: Quaternion: the inverse

norm(self)

Returns: float: the norm

normalized(self)

Returns: Quaternion: the quaternion scaled such that its norm is 1