quat - quaternions

A quat represents a quaternion type that can be used to store rotations. A quaternion contains four values of which one can be seen as the angle and the other three as the axis of rotation. The most common way to initialize a quaternion is by specifying an angle (in radians) and the axis of rotation:

# initialize the quaternion by specifying an angle and the axis of rotation
q = quat(0.5*pi, vec3(0,0,1))

# initialize by specifying a rotation matrix (as mat3 or mat4)
q = quat(R)

# all components are set to zero
q = quat()

(0.0000, 0.0000, 0.0000, 0.0000)

# set the w component
q = quat(2.5)

(0.5000, 0.0000, 0.0000, 0.0000)

# set all four components (w,x,y,z)
q = quat(1,0,0,0)
q = quat([1,0,0,0])
q = quat("1,0,0,0")

(1.0000, 0.0000, 0.0000, 0.0000)

Finally, you can initialize a quaternion with a copy of another quaternion:

q = quat(r)

Mathematical operations:

The mathematical operators are supported with the following combination of types:

quat  =  quat + quat
quat  =  quat - quat
quat  =  quat * quat
quat  = float * quat
quat  =  quat * float
quat  =  quat / float
quat  = -quat
quat  =  quat ** float = pow(quat, float)   (new in version 1.1)
quat  =  quat ** quat  = pow(quat, quat)    (new in version 1.1)

Additionally, you can compare quaternions with == and !=. Taking the absolute value will return the magnitude of the quaternion:

float = abs(q)

Methods:

conjugate(): Return the conjugate (w,-x,-y,-z) of the quaternion.

normalize(): Returns normalized quaternion. If the method is called on the null vector (where each component is zero) a ZeroDivisionError is raised.

inverse(): Return inverse of the quaternion.

toAngleAxis(): Returns a tuple containing the angle (in radians) and the axis of rotation.

fromAngleAxis(angle, axis): Initializes self from an angle (in radians) and an axis of rotation and returns self. New in version 1.1: The initialized quaternion will be a unit quaternion.

toMat3(): Convert the quaternion into a rotation matrix and return the matrix as a mat3.

toMat4(): Convert the quaternion into a rotation matrix and return the matrix as a mat4.

fromMat(matrix): Initialize self from a rotation matrix, given either as a mat3 or a mat4 and returns self. matrix must be a rotation matrix (i.e. the determinant is 1), if you have a matrix that's made up of other parts as well, call matrix.decompose() to get the rotation part.

dot(b): Returns the dot product of self with quaternion b.
New in version 1.1.

log(): Returns the natural logarithm of self.
New in version 1.1.

exp(): Returns the exponential of self.
New in version 1.1.

Related functions:

slerp(t, q0, q1): Performs a spherical linear interpolation between two quaternions q0 and q1. For t=0.0 the return value equals q0, for t=1.0 it equals q1. q0 and q1 must be unit quaternions.
New in version 1.1.

squad(t, a, b, c, d): Performs a spherical cubic interpolation between quaternion a and d where quaternion b and c define the shape of the interpolation curve. For t=0.0 the return value equals a, for t=1.0 it equals d. All quaternions must be unit quaternions.
New in version 1.1.