Quaternion¶

Represents a Quaternion rotation.

The Quaternion class provides a number of convenient functions and conversions.

import numpy as np
from pyrr import Quaternion, Matrix33, Matrix44, Vector3, Vector4

q = Quaternion()

# explicit creation
q = Quaternion.from_x_rotation(np.pi / 2.0)
q = Quaternion.from_matrix(Matrix33.identity())
q = Quaternion.from_matrix(Matrix44.identity())

# inferred conversions
q = Quaternion(Quaternion())
q = Quaternion(Matrix33.identity())
q = Quaternion(Matrix44.identity())

# apply one quaternion to another
q1 = Quaternion.from_y_rotation(np.pi / 2.0)
q2 = Quaternion.from_x_rotation(np.pi / 2.0)
q3 = q1 * q2

# extract a matrix from the quaternion
m33 = q3.matrix33
m44 = q3.matrix44

# convert from matrix back to quaternion
q4 = Quaternion(m44)

# rotate a quaternion by a matrix
q = Quaternion() * Matrix33.identity()
q = Quaternion() * Matrix44.identity()

# apply quaternion to a vector
v3 = Quaternion() * Vector3()
v4 = Quaternion() * Vector4()

# undo a rotation
q = Quaternion.from_x_rotation(np.pi / 2.0)
v = q * Vector3([1.,1.,1.])
# ~q is the same as q.conjugate
original = ~q * v
assert np.allclose(original, v)

# get the dot product of 2 Quaternions
dot = Quaternion() | Quaternion.from_x_rotation(np.pi / 2.0)

class pyrr.objects.quaternion.Quaternion¶

angle¶: Returns the angle around the axis of rotation of this Quaternion as a float.

axis¶: Returns the axis of rotation of this Quaternion as a Vector3.

conjugate¶

Returns the conjugate of this Quaternion.

This is a Quaternion with the opposite rotation.

cross(other)¶

Returns the cross of this Quaternion and another.

This is the equivalent of combining Quaternion rotations (like Matrix multiplication).

dot(other)¶: Returns the dot of this Quaternion and another.

exp()¶: Returns a new Quaternion representing the exponentional of this Quaternion

classmethod from_axis(axis, dtype=None)¶: Creates a new Quaternion from an axis with angle magnitude.

classmethod from_axis_rotation(axis, theta, dtype=None)¶: Creates a new Quaternion with a rotation around the specified axis.

classmethod from_eulers(eulers, dtype=None)¶: Creates a Quaternion from the specified Euler angles.

classmethod from_inverse_of_eulers(eulers, dtype=None)¶: Creates a Quaternion from the inverse of the specified Euler angles.

classmethod from_matrix(matrix, dtype=None)¶: Creates a Quaternion from the specified Matrix (Matrix33 or Matrix44).

classmethod from_x_rotation(theta, dtype=None)¶: Creates a new Quaternion with a rotation around the X-axis.

classmethod from_y_rotation(theta, dtype=None)¶: Creates a new Quaternion with a rotation around the Y-axis.

classmethod from_z_rotation(theta, dtype=None)¶: Creates a new Quaternion with a rotation around the Z-axis.

inverse¶: Returns the inverse of this quaternion.

is_identity¶: Returns True if the Quaternion has no rotation (0.,0.,0.,1.).

length¶: Returns the length of this Quaternion.

lerp(other, t)¶: Interpolates between quat1 and quat2 by t. The parameter t is clamped to the range [0, 1]

matrix33¶: Returns a Matrix33 representation of this Quaternion.

matrix44¶: Returns a Matrix44 representation of this Quaternion.

negative¶: Returns the negative of the Quaternion.

normalise()¶: normalizes this Quaternion in-place.

normalised¶: Returns a normalized version of this Quaternion as a new Quaternion.

normalize()¶: normalizes this Quaternion in-place.

normalized¶: Returns a normalized version of this Quaternion as a new Quaternion.

power(exponent)¶: Returns a new Quaternion representing this Quaternion to the power of the exponent.

slerp(other, t)¶: Spherically interpolates between quat1 and quat2 by t. The parameter t is clamped to the range [0, 1]

w¶

x¶

xw¶

xy¶

xyw¶

xyz¶

xyzw¶

xz¶

xzw¶

y¶

z¶