Quaternion¶

Provide functions for the creation and manipulation of Quaternions.

pyrr.quaternion.apply_to_vector(*args, **kwargs)¶

Rotates a vector by a quaternion.

Parameters:	quat (numpy.array) – The quaternion. vec (numpy.array) – The vector.
Return type:	numpy.array
Returns:	The vector rotated by the quaternion.
Raises:	ValueError – raised if the vector is an unsupported size

pyrr.quaternion.conjugate(*args, **kwargs)¶

Calculates a quaternion with the opposite rotation.

Parameters:	quat (numpy.array) – The quaternion.
Return type:	numpy.array.
Returns:	A quaternion representing the conjugate.

pyrr.quaternion.create(x=0.0, y=0.0, z=0.0, w=1.0, dtype=None)¶

pyrr.quaternion.create_from_axis(*args, **kwargs)¶

pyrr.quaternion.create_from_axis_rotation(*args, **kwargs)¶

pyrr.quaternion.create_from_eulers(*args, **kwargs)¶

Creates a quaternion from a set of Euler angles.

Eulers are an array of length 3 in the following order:: [roll, pitch, yaw]

pyrr.quaternion.create_from_inverse_of_eulers(*args, **kwargs)¶

Creates a quaternion from the inverse of a set of Euler angles.

Eulers are an array of length 3 in the following order:: [roll, pitch, yaw]

pyrr.quaternion.create_from_matrix(*args, **kwargs)¶

pyrr.quaternion.create_from_x_rotation(theta, dtype=None)¶

pyrr.quaternion.create_from_y_rotation(theta, dtype=None)¶

pyrr.quaternion.create_from_z_rotation(theta, dtype=None)¶

pyrr.quaternion.cross(*args, **kwargs)¶

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.

pyrr.quaternion.dot(quat1, quat2)¶

Calculate the dot product of quaternions.

This is the same as a vector dot product.

Parameters:	quat1 (numpy.array) – The first quaternion(s). quat2 (numpy.array) – The second quaternion(s).
Return type:	float, numpy.array
Returns:	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.

pyrr.quaternion.exp(*args, **kwargs)¶

Calculate the exponential of the quaternion

Parameters:	quat (numpy.array) – The quaternion.
Return type:	numpy.array.
Returns:	The exponential of the quaternion

class pyrr.quaternion.index¶

w = 3¶

x = 0¶

y = 1¶

z = 2¶

pyrr.quaternion.inverse(quat)¶

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.

Parameters:	quat (numpy.array) – The quaternion to invert.
Return type:	numpy.array.
Returns:	The inverse of the quaternion.

pyrr.quaternion.is_identity(quat)¶

pyrr.quaternion.is_non_zero_length(quat)¶

Checks if a quaternion is not zero length.

This is the opposite to ‘is_zero_length’. This is provided for readability.

Parameters:	quat (numpy.array) – The quaternion to check.
Return type:	boolean
Returns:	False if the quaternion is zero length, otherwise True.

See also

is_zero_length

pyrr.quaternion.is_zero_length(quat)¶

Checks if a quaternion is zero length.

Parameters:	quat (numpy.array) – The quaternion to check.
Return type:	boolean.
Returns:	True if the quaternion is zero length, otherwise False.

pyrr.quaternion.length(quat)¶

Calculates the length of a quaternion.

Parameters:	quat (numpy.array) – The quaternion to measure.
Return type:	float, numpy.array
Returns:	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.

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

pyrr.quaternion.negate(*args, **kwargs)¶

Calculates the negated quaternion.

This is essentially the quaternion * -1.0.

Parameters:	quat (numpy.array) – The quaternion.
Return type:	numpy.array
Returns:	The negated quaternion.

pyrr.quaternion.normalise(quat)¶

Ensure a quaternion is unit length (length ~= 1.0).

The quaternion is not changed in place.

Parameters:	quat (numpy.array) – The quaternion to normalize.
Return type:	numpy.array
Returns:	The normalized quaternion(s).

pyrr.quaternion.normalize(quat)¶

Ensure a quaternion is unit length (length ~= 1.0).

The quaternion is not changed in place.

Parameters:	quat (numpy.array) – The quaternion to normalize.
Return type:	numpy.array
Returns:	The normalized quaternion(s).

pyrr.quaternion.power(*args, **kwargs)¶

Multiplies the quaternion by the exponent.

The quaternion is not changed in place.

Parameters:	quat (numpy.array) – The quaternion. scalar (float) – The exponent.
Return type:	numpy.array.
Returns:	A quaternion representing the original quaternion to the specified power.

pyrr.quaternion.rotation_angle(quat)¶

Calculates the rotation around the quaternion’s axis.

Parameters:	quat (numpy.array) – The quaternion.
Return type:	float.
Returns:	The quaternion’s rotation about the its axis in radians.

pyrr.quaternion.rotation_axis(*args, **kwargs)¶

Calculates the axis of the quaternion’s rotation.

Parameters:	quat (numpy.array) – The quaternion.
Return type:	numpy.array.
Returns:	The quaternion’s rotation axis.

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

pyrr.quaternion.squared_length(quat)¶

Calculates the squared length of a quaternion.

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

Parameters:	quat (numpy.array) – The quaternion to measure.
Return type:	float, numpy.array
Returns:	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.