Quaternion¶

A unit quaternion in scalar-first convention [w, x, y, z]. The quaternion serves as the central hub for attitude conversions -- most cross-type conversions route through Quaternion internally.

Construction¶

The constructor normalizes automatically:

from astrojax import Quaternion

q = Quaternion(1.0, 0.0, 0.0, 0.0)   # identity rotation
q2 = Quaternion(1.0, 1.0, 1.0, 1.0)  # auto-normalized to unit length

Factory Methods¶

import jax.numpy as jnp

# From a 4-element vector (scalar-first by default)
q = Quaternion.from_vector(jnp.array([1.0, 0.0, 0.0, 0.0]))

# Scalar-last convention
q = Quaternion.from_vector(jnp.array([0.0, 0.0, 0.0, 1.0]), scalar_first=False)

Properties¶

The four quaternion components are accessible as read-only properties:

q = Quaternion(0.5, 0.5, 0.5, 0.5)
print(q.w, q.x, q.y, q.z)

Operations¶

Hamilton Product¶

Quaternion multiplication implements the Hamilton product, composing two rotations:

q1 = Quaternion(1.0, 0.0, 0.0, 0.0)
q2 = Quaternion(0.5, 0.5, 0.5, 0.5)

q3 = q1 * q2  # Hamilton product

Conjugate and Inverse¶

For a unit quaternion, the conjugate equals the inverse. For non-unit quaternions, inverse() divides by the squared norm:

qc = q2.conjugate()  # [w, -x, -y, -z]
qi = q2.inverse()     # conjugate / norm^2

Spherical Linear Interpolation (SLERP)¶

SLERP provides constant-speed interpolation along the shortest great-circle arc on the unit sphere. Falls back to linear interpolation when quaternions are nearly parallel:

q_mid = q1.slerp(q2, 0.5)  # halfway between q1 and q2

Arithmetic¶

Addition, subtraction, and negation are also supported:

q_sum = q1 + q2   # component-wise add, then renormalize
q_diff = q1 - q2  # component-wise subtract, then renormalize
q_neg = -q1       # negate vector part

Conversions¶

from astrojax import RotationMatrix, EulerAngle, EulerAngleOrder, EulerAxis

q = Quaternion(0.675, 0.42, 0.5, 0.71)

# To other representations
r = q.to_rotation_matrix()
e = q.to_euler_angle(EulerAngleOrder.ZYX)
ea = q.to_euler_axis()

# From other representations
q2 = Quaternion.from_rotation_matrix(r)
q3 = Quaternion.from_euler_angle(e)
q4 = Quaternion.from_euler_axis(ea)