Euler Axis (Axis-Angle)¶

A rotation defined by a unit axis vector and a rotation angle. The EulerAxis class stores a shape (3,) axis and a scalar angle, both in the configured float dtype. Angles are always stored in radians internally.

Construction¶

From Axis Array and Angle¶

import jax.numpy as jnp
from astrojax import EulerAxis

# 45-degree rotation about z-axis
ea = EulerAxis(jnp.array([0.0, 0.0, 1.0]), 45.0, use_degrees=True)

From Individual Components¶

ea = EulerAxis.from_values(0.0, 0.0, 1.0, 45.0, use_degrees=True)

From a 4-Element Vector¶

import jax.numpy as jnp

# Default: vector-first [x, y, z, angle]
ea = EulerAxis.from_vector(jnp.array([0.0, 0.0, 1.0, 0.7854]))

# Angle-first [angle, x, y, z]
ea = EulerAxis.from_vector(jnp.array([0.7854, 0.0, 0.0, 1.0]), vector_first=False)

Properties¶

ea = EulerAxis.from_values(0.0, 0.0, 1.0, 45.0, use_degrees=True)
print(ea.axis)   # [0.0, 0.0, 1.0]
print(ea.angle)  # ~0.7854 radians

Serialization¶

Export to a 4-element vector:

v = ea.to_vector()                           # [x, y, z, angle_rad]
v = ea.to_vector(use_degrees=True)           # [x, y, z, angle_deg]
v = ea.to_vector(vector_first=False)         # [angle_rad, x, y, z]

Conversions¶

from astrojax import Quaternion, RotationMatrix, EulerAngle, EulerAngleOrder

ea = EulerAxis.from_values(0.0, 0.0, 1.0, 45.0, use_degrees=True)

# To other representations
q = ea.to_quaternion()
r = ea.to_rotation_matrix()
e = ea.to_euler_angle(EulerAngleOrder.XYZ)

# From other representations
ea2 = EulerAxis.from_quaternion(q)
ea3 = EulerAxis.from_rotation_matrix(r)
ea4 = EulerAxis.from_euler_angle(e)

Zero rotation

When the rotation angle is zero, the axis is undefined. The conversion from quaternion returns a default axis of [1, 0, 0] in this case.