quaternion.md

Quaternion API

Class

Quaternion(w=0.0, x=0.0, y=0.0, z=0.0, v=None)

Represents a quaternion in scalar-first form: [w, x, y, z].

Initialization Parameters

• w: float | Quaternion | Vector3D | array-like
  • If v is None and w is numeric, w is scalar part.
  • If w is Quaternion, copies values.
  • If w is Vector3D, creates pure quaternion [0, x, y, z].
  • If w is length-4 array, interpreted as [w, x, y, z].
  • If w is length-3 array, interpreted as [0, x, y, z].
• x: float, default 0.0.
• y: float, default 0.0.
• z: float, default 0.0.
• v: optional alternate input source (Quaternion, Vector3D, length-3/4 array-like).

Common Operations

• q1 + q2, q1 - q2
• q1 * q2 (Hamilton product)
• q * Vector3D (vector promoted to pure quaternion)
• q * scalar, scalar * q
• q / scalar

Methods

• normalize()
  • In-place normalization to unit quaternion.

Properties

• q.v -> Vector3D: vector part (x, y, z).
• q.q -> np.ndarray: array [w, x, y, z].
• q.conjugate -> Quaternion: [w, -x, -y, -z].
• q.inverse -> Quaternion: conjugate / ||q||^2.
• q.norm -> float: quaternion magnitude.
• q.r33 -> np.ndarray: 3x3 rotation matrix.
• q.isZero -> bool: near-zero check using module epsilon.

Notes

• Many hot paths are optionally accelerated by pyIMU._qcore.
• Rotation convention in this project is NED.