Quaternion Construction

def __init__(self, *args, **kwargs):
    """
    Initialize a new Quaternion object.
    
    Supports multiple initialization methods:
    - No arguments: Identity quaternion (1, 0, 0, 0)
    - Single scalar: Real quaternion (scalar, 0, 0, 0)
    - Four scalars: Direct component specification (w, x, y, z)
    - Single sequence: Four-element array [w, x, y, z]
    - Another Quaternion: Copy constructor
    
    Keyword arguments:
    - scalar/vector: Separate real and imaginary parts
    - real/imaginary: Alternative names for scalar/vector
    - axis/angle or axis/radians or axis/degrees: Axis-angle representation
    - array: Four-element sequence [w, x, y, z]
    - matrix: 3x3 or 4x4 rotation/transformation matrix
    """

# Identity quaternion
q = Quaternion()  # (1, 0, 0, 0)

# From components
q = Quaternion(1, 0, 0, 0)  # (w, x, y, z)
q = Quaternion([1, 0, 0, 0])  # From array

# From scalar and vector parts
q = Quaternion(scalar=1, vector=[0, 0, 0])
q = Quaternion(real=1, imaginary=[0, 0, 0])

# From axis and angle
q = Quaternion(axis=[0, 1, 0], angle=1.57)  # Radians
q = Quaternion(axis=[0, 1, 0], radians=1.57)
q = Quaternion(axis=[0, 1, 0], degrees=90)

# From rotation matrix
import numpy as np
matrix = np.eye(3)
q = Quaternion(matrix=matrix)

# Copy constructor
q1 = Quaternion(1, 0, 0, 0)
q2 = Quaternion(q1)

@classmethod
def random(cls):
    """
    Generate a random unit quaternion.
    
    Uniformly distributed across the rotation space using method from:
    http://planning.cs.uiuc.edu/node198.html
    
    Returns:
        Quaternion: Random unit quaternion
    """

# Generate random rotation
random_q = Quaternion.random()
print(f"Random quaternion: {random_q}")
print(f"Is unit: {random_q.is_unit()}")

@classmethod
def _from_matrix(cls, matrix, rtol=1e-05, atol=1e-08):
    """
    Create quaternion from 3x3 rotation or 4x4 transformation matrix.
    
    Parameters:
        matrix: numpy array, 3x3 or 4x4 matrix
        rtol: relative tolerance for orthogonality check
        atol: absolute tolerance for orthogonality check
    
    Returns:
        Quaternion: Quaternion representing the same rotation
    
    Raises:
        ValueError: If matrix is not orthogonal or determinant != 1
        TypeError: If matrix is not numpy array
    """

@classmethod
def _from_axis_angle(cls, axis, angle):
    """
    Create quaternion from axis and angle representation.
    
    Parameters:
        axis: array-like, 3-vector rotation axis (will be normalized)
        angle: float, rotation angle in radians
    
    Returns:
        Quaternion: Quaternion representing the rotation
    
    Raises:
        ZeroDivisionError: If axis has zero length
    """

def _validate_number_sequence(self, seq, n):
    """
    Validate a sequence to be of a certain length and ensure it's a numpy array of floats.
    
    Parameters:
        seq: sequence to validate
        n: expected length
    
    Returns:
        numpy.ndarray: Validated array of floats
    
    Raises:
        ValueError: Invalid length or non-numeric value
    """

@staticmethod
def to_degrees(angle_rad):
    """
    Convert angle from radians to degrees.
    
    Parameters:
        angle_rad: float or None, angle in radians
    
    Returns:
        float or None: angle in degrees
    """

@staticmethod
def to_radians(angle_deg):
    """
    Convert angle from degrees to radians.
    
    Parameters:
        angle_deg: float or None, angle in degrees
    
    Returns:
        float or None: angle in radians
    """

# Angle conversion
degrees = Quaternion.to_degrees(3.14159)  # ~180.0
radians = Quaternion.to_radians(90)       # ~1.5708