import numpy as np


def jitter_landmark(landmark, distance_distribution, bias):
    """
    Jitters a 3D landmark such that the distances to the original landmark
    follow the specified distribution.

    Args:
    - landmark (tuple): A tuple containing the x, y, and z coordinates of the landmark.
    - distance_distribution (list): A list of Euclidean distances.

    Returns:
    - jittered_landmark (tuple): A tuple containing the jittered x, y, and z coordinates.
    """
    # Sample a random direction in 3D space
    direction = np.random.randn(3)

    # Normalize the direction vector to have unit length
    direction /= np.linalg.norm(direction)

    # Sample a distance from the specified distribution
    sampled_distance = np.random.choice(distance_distribution)

    # Calculate the jittered coordinates
    x, y, z = landmark
    jittered_x = x + sampled_distance * direction[0] * bias
    jittered_y = y + sampled_distance * direction[1] * bias
    jittered_z = z + sampled_distance * direction[2] * bias

    # Return the jittered landmark coordinates
    jittered_landmark = (jittered_x, jittered_y, jittered_z)

    # Calculate Euclidean distance between original and jittered landmarks
    euclidean_distance = np.linalg.norm(
        np.array(landmark) - np.array(jittered_landmark)
    )

    # Print the Euclidean distance
    print("Euclidean Distance to Original Landmark:", euclidean_distance)
    return jittered_landmark