Untitled

import numpy as np

def reflect_point_across_line(point, line_start, line_end):
    """
    Reflect a point across a line defined by two points (line_start, line_end).

    Args:
        point (array): The point to reflect (e.g., point 0).
        line_start (array): Starting point of the line (e.g., point 1).
        line_end (array): Ending point of the line (e.g., point 4).

    Returns:
        array: The reflected point coordinates.
    """
    # Convert to numpy arrays
    point = np.array(point)
    line_start = np.array(line_start)
    line_end = np.array(line_end)
    
    # Calculate the line vector
    line_vector = line_end - line_start
    
    # Normalize the line vector (to get the direction unit vector)
    line_unit_vector = line_vector / np.linalg.norm(line_vector)
    
    # Vector from line_start to the point
    point_vector = point - line_start
    
    # Project the point onto the line (dot product of point_vector with line_unit_vector)
    projection_length = np.dot(point_vector, line_unit_vector)
    projection = line_start + projection_length * line_unit_vector
    
    # Calculate the vector from the projected point to the original point
    reflection_vector = projection - point
    
    # Reflect the point across the line by adding the reflection vector to the projection
    reflected_point = projection + reflection_vector
    
    return reflected_point

def calculate_forehead_position_with_reflection(landmarks):
    """
    Calculate the forehead position by reflecting point 0 across the line formed by points 1 and 4.
    
    Args:
        landmarks (list): List of landmarks where each is (x, y, z) tuple.

    Returns:
        tuple: Estimated forehead position as (x, y, z).
    """
    # Get the coordinates for points 0, 1, and 4
    point_0 = landmarks[0]
    point_1 = landmarks[1]
    point_4 = landmarks[4]
    
    # Reflect point 0 across the line formed by point 1 and point 4
    forehead_position = reflect_point_across_line(point_0, point_1, point_4)
    
    return tuple(forehead_position)