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import numpy as np

def scale_polygons(polygons, original_size, new_size):
    """
    Scales a list of polygons to a new size while preserving the aspect ratio.
    
    Parameters:
        - polygons: a list of polygons, where each polygon is a list of points
        - original_size: the size of the original image as a tuple (height, width)
        - new_size: the desired size of the new image as a tuple (height, width)
        
    Returns:
        - a list of scaled polygons
    """
    # Calculate the aspect ratios of the original and new images
    original_aspect_ratio = original_size[1] / original_size[0]
    new_aspect_ratio = new_size[1] / new_size[0]

    # Calculate the scale factor based on the aspect ratio that changes the least
    if original_aspect_ratio < new_aspect_ratio:
        scale_factor = new_size[0] / original_size[0]
    else:
        scale_factor = new_size[1] / original_size[1]

    # Create an empty list to store the scaled polygons
    scaled_polygons = []

    # Iterate through each polygon in the list
    for polygon in polygons:
        # Create an empty list to store the scaled points of the polygon
        scaled_polygon = []
        
        # Iterate through each point in the polygon
        for point in polygon:
            # Scale the point using the scale factor and the center of the image
            center_x = original_size[1] / 2
            center_y = original_size[0] / 2
            scaled_x = (point[0] - center_x) * scale_factor + new_size[1] / 2
            scaled_y = (point[1] - center_y) * scale_factor + new_size[0] / 2
            scaled_point = [int(scaled_x), int(scaled_y)]
            
            # Append the scaled point to the scaled polygon
            scaled_polygon.append(scaled_point)
        
        # Append the scaled polygon to the list of scaled polygons
        scaled_polygons.append(scaled_polygon)
    
    return scaled_polygons