import numpy as np
import matplotlib.pyplot as plt

def douglas_peucker(points, epsilon):
    if len(points) <= 2:
        return points

    # Find the point with the maximum distance
    d_max = 0
    index = 0
    end = len(points) - 1

    for i in range(1, end):
        d = perpendicular_distance(points[i], points[0], points[end])
        if d > d_max:
            index = i
            d_max = d

    # If the maximum distance is greater than epsilon, recursively simplify
    result = []
    if d_max > epsilon:
        result += douglas_peucker(points[:index + 1], epsilon)
        result += douglas_peucker(points[index:], epsilon)
    else:
        result = [points[0], points[end]]

    return result

def perpendicular_distance(point, line_start, line_end):
    # Calculate the perpendicular distance of a point to a line
    return np.abs(np.cross(line_end - line_start, line_start - point)) / np.linalg.norm(line_end - line_start)

# Example usage
# Create a set of points representing a line
original_points = np.array([[0, 0], [1, 1], [2, 3], [3, 1], [4, 0], [5, 1], [6, -1], [7, -3]])
epsilon = 0.1
simplified_points = np.array(douglas_peucker(original_points, epsilon))


# Plot the original and simplified lines
plt.plot(original_points[:, 0], original_points[:, 1], label='Original Line')
simplified_points_array = np.array(simplified_points)
plt.plot(simplified_points_array[:, 0], simplified_points_array[:, 1], label='Simplified Line', linestyle='dashed')
plt.scatter(simplified_points[:, 0], simplified_points[:, 1], c='red', label='Simplified Points')

plt.legend()
plt.title('Douglas-Peucker Line Simplification')
plt.show()