import pygame
import math
import itertools

# Define constants
WHITE = (255, 255, 255)
BLACK = (0, 0, 0)
WIDTH, HEIGHT = 800, 600
CENTER = (WIDTH // 2, HEIGHT // 2)

# Define the tesseract vertices in 4D space
vertices = [-1, 1]
tesseract_vertices = [[x, y, z, w] for x in vertices for y in vertices
                      for z in vertices for w in vertices]

# Define the edges between vertices
edges = [(n, n ^ 1) for n in range(16) for bit in range(4) if n & (1 << bit)]

# Initialize Pygame
pygame.init()
screen = pygame.display.set_mode((WIDTH, HEIGHT))
clock = pygame.time.Clock()
running = True


# Projection functions
def project_4D_to_3D(x, y, z, w, rotation_xy, rotation_xz, rotation_xw):
    # Rotate in 4D space
    xz = x * math.cos(rotation_xz) - z * math.sin(rotation_xz)
    zx = z * math.cos(rotation_xz) + x * math.sin(rotation_xz)
    xy = xz * math.cos(rotation_xy) - y * math.sin(rotation_xy)
    yx = y * math.cos(rotation_xy) + xz * math.sin(rotation_xy)
    xw = xy * math.cos(rotation_xw) - w * math.sin(rotation_xw)
    wx = w * math.cos(rotation_xw) + xy * math.sin(rotation_xw)

    # 4D to 3D projection
    distance = 2
    factor = distance / (distance + wx)
    x3d = factor * yx
    y3d = factor * zx
    z3d = factor * w
    return x3d, y3d, z3d


def project_3D_to_2D(x, y, z):
    # 3D to 2D projection (ignoring z for simple orthographic projection)
    return int(CENTER[0] + x * 100), int(CENTER[1] + y * 100)


# Main loop
angle_xy = angle_xz = angle_xw = 0.0
while running:
    # Handle events
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            running = False

    # Update the rotation angles
    angle_xy += 0.01
    angle_xz += 0.01
    angle_xw += 0.01

    # Clear screen
    screen.fill(BLACK)

    # Draw the tesseract
    projected_2d_points: list = []
    for vertex in tesseract_vertices:
        x, y, z, w = vertex
        # Project the 4D point to 3D
        x3d, y3d, z3d = project_4D_to_3D(x, y, z, w, angle_xy, angle_xz,
                                         angle_xw)
        # Project the 3D point to 2D and store it
        projected_2d_points.append(project_3D_to_2D(x3d, y3d, z3d))

    # Draw the edges
    for edge in edges:
        start_pos = projected_2d_points[edge[0]]
        end_pos = projected_2d_points[edge[1]]
        pygame.draw.line(screen, WHITE, start_pos, end_pos, 1)

    # Update display
    pygame.display.flip()

    # Cap the frame rate
    clock.tick(30)

pygame.quit()