A tree’s shadow changes as the sun rises in the east and sets in the west

To simulate a tree’s shadow changing as the sun rises in the east and sets in the west, we can use Python 3 and the math library to calculate the angle of the sun’s position at a given time, and the Pygame library to draw the tree and its shadow.

Here is an example program that simulates the tree’s shadow changing throughout the day:

pythonCopy codeimport pygame
import math

# Initialize Pygame
pygame.init()

# Define colors
WHITE = (255, 255, 255)
BLACK = (0, 0, 0)
GREEN = (0, 255, 0)
BLUE = (0, 0, 255)

# Set up the window
WINDOW_WIDTH = 800
WINDOW_HEIGHT = 600
window = pygame.display.set_mode((WINDOW_WIDTH, WINDOW_HEIGHT))
pygame.display.set_caption("Tree Shadow Simulation")

# Set up the tree
TREE_HEIGHT = 200
TREE_WIDTH = 50
tree_rect = pygame.Rect((WINDOW_WIDTH - TREE_WIDTH) / 2, WINDOW_HEIGHT - TREE_HEIGHT, TREE_WIDTH, TREE_HEIGHT)

# Set up the sun
SUN_RADIUS = 20
sun_position = (WINDOW_WIDTH / 2, -SUN_RADIUS)

# Define the time of day in minutes (0 = midnight, 720 = noon, 1440 = midnight)
time_of_day = 0

# Define the function to calculate the sun's position based on the time of day
def calculate_sun_position(time_of_day):
    # Convert time of day to radians
    time_in_radians = (time_of_day / 1440) * 2 * math.pi

    # Calculate the sun's position based on the time of day
    x = (WINDOW_WIDTH / 2) + (WINDOW_WIDTH / 2 - SUN_RADIUS) * math.cos(time_in_radians)
    y = SUN_RADIUS + (WINDOW_HEIGHT / 2 - SUN_RADIUS) * math.sin(time_in_radians)

    return (x, y)

# Define the main loop
running = True
while running:
    # Handle events
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            running = False

    # Clear the screen
    window.fill(WHITE)

    # Draw the tree
    pygame.draw.rect(window, GREEN, tree_rect)

    # Draw the sun
    sun_position = calculate_sun_position(time_of_day)
    pygame.draw.circle(window, YELLOW, sun_position, SUN_RADIUS)

    # Calculate the angle of the sun's position
    dx = sun_position[0] - tree_rect.centerx
    dy = sun_position[1] - tree_rect.centery
    angle = math.atan2(dy, dx)

    # Calculate the length of the shadow
    shadow_length = TREE_HEIGHT / math.tan(angle)

    # Draw the shadow
    shadow_start = (tree_rect.centerx, tree_rect.centery)
    shadow_end = (shadow_start[0] + shadow_length * math.cos(angle), shadow_start[1] + shadow_length * math.sin(angle))
    pygame.draw.line(window, BLUE, shadow_start, shadow_end)

    # Update the display
    pygame.display.update()

    # Increment the time of day
    time_of_day += 1

    # Wrap the time of day back to 0 at midnight
    if time_of_day >= 1440:
        time_of_day = 0

# Clean up Pygame
pygame.quit()

This program defines the tree and the sun, calculates the position of the sun based on the time of day, calculates the angle of the sun’s position relative to the tree, and then calculates the length and position of the shadow. It