CircleIntersectionVisualizer.py

import math
import random
import tkinter as tk

# Configuration
WINDOW_WIDTH = 800
WINDOW_HEIGHT = 600
GRID_SIZE = 20
OFFSET = 200  # Offset from edges for circle positioning

# Create window
canvas = tk.Canvas(width=WINDOW_WIDTH, height=WINDOW_HEIGHT)
canvas.pack()


def calculate_intersection_points(x1, y1, r1, x2, y2, r2):
    """Calculate how many points two circles intersect at."""
    # Distance between centers
    distance = math.sqrt((x1 - x2) ** 2 + (y1 - y2) ** 2)
    
    # Identical circles
    if x1 == x2 and y1 == y2 and r1 == r2:
        return "infinite"
    
    # Circles are too far apart
    if distance > r1 + r2:
        return 0
    
    # One circle is inside the other without touching
    if distance < abs(r1 - r2):
        return 0
    
    # Circles touch externally or internally (exactly one point)
    if distance == r1 + r2 or distance == abs(r1 - r2):
        return 1
    
    # Circles intersect at two points
    return 2


def draw_circles():
    """Generate and draw two random circles, then calculate intersections."""
    canvas.delete("all")
    
    # Draw grid background
    for i in range(0, WINDOW_WIDTH, GRID_SIZE):
        for j in range(0, WINDOW_HEIGHT, GRID_SIZE):
            canvas.create_rectangle(
                i, j, i + GRID_SIZE, j + GRID_SIZE,
                fill="white", outline="lightgray"
            )
    
    # Generate random circle parameters
    x1, y1, r1 = random.randint(1, 10), random.randint(1, 10), random.randint(1, 10)
    x2, y2, r2 = random.randint(1, 10), random.randint(1, 10), random.randint(1, 10)
    
    # Scale and position circles
    scale = GRID_SIZE
    
    # Draw first circle
    canvas.create_oval(
        OFFSET + x1 * scale - r1 * scale,
        OFFSET + y1 * scale - r1 * scale,
        OFFSET + x1 * scale + r1 * scale,
        OFFSET + y1 * scale + r1 * scale,
        outline="blue", width=2
    )
    
    # Draw second circle
    canvas.create_oval(
        OFFSET + x2 * scale - r2 * scale,
        OFFSET + y2 * scale - r2 * scale,
        OFFSET + x2 * scale + r2 * scale,
        OFFSET + y2 * scale + r2 * scale,
        outline="red", width=2
    )
    
    # Calculate results
    distance = math.sqrt((x1 - x2) ** 2 + (y1 - y2) ** 2)
    intersection_count = calculate_intersection_points(x1, y1, r1, x2, y2, r2)
    
    # Display information
    canvas.create_text(
        WINDOW_WIDTH / 2, 30,
        text=f"Distance between centers: {distance:.2f}\nRadii: {r1} and {r2}",
        font=("Arial", 12)
    )
    
    canvas.create_text(
        WINDOW_WIDTH / 2, 80,
        text=f"Circles intersect at {intersection_count} point(s)",
        font=("Arial", 14, "bold")
    )


# Initial instruction text
canvas.create_text(
    WINDOW_WIDTH / 2, WINDOW_HEIGHT / 2,
    text="Click to generate random circles",
    font=("Arial", 16)
)

# Bind mouse click to generate circles
canvas.bind("<Button-1>", lambda event: draw_circles())
canvas.mainloop()