8. Enhancing Fall and Collision Behavior

The current ball movement uses constant velocity, lacking realistic deceleration during bounces. Introducing basic physics calculations improves the visual fidelity. While professional open-source physics angines like Box2D and PhysX offer advanced simulation capabilities, this section implements simplified physics manually.

1) Improved Display Function

A refined display function includes boundary checks to prevent the ball from moving outside screen limits. Multiple directional bounds can be added as needed.

void render_ball_animation(ball_object_t* ball)
{
    // Clamp position within screen bounds
    if (ball->state->y > SCREEN_HEIGHT - ball->state->radius)
        ball->state->y = SCREEN_HEIGHT - ball->state->radius;
    else if (ball->state->y < ball->state->radius)
        ball->state->y = ball->state->radius;
    else if (ball->state->x > SCREEN_WIDTH - ball->state->radius)
        ball->state->x = SCREEN_WIDTH - ball->state->radius;
    else if (ball->state->x < ball->state->radius)
        ball->state->x = ball->state->radius;

    cleardevice();
    fillcircle((int)ball->state->x, (int)ball->state->y, (int)ball->state->radius);
    Sleep(50);
}

2) Implementing Free-Fall Motion

Replace uniform downward motion with acceleration-based fall. Since mass is not modeled, a constant vertical acceleration simulates gravity.

Physics update logic:

• Velocity increases by acceleration per frame
• Position updates based on current velocity

ball->state->velocity_y += ball->state->gravity_accel;
ball->state->y += ball->state->velocity_y * 1; // 1 represents time delta (frame)

3) Adding Damped Bounce Effect

When the ball hits the bottom or top edge, apply energy loss via velocity scaling.

ball->state->velocity_y = -0.95f * ball->state->velocity_y;

4) Complete Falling and Bouncing Sequence

Combine physics update and collision response. Constants are now encapsulated within the animation structure for better maintainability.

void simulate_falling_ball(ball_object_t* ball)
{
    const float ENERGY_LOSS_FACTOR = 0.95f;
    
    ball->state->velocity_y += ball->state->gravity_accel;
    ball->state->y += ball->state->velocity_y;
    
    if (ball->state->y >= SCREEN_HEIGHT - ball->state->radius)
    {
        ball->state->velocity_y = -ENERGY_LOSS_FACTOR * ball->state->velocity_y;
    }
    
    render_ball_animation(ball);
}

9. Creating Parabolic Trajectory Animation

Now implement a more complex animation: parabolic motion.

1) Directional Velocity Components

Instead of using angles and trigonometry, define independent x and y velocity components directly in the state structure.

float velocity_x; // Horizontal speed
float velocity_y; // Vertical speed

2) Parabolic Motion Logic

The ball moves under simulated gravity and rebounds off walls with energy loss:

• Update position based on current velocities
• Apply gravity to vertical velocity
• Reverse direcsion and dampen speed upon wall collision

ball->state->x += ball->state->velocity_x;
ball->state->y += ball->state->velocity_y;
ball->state->velocity_y += GRAVITY; // Simulate gravitational pull

// Handle collisions
if (ball->state->x >= SCREEN_WIDTH - ball->state->radius || ball->state->x <= ball->state->radius)
    ball->state->velocity_x = -K * ball->state->velocity_x;
if (ball->state->y >= SCREEN_HEIGHT - ball->state->radius || ball->state->y <= ball->state->radius)
    ball->state->velocity_y = -K * ball->state->velocity_y;

3) Full Parabolic Animation Functon

void simulate_parabolic_motion(ball_object_t* ball)
{
    const float GRAVITY = 0.8f;
    const float K = 0.95f;
    
    ball->state->x += ball->state->velocity_x;
    ball->state->y += ball->state->velocity_y;
    ball->state->velocity_y += GRAVITY;
    
    // Wall collision detection and response
    if (ball->state->x >= SCREEN_WIDTH - ball->state->radius || ball->state->x <= ball->state->radius)
        ball->state->velocity_x = -K * ball->state->velocity_x;
    if (ball->state->y >= SCREEN_HEIGHT - ball->state->radius || ball->state->y <= ball->state->radius)
        ball->state->velocity_y = -K * ball->state->velocity_y;
    
    render_ball_animation(ball);
}

4) Main Loop Integration

Initialize initial velocity and run animation loop:

ball->state->velocity_x = 10.0f;
ball->state->velocity_y = 0.0f;

while (true)
{
    simulate_parabolic_motion(&ball);
    // simulate_falling_ball(&ball); // Alternative: use simple fall
}

This completes the core graphical behavior of the animated ball. Future improvements include refactoring the object structure to support multiple shapes, replacing Sleep() with a non-blocking timer system, and introducing callback function pointers for event handling. A finalized version will be made available later.