Physics Ball Simulation

1. Gravity (Acceleration)

Gravity is modeled as a constant downward acceleration vector (g) applied to each ball's vertical velocity (vy) per time step:

vy = vy + g

2. Bounciness (Restitution)

When a ball hits a boundary, it reflects its velocity vector. The coefficient of restitution (e) determines the percentage of kinetic energy retained. A bounce value of 0.75 means it keeps 75% of its speed, losing 25% to deformation and heat.

3. Mass & Density (m ∝ d · r³)

Real-world mass scales with volume (3D sphere). In this engine, mass (m) is calculated using the ball's radius (r) and density (d):

This cubic relation means doubling a ball's size increases its mass by 8x! Denser balls possess significantly higher momentum, easily pushing lighter balls aside.

4. Impulse-Based Collisions

Collisions are resolved in two phases:

• Positional Correction: Pushes overlapping balls apart slightly to prevent sinking or stickiness.
• Impulse Resolution: Applies equal and opposite forces (Newton's Third Law) along the collision normal to exchange momentum elastically.