Each die is a point mass under constant gravitational acceleration g, integrated with semi-implicit Euler: v += g·dt, x += v·dt. Floor and wall collisions invert the normal velocity component scaled by the restitution coefficient e (v' = -e·v) and apply Coulomb-like friction to the tangential component.
- Angular velocity decays by a friction factor each ground contact, mirroring how a tumbling cube sheds spin on impact.
- The die's showing face advances by one standard pip value (1↔6, 2↔5, 3↔4 opposite-face pairs) every quarter-turn of accumulated rotation, the same way a real cube's face changes each 90° tumble — so the final number is a deterministic function of the random launch spin, not a separate RNG call.
- A die "settles" once linear and angular speed both stay under threshold for 0.4s, matching the 3D version's settle condition.