Physikalische Grundlagen für Computerspiele

Maximilian Stark (, WS2018

Stand: 17.02.2019


Real-time physics

Modeling pyramid (bottom up)

  1. Geometric
  2. Kinematic
  3. **Physical**
  4. Behavioral
  5. Cognitive

Animation techniques


Mass spring systems

Numerical integration

Rigid Bodies



Fluid Simulation

Navier-Stokes equations, based on Euler


Smoothed Particle Hydrodynamics (SPH)

Smoothing kernels

Collision detection & response

Broad phase


Bounding Volume Hierarchies

Spatial partitioning

Narrow Phase

Contact & Friction

Position correction

Full RB simulation

  1. Integration
  2. Collision detection
    • Obtaining list of colliding object pairs
    • Usage of accelerated data structure
    • Minimal face-corner collisions
    • List building over time
      1. Timestep
        • Gather single deepest collections
      2. Timestep
        • Collision verification
        • Check of $v_{\text{rel}}$
  3. Penetration resolution
    • Sorted list, descending
    • Impulse based PosRot change
    • In theory: re-check for collisions
    • Usually finite time / attempts for resolution
      • Iterative Convergence
      • Priority based
  4. Velocity resolution
    • Sorted list, ascending $v_{\text{rel}}$
    • Recomputation of velocity for **all** objects colliding with either partner
    • Collision tolerance
      • Ignoring of small collisions
      • Minimal penetration depth & velocity
      • Only visual validity


Complex cloth simulation