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Computer Game Design and Development

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  1. Computer Game Design and Development Mathematics, Collision, and Physics Havok Destruction

  2. Overlap Bisection

  3. Limitations of Overlap Testing

  4. Intersection Testing

  5. Collision ApproximationsMinkowski Sum – sweep origin of X across Y

  6. Bounding Volumes AABB OBB

  7. Performance Possible collisionbetween R and B since overlap in all axis (2 in this case) Subdivide such that on averageone object in each cell.

  8. Terrain Collision • Heightmap information • Look up terrain height • 3 LERPs – Linear Interpretation between points • X • Z • Between x and z http://creators.xna.com/en-US/sample/collision3dheightmap

  9. Resolving Collision • Gross collision & subdivide if needed • Three phases • Prologue – ignore or trigger other events • Collision – point of impact, new velocities • Epilogue – destroy object, effects, damage

  10. Particle Physics Basics • Use consistent units (SI) • Particles • Position (p) in 3-space, vector3 (x,y,z) = p(t) • Velocity (v) = change in position over time, V(t) • Acceleration (a) = change in velocity over time, a(t) • Force (f) = results in change in acceleration over time, F(t) = ma(t) • Calculus • Derivatives and integrals go from one to another

  11. Collision Response (frictionless)

  12. Springs & Damping

  13. Friction

  14. Center of Mass

  15. Rigid Body CollisionCenter of Mass Consideration

  16. Physics Engines • Commercial • Game Dynamics SDK (Havok) • Renderware Physcis • NovodeX SDK • Free/Shareware • Open Dynamics Engine (ODE) • Tokamak Game Physics SDK • Newton Game Dynamics SDK

  17. Demo http://www.havok.com/content/view/584/96/ http://www.tokamakphysics.com/index.htm