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Comprehensive Guide to Computer Game Design and Development: Mathematics, Collision, Physics, and Havok

Explore advanced concepts in computer game design covering collision mathematics, physics simulations, Havok destruction, intersection testing, Minkowski sum, terrain collision with heightmaps, particle physics, friction, rigid body dynamics, and physics engines. Discover the intricacies of developing games with precise collision responses and accurate physics simulations.

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Comprehensive Guide to Computer Game Design and Development: Mathematics, Collision, Physics, and Havok

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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

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