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EECE 478

EECE 478. Game Physics. Collision Detection Object/Environment Object/Object Optimization Recursive dimensional clustering Chap. 8 Math for 3D…. Dynamic Simulation Eqns of motion Differential eqns Projectiles Friction Rotational forces Chap. 10&11. Game Physics.

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EECE 478

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  1. EECE 478 Game Physics

  2. Collision Detection Object/Environment Object/Object Optimization Recursive dimensional clustering Chap. 8 Math for 3D… Dynamic Simulation Eqns of motion Differential eqns Projectiles Friction Rotational forces Chap. 10&11 Game Physics

  3. Collision Detection Determine time and location of collisions, given: • Moving objects • Stationary environment

  4. Object Models Objects are collections of primitives • Spheres • Boxes • Planes Objects are articulated and hierarchical • Nested bounding volumes • Transform chains

  5. Environment Model Terrain and static elements • 2D+ spatial organization • Only small changes Therefore: • Can preprocess for optimization • Use quad/oct-trees or BSP trees • Object volumes compared to tree to determine possible collisions

  6. Object/EnvironmentCollisions • Use spatial partitioning to simplify • Identify possible collisions of dynamic object with static environment • Dynamic sphere vs. static plane • Dynamic box vs. static plane

  7. Sphere vs plane Plane = any surface with constant normal • Move plane by r and intersect w/point

  8. Box vs plane Determine effective radius reff of box • Box defined by vectors R, S and T

  9. Object vs Object Two moving objects with V1 and V2 • Stationary object • Moving object with V = V1-V2 • Only need moving + stationary

  10. Sphere vs Sphere Two spheres (P1,r1,V1) and (P2,r2,V2) • Find t where |P1(t)-P2(t)|= r1+ r2

  11. Rigid Body Motion Math for 3D Game Programming Chap. 10 & 11 Game Programming Gems Chap. 2.2

  12. Kinematics: T and R Kinematics models the motion of objects Objects have • Center of massrcm • Principle axesR0, R1, R2 • Velocityv = dr/dt • Acceleration a= dv/dt • Angular velocity  = d/dt

  13. Dynamics: F and A Dynamics models the actions created by application of forces • Momentum p = mv • Force Fnet = m(dv/dt) • Angular momentumL = r  p • Torque Nnet = r  dp/dt

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