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3D Physics Simulation

Steven Durant. 3D Physics Simulation. Contents. Equations Gravity Euler’s Method Simple Collisions Correct Collisions Efficiency Applications Screenshots. Gravity. F = G * M 1 * M 2 / R 2 Unavoidable efficiency of O(n 2 ). Euler’s Method. a = F / M ∆v = a * ∆t ∆p = v * ∆t.

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3D Physics Simulation

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  1. Steven Durant 3D Physics Simulation

  2. Contents • Equations • Gravity • Euler’s Method • Simple Collisions • Correct Collisions • Efficiency • Applications • Screenshots

  3. Gravity • F = G * M1 * M2 / R2 • Unavoidable efficiency of O(n2)

  4. Euler’s Method • a = F / M • ∆v = a * ∆t • ∆p = v * ∆t

  5. Simple (Elastic) Collisions • Check for collision via particle radius • Conservation of momentum • v1’ = v2 * M2 / M1 • v2’ = v1 * M1 / M2 • This method is flawed

  6. Correct Collisions • Find next collision based on time • O(n2) • Find distance between particles • Find distance moved into each other ∆d ∆D

  7. Correct Collisions • Find fraction of timestep until collision ∆t = 1 – ( ∆d / ∆D ) • Move both particles for the fraction • Use ∆t in Euler’s Equations • Calculate new velocities • Use conservation of momentum • Move both particles for the other fraction • Use (1-∆t) in Euler’s Equations

  8. Efficiency • Pruning pairs of particles • Pairs moving away from each other. • Pairs too far apart. • Pretend their velocities are towards each other • If they still won’t collide before the nearest collision then their real velocities don’t need to be used or checked.

  9. Application • Find out how long it would take for two apples on a frictionless table to collide by using realistic masses for the apples. • Put thousands of tiny little masses along a random distribution and see what the end product is. • Stuff orbiting each other? • One big blob?

  10. Screenshots

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