3D Physics Simulation

1
3D Physics Simulation

• Steven Durant

2
Contents

• Equations
• Gravity
• Eulers Method
• Simple Collisions
• Correct Collisions
• Efficiency
• Applications
• Screenshots

3
Gravity

• F G M1 M2 / R2
• Unavoidable efficiency of O(n2)

4
Eulers 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 Eulers Equations
• Calculate new velocities
• Use conservation of momentum
• Move both particles for the other fraction
• Use (1-?t) in Eulers 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 wont collide before the nearest
  collision then their real velocities dont 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