PARTICLE SYSTEMS 1 OUTLINE Newtonian Particles Meshes - - PowerPoint PPT Presentation

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PARTICLE SYSTEMS 1 OUTLINE Newtonian Particles Meshes - - PowerPoint PPT Presentation

Mar 19, 2024 264 likes •445 views

PARTICLE SYSTEMS 1 OUTLINE Newtonian Particles Meshes Efficiency Constraints 2 INTRODUCTION Most important of procedural methods Used to model Natural phenomena Clouds Terrain Plants

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SLIDE 1

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PARTICLE SYSTEMS

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SLIDE 2

OUTLINE

  • Newtonian Particles
  • Meshes
  • Efficiency
  • Constraints

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SLIDE 3

INTRODUCTION

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  • Most important of procedural methods
  • Used to model
  • Natural phenomena
  • Clouds
  • Terrain
  • Plants
  • Crowd Scenes
  • Real physical processes
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SLIDE 4

NEWTONIAN PARTICLE

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  • Particle system is a set of particles
  • Each particle is an ideal point mass
  • Six degrees of freedom
  • Position
  • Velocity
  • Each particle obeys Newtons’ law

f = ma

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SLIDE 5

FORCE VECTOR

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  • Independent Particles
  • Gravity
  • Wind forces
  • O(n) calulation
  • Coupled Particles O(n)
  • Meshes
  • Spring-Mass Systems
  • Coupled Particles O(n2)
  • Attractive and repulsive forces
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SLIDE 6

SOLUTION OF PARTICLE SYSTEMS

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float time, delta state[6n], force[3n]; state = initial_state(); for(time = t0; time<final_time, time+=delta) { force = force_function(state, time); state = ode(force, state, time, delta); render(state, time) }

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SLIDE 7

MESHES

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  • Connect each particle to its closest neighbors
  • O(n) force calculation
  • Use spring-mass system
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SLIDE 8

SPRING FORCES

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  • Assume each particle has unit mass and is connected to its neighbor(s) by a spring
  • Hooke’s law: force proportional to distance between the points
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SLIDE 9

SPRING DAMPING

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  • A pure spring-mass will oscillate forever
  • Must add a damping term
  • Must project velocity

·

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SLIDE 10

ATTRACTION AND REPULSION

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  • General case requires O(n2) calculation
  • In most problems, the drop off is such that not many particles contribute to the forces on

any given particle

  • Sorting problem: is it O(n log n)?
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SLIDE 11

BOXES

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  • Spatial subdivision technique
  • Divide space into boxes
  • Particle can only interact with particles in its box or the neighboring boxes
  • Must update which box a particle belongs to after each time step
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SLIDE 12

LINKED LISTS

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  • Each particle maintains a linked list of its neighbors
  • Update data structure at each time step
  • Must amortize cost of building the data structures initially
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SLIDE 13

PARTICLE FIELD CALCULATIONS

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  • Consider simple gravity
  • We don’t compute forces due to sun, moon, and other large bodies
  • Rather we use the gravitational field
  • Usually we can group particles into equivalent point masses
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SLIDE 14

CONSTRAINTS

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  • Easy in computer graphics to ignore physical reality
  • Surfaces are virtual
  • Must detect collisions separately if we want exact solution
  • Can approximate with

repulsive forces

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SLIDE 15

COLLISIONS

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Once we detect a collision, we can calculate new path Use coefficient of resititution Reflect vertical component May have to use partial time step

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SLIDE 16

CONTACT FORCES

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SLIDE 17

SUMMARY

  • Newtonian Particles
  • Meshes
  • Efficiency
  • Constraints

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