Simulation: Particle Systems

Course web page:

http://goo.gl/EB3aA

February 28, 2012 Lecture 5

Particle Systems

• Definition: Simulation of a set of similar, moving agents in a larger environment

• Scale usually such that aggregate motion of “swarm” is more apparent than internal agent motion

• Applications – Water, snow – Smoke, fire – Cloth – “Creatures”

• Basic loop: 1. Create, kill particles 2. Update positions based on:

• Previous positions, velocities, accelerations • Exterior and interior forces

3. Render particles

Fire: Each particle is a blended sprite

courtesy of S. Dunn

Particle/Agent Motion Factors • Global exterior forces such as gravity,

wind, pre-determined path, target position, etc.

• Interactions with fixed environment – Collisions – Friction

• Physical interactions with each other – Gravity, electrical attraction/repulsion – Spring connections – Collisions

• Interior “self determination” – Randomness – AI-like perception-action feedback

• Flocking, seeking with collision avoidance, etc.

Initial upward and outward velocity + gravity = water fountain

court

esy

of

Bla

ck B

elt S

yst

em

s

Smoke movie (turbulence…): Convection + invisible container =

smoke in a bottle

Particle Systems: Example

• Multiple “force phases”: 1. Pre-computed positions (e.g.,

face shape “attracts” particles to it)

2. Gravity as particles drop

3. Collision with plane to make them bounce

4. Wind vortex (not clear if this is physical simulation or just a 3-D surface with rotation)

5. Randomness as particles “buzz”

6. Back to face

from K. Sims movie “Particle Dreams” (1988)

Play particle75_1_89.mov

Particle Systems at the Movies

• First notable use (and coinage of name) was by W. Reeves in “Star Trek II: Wrath of Khan” (1982) for the “Genesis” effect

Particle are created, they move, and then go extinct (so the effect is localized) http://www.youtube.com/watch?v=QXbWCrzWJo4

Particle Systems at the Movies

“XXX” (2002) Avalanche effect by Digital Domain ~150,000 particles with matchmove

http://www.youtube.com/watch?v=5lWqNMC6YRs [~3:15 in]

Flocking with Interior Motion: Example

(Not the same algorithm as the Reynolds paper)

courtesy of D. Brogan

Flocking (C. Reynolds, SIGGRAPH 1987)

• Particles for simulating simple creatures: boids – Birds in flock – Fish in school – Etc.

• Not passive—forces are internally generated – Can be combined with external forces

• “Intentions” of each boid depend on characteristics of local environment

from C. Reynolds

Flocking: Local Environment

• Simulating vision in “murky water”, each boid only influenced by boids in neighborhood:

– Detection distance less than some threshold

– Angle from heading within peripheral vision range

courtesy of C. Reynolds

Boid Flocking Behaviors

• Basic (in priority order) – Collision Avoidance: Steer away

from too-close flockmates/obstacles

– Velocity Matching: Align direction and speed with nearby flockmates

– Flock Centering: Attempt to stay close to nearby flockmates

• More control: – Have leader(s) that don’t follow rules

above trace spline path to “guide” things

– Randomness and awareness of fixed obstacles in environment

courtesy of C. Reynolds

Collision avoidance

Velocity matching

Centering

Flocking Behaviors: Details

• Each behavior generates an acceleration a(t) directly (no consideration of mass)

• Electric charge-like model is followed: – Attractions and repulsions allowed

– Magnitude of induced acceleration falls off with inverse square of distance (0 outside neighborhood)

• Component accelerations are combined with weights for “personality” control: a(t) = wavoidaavoid(t) + wmatchamatch(t) + wcenteracenter(t)

Flocking: Example

Flocking with more complicated particles

Flocking examples: What’s Involved Here?

CrowdMaker Maya plugin (test_1000, test_Crowd) Environment awareness, leader

court

esy

of

C.

Reynold

s

court

esy

of

A.

Rin

ald

i

PSCrowd (demo for PS3; 5,000 fish: fishHiRes) Inverse kinematics?

Advanced Flocking at the Movies

courtesy of massivesoftware.com

“The Two Towers” (2002) Soldiers in battle scenes are articulated particles that each run small AI program to guide motion, actions http://www.youtube.com/watch?v=Rn6suNh5Gn0 (2:00-3:00) Play egyptbattle, weta-kong

courtesy of lordoftherings.net

Particle Systems: Steps

1. Create new particles and initialize their states

– Position, velocity, etc.

2. Delete “expired” particles

3. Update particle states based on forces both physical & virtual

4. Render particles

Particle Creation and Deletion

• Creation: Where? – Fixed source—e.g., fountain, top of waterfall

– Low density areas (to ensure adequate coverage)

– On object surface

– Along user-designated curve

• Deletion: Why? – Fixed lifetime ended

– Left bounding box

– Local density over threshold (e.g., have enough already for realistic effect)

Particle Update

• Given particle state at time t consisting of position, velocity, etc., how do we compute new values at time x(t + Δt) ?

• Typically, we don’t have an explicit parametric function x(t) that we can just evaluate for any t – E.g., a spline curve

• Rather, we have a set of forces and an initial value for the particle state

• We have to simulate the action of the forces on the particle to “see what happens”!

Forces

• Unary: “Global” forces applied to particles independently – Gravity: Can regard as constant acceleration in downward

direction:

fgravity(t) = m g

– Drag: Resistance to motion through medium proportional to speed:

fdrag(t) = -kd v(t)

• n-ary: Interaction forces between particles – Gravitational attraction – Electrical charge – Springs

Based on proximity

Specific to connected particles

n-ary Forces: Springs

• 2 connected particles a and b exert force on one another proportional to displace-ment from resting length r of spring

• Assuming time t, let Δx = xa – xb , d = Δx/|Δx|, and Δv = va – vb . Then the force on a is (where fb = –fa):

spring constant (“stiffness”)

damping constant (like “spring drag”)

a b

See molecule examples at http://www.myphysicslab.com

Collisions

courtesy of D. Baraff, Pixar

Collisions

• Penalty method – Spring-like force

proportional to penetration distance pushes particle out of object interior

• Hard collisions – Detect intersection point explicitly, treat

like a reflection (note that initial velocity vector points toward surface):

See collision examples (with many more tips) at http://www.myphysicslab.com

Collision Examples

courtesy of R. Fedkiw

plank rings

Spring systems

• Networks of particles connected by springs can be used to simulate objects with elastic properties – 1-D: Rope, hair, grass

– 2-D: Cloth

– 3-D: Deformable (aka rubber) objects

Spring networks for cloth Angular springs for hair: Stiffness More “body”

court

esy

of

M. Kass

court

esy

of

J. B

arb

ic

Squishy “jello”

Hair examples

court

esy

of

A.

Selle

No hair-hair adhesion: Basically like thin ropes

With “stiction”: A bit like wet hair--sticky

Cloth Simulation I (Curtain)

courtesy of R. Bridson (http://www.cs.ubc.ca/~rbridson)

Cloth Simulation II (Table)

courtesy of R. Bridson (http://www.cs.ubc.ca/~rbridson)

Cloth simulation III (cloth2008 – 0:53)

courtesy of R. Bridson (http://www.cs.ubc.ca/~rbridson)

Deformable 3-D objects: “Jello cube”

http://www.youtube.com/watch?v=qWJ6mgkOF-c

Deformable 3-D objects: Variable stiffness*

armadillo: High stiffness Low stiffness

courtesy of R. Fedkiw

*Technically, a non-mass-spring technique was used for these videos