Simulation: Particle Systems

Transcription

1 Simulation: Particle Systems Course web page: February 28, 2012 Lecture 5

2 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: courtesy of S. Dunn 1. Create, kill particles Fire: Each particle is a blended sprite 2. Update positions based on: Previous positions, velocities, accelerations Exterior and interior forces 3. Render particles

3 courtesy of Black Belt Systems 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. Smoke movie (turbulence ): Convection + invisible container = smoke in a bottle Initial upward and outward velocity + gravity = water fountain

4 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

5 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)

6 Particle Systems at the Movies XXX (2002) Avalanche effect by Digital Domain ~150,000 particles with matchmove [~3:15 in]

7 Flocking with Interior Motion: Example (Not the same algorithm as the Reynolds paper) courtesy of D. Brogan

8 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

9 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

10 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 Collision avoidance Velocity matching Centering courtesy of C. Reynolds

11 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) = w avoid a avoid (t) + w match a match (t) + w center a center (t)

12 Flocking: Example

13 Flocking with more complicated particles

14 courtesy of A. Rinaldi CrowdMaker Maya plugin (test_1000, test_crowd) Environment awareness, leader PSCrowd (demo for PS3; 5,000 fish: fishhires) Inverse kinematics? courtesy of C. Reynolds Flocking examples: What s Involved Here?

15 Advanced Flocking at the Movies courtesy of lordoftherings.net The Two Towers (2002) Soldiers in battle scenes are articulated particles that each run small AI program to guide motion, actions (2:00-3:00) courtesy of massivesoftware.com Play egyptbattle, weta-kong

16 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

17 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)

18 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!

19 Forces Unary: Global forces applied to particles independently Gravity: Can regard as constant acceleration in downward direction: f gravity (t) = m g Drag: Resistance to motion through medium proportional to speed: f drag (t) = -k d v(t) n-ary: Interaction forces between particles Gravitational attraction Electrical charge Springs Based on proximity Specific to connected particles

20 n-ary Forces: Springs a b 2 connected particles a and b exert force on one another proportional to displacement from resting length r of spring Assuming time t, let Δx = x a x b, d = Δx/ Δx, and Δv = v a v b. Then the force on a is (where f b = f a ): spring constant ( stiffness ) damping constant (like spring drag ) See molecule examples at

21 Collisions courtesy of D. Baraff, Pixar

22 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

23 Collision Examples plank rings courtesy of R. Fedkiw

24 courtesy of M. Kass courtesy of J. Barbic 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 Angular springs for hair: Stiffness More body Spring networks for cloth Squishy jello

25 courtesy of A. Selle Hair examples No hair-hair adhesion: Basically like thin ropes With stiction : A bit like wet hair--sticky

26 Cloth Simulation I (Curtain) courtesy of R. Bridson (

27 Cloth Simulation II (Table) courtesy of R. Bridson (

28 Cloth simulation III (cloth2008 0:53) courtesy of R. Bridson (

29 Deformable 3-D objects: Jello cube

30 Deformable 3-D objects: Variable stiffness* courtesy of R. Fedkiw armadillo: High stiffness Low stiffness *Technically, a non-mass-spring technique was used for these videos