Advanced Algorithms. Particle Systems. Reading. What is a Particle System?

Transcription

1 Advanced Algorithms Particle Systems CMPT 466 Computer Animation Torsten Möller Hierarchical Kinematic Modeling Forward Kinematics Inverse Kinematics Rigid Body Constraints Basic Particle Forces Collision Controlling Groups of Objects particle systems flocking behaviour Reading Chapter 4 of Parents book William T. Reeves, "Particle Systems - A Technique for Modeling a Class of Fuzzy Objects", pp , (SIGGRAPH 83). "Particle Animation and Rendering Using Data Parallel Computation", Karl Sims, pp (SIGGRAPH 90) What is a Particle System? Simply a series of individual particles Velocity Position Color Lifetime Used to model complex systems Fire Smoke Fireworks Planets

2 Particle Systems Example Create fuzzy objects and objects whose behavior changes with time tradeoff between physical simulation and animator control: want motion to be physically correct want to have complete control available It doesn t have to be a dot Particle Systems work The right way - perform complete physical simulations, and determine the forces to apply to achieve the desired motion. This is difficult. Both of these are non-trivial. A practical way - Combine dynamic simulation with kinematic control by providing several levels of operations along this spectrum.

3 Particle Systems Essence of this approach: positions are generated automatically evolution of particles is controlled automatically individual particles affect final image directly Particle Systems Scale usually such that aggregate motion of swarm is more apparent than internal agent motion Basic loop: Create, kill particles Update positions based on: Previous positions, velocities, accelerations Exterior and interior forces Render particles Particle Motion Motion may be driven by: Global exterior forces such as gravity, wind, predetermined path or target position, etc. Contact interactions with environment Collisions Friction Physical interactions with each other Gravity, electrical attraction/ repulsion Spring connections Collisions Interior self determination AI-like perception-action feedback Randomness courtesy of Black Belt Systems Initial upward and outward velocity + gravity = water fountain Particle Systems: Example Combination of gravity, wind vortex, collision forces, and pre-computed positions (e.g., face shape attracts particles to it) from K. Sims movie Particle Dreams (1988)

4 Particle Systems at the Movies 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) XXX (2002) Avalanche effect by Digital Domain ~150,000 particles Particle Systems at the Movies Particle Systems 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 Differ from other representations: clouds of particles define objects volume (NO explicit boundary) not static - particles are born / change and move / die non deterministic stochastic processes create and change appearance and shape of particles courtesy of massivesoftware.com

5 Particle Systems For each frame in a particle system s lifetime, we must: generate new particles assign new particle s attribute remove particles past their lifetime move and transform remaining particles render the image particles systems can be trees, i.e. each particle is actually another P.S. Particle Systems Reaction to environment Aging: Time-varying attributes birth Source death Particles - Generation Number of particles affects the density of the image 2 ways of controlling # of particles: control mean # and variance: N parts = N mean + Rand()*Var parts (Rand - random variable often between 0 and 1) make # of particles depend on screen size of object: N parts = (N mean + Rand()*Var parts )* f(scr.area) Particles - Generation grow and shrink intensity of system of particles: N mean = N init +!N mean * (f-f 0 ) (where f is the frame number)

6 Modeling The Particle We know each particle is independent Have the following attributes X and Y coordinates X velocity Y velocity Color, Size (or image) Lifetime Shape Each particle may start with the same or different location Each particle usually starts out with a different x and y velocity Particle - Attributes These shapes positioned, oriented in a 3D world initial position of particle is with respect to shape of particle system Particle - Attributes shape of a system may constrain direction of initial velocity for a sphere - particles move outward from center for a disk - they move upward (maybe with an ejection angle) Particle - Attributes compute speed by: speed init = speed mean + Rand()*Var speed

7 Particle Systems Levels of operations between explicit kinematic control and physically based simulations position operations (kinematics) velocity operations acceleration operations (dynamics) simulate time increment Particle - Dynamics To move particle, add velocity vector can add acceleration factor to simulate gravity particles can change color, transparency and size over time control these changes by global or local rate-of-change parameters Forces Unary: gravity, viscosity N-ary: spring, etc. Environmental: repulsion forces, reaction to collisions Motion with Dynamics simulate time increment Dt: A = F/m, if using forces V = V + A!t P = P + V!t works ok, if!t is small enough that the acceleration and velocity are nearly constant over!t.

8 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 Based on proximity Electrical charge Springs Specific to connected particles n-ary Forces: Springs 2 connected particles a and b exert force on one another proportional to displacement from resting length r of spring Assuming time t, let a b!x = x a - x b, d = displacement, and!v = v a - v b Then the force on a is: f a = "[ k s ( #x " r) + k d #v $ d]d spring constant damping constant ( stiffness ) (like spring drag ) Spring systems Cloth Simulation I Networks of particles connected by springs can be used to simulate objects with elastic properties For example 1-D: Rope, hair 2-D: Cloth 3-D: Jello courtesy of M. Kass Angular springs for hair: Stiffness! More body courtesy of F. Pfenning Spring networks for cloth courtesy of R. Bridson (

9 Cloth Simulation II Cloth Simulation III courtesy of R. Bridson ( courtesy of R. Bridson ( More cloth simulations Particle Physics Accumulate forces Calculate acceleration Assume constant acceleration over delta time Average velocity = (v old + v old +a*dt)/2 = v old + a*dt/2 Position new = position old + v*dt+a*dt2/2 (More than just spring systems are used here) from creators unknown

10 Euler and RK Integration First order (linear) approximation using a step size of!t : ( ) = x( t) + "tf ( x,t) x t + "t Passive Update: Steps Particle is initialized when created with x(t) = x 0 and v(t) = v 0 So assume we have x(t) and v(t); now we want: x(t + dt): Integrate v(t) with ODE solver v(t + dt): Integrate f(t)/m with ODE solver Just need to sum component forces acting on particle at time t to get net force f(t). For example, for a cannonball shot through the air: f(t) = f gravity (t) + f drag (t) +... from Numerical Recipes Particle - Extinction Lifetime assigned as initial attribute often described in frames compute by Lifetime = Life mean + Rand()*Var life delete particle if intensity drops below a treshold delete particle if it goes outside an area of interest Particle - Rendering In general a difficult task (e.g. to ray trace several million particles!) problems: particles can be transparent can obscure other particles and/or other objects can cast shadows on other particles and/or other objects can interact with other objects

11 Particle - Rendering simplifying approaches are used assume each particle is a separate point light particles have cumulative effect on pixel if particles are moving, can represent as short line (a kind of motion blur - this also helps reduce strobing - i.e. temporal aliasing) render separately from other types of objects and composite various scene parts Some Code class Particle { double x, y, xvel, yvel; int lifecounter; Particle(int startx, int starty, int velx, int vely){ x = startx; y = starty; xvel = velx; yvel = vely; lifecounter = 0; The Only Particle Behavior A particle should know how to update its position: void updateposition( ) { x = x+xvel; y = y+yvel; yvel = yvel + GRAVITY+FORCES; lifecounter = lifecounter + 1; if (lifecounter > 100) isalive = false; public class ParticleSystem { Particle[ ] particles; final static double GRAVITY = 0.1; int x, y; int particlesalive; Some Code ParticleSystem(int numparticles, int startx, int starty) { particles = new Particle[numParticles]; x = startx; y = starty; for (int i = 0; i < numparticles; i++) { double rand = Math.random( )*2* ; double randx = Math.cos(rand)*5; double randy = Math.sin(rand)*5; particles[i] = new Particle(x, y, randx, randy);

12 The Only Particle System Behavior public void updatesystem() { particlesalive = 0; for (int i = 0; i<particles.length; i++) { // Tell particles to update themselves particles[i].updateposition(); // Count particles left in system if (particles[i].isalive) { particlesalive++; Putting it All Together ParticleSystem p while (true) { for all particles in p draw p p.updatesystem( ); More Complex Systems What we saw before works for individual systems, like a firework To create a series of fireworks, bring to life several particle systems! Must keep track of which systems are still active Serious slowdown Serious garbage potential Particle - Genesis Generate collections of particles on concentric circles on planet surface each particle position used as location for new particle system of a different type

13 Particle - Genesis position computed by adding velocity vector to previous position Particle - Genesis velocity vector can be updated with acceleration vector (e.g. to account for gravity) choose randomly: placing on disk generation rate initial velocity lifetime Particle - Genesis color started primarily red, with some green and blue. Altered over time to fade away, with red lasting longer to give effect of cooling of white-hot material Flocking (C. Reynolds, SIGGRAPH 1987) Particles for simulating simple creatures: boids Birds in flock Other work Fish in school Brogan, Etc. hodgins from C. Reynolds Not passive forces are internally generated Can be combined with external forces Intentions of each boid depend on characteristics of local environment

14 Geometric objects Many objects Flocking Simple motion - e.g., local rules, more physics, collision avoidance Consider other members. Local Control Perception Physics Reasoning and Reaction Flocking: Local Environment Boid Flocking Behaviors Simulating vision in murky water, each boid only influenced by boids in neighborhood: Distance less than some threshold Angle from heading within peripheral vision range Basic (in priority order) Collision Avoidance: Steer away from too-close flockmates 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 courtesy of C. Reynolds

15 Local Perception Limited field of view - modified by speed Importance by distance, proximity, angle Avoid bumping into neighbors Stay close to neighbors Match velocity of neighbors Draft behind member immediately ahead Global Perception General migratory urge Drawn to flock center Follow designated leader Not realistic, but facilitates control Physics Flight - thrust, lift, drag, gravity Perception Forces - flock centering, migration urge, etc. Other Forces - wind, collision avoidance Flocking Behaviors: Physics 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)

16 Negotiating the Motion Collision Avoidance Collision Avoidance Collision Avoidance

17 Steer To Avoid - Simulating Sight Steer to closest point on boundary sphere Steer to closest point on boundary of silhouette Steer to first non-intersecting feeler Steer to closest background point of projection. Flocking - Recap Fewer members than in particle systems Knowledge of, and reaction to, other members More physics - modeling flight, banking, etc. More intelligence - reasoning about path Emergent Behavior - global behavior from local rules