Stephen Chenney, University of WisconsinPlausible Simulation Uncertainty, Efficiency, and Desired Outcomes Stephen Chenney University of Wisconsin

Stephen Chenney, University of WisconsinPlausible Simulation Thought Experiments When someone says “I’ll be there in 10 minutes”, what do you expect? How long do you wait for someone who is late? Why?

Stephen Chenney, University of WisconsinPlausible Simulation What is Simulation? Simulation for graphics supports an experience, a story, a feeling … –It does NOT answer “What if?” questions A round ball bouncing on a flat table: Science says:Experience says:

Stephen Chenney, University of WisconsinPlausible Simulation Plausible Simulation (Barzel, Hughes, Wood 96) Many renditions of a single event may appear “plausible” –Reality is a messy thing we can’t hope to accurately model –People are poor observers and can be easily fooled Go for the right experience –But NOT the right “physics”

Stephen Chenney, University of WisconsinPlausible Simulation Physics is Messy Simulation models typically ignore messy parts of reality –Rough, dirty surfaces –Atmospheric effects –Collision response Imperfections lead to important effects Plausible simulation captures global effects of local imperfections

Stephen Chenney, University of WisconsinPlausible Simulation Viewers are Hopeless Film-makers have always known It is hard for a viewer to anticipate the correct outcome –Sometimes they have insufficient information –Viewers are often dead wrong (sound travels through a vacuum?) Plausible simulation produces reasonable, but not “correct” outcomes

Stephen Chenney, University of WisconsinPlausible Simulation Implications Realistic physics includes imperfections A given scenario might have many good outcomes We choose specific simulations

Stephen Chenney, University of WisconsinPlausible Simulation Choosing Favorites Efficiency: Choose a simulation that is cheap to compute Direction: Choose an answer that meets the director’s goals

Stephen Chenney, University of WisconsinPlausible Simulation Simulation Culling Large dynamic environments are costly Reduce cost by ignoring out-of-view motion Aim to retain plausibility

Stephen Chenney, University of WisconsinPlausible Simulation Stop Sign World (CAF2001) Medieval city –Can’t see far Car behavior: –Drive along streets –Queue behind other cars –Stop at stop signs –One car through intersection at a time –Random choices for where to turn

Stephen Chenney, University of WisconsinPlausible Simulation Plausibility? What determines plausibility? –Visible traffic densities –Measurable travel times –In view behavior What determines these things? –Knowledge of car locations –Accurate in-view simulation

Stephen Chenney, University of WisconsinPlausible Simulation Strategy Jump out-of-view cars from place to place Don’t simulate braking, turning, accelerating, wheels, … If we get the jumps right, we get the right results

Stephen Chenney, University of WisconsinPlausible Simulation Direct Comparisons Our jump-cars model generates different simulations –The timing of some jumps is not exact Direct comparison will thus find major differences –But one simulation is really no better than the other However, the statistics will be the same

Stephen Chenney, University of WisconsinPlausible Simulation Measuring Plausibility We wish to reason about many outcomes from a single phenomenon Probability and statistics are the tool Measure statistics from the reference solution Compare to the cheaper solution

Stephen Chenney, University of WisconsinPlausible Simulation City Plausibility

Stephen Chenney, University of WisconsinPlausible Simulation Faster too!

Stephen Chenney, University of WisconsinPlausible Simulation Proxy Simulations Replace an out of view simulation with one that produces a similar event stream, a proxy What are the events? –An author decides What does similar mean? –Statistically the same What is the proxy? –Discrete event models Proxy dynamics Dynamics

Stephen Chenney, University of WisconsinPlausible Simulation Path Planning (ACF2001) Path planning is a large part of game AI Biggest cost is avoiding other moving objects –Typically requires checking for local neighbors on every frame

Stephen Chenney, University of WisconsinPlausible Simulation Fast Path Planning Static obstacles can be pre-processed –Pre-process: Shortest path b/w every pair of obstacle vertices; space broken into regions that see the same obstacle vertices –At run time: Find shortest path between vertex viz from start and one viz from end Dynamic objects handled at run time –If blocked, delay and wait for one to move –If nobody moves, re-plan –If objects are temporarily static, plan around them wait

Stephen Chenney, University of WisconsinPlausible Simulation The Path Planning Proxy The static component is fast enough – roughly constant time per command Events are arrival at intermediate nodes Problem: Time between waypoints depends on everyone else Time? dt?

Stephen Chenney, University of WisconsinPlausible Simulation Event Timing Avoiding other moving objects can only delay your journey –Each “collision” adds something to your travel time Same for re-planning around temporarily static objects Model this delay as a random variable –Explicitly ensure same statistics

Stephen Chenney, University of WisconsinPlausible Simulation Runtime Proxy Spatial subdivision on the world Test for overlaps in objects’ paths For each overlap, sample a delay and add it to the travel time to the next waypoint 2 delays 1 delay

Stephen Chenney, University of WisconsinPlausible Simulation Performance Increase the possible number of real-time objects by 100x But, some changes in behavior: –Completely blocked paths are not detected –Not all statistics are same

Stephen Chenney, University of WisconsinPlausible Simulation Other Work on Culling Techniques for culling objects that don’t move far: –CF97, CIF99 Techniques for simulation Level-Of-Detail: –Hopping robots (CH97), some look at stats to verify plausibility –Graceful degradation of collision response (DO2000) with subsequent user studies –Particle systems (OFL2001), no look at plausibility

Stephen Chenney, University of WisconsinPlausible Simulation Culling Conclusions Verify plausibility by looking at statistics Or explicitly use statistics to do out- of-view Massive speedups if we replace accurate with plausible simulation

Stephen Chenney, University of WisconsinPlausible Simulation Choosing Favorites Efficiency: Choose a simulation that is cheap to compute Direction: Choose an answer that meets the director’s goals

Stephen Chenney, University of WisconsinPlausible Simulation Directing Animations Plausibility is great for control Lots of options – choose the one that gives the desired outcome Two domains: –Collision intensive rigid-body systems –Group behaviors

Stephen Chenney, University of WisconsinPlausible Simulation Incorporating Plausibility Add sources of randomness to a simulation model –Intended to capture unknowns in the environment –Or inserted specifically for control, relying on poor perception The result is a probability distribution over simulations

Stephen Chenney, University of WisconsinPlausible Simulation Animation Distributions Model the uncertainty in the world. E.g. table with independent Gaussian normals. θ0θ0 θ1θ1  

Stephen Chenney, University of WisconsinPlausible Simulation Directing Choosing values for each random variable gives us an animation –Plausible choices (high probability) give plausible animations To also meet constraints, choose values that also give the desired outcome –Ideally, sample from p world (A|constraints) –Many possible choices

Stephen Chenney, University of WisconsinPlausible Simulation Constrained Sampling Restrict ourselves to choices for normals that meet constraints Problem: Which normals meet the constraints? θ0θ0 θ1θ1 

Stephen Chenney, University of WisconsinPlausible Simulation Sampling With Constraints Cannot, in general, sample directly –No direct method to satisfy the constraints Construct a new distribution –Animation satisfies constraints  high probability –Probability encodes the quality of a world and an outcome –In other words, only things that do what we want are plausible

Stephen Chenney, University of WisconsinPlausible Simulation New Ball Distribution θ0θ0 θ1θ1  d

Stephen Chenney, University of WisconsinPlausible Simulation Markov chain Monte Carlo (MCMC) Generates samples from complex distributions, like p(A) –Originated in statistical physics –Metropolis rendering - Veach 97 –Constrained terrain - Szeliski & Terzopoulos 89 Chain of samples localizes high- probability regions (good animations)

Stephen Chenney, University of WisconsinPlausible Simulation MCMC Algorithm

Stephen Chenney, University of WisconsinPlausible Simulation Properties of MCMC Generates a sequence of animations distributed according to p(A) –Certain technical conditions (ergodicity) must be met If p(A) encodes plausibility, we will see plausible animations

Stephen Chenney, University of WisconsinPlausible Simulation Proposal Strategies Current  Candidate animation Aims: –Rapid exploration of state space –High probability of acceptance –E.g. Change some normals Exploit domain specific knowledge

Stephen Chenney, University of WisconsinPlausible Simulation Dice Dice are so hard to control that we use them as random number generators Bspline table Slightly random initial conditions Control final position and orientation

Stephen Chenney, University of WisconsinPlausible Simulation Spelling Balls Multi-body interactions Randomly perturbed boxes Balls from random positions

Stephen Chenney, University of WisconsinPlausible Simulation Bowling Random initial ball location and speed –Different styles arise in samples Perturbed pin locations Won’t do “impossible” things

Stephen Chenney, University of WisconsinPlausible Simulation Rigid Body Conclusions Plausibility can be ensured through the choice of algorithm –MCMC guarantees that the results come from the correct distribution –The distribution is constructed to encode plausibility Best when there are likely to be lots of solutions isolated in state-space Possible to include domain specific knowledge, if available

Stephen Chenney, University of WisconsinPlausible Simulation Constrained Flocks Problem: Make a simulated flock meet hard constraints –Randomness in agents’ motion Strategy: –Initial guess ensures constraints are satisfied –Iterative phase makes the result plausible t=0 t=5

Stephen Chenney, University of WisconsinPlausible Simulation Measuring Plausibility Extract random components implied by the motion Look at the probability of seeing such random vectors Align + Cohere + Collision + Separate Observed  = Random

Stephen Chenney, University of WisconsinPlausible Simulation Flocking Conclusions Sometimes easier to enforce constraints then fix plausibility But need ways to measure plausibility of complex behaviors –Statistics give us the tools Needed: Better ways to compare distributions; exploration of which statistics are important

Stephen Chenney, University of WisconsinPlausible Simulation Other Work Popović: Alternate solution methods for constrained collisions –Interactive speeds, but more restricted domain (lower energy, fewer bodies) O’Sullivan et.al.: Perceptual measurements of what’s plausible –Talk in SIGGRAPH 2003

Stephen Chenney, University of WisconsinPlausible Simulation Summary Plausibility offers efficiency and control 4 ways to measure/verify plausibility –Verify by measuring statistics –Ensure by building correct stats into model –Retain by sampling according to probably outcomes –Measure by comparing statistics

Stephen Chenney, University of WisconsinPlausible Simulation It should be possible… Merging efficiency and control –Exploit culling for control – make the car run the red light in front of the driver –Real-time adaptation of game difficulty User interfaces –Saying what you want is hard –Presenting and categorizing classes of solutions is difficult (Marks et al 96)

Stephen Chenney, University of WisconsinPlausible Simulation Acknowledgements Funded by ONR MURI N and NSF CCR Thanks to D.A. Forsyth, Okan Arikan, Matt Anderson, Eric McDaniel and Andrew Selle

Stephen Chenney, University of WisconsinPlausible Simulation References ACF2001: Okan Arikan and Stephen Chenney and D. A. Forsyth, "Efficient Multi- Agent Path Planning", Eurographics Workshop on Animation and Simulation, pp , 2001 CAF2001: Stephen Chenney and Okan Arikan and D.A.Forsyth, "Proxy Simulations For Efficient Dynamics", Proceedings of Eurographics, Short Presentations, 2001 CF97: Stephen Chenney and David Forsyth, "View-Dependent Culling of Dynamic Systems in Virtual Environments", Symposium on Interactive 3D Graphics, pp55-58, 1997 CIF99: Stephen Chenney and Jeffrey Ichnowski and David Forsyth, "Dynamics Modeling and Culling", IEEE CGA, 19(2), pp 79-87, 1999 CF2000: Stephen Chenney and D.A. Forsyth, "Sampling Plausible Solutions to Multi- body Constraint Problems", SIGGRAPH, pp , 2000 CO96: Deborah A. Carlson and Jessica K. Hodgins, ”Simulation Levels of Detail for Real-time Animation", Graphics Interface '97, pp 1-8, 1997 DO2000: J. Dingliana and C. O’Sullivan, “Graceful Degradation of Collision Handling in Physically Based Animation”, Computer Graphics Forum. Vol 19(2000), Number 3, pp OFL2001: David A. O'Brien, Susan Fisher and Ming Lin, "Simulation Level of Detail for Automatic Simplification of Particle System Dynamics", Computer Animation, 2001

Stephen Chenney, University of WisconsinPlausible Simulation Traffic Efficiency

Stephen Chenney, University of WisconsinPlausible Simulation Event Timing

Stephen Chenney, University of WisconsinPlausible Simulation Planning Dynamics Time

Stephen Chenney, University of WisconsinPlausible Simulation Planning Efficiency Efficiency: Ratio of in-view work to total work