January 30th & 31st
[Graphics] [Physics] [Speaker Bios]
This information is subject to change.
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PHYSICS SEMINAR SCHEDULE January 30th & 31st [Graphics] [Physics] [Speaker Bios] This information is subject to change. |
Simulating flowing, squishy, misty, windy, bouncy, stretchy, breakable, decidedly-non-rigid stuff. |
In the ongoing race to get the coolest, most interactive, and most immersive technologies into high end games, continuum dynamics stands as the next physics hurdle for top developers to understand and overcome. While it is going to take time before an entire game world is simulated using continuum equations, the technology is starting to show up in game special effects, including water simulations, moving fog and smoke, cloth, soft and breakable objects, and even simulated fire and explosions. Understanding the underlying continuum equations, and how to numerically simulate them in a fast and stable way, is crucial to getting these special effects to be far more compelling than the traditional lame hacks. This intuitive mathematical understanding is also critically important as we move forward as an industry and continuum simulations become more central to gameplay. This seminar will study continuum dynamics in depth, including the dynamics of fluids (gasses and liquids) and solids (deformable and breakable objects). We will focus on both the core mathematics of the field and on implementing simulations for specific special effects based on the continuum dynamics equations. Extended question and answer periods and peer discussion sessions ensure attendees can hone in on specific issues related to their projects. |
| Prerequisites: Physics seminar attendees are expected to have a good understanding of rigid body mechanics, single- and multi-variable/vector calculus, ordinary differential equations, and taking partial derivatives and Jacobians (but not necessarily partial differential equations, which we'll cover). Familiarity with linear algebra and numerical linear algebra is important. |
| Mathematical Foundations of Continuum Dynamics How do we write the equations for a specific continuum dynamical system, whether it's a fluid, a solid, or a general equation describing a time- and space-varying effect? After writing the equations, how do we break them down and solve them on a computer? What are the general and specific characteristics and tradeoffs of different formulations, discretizations, and integration techniques? |
| PDEs for Modeling Continuum Effects January 30, 2001 9:15 AM to 10:00 AM (45 minutes) Chris Hecker Partial Differential Equations form the basis for modeling almost all physical phenomena in continuum dynamics. This short introduction lecture positions PDEs as tools for creating mathematical models for physical effects. We briefly discuss differential equations in general, the transition from ODEs to PDEs, and we introduce the symbols and terminology for the seminar. This lecture serves as a roadmap for the mathematics of PDEs and provides context for the PDEs discussed in more depth in later sessions. |
| Numerical Solution of PDEs: Discretization, Meshing, & Simulation January 30, 2001 10:00 AM to 10:45 AM (45 minutes) Chris Hecker Once we have a set of PDEs describing the physical phenomenon we're trying to model, we have to solve the equations in real time to create animation. Unfortunately, almost all of the PDEs we'd like to solve do not have analytical solutions, so we must numerical integrate them. To numerically integrate a PDE, we must discretize the continuous equation so that a computer can operate upon it. We discuss examples of how to turn an infinite dimensional PDE into a finite dimension discretized equation that we can solve numerically. |
| PDE Integration Techniques, Part 1: Basics and Iterative Solvers January 30, 2001 11:00 AM to 12:00 PM (1 hour) Van Emden Henson Discretized PDEs form large sparse linear systems that need to be solved numerically. This session covers the basics of large scale numerical linear system solving. The subtleties and different forms of iterative solvers are covered, and the theoretical and practical underpinnings of the techniques are discussed. Runtime performance and stability are always at the forefront of discussion. |
| PDE Integration Techniques, Part 2: Multigrid January 30, 2001 1:00 PM to 2:00 PM (1 hour) Van Emden Henson There's a relatively new large-scale linear system solution technique called "multigrid" that's been hugely successful in recent years, and it's becoming one of the most imporant numerical techniques for solving PDEs. This lecture builds on Part 1 and extends that material to multigrid and the subtleties of implementing it efficiently. |
| Fluids The study of fluids, which includes both liquids and gasses, is rich in complexity, subtlety, and luckily, in opportunities for simplification. Truly understanding the structure of the equations governing fluid behavior and ways of simulating those equations on a computer allows us to make simplifications with known tradeoffs, as opposed to hacks that blow up in unforseen ways. Multiple fluids interacting, like water and air with a free boundary/interface between them, present another set of problems and open issues beyond simply simulating an individual fluid in a closed volume. |
| Equations and Variables of Fluid Dynamics January 30, 2001 2:00 PM to 2:30 PM (30 minutes) Chris Hecker This short session introduces the main equations, concepts, and variables in fluid dynamics. It gets everyone on a level playing field for communicating during the following fluids lectures. |
| Implementing a Liquid Simulator January 30, 2001 2:30 PM to 3:30 PM (1 hour) Nick Foster This lecture introduces liquid numerical simulation by discussing the implementation of a complete simulator. Foster will cover the dynamics equations, their discretization, and the subtleties of implementing the solver in code. Lessons learned from implementing multiple liquid simulators will be covered in depth. |
| Fluid Interface Tracking Methods January 30, 2001 3:45 PM to 4:45 PM (1 hour) Ron Fedkiw Liquids are dynamically interesting in and of themselves, but they're even more interesting when the liquid and the open air (and possibly other types of liquids) can interact, intermix, splash, and flow around. This simulation of the free boundary--or interface--is a complex and subtle problem in addition to the problems of simulating the fluids in the first place. A number of competing interface tracking and simulating techniques all have advantages and disadvantages, and there's no clear winner at this point. This lecture will discuss some of the techniques and their tradeoffs. |
| Liquid and Gas Integration Schemes: Stability and Performance January 30, 2001 4:45 PM to 5:45 PM (1 hour) Jos Stam The same terms in the fluids equations that make liquids and gasses so dynamically interesting are the ones that cause lots of troubles for numerical integrators. Stiffness, nonlinearity, and slow convergence of iterative methods are all commonly encountered problems. This lecture discusses why these problems show up, and covers practical techniques and different approaches for dealing with them in your games. |
| Fluid Wrapup, Survey of Simplifications for Special Effects, Peer Discussion January 30, 2001 6:00 PM to 7:00 PM (1 hour) Ron Fedkiw, Chris Hecker, Everybody Batting cleanup for the day, Fedkiw will fill in some of the inevitable cracks in the coverage of the day's fluid discussions. Compressibility and its importance to fluid behavior will be covered informally. We'll then take the fluid equations apart, surveying common simplifications that can greatly reduce the computational overhead of a simulation in exchange for reducing its expressiveness. This survey blends into a peer discussion on fluids and their applicability to game special effects today. |
| Solids High end games are finally simulating ideal rigid bodies with some degree of accuracy and consistency. Now end-users and designers want to bend those bodies, blow them up, drape cloth over them, or break them under loads to take the player's experience to the next level. |
| Solid Body PDEs: Formulation & Discretization January 31, 2001 9:15 AM to 10:30 AM (1.25 hours) James O'Brien This lecture will present the PDEs of solid body continuum dynamics, including how the equations are derived, and how solids differ from fluids mathematically. There is a very rich set of discretizations available for solid PDEs, and we'll discuss a number of them and their tradeoffs. Finally, simplifications to the complete solid PDEs will be presented and discussed. |
| Subtleties in Cloth Simulation and Integration January 31, 2001 10:45 AM to 12:00 PM (1.25 hours) David Baraff Cloth simulation is one of the first continuum effects game developers have tried to implement in production code. However, robust cloth that exhibits the nonlinear, anisotropic, and stiff properties of real cloth requires far more than just a mass-spring system and an implicit integrator. This lecture will discuss some of the subtleties of simulating cloth robustly, and will focus on integration aspects of the problem. |
| Fast Simulation of Elastostatic Deformable Models January 31, 2001 1:30 PM to 2:30 PM (1 hour) Doug James For real time physics simulation in games, it often makes sense to do as much work ahead of time as possible. When simulating relatively stiff deformable objects, linear elastostatic models have the nice property that most of their behavior can be described by precomputed deformations, which in turn helps avoid redundant runtime computation. In this lecture, I will discuss these models and their fast solution methods in detail, and so show how precomputed deformations combined with the principle of linear superposition can produce substantial runtime speed-ups. |
| Deformable Body Techniques for Cartoon Simulation January 31, 2001 2:30 PM to 3:30 PM (1 hour) David Wu Cartoon rendering has gotten a lot of attention lately, but cartoon simulation has lagged behind. This talk describes a deformable body model that serves as the foundation for a game situated in a cartoon universe. The scope of this model is the simulation of characters, animals, vehicles and various other animated objects in a real time interactive setting. The continuum dynamics of Cartoon characters are approximated by a discrete representation of model space consisting of piecewise linear tetrahedral elements. Character joints, contacts, collision and other constraints are modeled as potentials. The resulting system of (stiff) ODE's are discretized in time via a fixed step-size implicit Euler scheme. |
| Hybrids Systems that are both fluids and solids, or neither. |
| Advanced Techniques for Mass-Spring Simulations
Survey and Discussion January 31, 2001 3:45 PM to 4:00 PM (15 minutes) Chris Hecker, Everybody Mass-Spring simulations, especially as naively implemented by some games, are much maligned as a hack. Instability in the face of stiffness is a common problem, as is lack of volume preservation and nonuniform handling of self-intersections and non-particle collisions and contacts. There has been work lately on making mass-spring simulations better behaved and more accurate. This session covers 5 recent papers on advanced mass-spring techniques, and we'll discuss their advantages and disadvantages. |
| Fracture, Tearing, Collision, Contact Manifolds, and Mixing Simulations Discussion January 31, 2001 4:00 PM to 4:45 PM (45 minutes) James O'Brien, David Baraff, Everybody Objects are simply more interesting when you can break them. But what does "breaking" mean, mathematically? This session discusses the mathematics of breaking and tearing, and surveys the current state of the art in destroying nicely constructed continuum solids. And, as if simply simulating solid continuum dynamics wasn't difficult enough, we have to figure out how to make flexible and breakable bodies interact with our game worlds. There are many open problems in this area, especially when you add in the requirement that the solids interact with the fluids. We'll cover the common approaches and simplifications, like uncoupling the differing simulations, and discuss their problems. |
| Smoothed Particles and Adaptive Simulation January 31, 2001 4:45 PM to 5:45 PM (1 hour) Mathieu Desbrun Is lava a fluid or a solid? These hybrid systems are interesting, and have similarities to both solids and fluids. This session covers two models that use adaptive techniques for simulating goopy lava-like materials and soft bodies. |
| Massive Scale Particle Simulations January 31, 2001 6:00 PM to 7:00 PM (1 hour) Rob Thacker Most game developers implemented a particle system simulator as their first physics project. And, although rendering particle systems is quite advanced and has gotten a lot of attention, simulating particle systems has not made the same leaps and our simulators are still very naive. It's time to push the state of the art forward in game particle simulators. Although it may seem like celestial mechanics doesn't have much in common with game development, researchers in that field have been simulating incredibly huge particle systems for years, and have developed many advanced algorithms for particle management, force aggregation, and stable integration. We'll hear a survey from that field and discuss applying the techniques to game simulators. |
| Contact info@techsem.com or call us at 310/ 375-6602. |