Data-driven simulation demands good training data drawn from a vast space of possible simulations. While fully sampling these large spaces is infeasible, we observe that in practical applications, such as gameplay, users explore only a vanishingly small subset of the dynamical state space. In this paper we present a sampling approach that takes advantage of this observation by concentrating precomputation around the states that users are most likely to encounter. We demonstrate our technique in a prototype self-refining game whose dynamics improve with play, ultimately providing realistically rendered, rich fluid dynamics in real time on a mobile device. Our results show that our analytics-driven training approach yields lower model error and fewer visual artifacts than a heuristic training strategy.

The central argument against data-driven methods in computer graphics rests on the curse of dimensionality: it is intractable to precompute "everything" about a complex space. In this paper, we challenge that assumption by using several thousand CPU-hours to perform a massive exploration of the space of secondary clothing effects on a character animated through a large motion graph. Our system continually explores the phase space of cloth dynamics, incrementally constructing a secondary cloth motion graph that captures the dynamics of the system. We find that it is possible to sample the dynamical space to a low visual error tolerance and that secondary motion graphs containing tens of gigabytes of raw mesh data can be compressed down to only tens of megabytes. These results allow us to capture the effect of high-resolution, off-line cloth simulation for a rich space of character motion and deliver it efficiently as part of an interactive application.

We propose a new method for the large-scale collection and analysis of drawings by using a mobile game specifically designed to collect such data. Analyzing this crowdsourced drawing database, we build a spatially varying model of artistic consensus at the stroke level. We then present a surprisingly simple stroke-correction method which uses our artistic consensus model to improve strokes in real-time. Importantly, our auto-corrections run interactively and appear nearly invisible to the user while seamlessly preserving artistic intent. Closing the loop, the game itself serves as a platform for large-scale evaluation of the effectiveness of our stroke correction algorithm.

This paper extends Galerkin projection to a large class of non-polynomial functions typically encountered in graphics. We demonstrate the broad applicability of our approach by applying it to two strikingly different problems: fluid simulation and radiosity rendering, both using deforming meshes. Standard Galerkin projection cannot efficiently approximate these phenomena. Our approach, by contrast, enables the compact representation and approximation of these complex non-polynomial systems, including quotients and roots of polynomials. We rely on representing each function to be model-reduced as a composition of tensor products, matrix inversions, and matrix roots. Once a function has been represented in this form, it can be easily model-reduced, and its reduced form can be evaluated with time and memory costs dependent only on the dimension of the reduced space.

Incorporating the individual and collective problem solving skills of non-experts into the scientific discovery process could potentially accelerate the advancement of science. This paper discusses the design process used for Foldit, a multiplayer online biochemistry game that presents players with computationally difficult protein folding problems in the form of puzzles, allowing ordinary players to gain expertise and help solve these problems. The principle challenge of designing such scientific discovery games is harnessing the enormous collective problem-solving potential of the game playing population, who have not been previously introduced to the specific problem, or, often, the entire scientific discipline. To address this challenge, we took an iterative approach to designing the game, incorporating feedback from players and biochemical experts alike. Feedback was gathered both before and after releasing the game, to create the rules, interactions, and visualizations in Foldit that maximize contributions from game players. We present several examples of how this approach guided the game's design, and allowed us to improve both the quality of the gameplay and the application of player problem-solving.

We present a technique for learning clothing models that enables the simultaneous animation of thousands of detailed garments in real-time. This surprisingly simple conditional model learns and preserves the key dynamic properties of a cloth motion along with folding details. Our approach requires no a priori physical model, but rather treats training data as a "black box." We show that the models learned with our method are stable over large time-steps and can approximately resolve cloth-body collisions. We also show that within a class of methods, no simpler model covers the full range of cloth dynamics captured by ours. Our method bridges the current gap between skinning and physical simulation, combining benefits of speed from the former with dynamic effects from the latter. We demonstrate our approach on a variety of apparel worn by male and female human characters performing a varied set of motions typically used in video games ( e.g. , walking, running, jumping, etc. ).

We present a new approach to fluid simulation that balances the speed of model reduction with the flexibility of grid-based methods. We construct a set of composable reduced models, or tiles , which capture spatially localized fluid behavior. We then precompute coupling terms so that these models can be rearranged at runtime. To enforce consistency between tiles, we introduce constraint reduction . This technique modifies a reduced model so that a given set of linear constraints can be fulfilled. Because dynamics and constraints can be solved entirely in the reduced space, our method is extremely fast and scales to large domains.

We present a new approach to realtime character animation with interactive control. Given a corpus of motion capture data and a desired task, we automatically compute near-optimal controllers using a low-dimensional basis representation. We show that these controllers produce motion that fluidly responds to several dimensions of user control and environmental constraints in realtime. Our results indicate that very few basis functions are required to create high-fidelity character controllers which permit complex user navigation and obstacle-avoidance tasks.

We present a real-time crowd model based on continuum dynamics. In our model, a dynamic potential field simultaneously integrates global navigation with moving obstacles such as other people, efficiently solving for the motion of large crowds without the need for explicit collision avoidance. Simulations created with our system run at interactive rates, demonstrate smooth flow under a variety of conditions, and naturally exhibit emergent phenomena that have been observed in real crowds.

We present a new model reduction approach to fluid simulation, enabling large, real-time, detailed flows with continuous user interaction. Our reduced model can also handle moving obstacles immersed in the flow. We create separate models for the velocity field and for each moving boundary, and show that the coupling forces may be reduced as well. Our results indicate that surprisingly few basis functions are needed to resolve small but visually important features such as spinning vortices.

We describe a novel method for controlling physics-based fluid simulations through gradient-based nonlinear optimization. Using a technique known as the adjoint method , derivatives can be computed efficiently, even for large 3D simulations with millions of control parameters. In addition, we introduce the first method for the full control of free-surface liquids. We show how to compute adjoint derivatives through each step of the simulation, including the fast marching algorithm, and describe a new set of control parameters specifically designed for liquids.

We describe a method for controlling smoke simulations through user-specified keyframes. To achieve the desired behavior, a continuous quasi-Newton optimization solves for appropriate "wind" forces to be applied to the underlying velocity field throughout the simulation. The cornerstone of our approach is a method to efficiently compute exact derivatives through the steps of a fluid simulation. We formulate an objective function corresponding to how well a simulation matches the user's keyframes, and use the derivatives to solve for force parameters that minimize this function. For animations with several keyframes, we present a novel multiple-shooting approach. By splitting large problems into smaller overlapping subproblems, we greatly speed up the optimization process while avoiding certain local minima.