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Visual quality, low computational cost, and numerical stability are foremost goals in computer animation. An important ingredient in achieving these goals is the conservation of fundamental motion invariants. For example, rigid and deformable body simulation has benefited greatly from conservation of linear and angular momenta. In the case of fluids, however, none of the current techniques focuses on conserving invariants, and consequently, they often introduce a visually disturbing numerical diffusion of vorticity. Visually just as important is the resolution of complex simulation domains. Doing so with regular (even if adaptive) grid techniques can be computationally delicate. In this paper, we propose a novel technique for the simulation of fluid flows. It is designed to respect the defining differential properties, i.e., the conservation of circulation along arbitrary loops as they are transported by the flow. Consequently, our method offers several new and desirable properties: (1) arbitrary simplicial meshes (triangles in 2D, tetrahedra in 3D) can be used to define the fluid domain; (2) the computations are efficient due to discrete operators with small support; (3) the method is stable for arbitrarily large time steps; (4) it preserves discrete circulation avoiding numerical diffusion of vorticity; and (5) its implementation is straightforward.

Figure 1: Tracking enables artistic expression and physical simulation to work hand-in-hand, as demonstrated in our animation of a character’s unfortunate event. We begin (left to right) with the artist’s animation, automatically generate a set of Petrov-Galerkin test functions (visualized as colored patches), and then solve the constrained Lagrangian mechanics equations to flesh out wrinkles and folds. We combine the often opposing forces of artistic freedom and mathematical determinism to enrich a given animation or simulation of a surface with physically based detail. We present a process called tracking, which takes as input a rough animation or simulation and enhances it with physically simulated detail. Building on the foundation of constrained Lagrangian mechanics, we propose weak-form constraints for tracking the input motion. This method allows the artist to choose where to add details such as characteristic wrinkles and folds of various thin shell materials and dynamical effects of physical forces. We demonstrate multiple applications ranging from enhancing an artist’s animated character to guiding a simulated inanimate object.

Animation techniques for controlling passive simulation are commonly based on an optimization paradigm: the user provides goals a priori, and sophisticated numerical methods minimize a cost function that represents these goals. Unfortunately, for multibody systems with discontinuous contact events these optimization problems can be highly nontrivial to solve, and many-hour offline optimizations, unintuitive parameters, and convergence failures can frustrate end-users and limit usage. On the other hand, users are quite adaptable, and systems which provide interactive feedback via an intuitive interface can leverage the user’s own abilities to quickly produce interesting animations. However, the online computation necessary for interactivity limits scene complexity in practice. We introduce Many-Worlds Browsing, a method which circumvents these limits by exploiting the speed of multibody simulators to compute numerous example simulations in parallel (offline and online), and allow the user to browse and modify them interactively. We demonstrate intuitive interfaces through which the user can select among the examples and interactively adjust those parts of the scene that do not match his requirements. We show that using a combination of our techniques, unusual and interesting results can be generated for moderately sized scenes with under an hour of user time. Scalability is demonstrated by sampling much larger scenes using modest offline computations.

Control of physical simulation has become a popular topic in the field of computer graphics. Keyframe control has been applied to simulations of rigid bodies, smoke, liquid, flocks, and finite element-based elastic bodies. In this paper, we create a framework for controlling systems of interacting particles – paying special attention to simulations of cloth and flocking behavior. We introduce a novel integrator-swapping approximation in order to apply the adjoint method to linearized implicit schemes appropriate for cloth simulation. This allows the control of cloth while avoiding computationally infeasible derivative calculations. Meanwhile, flocking control using the adjoint method is significantly more efficient than currently-used methods for constraining group behaviors, allowing the controlled simulation of greater numbers of agents in fewer optimization iterations. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Physically based modeling; I.3.7 [Computer Graphics]: Animation; I.6.8 [Simulation and Modeling]: Animation;

In this article, we propose techniques for modeling and rendering of heterogeneous translucent materials that enable acquisition from measured samples, interactive editing of material attributes, and real-time rendering. The materials are assumed to be optically dense such that multiple scattering can be approximated by a diffusion process described by the diffusion equation. For modeling heterogeneous materials, we present the inverse diffusion algorithm for acquiring material properties from appearance measurements. This modeling algorithm incorporates a regularizer to handle the ill-conditioning of the inverse problem, an adjoint method to dramatically reduce the computational cost, and a hierarchical GPU implementation for further speedup. To render an object with known material properties, we present the polygrid diffusion algorithm, which solves the diffusion equation with a boundary condition defined by the given illumination environment. This rendering technique is based on representation of an object by a polygrid, a grid with regular connectivity and an irregular shape, which facilitates solution of the diffusion equation in arbitrary volumes. Because of the regular connectivity, our rendering algorithm can be implemented on the GPU for real-time performance. We demonstrate our techniques by capturing materials from physical samples and performing real-time rendering and editing with these materials.

original motion exemplar synthesized detail motion combined motion field original density field final density field Figure 1: Motion field texture synthesis. Given a low-resolution motion field and an input exemplar, we synthesize a high-resolution detailed motion field that resembles the exemplar while follows the local orientation of the low-resolution field. This synthesized detail motion field is then combined with the original low-res motion field to produce the final motion. Our method can produce non-physics-based artistic effects such as fluids with heart-shaped motions. A variety of animation effects such as herds and fluids contain detailed motion fields characterized by repetitive structures. Such detailed motion fields are often visually important, but tedious to specify manually or expensive to simulate computationally. Due to the repetitive nature, some of these motion fields (e.g. turbulence in fluids) could be synthesized by procedural texturing, but procedural texturing is known for its limited generality. We apply example-based texture synthesis for motion fields. Our

Physically based simulation of rigid body dynamics is commonly done by time-stepping systems forward in time. In this paper, we propose methods to allow time-stepping rigid body systems backward in time. Unfortunately, reverse-time integration of rigid bodies involving frictional contact is mathematically ill-posed, and can lack unique solutions. We instead propose time-reversed rigid body integrators that can sample possible solutions when unique ones do not exist. We also discuss challenges related to dissipation-related energy gain, sensitivity to initial conditions, stacking, constraints and articulation, rolling, sliding, skidding, bouncing, high angular velocities, rapid velocity growth from micro-collisions, and other problems encountered when going against the usual flow of time.

this dissertation is drawn from the two publications, "Melting and Flowing" [8] and "Rigid Fluid: Animating the Interplay Between Rigid Bodies and Fluid" [7]. I am extremely grateful to my coauthors, Greg Turk, Peter Mucha and Brooks Van Horn, without whose help those articles would not exist

Visual quality, low computational cost, and numerical stability are foremost goals in computer animation. An important ingredient in achieving these goals is the conservation of fundamental motion invariants. For example, rigid and deformable body simulation has benefited greatly from conservation of linear and angular momenta. In the case of fluids, however, none of the current techniques focuses on conserving invariants, and consequently they often introduce a visually disturbing numerical diffusion of vorticity. Visually just as important is the resolution of complex simulation domains. Doing so with regular (even if adaptive) grid techniques can be computationally delicate. In this thesis we describe a novel technique for the simulation of fluid flows. It is designed to respect the defining differential properties, i.e., the conservation of circulation along arbitrary loops as they are transported by the flow. Consequently, our method offers several new and desirable properties: (1) arbitrary simplicial meshes (triangles in 2D, tetrahedra in 3D) can be used to define the fluid domain; (2) the computations are efficient due to discrete operators with small support; (3) the method is stable for arbitrarily large time steps; (4) it preserves discrete circulation avoiding numerical diffusion of vorticity; and (5) its implementation is straightforward. iv