Month: July 2011

A Level-set Method for Skinning Animated Particle Data

Haimasree Bhattacharya, Yue Gao, Adam W. Bargteil

In this paper, we present a straightforward, easy to implement method for particle skinning—generating surfaces from animated particle data. We cast the problem in terms of constrained optimization and solve the optimization using a level-set approach. The optimization seeks to minimize the thin-plate energy of the surface, while staying between surfaces defined by the union of spheres centered at the particles. Our approach skins each frame independently while preserving the temporal coherence of the underlying particle animation. Thus, it is well-suited for environments where particle skinning is treated as a post-process, with each frame generated in parallel. We demonstrate our method on data generated by a variety of fluid simulation techniques and simple particle systems.

A Level-set Method for Skinning Animated Particle Data

Eulerian Solid Simulation with Contact

David I. W. Levin, Joshua Litven, Garrett L. Jones, Shinjiro Sueda, Dinesh K. Pai

Simulating viscoelastic solids undergoing large, nonlinear deformations in close contact is challenging. In addition to inter-object contact, methods relying on Lagrangian discretizations must handle degenerate cases by explicitly remeshing or resampling the object. Eulerian methods, which discretize space itself, provide an interesting alternative due to the fixed nature of the discretization. In this paper we present a new Eulerian method for viscoelastic materials that features a collision detection and resolution scheme which does not require explicit surface tracking to achieve accurate collision response. Time-stepping with contact is performed by the efficient solution of large sparse quadratic programs; this avoids constraint sticking and other difficulties. Simulation and collision processing can share the same uniform grid, making the algorithm easy to parallelize. We demonstrate an implementation of all the steps of the algorithm on the GPU. The method is effective for simulation of complicated contact scenarios involving multiple highly deformable objects, and can directly simulate volumetric models obtained from medical imaging techniques such as CT and MRI.

Eulerian Solid Simulation with Contact

Sensitive Couture for Interactive Garment Editing and Modeling

Nobuyuki Umetani, Danny M. Kaufman, Takeo Igarashi, Eitan Grinspun

We present a novel interactive tool for garment design that enables, for the first time, interactive bidirectional editing between 2D patterns and 3D high-fidelity simulated draped forms. This provides a continuous, interactive, and natural design modality in which 2D and 3D representations are simultaneously visible and seamlessly maintain correspondence. Artists can now interactively edit 2D pattern designs and immediately obtain stable accurate feedback online, thus enabling rapid prototyping and an intuitive understanding of complex drape form.

Sensitive Couture for Interactive Garment Editing and Modeling

Physics-inspired Upsampling for Cloth Simulation in Games

Ladislav Kavan, Dan Gerszewski, Peter-Pike Sloan, Adam W. Bargteil

We propose a method for learning linear upsampling operators for physically-based cloth simulation, allowing us to enrich coarse meshes with mid-scale details in minimal time and memory budgets, as required in computer games. In contrast to classical subdivision schemes, our operators adapt to a specific context (e.g. a flag flapping in the wind or a skirt worn by a character), which allows them to achieve higher detail. Our method starts by pre-computing a pair of coarse and fine training simulations aligned with tracking constraints using harmonic test functions. Next, we train the upsampling operators with a new regularization method that enables us to learn mid-scale details without overfitting. We demonstrate generalizability to unseen conditions such as different wind velocities or novel character motions. Finally, we discuss how to re-introduce high frequency details not explainable by the coarse mesh alone using oscillatory modes.

Physics-inspired Upsampling for Cloth Simulation in Games

Element-Wise Mixed Implicit-Explicit Integration for Stable Dynamic Simulation of Deformable Objects

Basil Fierz, Jonas Spillman, Matthias Harders

In order to evolve a deformable object in time, the underlying equations of motion have to be numerically integrated. This is commonly done by employing either an explicit or an implicit integration scheme. While explicit methods are only stable for small time steps, implicit methods are unconditionally stable. In this paper, we present a novel methodology to combine explicit and implicit linear integration approaches, based on element-wise stability considerations. First, we detect the ill-shaped simulation elements which hinder the stable explicit integration of the element nodes as a pre-computation step. These nodes are then simulated implicitly, while the remaining parts of the mesh are explicitly integrated. As a consequence, larger integration time steps than in purely explicit methods are possible, while the computation time per step is smaller than in purely implicit integration. During modifications such as cutting or fracturing, only newly created or modified elements need to be reevaluated, thus making the technique usable in real-time simulations. In addition, our method reduces problems due to numerical dissipation.

Element-Wise Mixed Implicit-Explicit Integration for Stable Dynamic Simulation of Deformable Objects

A Particle-based Method for Preserving Fluid Sheets

Ryoichi Ando, Reiji Tsuruno

We present a new particle-based method that explicitly preserves thin fluid sheets for animating liquids. Our primary contribution is a meshless particle-based framework that splits at thin points and collapses at dense points to prevent the breakup of liquid. In contrast to existing surface tracking methods, the proposed framework does not suffer from numerical diffusion or tangles, and robustly handles topology changes by the meshless representation. As the underlying fluid model, we use Fluid-Implicit-Particle (FLIP) with weak spring forces to generate smooth particle-based liquid animation that maintains an even spatial particle distribution in the presence of eddying or inertial motions. The thin features are detected by examining stretches of distributions of neighboring particles by performing Principle Component Analysis (PCA), which is used to reconstruct thin surfaces with anisotropic kernels. Our algorithm is intuitively implemented, easy to parallelize and capable of producing visually complex thin liquid animations.

A Particle-based Method for Preserving Fluid Sheets

SPH Granular Flow with Friction and Cohesion

Ivan Alduan, Miguel Otaduy

Combining mechanical properties of solids and fluids, granular materials pose important challenges for the design of algorithms for realistic animation. In this paper, we present a simulation algorithm based on smoothed particle hydrodynamics (SPH) that succeeds in modeling important features of the behavior of granular materials. These features are unilateral incompressibility, friction and cohesion. We extend an existing unilateral incompressibility formulation to be added at almost no effort to an existing SPH-based algorithm for fluids. The main advantages of this extension are the ease of implementation, the lack of grid artifacts, and the simple two-way coupling with other objects. Our friction and cohesion models can also be incorporated in a seamless manner in the overall SPH simulation algorithm.

SPH Granular Flow with Friction and Cohesion

Physics-based Character Skinning using Multi-Domain Subspace Deformations

Theodore Kim, Doug L. James

We propose a domain-decomposition method to simulate articulated deformable characters entirely within a subspace framework. The method supports quasistatic and dynamic deformations, nonlinear kinematics and materials, and can achieve interactive time-stepping rates. To avoid artificial rigidity, or “locking,” associated with coupling low-rank domain models together with hard constraints, we employ penalty-based coupling forces. The multi-domain subspace integrator can simulate deformations efficiently, and exploits efficient subspace-only evaluation of constraint forces between rotated domains using the so-called Fast Sandwich Transform (FST). Examples are presented for articulated characters with quasistatic and dynamic deformations, and interactive performance with hundreds of fully coupled modes. Using our method, we have observed speedups of between three and four orders of magnitude over full-rank, unreduced simulations.

Physics-based Character Skinning using Multi-Domain Subspace Deformations

Mass and Momentum Conservation for Fluid Simulation

Michael Lentine, Mridul Aanjaneya, Ronald Fedkiw

Momentum conservation has long been used as a design principle for solid simulation (e.g. collisions between rigid bodies, mass-spring elastic and damping forces, etc.), yet it has not been widely used for fluid simulation. In fact, semi-Lagrangian advection does not conserve momentum, but is still regularly used as a bread and butter method for fluid simulation. In this paper, we propose a modification to the semi-Lagrangian method in order to make it fully conserve momentum. While methods of this type have been proposed earlier in the computational physics literature, they are not necessarily appropriate for coarse grids, large time steps or inviscid flows, all of which are common in graphics applications. In addition, we show that the commonly used vorticity confinement turbulence model can be modified to exactly conserve momentum as well. We provide a number of examples that illustrate the benefits of this new approach, both in conserving fluid momentum and passively advected scalars such as smoke density. In particular, we show that our new method is amenable to efficient smoke simulation with one time step per frame, whereas the traditional non-conservative semi-Lagrangian method experiences serious artifacts when run with these large time steps, especially when object interaction is considered.

Mass and Momentum Conservation for Fluid Simulation

Mathematical Foundation of the Optimization-Based Fluid Animation Method

Kenny Erleben, Marek Misztal, J. Andreas Baerentzen

We present the mathematical foundation of a fluid animation method for unstructured meshes. Key contributions not previously treated are the extension to include diffusion forces and higher order terms of non-linear force approximations. In our discretization we apply a fractional step method to be able to handle advection in a numerically simple Lagrangian approach. Following this a finite element method is used for the remaining terms of the fractional step method. The key to deriving a discretization for the diffusion forces lies in restating the momentum equations in terms of a Newtonian stress tensor. Rather than applying a straightforward temporal finite difference method followed by a projection method to enforce incompressibility as done in the stable fluids method, the last step of the fractional step method is rewritten as an optimization problem to make it easy to incorporate non-linear force terms such as surface tension.

Mathematical Foundation of the Optimization-Based Fluid Animation Method