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

Procedural Fluid Modeling of Explosion Phenomena Based on Physical Properties

Genichi Kawada, Takashi Kanai

We propose a method to procedurally model the fluid flows of explosion phenomena by taking physical properties into account. Explosion flows are always quite difficult to control, because they easily disturb each other and change rapidly. With this method, the target flows are described by control paths, and the propagation flows are controlled by following these paths. We consider the physical properties, which are the propagations of the pressure generated by the ignition, the detonation state caused by the pressure and the fuel combustions. Velocity, density, temperature and pressure fields are generated procedurally, and the fluid flows are computed from these four fields based on grid-based fluid simulations. Using this method, we can achieve a fluid motion that closely resembles one generated solely through simulation. This method realizes the modeling of flows controlled frame by frame and follows the flow’s physical properties.

Procedural Fluid Modeling of Explosion Phenomena Based on Physical Properties

A Simple Finite Volume Method for Adaptive Viscous Liquids

Christopher Batty, Ben Houston

We present the first spatially adaptive Eulerian fluid animation method to support challenging viscous liquid effects such as folding, coiling, and variable viscosity. We propose a tetrahedral node-based embedded finite volume method for fluid viscosity, adapted from popular techniques for Lagrangian deformable objects. Applied in an Eulerian fashion with implicit integration, this scheme stably and efficiently supports high viscosity fluids while yielding symmetric positive definite linear systems. To integrate this scheme into standard tetrahedral mesh-based fluid simulators, which store normal velocities on faces rather than velocity vectors at nodes, we offer two methods to reconcile these representations. The first incorporates a mapping between different degrees of freedom into the viscosity solve itself. The second uses a FLIP-like approach to transfer velocity data between nodes and faces before and after the linear solve. The former offers tighter coupling by enabling the linear solver to act directly on the face velocities of the staggered mesh, while the latter provides a sparser linear system and a simpler implementation. We demonstrate the effectiveness of our approach with animations of spatially varying viscosity, realistic rotational motion, and viscous liquid buckling and coiling.

A Simple Finite Volume Method for Adaptive Viscous Liquids

Robust Real-Time Deformation of Incompressible Surface Meshes

Raphael Diziol, Jan Bender, Daniel Bayer

We introduce an efficient technique for robustly simulating incompressible objects with thousands of elements in real-time. Instead of considering a tetrahedral model, commonly used to simulate volumetric bodies, we simply use their surfaces. Not requiring hundreds or even thousands of elements in the interior of the object enables us to simulate more elements on the surface, resulting in high quality deformations at low computation costs. The elasticity of the objects is robustly simulated with a geometrically motivated shape matching approach which is extended by a fast summation technique for arbitrary triangle meshes suitable for an efficient parallel computation on the GPU. Moreover, we present an oscillation-free and collision-aware volume constraint, purely based on the surface of the incompressible body. The novel heuristic we propose in our approach enables us to conserve the volume, both globally and locally. Our volume constraint is not limited to the shape matching method and can be used with any method simulating the elasticity of an object. We present several examples which demonstrate high quality volume conserving deformations and compare the run-times of our CPU implementation, as well as our GPU implementation with similar methods.

Robust Real-Time Deformation of Incompressible Surface Meshes

Graph-based Fire Synthesis

Yubo Zhang, Carlos Correa, Kwan-Liu Ma

We present a novel graph-based data-driven technique for cost-effective fire modeling. This technique allows composing long animation sequences using a small number of short simulations. While traditional techniques such as motion graphs and motion blending work well for character motion synthesis, they cannot be trivially applied to fluids to produce results with physically consistent properties which are crucial to the visual appearance of fluids. Motivated by the motion graph technique used in character animations, we introduce a new type of graph which can be applied to create various fire phenomena. Each graph node consists of a group of compact spatialtemporal flow pathlines instead of a set of volumetric state fields. Consequently, achieving smooth transitions between discontinuous graph nodes for modeling turbulent fires becomes feasible and computationally efficient.The synthesized particle flow results allow direct particle controls which is much more flexible than a full volumetric representation of the simulation output. The accompanying video shows the versatility and potential power of this new technique for synthesizing realtime complex fire at the quality comparable to production animations.

Graph-based Fire Synthesis

SCA 2011

The draft program for SCA 2011 is online here. Ke-Sen Huang maintains links to the full set of papers here.  Many of the papers involve physical simulation, including:

Two-Scale Particle Simulation

We propose a two-scale method for particle-based fluids that allocates computing resources to regions of the fluid where complex flow behavior emerges. Our method uses a low- and a high-resolution simulation that run at the same time. While in the coarse simulation the whole fluid is represented by large particles, the fine level simulates only a subset of the fluid with small particles. The subset can be arbitrarily defined and also dynamically change over time to capture complex flows and small-scale surface details. The low- and high-resolution simulations are coupled by including feedback forces and defining appropriate boundary conditions. Our method offers the benefit that particles are of the same size within each simulation level. This avoids particle splitting and merging processes, and allows the simulation of very large resolution differences without any stability problems. The model is easy to implement, and we show how it can be integrated into a standard SPH simulation as well as into the incompressible PCISPH solver. Compared to the single-resolution simulation, our method produces similar surface details while improving the efficiency linearly to the achieved reduction rate of the particle number.

Two-Scale Particle Simulation

Efficient Elasticity for Character Skinning with Contact and Collisions

We present a new algorithm for near-interactive simulation of skeleton driven, high resolution elasticity models. Our methodology is used for soft tissue deformation in character animation. The algorithm is based on a novel discretization of corotational elasticity over a hexahedral lattice. Within this framework we enforce positive definiteness of the stiffness matrix to allow efficient quasistatics and dynamics. In addition, we present a multigrid method that converges with very high efficiency. Our design targets performance through parallelism using a fully vectorized and branch-free SVD algorithm as well as a stable one-point quadrature scheme. Since body collisions, self collisions and soft-constraints are necessary for real-world examples, we present a simple framework for enforcing them. The whole approach is demonstrated in an end-to-end production-level character skinning system.

Efficient Elasticity for Character Skinning with Contact and Collisions