Physics-Based Animation

Our goal is to simulate the full hair geometry, consisting of ap- proximately one hundred thousand hairs on a typical human head. This will require scalable methods that can simulate every hair as opposed to only a few guide hairs. Novel to this approach is that the individual hair/hair interactions can be modeled with physical parameters (friction, static attraction, etc.) at the scale of a single hair as opposed to clumped or continuum interactions. In this vein, we first propose a new altitude spring model for preventing col- lapse in the simulation of volumetric tetrahedra, and we show that it is also applicable both to bending in cloth and torsion in hair. We demonstrate that this new torsion model for hair behaves in a fashion similar to more sophisticated models with significantly reduced computational cost. For added efficiency, we introduce a semi-implicit discretization of standard springs that makes them truly linear in multiple spatial dimensions and thus unconditionally stable without requiring Newton-Raphson iteration. We also simu- late complex hair/hair interactions including sticking and clumping behavior, collisions with objects (e.g. head and shoulders) and self- collisions. Notably, in line with our goal to simulate the full head of hair, we do not generate any new hairs at render time.

A Mass Spring Model for Hair Simulation

Knitted fabric is widely used in clothing because of its unique and stretchy behavior, which is fundamentally different from the behavior of woven cloth. The properties of knits come from the nonlinear, three-dimensional kinematics of long, inter-looping yarns, and despite significant advances in cloth animation we still do not know how to simulate knitted fabric faithfully. Existing cloth simulators mainly adopt elastic-sheet mechanical models inspired by woven materials, focusing less on the model itself than on important simulation challenges such as efficiency, stability, and robustness. We define a new computational model for knits in terms of the motion of yarns, rather than the motion of a sheet. Each yarn is modeled as an inextensible, yet otherwise flexible, B-spline tube. To simulate complex knitted garments, we propose an implicit-explicit integrator, with yarn inextensibility constraints imposed using efficient projections. Friction among yarns is approximated using rigid-body velocity filters, and key yarn-yarn interactions are mediated by stiff penalty forces. Our results show that this simple model predicts the key mechanical properties of different knits, as demonstrated by qualitative comparisons to observed deformations of actual samples in the laboratory, and that the simulator can scale up to substantial animations with complex dynamic motion.

Simulating Knitted Cloth at the Yarn Level

We present a fully implicit Eulerian technique for simulating free surface viscous liquids which eliminates artifacts in previous approaches, efficiently supports variable viscosity, and allows the simulation of more compelling viscous behaviour than previously achieved in graphics. Our method exploits a variational principle which automatically enforces the complex boundary condition on the shear stress at the free surface, while giving rise to a simple discretization with a symmetric positive definite linear system. We demonstrate examples of our technique capturing realistic buckling, folding and coiling behavior. In addition, we explain how to handle domains whose boundary comprises both ghost fluid Dirichlet and variational Neumann parts, allowing correct behaviour at free surfaces and solid walls for both our viscous solve and the variational pressure projection of [Batty et al. 2007].

Accurate Viscous Free Surfaces for Buckling, Coiling and Rotating Liquids

We propose a simulation technique for elastically deformable objects based on the discontinuous Galerkin finite element method (DG FEM). In contrast to traditional FEM, it overcomes the restrictions of conforming basis functions by allowing for discontinuous elements with weakly enforced continuity constraints. This added flexibility enables the simulation of arbitrarily shaped, convex and non-convex polyhedral elements, while still using simple polynomial basis functions. For the accurate strain integration over these elements we propose an analytic technique based on the divergence theorem. Being able to handle arbitrary elements eventually allows us to derive simple and efficient techniques for volumetric mesh generation, adaptive mesh refinement, and robust cutting.

Flexible Simulation of Deformable Models using Discontinuous Galerkin FEM

We present an efficient method for visual simulations of shock phenomena in compressible, inviscid fluids. Our algorithm is derived from one class of the finite volume method especially designed for capturing shock propagation, but offers improved efficiency through physically-based simplification and adaptation for graphical rendering. Our technique is well suited for parallel implementation on multicore architectures and is also capable of handling complex, bidirectional object-shock interactions stably and robustly. We describe its applications to various visual effects, including explosion, sonic booms and turbulent flows.

Visual Simulation of Shockwaves

We present a novel wavelet method for the simulation of fluids at high spatial resolution. The algorithm enables large- and small-scale detail to be edited separately, allowing high-resolution detail to be added as a post-processing step. Instead of solving the Navier-Stokes equations over a highly refined mesh, we use the wavelet decomposition of a low-resolution simulation to determine the location and energy characteristics of missing high-frequency components. We then synthesize these missing components using a novel incompressible turbulence function, and provide a method to maintain the temporal coherence of the resulting structures. There is no linear system to solve, so the method parallelizes trivially and requires only a few auxiliary arrays. The method guarantees that the new frequencies will not interfere with existing frequencies, allowing animators to set up a low resolution simulation quickly and later add details without changing the overall fluid motion.

Wavelet Turbulence for Fluid Simuation

Robust treatment of complex collisions is a challenging problem in cloth simulation. Some state of the art methods resolve collisions iteratively, invoking a fail-safe when a bound on iteration count is exceeded. The best-known fail-safe rigidifies the contact region, causing simulation artifacts. We present a fail-safe that cancels impact but not sliding motion, considerably reducing artificial dissipation. We equip the proposed fail-safe with an approximation of Coulomb friction, allowing finer control of sliding dissipation.

Robust Treatment of Simultaneous Collisions

We propose a hybrid method for simulating multiphase fluids such as bubbly water. The appearance of subgrid visual details is improved by incorporating a new bubble model based on smoothed particle hydrodynamics (SPH) into an Eulerian grid-based simulation that handles background flows of large bodies of water and air. To overcome the difficulty in simulating small bubbles in the context of the multiphase flows on a coarse grid, we heuristically model the interphase properties of water and air by means of the interactions between bubble particles. As a result, we can animate lively motion of bubbly water with small scale details efficiently.

Bubbles Alive

Spline joints are a novel class of joints that can model general scleronomic constraints for multibody dynamics based on the minimalcoordinates formulation. The main idea is to introduce spline curves and surfaces in the modeling of joints: We model 1-DOF joints using splines on SE(3), and construct multi-DOF joints as the product of exponentials of splines in Euclidean space. We present efficient recursive algorithms to compute the derivatives of the spline joint, as well as geometric algorithms to determine optimal parameters in order to achieve the desired joint motion. Our spline joints can be used to create interesting new simulated mechanisms for computer animation and they can more accurately model complex biomechanical joints such as the knee and shoulder.

Spline Joints for Multibody Dynamics

This paper presents the simulation of fluid flowing through a porous deformable material. We introduce the physical principles governing porous flow, expressed by the Law of Darcy, into the Smoothed Particle Hydrodynamics (SPH) framework for simulating fluids and deformable objects. Contrary to previous SPH approaches, we simulate porous flow at a macroscopic scale, making abstraction of individual pores or cavities inside the material. Thus, the number of computational elements is kept low, while at the same time realistic simulations can be achieved. Our algorithm models the changing behavior of the wet material as well as the full two-way coupling between the fluid and the porous material. This enables various new effects, such as the simulation of sponge-like elastic bodies and water-absorbing sticky cloth.

Porous Flow in Particle-Based Fluid Simulation