We introduce a simple turbulence model for smoke animation, qualitatively capturing the transport, diffusion, and spectral cascade of turbulent energy unresolved on a typical simulation grid. We track the mean kinetic energy per octave of turbulence in each grid cell, and a novel “net rotation” variable for modeling the self-advection of turbulent eddies. These additions to a standard fluid solver drive a procedural post-process, layering plausible dynamically evolving turbulent details on top of the large-scale simulated motion. Finally, to make the most of the simulation grid before jumping to procedural sub-grid models, we propose a new multistep predictor to alleviate the nonphysical dissipation of angular momentum in standard graphics fluid solvers.
Month: May 2008
Image-based Collision Detection and Response between Arbitrary Volume Objects
We present a new image-based method to process contacts between objects bounded by triangular surfaces. Unlike previous methods, it relies on image-based volume minimization, which eliminates complex geometrical computations and robustly handles deep intersections. The surfaces are rasterized in three orthogonal directions, and intersections are detected based on pixel depth and normal orientation. Per-pixel contact forces are computed and accumulated at the vertices. We show how to compute pressure forces which serve to minimize the intersection volume, as well as friction forces. No geometrical precomputation is required, which makes the method efficient for both deformable and rigid objects. We demonstrate it on rigid, skinned, and particle-based physical models with detailed surfaces in contacts at interactive frame rates.
Image-based Collision Detection and Response between Arbitrary Volume Objects
Robust High-Resolution Cloth using Parallelism, History-Based Collisions and Accurate Friction
In this paper we simulate high resolution cloth consisting of up to 2 million triangles which allows us to achieve highly detailed folds and wrinkles. Since the level of detail is also influenced by object collision and self collision, we propose a more accurate model for cloth-object friction. We also propose a robust history-based repulsion/collision framework where repulsions are treated accurately and efficiently on a per time step basis. Distributed memory parallelism is used for both time evolution and collisions and we specifically address Gauss-Seidel ordering of repulsion/collision response. This algorithm is demonstrated by several high-resolution and high-fidelity simulations.
Robust High-Resolution Cloth using Parallelism, History-Based Collisions and Accurate Friction
A Mass Spring Model for Hair Simulation
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.
Simulating Knitted Cloth at the Yarn Level
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.
Accurate Viscous Free Surfaces for Buckling, Coiling and Rotating Liquids
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
Flexible Simulation of Deformable Models using Discontinuous Galerkin FEM
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
Visual Simulation of Shockwaves
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.
Wavelet Turbulence for Fluid Simulation
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.
Robust Treatment of Simultaneous Collisions
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.