Physics-Based Animation

Linxu Fan, Lloyd M. Chitalu, Taku Komura

Large-scale topological changes play a key role in capturing the fine debris of fracturing virtual brittle material. Real-world, tough brittle fractures have dynamic branching behaviour but numerical simulation of this phenomena is notoriously challenging. In order to robustly capture these
visual characteristics, we simulate brittle fracture by combining elastodynamic continuum mechanical models with rigid-body methods: A continuum damage mechanics (CDM) problem is solved, following rigid-body impact, to simulate crack propagation by tracking a damage field. We combine the result of this elastostatic continuum model with a novel technique to approximate cracks as a non-manifold mid-surface, which enables accurate and robust modelling of material fragment volumes to compliment fast-and-rigid shatter effects. For enhanced realism, we add fracture detail, incorporating particle damage-time to inform localised perturbation of the crack surface with artistic control. We evaluate our method with numerous examples and comparisons, showing that it produces a breadth of brittle material fracture effects and with low simulation resolution to require much less time compared to fully elastodynamic simulations.

Simulating Brittle Fracture with Material Points

Zhen Chen, Hsiao-yu Chen, Danny M Kaufman, Mélina Skouras, Etienne Vouga

We propose a new model and algorithm to capture the high-definition statics of thin shells via coarse meshes. This model predicts global, fine-scale wrinkling at frequencies much higher than the resolution of the coarse mesh; moreover, it is grounded in the geometric analysis of elasticity, and does not require manual guidance, a corpus of training examples, nor tuning of ad hoc parameters. We first approximate the coarse shape of the shell using tension field theory, in which material forces do not resist compression. We then augment this base mesh with wrinkles, parameterized by an amplitude and phase field that we solve for over the base mesh, which together characterize the geometry of the wrinkles. We validate our approach against both physical experiments and numerical simulations, and we show that our algorithm produces wrinkles qualitatively similar to those predicted by traditional shell solvers requiring orders of magnitude more degrees of freedom.

Fine Wrinkling on Coarsely Meshed Thin Shells

Michael Tao, Christopher Batty, Mirela Ben-Chen, Eugene Fiume, David I. W. Levin

The comprehensive visual modeling of fluid motion has historically been a challenging task, due in no small part to the difficulties inherent in geometries that are non-manifold, open, or thin. Modern geometric cut-cell mesh generators have been shown to produce, both robustly and quickly, workable volumetric elements in the presence of these problematic geometries, and the resulting volumetric representation would seem to offer an ideal infrastructure with which to perform fluid simulations. However, cut-cell mesh elements are general polyhedra that often contain holes and are non-convex; it is therefore difficult to construct the explicit function spaces required to employ standard functional discretizations, such as the Finite Element Method. The Virtual Element Method (VEM) has recently emerged as a functional discretization that successfully operates with complex polyhedral elements through a weak formulation of its function spaces. We present a novel cut-cell fluid simulation framework that exactly represents boundary geometry during the simulation. Our approach enables, for the first time, detailed fluid simulation with “in-the-wild” obstacles, including ones that contain non-manifold parts, self-intersections, and extremely thin features. Our key technical contribution is the generalization of the Particle-In-Cell fluid simulation methodology to arbitrary polyhedra using VEM. Coupled with a robust cut-cell generation scheme, this produces a fluid simulation algorithm that can operate on previously infeasible geometries without requiring any additional mesh modification or repair.

VEMPIC: Particle-in-Polyhedron Fluid Simulation for Intricate Solid Boundaries

Alejandro Rodriguez, Gabriel Cirio

Seams play a fundamental role in the way a garment looks, fits, feels and behaves. Seams can have very different shapes and mechanical properties depending on how fabric is overlapped, folded and stitched together, with garment designers often choosing specific seam and stitch type combinations depending on the appearance and behavior they want for the garment. Yet, virtually all 3D CAD tools for fashion and visual effects ignore most of the visual and mechanical complexity of seams, and just treat them as joint edges, their simplest possible form, drastically limiting the fidelity of digital garments. In this paper, we present a method that models seams following their true, real-life construction. Each seam brings together and overlaps the fabric pieces to be sewn, folds the fabric according to the type of seam, and stitches the resulting assembly following the type of stitch. To avoid dealing with the complexities of folding in 3D space, we cast the problem into a sequence of simpler 2D problems where we can easily shape the seam and produce a result free of self-intersections, before lifting the folded geometry back to 3D space. We run a series of constrained optimizations to enforce spatial properties in these 2D settings, allowing us to treat asymmetric seams, gatherings and overlapping construction orders. Using a variety of common seams and stitches, we show how our approach substantially improves the visual appearance of full garments, for a better and more predictive digital replica.

True Seams: Modeling Seams in Digital Garments

Botao Wu, Zhendong Wang, Huamin Wang

In this paper, we wish to push the limit of real-time cloth and deformable body simulation to a higher level with 50K to 500K vertices, based on the development of a novel GPU-based multilevel additive Schwarz (MAS) preconditioner. Similar to other preconditioners under the MAS framework, our preconditioner naturally adopts multilevel and domain decomposition concepts. But contrary to previous works, we advocate the use of small, non-overlapping domains that can well explore the parallel computing power on a GPU. Based on this idea, we investigate and invent a series of algorithms for our preconditioner, including multilevel domain construction using Morton codes, low-cost matrix precomputation by one-way Gauss-Jordan elimination, and conflict-free symmetric-matrix-vector multiplication in runtime preconditioning. The experiment shows that our preconditioner is effective, fast, cheap to precompute and scalable with respect to stiffness and problem size. It is compatible with many linear and nonlinear solvers used in cloth and deformable body simulation with dynamic contacts, such as PCG, accelerated gradient descent and L-BFGS. On a GPU, our preconditioner speeds up a PCG solver by approximately a factor of four, and its CPU version outperforms a number of competitors, including ILU0 and ILUT.

A GPU-Based Multilevel Additive Schwarz Preconditioner for Cloth and Deformable Body Simulation

Alexandre Mercier-Aubin, Alexander Winter, David I.W. Levin, Paul G. Kry

We present a method for reducing the computational cost of elastic solid simulation by treating connected sets of non-deforming elements as rigid bodies. Non-deforming elements are identified as those where the strain rate squared Frobenius norm falls below a threshold for several frames. Rigidification uses a breadth first search to identify connected components while avoiding connections that would form hinges between rigid components. Rigid elements become elastic again when their approximate strain velocity rises above a threshold, which is fast to compute using a single iteration of conjugate gradient with a fixed Laplacian-based incomplete Cholesky preconditioner. With rigidification, the system size to solve at each time step can be greatly reduced, and if all elastic element become rigid, it reduces to solving the rigid body system. We demonstrate our results on a variety of 2D and 3D examples, and show that our method is likewise especially beneficial in contact rich examples.

Adaptive Rigidification of Elastic Solids

Wei Li, Yihui Ma, Xiaopei Liu, Mathieu Desbrun

Real-life multiphase flows exhibit a number of complex and visually appealing behaviors, involving bubbling, wetting, splashing, and glugging. However, most state-of-the-art simulation techniques in graphics can only demonstrate a limited range of multiphase flow phenomena, due to their inability to handle the real water-air density ratio and to the large amount of numerical viscosity introduced in the flow simulation and its coupling with the interface. Recently, kinetic-based methods have achieved success in simulating large density ratios and high Reynolds numbers efficiently; but their memory overhead, limited stability, and numerically-intensive treatment of coupling with immersed solids remain enduring obstacles to their adoption in movie productions. In this paper, we propose a new kinetic solver to couple the incompressible Navier-Stokes equations with a conservative phase-field equation which remedies these major practical hurdles. The resulting two-phase immiscible fluid solver is shown to be efficient due to its massively-parallel nature and GPU implementation, as well as very versatile and reliable because of its enhanced stability to large density ratios, high Reynolds numbers, and complex solid boundaries. We highlight the advantages of our solver through various challenging simulation results that capture intricate and turbulent air-water interaction, including comparisons to previous work and real footage.

Efficient Kinetic Simulation of Two-Phase Flows

Lei Lan, Danny M. Kaufman, Minchen Li, Chenfanfu Jiang, Yin Yang

Simulating stiff materials in applications where deformations are either not significant or else can safely be ignored is a fundamental task across fields. Rigid body modeling has thus long remained a critical tool and is, by far, the most popular simulation strategy currently employed for modeling stiff solids. At the same time, rigid body methods continue to pose a number of well known challenges and trade-offs including intersections, instabilities, inaccuracies, and/or slow performances that grow with contact-problem complexity. In this paper we revisit the stiff body problem and present ABD, a simple and highly effective affine body dynamics framework, which significantly improves state-of-the-art for simulating stiff-body dynamics. We trace the challenges in rigid-body methods to the necessity of linearizing piecewise-rigid trajectories and subsequent constraints. ABD instead relaxes the unnecessary (and unrealistic) constraint that each body’s motion be exactly rigid with a stiff orthogonality potential, while preserving the rigid body model’s key feature of a small coordinate representation. In doing so ABD replaces piecewise linearization with piecewise linear trajectories. This, in turn, combines the best of both worlds: compact coordinates ensure small, sparse system solves, while piecewise-linear trajectories enable efficient and accurate constraint (contact and joint) evaluations. Beginning with this simple foundation, ABD preserves all guarantees of the underlying IPC model we build it upon, e.g., solution convergence, guaranteed non-intersection, and accurate frictional contact. Over a wide range and scale of simulation problems we demonstrate that ABD brings orders of magnitude performance gains (two- to three-orders on the CPU and an order more when utilizing the GPU, obtaining 10, 000× speedups) over prior IPC-based methods, while maintaining simulation quality and nonintersection of trajectories. At the same time ABD has comparable or faster timings when compared to state-of-the-art rigid body libraries optimized for performance without guarantees, and successfully and efficiently solves challenging simulation problems where both classes of prior rigid body simulation methods fail altogether.

Affine Body Dynamics: Fast, Stable & Intersection-free Simulation of Stiff Materials

Lei Lan, Guanqun Ma, Yin Yang, Changxi Zheng, Minchen Li, Chenfanfu Jiang

We present a GPU algorithm for deformable simulation. Our method offers good computational efficiency and penetration-free guarantee at the same time, which are not common with existing techniques. The main idea is an algorithmic integration of projective dynamics (PD) and incremental potential contact (IPC). PD is a position-based simulation framework, favored for its robust convergence and convenient implementation. We show that PD can be employed to handle the variational optimization with the interior point method e.g., IPC. While conceptually straightforward, this requires a dedicated rework over the collision resolution and the iteration modality to avoid incorrect collision projection with improved numerical convergence. IPC exploits a barrier-based formulation, which yields an infinitely large penalty when the constraint is on the verge of being violated. This mechanism guarantees intersection-free trajectories of deformable bodies during the simulation, as long as they are apart at the rest configuration. On the downside, IPC brings a large amount of nonlinearity to the system, making PD slower to converge. To mitigate this issue, we propose a novel GPU algorithm named A-Jacobi for faster linear solve at the global step of PD. A-Jacobi is based on Jacobi iteration, but it better harvests the computation capacity on modern GPUs by lumping several Jacobi steps into a single iteration. In addition, we also re-design the CCD root finding procedure by using a new minimum-gradient Newton algorithm. Those saved time budgets allow more iterations to accommodate stiff IPC barriers so that the result is both realistic and collision-free. Putting together, our algorithm simulates complicated models of both solids and shells on the GPU at an interactive rate or even in real time.

Penetration-free Projective Dynamics on the GPU

Ziyin Qu, Minchen Li, Fernando de Goes, Chenfanfu Jiang

This paper introduces a new weighting scheme for particle-grid transfers that generates hybrid Lagrangian/Eulerian fluid simulations with uniform particle distributions and precise volume control. At its core, our approach reformulates the construction of Power Particles [de Goes et al . 2015] by computing volume-constrained density kernels. We employ these optimized kernels as particle domains within the Generalized Interpolation Material Point method (GIMP) in order to incorporate Power Particles into the Particle-In-Cell framework, hence the name the Power Particle-In-Cell method. We address the construction of volume-constrained density kernels as a regularized optimal transportation problem and describe an iterative solver based on localized Gaussian convolutions that leads to a significant performance speedup compared to [de Goes et al . 2015]. We also present novel extensions for handling free surfaces and solid obstacles that bypass the need for cell clipping and ghost particles. We demonstrate the advantages of our transfer weights by improving hybrid schemes for fluid simulation such as the Fluid Implicit Particle (FLIP) method and the Affine Particle-In-Cell (APIC) method with volume preservation and robustness to varying particle-per-cell ratio, while retaining low numerical dissipation, conserving linear and angular momenta, and avoiding particle reseeding or post-process relaxations.

The Power Particle-In-Cell Method