Remeshing-free Graph-based Finite Element Method for Fracture Simulation

Fracture produces new mesh fragments that introduce additional degrees of freedom in the system dynamics. Existing finite element method (FEM) based solutions suffer from increasing computational cost as the system matrix size increases. We solve this problem by presenting a graph-based FEM model for fracture simulation that is remeshing-free and easily scales to high-resolution meshes. Our algorithm models fracture on the graph induced in a volumetric mesh with tetrahedral elements. We relabel the edges of the graph using a computed damage variable to initialize and propagate fracture. We prove that non-linear, hyper-elastic strain energy density is expressible entirely in terms of the edge lengths of the induced graph. This allows us to reformulate the system dynamics for the relabelled graph without changing the size of the system dynamics matrix and thus prevents the computational cost from blowing up. The fractured surface has to be reconstructed explicitly only for visualization purposes. We simulate standard laboratory experiments from structural mechanics and compare the results with corresponding real-world experiments. We fracture objects made of a variety of brittle and ductile materials, and show that our technique offers stability and speed that is unmatched in current literature.     

The Matchstick Model for Anisotropic Friction Cones

Inspired by frictional behaviour that is observed when sliding matchsticks against one another at different angles, we propose a phenomenological anisotropic friction model for structured surfaces. Our model interpolates isotropic and anisotropic elliptical Coulomb friction parameters for a pair of surfaces with perpendicular and parallel structure directions (e.g. the wood grain direction). We view our model as a special case of an abstract friction model that produces a cone based on state information, specifically the relationship between structure directions. We show how our model can be integrated into LCP and NCP-based simulators using different solvers with both explicit and fully implicit time-integration. The focus of our work is on symmetric friction cones, and we therefore demonstrate a variety of simulation scenarios where the friction structure directions play an important part in the resulting motions. Consequently, authoring of friction using our model is intuitive and we demonstrate that our model is compatible with standard authoring practices, such as texture mapping.     

Inflatable Models

A physically-based model is presented for the simulation of a new type of deformable objects-inflatable objects, such as shaped balloons, which consist of pressurized air enclosed by an elastic surface. These objects have properties inherent in both 3D and 2D elastic bodies, as they demonstrate the behaviour of 3D shapes using 2D formulations. As there is no internal structure in them, their behaviour is substantially different from the behaviour of deformable solid objects. We use one of the few available models for deformable surfaces, and enhance it to include the forces of internal and external pressure. These pressure forces may also incorporate buoyancy forces, to allow objects filled with a low density gas to float in denser media. The obtained models demonstrate rich dynamic behaviour, such as bouncing, floating, deflation and inflation.     

Direct Position‐Based Solver for Stiff Rods

In this paper, we present a novel direct solver for the efficient simulation of stiff, inextensible elastic rods within the position‐based dynamics (PBD) framework. It is based on the XPBD algorithm, which extends PBD to simulate elastic objects with physically meaningful material parameters. XPBD approximates an implicit Euler integration and solves the system of non‐linear equations using a non‐linear Gauss–Seidel solver. However, this solver requires many iterations to converge for complex models and if convergence is not reached, the material becomes too soft. In contrast, we use Newton iterations in combination with our direct solver to solve the non‐linear equations which significantly improves convergence by solving all constraints of an acyclic structure (tree), simultaneously. Our solver only requires a few Newton iterations to achieve high stiffness and inextensibility. We model inextensible rods and trees using rigid segments connected by constraints. Bending and twisting constraints are derived from the well‐established Cosserat model. The high performance of our solver is demonstrated in highly realistic simulations of rods consisting of multiple 10 000 segments. In summary, our method allows the efficient simulation of stiff rods in the PBD framework with a speedup of two orders of magnitude compared to the original XPBD approach.     

Monolithic Friction and Contact Handling for Rigid Bodies and Fluids Using SPH

We propose a novel monolithic pure SPH formulation to simulate fluids strongly coupled with rigid bodies. This includes fluid incompressibility, fluid–rigid interface handling and rigid–rigid contact handling with a viable implicit particle-based dry friction formulation. The resulting global system is solved using a new accelerated solver implementation that outperforms existing fluid and coupled rigid–fluid simulation approaches. We compare results of our simulation method to analytical solutions, show performance evaluations of our solver and present a variety of new and challenging simulation scenarios.     

Physically‐based forehead animation including wrinkles

Physically‐based animation techniques enable more realistic and accurate animation to be created. We present a fully physically‐based approach for efficiently producing realistic‐looking animations of facial movement, including animation of expressive wrinkles. This involves simulation of detailed voxel‐based models using a graphics processing unit‐based total Lagrangian explicit dynamic finite element solver with an anatomical muscle contraction model, and advanced boundary conditions that can model the sliding of soft tissue over the skull. The flexibility of our approach enables detailed animations of gross and fine‐scale soft‐tissue movement to be easily produced with different muscle structures and material parameters, for example, to animate different aged skins. Although we focus on the forehead, our approach can be used to animate any multi‐layered soft body. © 2014 The Authors. Computer Animation and Virtual Worlds published by John Wiley & Sons, Ltd.     

Accelerating Liquid Simulation With an Improved Data-Driven Method

In physics-based liquid simulation for graphics applications, pressure projection consumes a significant amount of computational time and is frequently the bottleneck of the computational efficiency. How to rapidly apply the pressure projection and at the same time how to accurately capture the liquid geometry are always among the most popular topics in the current research trend in liquid simulations. In this paper, we incorporate an artificial neural network into the simulation pipeline for handling the tricky projection step for liquid animation. Compared with the previous neural-network-based works for gas flows, this paper advocates new advances in the composition of representative features as well as the loss functions in order to facilitate fluid simulation with free-surface boundary. Specifically, we choose both the velocity and the level-set function as the additional representation of the fluid states, which allows not only the motion but also the boundary position to be considered in the neural network solver. Meanwhile, we use the divergence error in the loss function to further emulate the lifelike behaviours of liquid. With these arrangements, our method could greatly accelerate the pressure projection step in liquid simulation, while maintaining fairly convincing visual results. Additionally, our neutral network performs well when being applied to new scene synthesis even with varied boundaries or scales.     

Multi-Segment Foot for Human Modelling and Simulation

Realistic modelling of a human-like character is one of the main topics in computer graphics to simulate human motion physically and also look realistically. Of the body parts, a human foot interacts with the ground, and plays an essential role in weight transmission, balancing posture and assisting ambulation. However, in the previous researches, the foot model was often simplified into one or two rigid bodies connected by a revolute joint. We propose a new foot model consisting of multiple segments to reproduce human foot shape and its functionality accurately. Based on the new model, we develop a foot pose controller that can reproduce foot postures that are generally not obtained in motion capture data. We demonstrate the validity of our foot model and the effectiveness of our foot controller with a variety of foot motions in a physics-based simulation.     

Enhanced rig‐space simulation

Rig‐space physics a finite element method(FEM) based simulation technique that aims at adding secondary motion on a character while maintaining seamless cooperation with traditional animation pipelines. We enhance the rig‐space physics by introducing several techniques, including general field interaction, proportional‐derivative control, and improved material control. This allows an animator to perform various interferences to the simulation process and create more abundant animation effects. Moreover, we also improve the numerical stability of the simulation algorithm by prepending a conjugate gradient procedure. Copyright © 2016 John Wiley & Sons, Ltd.     

Controller Design for Multi‐Skilled Bipedal Characters

Developing motions for simulated humanoids remains a challenging problem. While there exists a multitude of approaches, few of these are reimplemented or reused by others. The predominant focus of papers in the area remains on algorithmic novelty, due to the difficulty and lack of incentive to more fully explore what can be accomplished within the scope of existing methodologies. We develop a language, based on common features found across physics‐based character animation research, that facilitates the controller authoring process. By specifying motion primitives over a number of phases, our language has been used to design over 25 controllers for motions ranging from simple static balanced poses, to highly dynamic stunts. Controller sequencing is supported in two ways. Naive integration of controllers is achieved by using highly stable pose controllers (such as a standing or squatting) as intermediate transitions. More complex controller connections are automatically learned through an optimization process. The robustness of our system is demonstrated via random walkthroughs of our integrated set of controllers.     

Numerical Coarsening with Neural Shape Functions

We propose to use nonlinear shape functions represented as neural networks in numerical coarsening to achieve generalization capability as well as good accuracy. To overcome the challenge of generalization to different simulation scenarios, especially nonlinear materials under large deformations, our key idea is to replace the linear mapping between coarse and fine meshes adopted in previous works with a nonlinear one represented by neural networks. However, directly applying an end-to-end neural representation leads to poor performance due to over-huge parameter space as well as failing to capture some intrinsic geometry properties of shape functions. Our solution is to embed geometry constraints as the prior knowledge in learning, which greatly improves training efficiency and inference robustness. With the trained neural shape functions, we can easily adopt numerical coarsening in the simulation of various hyperelastic models without any other preprocessing step required. The experiment results demonstrate the efficiency and generalization capability of our method over previous works.     

基于物理模型的烟雾实时模拟

本文提出了一种基于物理模型的烟雾的实时数值模拟方法.真实感和实时性是计算机图形学追求的两个目标.传统的动画技术生成的物体运动是虚拟的,并不能完全反映物体的真实运动.与传统的动画技术相比,基于物理的动画更能表现运动的真实性.在用非粘性不可压欧拉方程表示烟雾的物理模型的基础上,利用破开算子法将其分解成外力项、对流项和投影项分别进行求解,每一步都稳定,因而整个求解也就稳定.求解过程的稳定性保证了模拟可以用大时间步长,也就保证了模拟的实时性.与传统的方法相比,能同时满足计算机图形学的真实感和实时性要求.     

Anisotropic Strain Limiting for Quadrilateral and Triangular Cloth Meshes

The cloth simulation systems often suffer from excessive extension on the polygonal mesh, so an additional strain‐limiting process is typically used as a remedy in the simulation pipeline. A cloth model can be discretized as either a quadrilateral mesh or a triangular mesh, and their strains are measured differently. The edge‐based strain‐limiting method for a quadrilateral mesh creates anisotropic behaviour by nature, as discretization usually aligns the edges along the warp and weft directions. We improve this anisotropic technique by replacing the traditionally used equality constraints with inequality ones in the mathematical optimization, and achieve faster convergence. For a triangular mesh, the state‐of‐the‐art technique measures and constrains the strains along the two principal (and constantly changing) directions in a triangle, resulting in an isotropic behaviour which prohibits shearing. Based on the framework of inequality‐constrained optimization, we propose a warp and weft strain‐limiting formulation. This anisotropic model is more appropriate for textile materials that do not exhibit isotropic strain behaviour.     

Primal‐Dual Optimization for Fluids

We apply a novel optimization scheme from the image processing and machine learning areas, a fast Primal‐Dual method, to achieve controllable and realistic fluid simulations. While our method is generally applicable to many problems in fluid simulations, we focus on the two topics of fluid guiding and separating solid‐wall boundary conditions. Each problem is posed as an optimization problem and solved using our method, which contains acceleration schemes tailored to each problem. In fluid guiding, we are interested in partially guiding fluid motion to exert control while preserving fluid characteristics. With our method, we achieve explicit control over both large‐scale motions and small‐scale details which is valuable for many applications, such as level‐of‐detail adjustment (after running the coarse simulation), spatially varying guiding strength, domain modification, and resimulation with different fluid parameters. For the separating solid‐wall boundary conditions problem, our method effectively eliminates unrealistic artefacts of fluid crawling up solid walls and sticking to ceilings, requiring few changes to existing implementations. We demonstrate the fast convergence of our Primal‐Dual method with a variety of test cases for both model problems.     

Performance‐driven muscle‐based facial animation

We describe a system to synthesize facial expressions by editing captured performances. For this purpose, we use the actuation of expression muscles to control facial expressions. We note that there have been numerous algorithms already developed for editing gross body motion. While the joint angle has direct effect on the configuration of the gross body, the muscle actuation has to go through a complicated mechanism to produce facial expressions. Therefore,we devote a significant part of this paper to establishing the relationship between muscle actuation and facial surface deformation. We model the skin surface using the finite element method to simulate the deformation caused by expression muscles. Then, we implement the inverse relationship, muscle actuation parameter estimation, to find the muscle actuation values from the trajectories of the markers on the performer's face. Once the forward and inverse relationships are established, retargeting or editing a performance becomes an easy job. We apply the original performance data to different facial models with equivalent muscle structures, to produce similar expressions. We also produce novel expressions by deforming the original data curves of muscle actuation to satisfy the key‐frame constraints imposed by animators.Copyright © 2001 John Wiley & Sons, Ltd.     

Detail‐Preserving Explicit Mesh Projection and Topology Matching for Particle‐Based Fluids

We propose a new explicit surface tracking approach for particle‐based fluid simulations. Our goal is to advect and update a highly detailed surface, while only computing a coarse simulation. Current explicit surface methods lose surface details when projecting on the isosurface of an implicit function built from particles. Our approach uses a detail‐preserving projection, based on a signed distance field, to prevent the divergence of the explicit surface without losing its initial details. Furthermore, we introduce a novel topology matching stage that corrects the topology of the explicit surface based on the topology of an implicit function. To that end, we introduce an optimization approach to update our explicit mesh signed distance field before remeshing. Our approach is successfully used to preserve the surface details of melting and highly viscous objects, and shown to be stable by handling complex cases involving multiple topological changes. Compared to the computation of a high‐resolution simulation, using our approach with a coarse fluid simulation significantly reduces the computation time and improves the quality of the resulting surface.     

A deformable body model for surgical simulation

We propose a deformable body model in order to simulate the dynamic behaviour of human organs in surgical simulators. It is based on a spring surface mesh, fitted with a virtual rigid component which does not interact with the environment and provides the structure with a rigid behaviour. This specific structure is intended to be physically based and interactive but also to support dynamic alteration such as incisions, under several constraints: mechanical realism, robustness and real time. Moreover, interactions are taken into account by a 4D collision detection algorithm between polygonal objects, and reponse is computed analytically. Copyright © 2000 John Wiley & Sons, Ltd.     

Realistic and stable simulation of turbulent details behind objects in smoothed‐particle hydrodynamics fluids

This paper presents a novel realistic and stable turbulence synthesis method to simulate the turbulent details generated behind objects in smoothed particle hydrodynamics (SPH) fluids. Firstly, by approximating the boundary layer theory on the fly in SPH fluids, we propose a vorticity production model to identify which fluid particles shed from object surfaces and which are seeded as vortex particles. Then, we employ an SPH‐like summation interpolant formulation of the Biot–Savart law to calculate the fluctuating velocities stemming from the generated vorticity field. Finally, the stable evolution of the vorticity field is achieved by combining an implicit vorticity diffusion technique and an artificial dissipation term. Moreover, in order to efficiently catch turbulent details for rendering, we propose an octree‐based adaptive surface reconstruction method for particle‐based fluids. The experiment results demonstrate that our turbulence synthesis method provides an effect way to model the obstacle‐induced turbulent details in SPH fluids and can be easily added to existing particle‐based fluid–solid coupling pipelines. Copyright © 2014 John Wiley & Sons, Ltd.     

Stable and Fast Fluid–Solid Coupling for Incompressible SPH

The solid boundary handling has been a research focus in physically based fluid animation. In this paper, we propose a novel stable and fast particle method to couple predictive–corrective incompressible smoothed particle hydrodynamics and geometric lattice shape matching (LSM), which animates the visually realistic interaction of fluids and deformable solids allowing larger time steps or velocity differences. By combining the boundary particles sampled from solids with a momentum‐conserving velocity‐position correction scheme, our approach can alleviate the particle deficiency issues and prevent the penetration artefacts at the fluid–solid interfaces simultaneously. We further simulate the stable deformation and melting of solid objects coupled to smoothed particle hydrodynamics fluids based on a highly extended LSM model. In order to improve the time performance of each time step, we entirely implement the unified particle framework on GPUs using compute unified device architecture. The advantages of our two‐way fluid–solid coupling method in computer animation are demonstrated via several virtual scenarios.     

Turbulent Details Simulation for SPH Fluids via Vorticity Refinement

A major issue in smoothed particle hydrodynamics (SPH) approaches is the numerical dissipation during the projection process, especially under coarse discretizations. High‐frequency details, such as turbulence and vortices, are smoothed out, leading to unrealistic results. To address this issue, we introduce a vorticity refinement (VR) solver for SPH fluids with negligible computational overhead. In this method, the numerical dissipation of the vorticity field is recovered by the difference between the theoretical and the actual vorticity, so as to enhance turbulence details. Instead of solving the Biot‐Savart integrals, a stream function, which is easier and more efficient to solve, is used to relate the vorticity field to the velocity field. We obtain turbulence effects of different intensity levels by changing an adjustable parameter. Since the vorticity field is enhanced according to the curl field, our method can not only amplify existing vortices, but also capture additional turbulence. Our VR solver is straightforward to implement and can be easily integrated into existing SPH methods.