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.     

Functionality‐Driven Musculature Retargeting

We present a novel retargeting algorithm that transfers the musculature of a reference anatomical model to new bodies with different sizes, body proportions, muscle capability, and joint range of motion while preserving the functionality of the original musculature as closely as possible. The geometric configuration and physiological parameters of musculotendon units are estimated and optimized to adapt to new bodies. The range of motion around joints is estimated from a motion capture dataset and edited further for individual models. The retargeted model is simulation‐ready, so we can physically simulate muscle‐actuated motor skills with the model. Our system is capable of generating a wide variety of anatomical bodies that can be simulated to walk, run, jump and dance while maintaining balance under gravity. We will also demonstrate the construction of individualized musculoskeletal models from bi‐planar X‐ray images and medical examination.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

DYVERSO: A Versatile Multi‐Phase Position‐Based Fluids Solution for VFX

Many impressive fluid simulation methods have been presented in research papers before. These papers typically focus on demonstrating particular innovative features, but they do not meet in a comprehensive manner the production demands of actual VFX pipelines. VFX artists seek methods that are flexible, efficient, robust and scalable, and these goals often conflict with each other. In this paper, we present a multi‐phase particle‐based fluid simulation framework, based on the well‐known Position‐Based Fluids (PBF) method, designed to address VFX production demands. Our simulation framework handles multi‐phase interactions robustly thanks to a modified constraint formulation for density contrast PBF. And, it also supports the interaction of fluids sampled at different resolutions. We put special care on data structure design and implementation details. Our framework highlights cache‐efficient GPU‐friendly data structures, an improved spatial voxelization technique based on Z‐index sorting, tuned‐up simulation algorithms and two‐way‐coupled collision handling based on VDB fields. Altogether, our fluid simulation framework empowers artists with the efficiency, scalability and versatility needed for simulating very diverse scenes and effects.     

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.     

Muscle‐Based Control for Character Animation

Muscle‐based control is transforming the field of physics‐based character animation through the integration of knowledge from neuroscience, biomechanics and robotics, which enhance motion realism. Since any physics‐based animation system can be extended to a muscle‐actuated system, the possibilities of growth are tremendous. However, modelling muscles and their control remains a difficult challenge. We present an organized review of over a decade of research in muscle‐based control for character animation, its fundamental concepts and future directions for development. The core of this review contains a classification of control methods, tables summarizing their key aspects and popular neuromuscular functions used within these controllers, all with the purpose of providing the reader with an overview of the field.     

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.     

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.     

Boundary Handling at Cloth–Fluid Contact

We present a robust and efficient method for the two‐way coupling between particle‐based fluid simulations and infinitesimally thin solids represented by triangular meshes. Our approach is based on a hybrid method that combines a repulsion force approach with a continuous intersection handling to guarantee that no penetration occurs. Moreover, boundary conditions for the tangential component of the fluid's velocity are implemented to model the different slip conditions. The proposed method is particularly useful for dynamic surfaces, like cloth and thin shells. In addition, we demonstrate how standard fluid surface reconstruction algorithms can be modified to prevent the calculated surface from intersecting close objects. For both the two‐way coupling and the surface reconstruction, we take into account that the fluid can wet the cloth. We have implemented our approach for the bidirectional interaction between liquid simulations based on Smoothed Particle Hydrodynamics (SPH) and standard mesh‐based cloth simulation systems.     

Parallel Surface Reconstruction for Particle‐Based Fluids

This paper presents a novel method that improves the efficiency of high‐quality surface reconstructions for particle‐based fluids using Marching Cubes. By constructing the scalar field only in a narrow band around the surface, the computational complexity and the memory consumption scale with the fluid surface instead of the volume. Furthermore, a parallel implementation of the method is proposed. The presented method works with various scalar field construction approaches. Experiments show that our method reconstructs high‐quality surface meshes efficiently even on single‐core CPUs. It scales nearly linearly on multi‐core CPUs and runs up to fifty times faster on GPUs compared to the original scalar field construction approaches.     

Boundary‐dominant flower blooming simulation

This paper presents a new physics‐based simulation method for flower blossom, which is based on biological observations that flower opening is usually driven by a boundary‐dominant morphological transition in a curved petal. We use an elastic triangular mesh representing a flower petal and adopt in‐plane expansion to induce global bending. Out‐of‐plane curl plays an auxiliary role in reducing the curvatures of cross‐sections. We also propose to adapt semi‐implicit Euler time integrator for fast simulation results, which has intrinsic damping and at least one order precision. Our system allows users to control the blossoming process by simply specifying a growth curve, which is easy to design because of the boundary‐dominant property. Experimental results show that our physics‐based system runs faster and generates more realistic and convincing blossom results than the existing simulation methods. Copyright © 2015 John Wiley & Sons, Ltd.     

Discrete‐Valued Model Predictive Control Using Sum‐of‐Absolute‐Values Optimization

In this paper, we propose a new design method of discrete‐valued model predictive control for continuous‐time linear time‐invariant systems based on sum‐of‐absolute‐values (SOAV) optimization. The finite‐horizon discrete‐valued control design is formulated as an SOAV optimal control, which is an expansion of L¹ optimal control. It is known that under the normality assumption, the SOAV optimal control exists and takes values in a fixed finite alphabet set if the initial state lies in a subset of the reachable set. In this paper, we analyze the existence and discreteness property for systems that do not necessarily satisfy the normality assumption. Then, we extend the finite‐horizon SOAV optimal control to infinite‐horizon model predictive control (MPC). We give sufficient conditions for the recursive feasibility and the stability of the MPC‐based feedback system in the presence of bounded noise. Simulation results show the effectiveness of the proposed method.     

An Implicit SPH Formulation for Incompressible Linearly Elastic Solids

We propose a novel smoothed particle hydrodynamics (SPH) formulation for deformable solids. Key aspects of our method are implicit elastic forces and an adapted SPH formulation for the deformation gradient that—in contrast to previous work—allows a rotation extraction directly from the SPH deformation gradient. The proposed implicit concept is entirely based on linear formulations. As a linear strain tensor is used, a rotation‐aware computation of the deformation gradient is required. In contrast to existing work, the respective rotation estimation is entirely realized within the SPH concept using a novel formulation with incorporated kernel gradient correction for first‐order consistency. The proposed implicit formulation and the adapted rotation estimation allow for significantly larger time steps and higher stiffness compared to explicit forms. Performance gain factors of up to one hundred are presented. Incompressibility of deformable solids is accounted for with an ISPH pressure solver. This further allows for a pressure‐based boundary handling and a unified processing of deformables interacting with SPH fluids and rigids. Self‐collisions are implicitly handled by the pressure solver.     

The creation of a high‐fidelity finite element model of the kidney for use in trauma research

A detailed finite element model of the human kidney for trauma research has been created directly from the National Library of Medicine Visible Human Female (VHF) Project data set. An image segmentation and organ reconstruction software package has been developed and employed to transform the 2D VHF images into a 3D polygonal representation. Non‐uniform rational B‐spline (NURBS) surfaces were then mapped to the polygonal surfaces, and were finally utilized to create a robust 3D hexahedral finite element mesh within a commercially available meshing software. The model employs a combined viscoelastic and hyperelastic material model to successfully simulate the behaviour of biological soft tissues. The finite element model was then validated for use in biomechanical research. Copyright © 2002 John Wiley & Sons, Ltd.