Fluid Simulation with Articulated Bodies

We present an algorithm for creating realistic animations of characters that are swimming through fluids. Our approach combines dynamic simulation with data-driven kinematic motions (motion capture data) to produce realistic animation in a fluid. The interaction of the articulated body with the fluid is performed by incorporating joint constraints with rigid animation and by extending a solid/fluid coupling method to handle articulated chains. Our solver takes as input the current state of the simulation and calculates the angular and linear accelerations of the connected bodies needed to match a particular motion sequence for the articulated body. These accelerations are used to estimate the forces and torques that are then applied to each joint. Based on this approach, we demonstrate simulated swimming results for a variety of different strokes, including crawl, backstroke, breaststroke, and butterfly. The ability to have articulated bodies interact with fluids also allows us to generate simulations of simple water creatures that are driven by simple controllers.     

Real-Time Physics-Based 3D Biped Character Animation Using an Inverted Pendulum Model

We present a physics-based approach to generate 3D biped character animation that can react to dynamical environments in real time. Our approach utilizes an inverted pendulum model to online adjust the desired motion trajectory from the input motion capture data. This online adjustment produces a physically plausible motion trajectory adapted to dynamic environments, which is then used as the desired motion for the motion controllers to track in dynamics simulation. Rather than using Proportional-Derivative controllers whose parameters usually cannot be easily set, our motion tracking adopts a velocity-driven method which computes joint torques based on the desired joint angular velocities. Physically correct full-body motion of the 3D character is computed in dynamics simulation using the computed torques and dynamical model of the character. Our experiments demonstrate that tracking motion capture data with real-time response animation can be achieved easily. In addition, physically plausible motion style editing, automatic motion transition, and motion adaptation to different limb sizes can also be generated without difficulty.     

A simple approximation to rigid body dynamics for computer animation

Recently, the dynamics of linked articulated rigid bodies has become a valuable tool for making realistic three-dimensional computer animations. An exact treatment of rigid body dynamics, however, is based on rather non-intuitive results from classical mechanics (e.g. the Euler equations for rotating bodies) and it relies heavily on sophisticated numerical schemes to solve (large) sets of coupled non-linear algebraic and differential equations. As a result, articulated rigid bodies are not yet supported by most real-time animation systems. This paper discusses an approach to rigid body dynamics which is based on (both conceptually and algorithmically much simpler) point mechanics; this gives rise to an asymptotically exact numerical scheme (NSI) which is useful in the context of real-time animation, provided that the number of degrees of freedom of the simulated system is not too large. Based on NSI, a second scheme (NS2) is derived which is useful for approximating the motions of linked articulated rigid bodies; NS2 turns out to be sufficiently fast to give at least qualitative results in real-time simulation. In general, the algorithm NS2 is not necessarily (asymptotically) exact, but a quantitative analysis shows that in the absence of reaction forces it conserves angular momentum.     

Forward dynamics based realistic animation of rigid bodies

This paper presents a new methodology for model and control of the motion of an (articulated) rigid body for the purposes of animation. The technique uses a parameter optimization method for forward dynamic simulation to obtain a good set of values for the control variables of the system. We model articulated rigid bodies using a moderate number of control nodes, and we linearly interpolate control values between adjacent pairs of these nodes. The interpolated control values are used to determine the forces/torques for the body actuators. We can control total motion duration time, and the control is more flexible than in any other dynamics based animation techniques. We employ a parameter optimization, (or nonlinear programming) method to find a good set of values for the control nodes. We extend this method by using a musculotendon skeletal model for the human body instead of the more commonly used robot model to provide more accurate human motion simulations. Skeletal and musculotendon dynamics enable us to do the human body animation more accurately than ever because the muscle force depends on the geometry of a human as well as on differential kinematic parameters. We show various levels of motion control for forward dynamics animation: ranging from piecewise linear forces/torques control for joints to muscle activation signal control for muscles to generate highly nonlinear forces/torques. This spectrum of control levels provides various nonlinear resulting motions to animators to allow them to achieve effective motion control and physically realistic motion simultaneously. Because our algorithms are heavily dependent on parameter optimization, and since the optimization technique may have difficulty finding a global optimum, we provide a modified optimization method along with various techniques to reduce the search space size. Our parameter optimization based forward dynamic animation and musculotendon dynamics based animation present the first use of such techniques in animation research to date.     

Psychological Evidence for Unconscious Processing of Detail in Real‐time Animation of Multiple Characters

Detailed animation of 3D articulated body models is in principle desirable but is also a highly resource‐intensive task. Resource limitations are particularly critical in 3D visualizations of multiple characters in real‐time game sequences. We investigated to what extent observers perceptually process the level of detail in naturalistic character animations. Only if such processing occurs would it be justified to spend valuable resources on richness of detail. An experiment was designed to test the effectiveness of 3D body animation. Observers had to judge the level of overall skill exhibited by four simulated soccer teams. The simulations were based on recorded RoboCup simulation league games. Thus objective skill levels were known from the teams' placement in the tournament. The animations' level of detail was varied in four increasing steps of modelling complexity. Results showed that observers failed to notice the differences in detail. Nonetheless, clear effects of character animation on perceived skill were found. We conclude that character animation co‐determines perceptual judgements even when observers are completely unaware of these manipulations. Copyright © 2000 John Wiley & Sons, Ltd.     

Dynamically refining animated triangle meshes for rendering

We present a method to dynamically apply local refinements to an irregular triangle mesh as it deforms in real time. The method increases surface smoothness in regions of high deformation by splitting triangles in a fashion similar to one or two steps of Loop subdivision. The refinement is computed for an arbitrary triangle mesh, and the subdivided triangles are simply passed to the rendering engine, leaving the mesh itself unchanged. The algorithm can thus be easily plugged into existing systems to enhance the visual appearance of animated meshes. The refinement step has very low computational overhead and is easy to implement. We demonstrate the use of the algorithm in a physics-based facial animation system.     

Markov-Type Vector Field for endless surface animation of water stream

In this paper, we propose a hybrid (physical-stochastic) model of surface element (surfel) fluctuations for the visual simulation of an endlessly running water surface. This model comprises two main phases: preprocessing and endless animation phases. First, we simulate a physics-based method for a specific period of time during the preprocessing phase. We construct a stochastic vector field in the simulation, referred to as a Markov-Type Vector Field (MTVF), using only the surface values of the fluid flow. Next, we import the MTVF data into the main endless animation phase and create a surface fluctuation animation by surfels and temporary velocity field modeling of the MTVF using a random sample. In our approach, the surfel edges that cover the fluid flow domain are transferred simply via a temporary single velocity and the new flow surface is determined directly based on their positions. MTVF allows us to generate a water surface animation endlessly in real time without the time-consuming processes of solving the corresponding physical equations. We describe the MTVF construction method and the endless surface animation steps, as well as present the results of experiments that demonstrate the plausibility of our method.     

Online Motion Capture Marker Labeling for Multiple Interacting Articulated Targets

In this paper, we propose an online motion capture marker labeling approach for multiple interacting articulated targets. Given hundreds of unlabeled motion capture markers from multiple articulated targets that are interacting each other, our approach automatically labels these markers frame by frame, by fitting rigid bodies and exploiting trained structure and motion models. Advantages of our approach include: 1) our method is an online algorithm, which requires no user interaction once the algorithm starts. 2) Our method is more robust than traditional the closest point-based approaches by automatically imposing the structure and motion models. 3) Due to the use of the structure model which encodes the rigidity of each articulated body of captured targets, our method can recover missing markers robustly. Our approach is efficient and particularly suited for online computer animation and video game applications.     

Geometric Stiffness for Real‐time Constrained Multibody Dynamics

This paper focuses on the stable and efficient simulation of articulated rigid body systems for real‐time applications. Specifically, we focus on the use of geometric stiffness which can dramatically increase simulation stability. We examine several numerical problems with the inclusion of geometric stiffness in the equations of motion, as proposed by previous work, and address these issues by introducing a novel method for efficiently building the linear system. This offers improved tractability and numerical efficiency. Furthermore, geometric stiffness tends to significantly dissipate kinetic energy. We propose an adaptive damping scheme, inspired by the geometric stiffness, that uses a stability criterion based on the numerical integrator to determine the amount of non‐constitutive damping required to stabilize the simulation. With this approach, not only is the dynamical behavior better preserved, but the simulation remains stable for mass ratios of 1,000,000‐to‐1 at time steps up to 0.1 s. We present a number of challenging scenarios to demonstrate that our method improves efficiency, and that it increases stability by orders of magnitude compared to previous work.     

基于Kinect的人体姿态估计优化和动画生成

为了生成更准确流畅的虚拟人动画,采用Kinect设备捕获三维人体姿态数据的同时,使用单目人体三维姿态估计算法对Kinect的彩色信息进行骨骼点数据推理,从而实时优化人体姿态估计效果,并驱动虚拟人物模型生成动画。首先,提出了一种时空优化的骨骼点数据处理方法,以提高单目估计人体三维姿态的稳定性;其次,提出了一种Kinect和遮挡鲁棒姿势图（ORPM）算法融合的人体姿态估计方法来解决Kinect的遮挡问题;最后,研制了基于四元数向量插值和逆向运动学约束的虚拟人动画系统,其能够进行运动仿真和实时动画生成。与仅利用Kinect捕获人体运动来生成动画的方法相比,所提方法的人体姿态估计数据鲁棒性更强,具备一定的防遮挡能力,而与基于ORPM算法的动画生成方法相比,所提方法生成的动画在帧率上提高了两倍,效果更真实流畅。     

Principal Geodesic Analysis in the Space of Discrete Shells

Important sources of shape variability, such as articulated motion of body models or soft tissue dynamics, are highly nonlinear and are usually superposed on top of rigid body motion which must be factored out. We propose a novel, nonlinear, rigid body motion invariant Principal Geodesic Analysis (PGA) that allows us to analyse this variability, compress large variations based on statistical shape analysis and fit a model to measurements. For given input shape data sets we show how to compute a low dimensional approximating submanifold on the space of discrete shells, making our approach a hybrid between a physical and statistical model. General discrete shells can be projected onto the submanifold and sparsely represented by a small set of coefficients. We demonstrate two specific applications: model‐constrained mesh editing and reconstruction of a dense animated mesh from sparse motion capture markers using the statistical knowledge as a prior.     

Interactive motion mapping for real‐time character control

It is now possible to capture the 3D motion of the human body on consumer hardware and to puppet in real time skeleton‐based virtual characters. However, many characters do not have humanoid skeletons. Characters such as spiders and caterpillars do not have boned skeletons at all, and these characters have very different shapes and motions. In general, character control under arbitrary shape and motion transformations is unsolved ‐ how might these motions be mapped? We control characters with a method which avoids the rigging‐skinning pipeline — source and target characters do not have skeletons or rigs. We use interactively‐defined sparse pose correspondences to learn a mapping between arbitrary 3D point source sequences and mesh target sequences. Then, we puppet the target character in real time. We demonstrate the versatility of our method through results on diverse virtual characters with different input motion controllers. Our method provides a fast, flexible, and intuitive interface for arbitrary motion mapping which provides new ways to control characters for real‐time animation.     

GPU rigid skinning based on a refined skeletonization method

In this paper, we present a skeletal rigid skinning approach. First, we describe a skeleton extraction technique that produces refined skeletons appropriate for animation from decomposed character models. Then, to avoid the artifacts generated in previous skinning approaches and the associated high training costs, we develop an efficient and robust rigid skinning technique that applies blending patches around joints. To achieve real time animation, we have adapted all steps of our rigid skinning algorithm so that they are performed efficiently on the GPU. Finally, we present an evaluation of our methods against four criteria: efficiency, quality, scope, and robustness. Copyright © 2010 John Wiley & Sons, Ltd.     

基于超节点LDL分解的大规模结构计算

采用列压缩稀疏(Compressed Sparse Column,CSC)矩阵存储策略对矩阵LDL分解前进行填充元优化排序;基于消去树进行LDL符号分解,使之独立于数值分解,避免多余的内存消耗,减少不必要的数值运算.利用矩阵非零元的分布特性分析并实现超节点LDL分解算法,将稀疏矩阵的分解运算变为一系列稠密矩阵运算,并使用优化的BLAS函数库加速分解.测试表明:算法在成倍地提高计算速度的同时进一步降低内存消耗,适用于大规模的结构计算.     

Reconstructing Animated Meshes from Time‐Varying Point Clouds

In this paper, we describe a novel approach for the reconstruction of animated meshes from a series of time‐deforming point clouds. Given a set of unordered point clouds that have been captured by a fast 3‐D scanner, our algorithm is able to compute coherent meshes which approximate the input data at arbitrary time instances. Our method is based on the computation of an implicit function in ?⁴ that approximates the time‐space surface of the time‐varying point cloud. We then use the four‐dimensional implicit function to reconstruct a polygonal model for the first time‐step. By sliding this template mesh along the time‐space surface in an as‐rigid‐as‐possible manner, we obtain reconstructions for further time‐steps which have the same connectivity as the previously extracted mesh while recovering rigid motion exactly. The resulting animated meshes allow accurate motion tracking of arbitrary points and are well suited for animation compression. We demonstrate the qualities of the proposed method by applying it to several data sets acquired by real‐time 3‐D scanners.     

Learnt inverse kinematics for animation synthesis

Existing work on animation synthesis can be roughly split into two approaches, those that combine segments of motion-capture data, and those that perform inverse kinematics. In this paper, we present a method for performing animation synthesis of an articulated object (e.g. human body and a dog) from a minimal set of body joint positions, following the approach of inverse kinematics. We tackle this problem from a learning perspective. Firstly, we address the need for knowledge on the physical constraints of the articulated body, so as to avoid the generation of a physically impossible poses. A common solution is to heuristically specify the kinematic constraints for the skeleton model. In this paper however, the physical constraints of the articulated body are represented using a hierarchical cluster model learnt from a motion capture database. Additionally, we shall show that the learnt model automatically captures the correlation between different joints through simultaneous modelling of their angles. We then show how this model can be utilised to perform inverse kinematics in a simple and efficient manner. Crucially, we describe how IK is carried out from a minimal set of end-effector positions. Following this, we show how this “learnt inverse kinematics” framework can be used to perform animation syntheses on different types of articulated structures. To this end, the results presented include the retargeting of a flat surface walking animation to various uneven terrains to demonstrate the synthesis of a full human body motion from the positions of only the hands, feet and torso. Additionally, we show how the same method can be applied to the animation synthesis of a dog using only its feet and torso positions.     

A factorization-based approach for articulated nonrigid shape, motion and kinematic chain recovery from video

Recovering articulated shape and motion, especially human body motion, from video is a challenging problem with a wide range of applications in medical study, sport analysis and animation, etc. Previous work on articulated motion recovery generally requires prior knowledge of the kinematic chain and usually does not concern the recovery of the articulated shape. The non-rigidity of some articulated part, e.g. human body motion with nonrigid facial motion, is completely ignored. We propose a factorization-based approach to recover the shape, motion and kinematic chain of an articulated object with nonrigid parts altogether directly from video sequences under a unified framework. The proposed approach is based on our modeling of the articulated non-rigid motion as a set of intersecting motion subspaces. A motion subspace is the linear subspace of the trajectories of an object. It can model a rigid or non-rigid motion. The intersection of two motion subspaces of linked parts models the motion of an articulated joint or axis. Our approach consists of algorithms for motion segmentation, kinematic chain building, and shape recovery. It handles outliers and can be automated. We test our approach through synthetic and real experiments and demonstrate how to recover articulated structure with non-rigid parts via a single-view camera without prior knowledge of its kinematic chain.     

An Algorithm with Logarithmic Time Complexity for Interactive Simulation of Hierarchically Articulated Bodies Using a Distributed-memory Architecture

The dynamic simulation of large systems of hierarchically articulated bodies is very time-consuming and cannot be done in real time using current one-processor workstations. This paper discusses the parallelization of dynamic simulation algorithms for such systems. First, the methods used in computer animation for solving initial-value problems are compared. Using test suites based on articulated bodies, the Gear method for non-stiff problems is identified as the solver with the least right-hand-side evaluations of the differential equations for the executed tests. On the basis of this method and the articulated-body method, a ‘simulation engine’ for distributed-memory architectures is presented. By reimplementing the Gear method and rearranging its parts, logarithmic time complexity is achieved for hierarchically articulated bodies. By using the simulation engine, interactive, physically based animation of large articulated figures is possible.     

Tracking and Motion Estimation of the Articulated Object: a Hierarchical Kalman Filter Approach

Real-time motion capture plays a very important role in various applications, such as 3D interface for virtual reality systems, digital puppetry, and real-time character animation. In this paper we challenge the problem of estimating and recognizing the motion of articulated objects using theoptical motion capturetechnique. In addition, we present an effective method to control the articulated human figure in realtime.The heart of this problem is the estimation of 3D motion and posture of an articulated, volumetric object using feature points from a sequence of multiple perspective views. Under some moderate assumptions such as smooth motion and known initial posture, we develop a model-based technique for the recovery of the 3D location and motion of a rigid object using a variation of Kalman filter. The posture of the 3D volumatric model is updated by the 2D image flow of the feature points for all views. Two novel concepts – the hierarchical Kalman filter (KHF) and the adaptive hierarchical structure (AHS) incorporating the kinematic properties of the articulated object – are proposed to extend our formulation for the rigid object to the articulated one. Our formulation also allows us to avoid two classic problems in 3D tracking: the multi-view correspondence problem, and the occlusion problem. By adding more cameras and placing them appropriately, our approach can deal with the motion of the object in a very wide area. Furthermore, multiple objects can be handled by managing multiple AHSs and processing multiple HKFs.We show the validity of our approach using the synthetic data acquired simultaneously from the multiple virtual camera in a virtual environment (VE) and real data derived from a moving light display with walking motion. The results confirm that the model-based algorithm works well on the tracking of multiple rigid objects.     

Rank 1 weighted factorization for 3D structure recovery: algorithms and performance analysis

The paper describes the rank 1 weighted factorization solution to the structure from motion problem. This method recovers the 3D structure from the factorization of a data matrix that is rank 1 rather than rank 3. This matrix collects the estimates of the 2D motions of a set of feature points of the rigid object. These estimates are weighted by the inverse of the estimates error standard deviation so that the 2D motion estimates for "sharper" features, which are usually well-estimated, are given more weight, while the noisier motion estimates for "smoother" features are weighted less. We analyze the performance of the rank 1 weighted factorization algorithm to determine what are the most suitable 3D shapes or the best 3D motions to recover the 3D structure of a rigid object from the 2D motions of the features. Our approach is developed for the orthographic camera model. It avoids expensive singular value decompositions by using the power method and is suitable to handle dense sets of feature points and long video sequences. Experimental studies with synthetic and real data illustrate the good performance of our approach.