Multi‐layer Lattice Model for Real‐Time Dynamic Character Deformation

Due to the recent advancement of computer graphics hardware and software algorithms, deformable characters have become more and more popular in real‐time applications such as computer games. While there are mature techniques to generate primary deformation from skeletal movement, simulating realistic and stable secondary deformation such as jiggling of fats remains challenging. On one hand, traditional volumetric approaches such as the finite element method require higher computational cost and are infeasible for limited hardware such as game consoles. On the other hand, while shape matching based simulations can produce plausible deformation in real‐time, they suffer from a stiffness problem in which particles either show unrealistic deformation due to high gains, or cannot catch up with the body movement. In this paper, we propose a unified multi‐layer lattice model to simulate the primary and secondary deformation of skeleton‐driven characters. The core idea is to voxelize the input character mesh into multiple anatomical layers including the bone, muscle, fat and skin. Primary deformation is applied on the bone voxels with lattice‐based skinning. The movement of these voxels is propagated to other voxel layers using lattice shape matching simulation, creating a natural secondary deformation. Our multi‐layer lattice framework can produce simulation quality comparable to those from other volumetric approaches with a significantly smaller computational cost. It is best to be applied in real‐time applications such as console games or interactive animation creation.     

Skeleton-based Variational Mesh Deformations

In this paper, a new free-form shape deformation approach is proposed. We combine a skeleton-based mesh deformation technique with discrete differential coordinates in order to create natural-looking global shape deformations. Given a triangle mesh, we first extract a skeletal mesh, a two-sided Voronoibased approximation of the medial axis. Next the skeletal mesh is modified by free-form deformations. Then a desired global shape deformation is obtained by reconstructing the shape corresponding to the deformed skeletal mesh. The reconstruction is based on using discrete differential coordinates. Our method preserves fine geometric details and original shape thickness because of using discrete differential coordinates and skeleton-based deformations. We also develop a new mesh evolution technique which allow us to eliminate possible global and local self-intersections of the deformed mesh while preserving fine geometric details. Finally, we present a multi-resolution version of our approach in order to simplify and accelerate the deformation process. In addition, interesting links between the proposed free-form shape deformation technique and classical and modern results in the differential geometry of sphere congruences are established and discussed.     

Multi‐Resolution Cloth Simulation

We propose a novel, multi‐resolution method to efficiently perform large‐scale cloth simulation. Our cloth simulation method is based on a triangle‐based energy model constructed from a cloth mesh. We identify that solutions of the linear system of cloth simulation are smooth in certain regions of the cloth mesh and solve the linear system on those regions in a reduced solution space. Then we reconstruct the original solutions by performing a simple interpolation from solutions computed in the reduced space. In order to identify regions where solutions are smooth, we propose simplification metrics that consider stretching, shear, and bending forces, as well as geometric collisions. Our multi‐resolution method can be applied to many existing cloth simulation methods, since our method works on a general linear system. In order to demonstrate benefits of our method, we apply our method into four large‐scale cloth benchmarks that consist of tens or hundreds of thousands of triangles. Because of the reduced computations, we achieve a performance improvement by a factor of up to one order of magnitude, with a little loss of simulation quality.     

Inverse Modelling of Incompressible Gas Flow in Subspace

This paper advocates a novel method for modelling physically realistic flow from captured incompressible gas sequence via modal analysis in frequency‐constrained subspace. Our analytical tool is uniquely founded upon empirical mode decomposition (EMD) and modal reduction for fluids, which are seamlessly integrated towards a powerful, style‐controllable flow modelling approach. We first extend EMD, which is capable of processing 1D time series but has shown inadequacies for 3D graphics earlier, to fit gas flows in 3D. Next, frequency components from EMD are adopted as candidate vectors for bases of modal reduction. The prerequisite parameters of the Navier–Stokes equations are then optimized to inversely model the physically realistic flow in the frequency‐constrained subspace. The estimated parameters can be utilized for re‐simulation, or be altered toward fluid editing. Our novel inverse‐modelling technique produces real‐time gas sequences after precomputation, and is convenient to couple with other methods for visual enhancement and/or special visual effects. We integrate our new modelling tool with a state‐of‐the‐art fluid capturing approach, forming a complete pipeline from real‐world fluid to flow re‐simulation and editing for various graphics applications.     

A criterion on inclusion of stress stiffening effects in flexible multibody dynamic system simulation

This paper presents a criterion on inclusion of stress stiffening effects in dynamic simulation of flexible multibody systems. The proposed criterion examines numerically the eigenvalue variation of the total modal stiffness matrix that is a combination of the modal stress stiffness matrix and the conventional linear modal stiffness matrix prior to actual dynamic simulation. If the variation is sufficiently large for any flexible body in the multibody system, then stress stiffening effects must be included in dynamic simulation of flexible multibody systems for accurate prediction of dynamic behavior. Since the criterion uses the most general stress stiffness matrix contributed from applied and constraint reaction loads as well as from a system of 12 inertial loads, this criterion is applicable to any general flexible multibody dynamic system. Several numerical results are presented to show the effectiveness of the proposed criterion.     

热测地场控制的近似刚性网格变形技术

为保持三维模型局部细节,修正近似刚性网格变形算法(ARAP)应用于大尺度以及 非完全刚性变形中出现的扭曲、翻折问题,提出了一种基于测地场约束的近似刚性变形方法。 首先对模型进行 Laplacian 变形,并通过奇异值分解求得局部单位的旋转矩阵,计算模型刚性变 形能量;然后通过求解稀疏线性系统,更新变形点,再通过求解两次稀疏线性系统,计算变形 过程中产生的测地场偏差,并修正变形网格,得到与原始网格测地场接近的变形结果;反复迭 代上述步骤,直到热测地场偏差满足一定要求,获得最终变形结果。结果表明,该方法能在网 格变形过程中快速地完成网格点修正功能,在应用于大尺度变形中也能有效地避免网格出现翻 折问题。     

Automatic Conversion of Mesh Animations into Skeleton-based Animations

Recently, it has become increasingly popular to represent animations not by means of a classical skeleton‐based model, but in the form of deforming mesh sequences. The reason for this new trend is that novel mesh deformation methods as well as new surface based scene capture techniques offer a great level of flexibility during animation creation. Unfortunately, the resulting scene representation is less compact than skeletal ones and there is not yet a rich toolbox available which enables easy post‐processing and modification of mesh animations. To bridge this gap between the mesh‐based and the skeletal paradigm, we propose a new method that automatically extracts a plausible kinematic skeleton, skeletal motion parameters, as well as surface skinning weights from arbitrary mesh animations. By this means, deforming mesh sequences can be fully‐automatically transformed into fullyrigged virtual subjects. The original input can then be quickly rendered based on the new compact bone and skin representation, and it can be easily modified using the full repertoire of already existing animation tools.     

Nonlinear dynamics by mode superposition

A mode superposition technique for approximately solving nonlinear initial-boundary-value problems of structural dynamics is discussed, and results for examples involving large deformation are compared to those obtained with implicit direct integration methods such as the Newmark generalized acceleration and Houbolt backward-difference operators. The initial natural frequencies and mode shapes are found by inverse power iteration with the trial vectors for successively higher modes being swept by Gram—Schmidt orthonormalization at each iteration. The subsequent modal spectrum for nonlinear states is based upon the tangent stiffness of the structure and is calculated by a subspace iteration procedure that involves matrix multiplication only, using the most recently computed spectrum as an initial estimate. Then, a precise time integration algorithm that has no artificial damping or phase velocity error for linear problems is applied to the uncoupled modal equations of motion. Squared-frequency extrapolation is examined for nonlinear problems as a means by which these qualities of accuracy and precision can be maintained when the state of the system (and, thus, the modal spectrum) is changing rapidly.The results indicate that a number of important advantages accrue to nonlinear mode superposition: (a) there is no significant difference in total solution time between mode superposition and implicit direct integration analyses for problems having narrow matrix half-bandwidth (in fact, as bandwidth increases, mode superposition becomes more economical), (b) solution accuracy is under better control since the analyst has ready access to modal participation factors and the ratios of time step size to modal period, and (c) physical understanding of nonlinear dynamic response is improved since the analyst is able to observe the changes in the modal spectrum as deformation proceeds.     

Sparse Localized Decomposition of Deformation Gradients

Sparse localized decomposition is a useful technique to extract meaningful deformation components out of a training set of mesh data. However, existing methods cannot capture large rotational motion in the given mesh dataset. In this paper we present a new decomposition technique based on deformation gradients. Given a mesh dataset, the deformation gradient field is extracted, and decomposed into two groups: rotation field and stretching field, through polar decomposition. These two groups of deformation information are further processed through the sparse localized decomposition into the desired components. These sparse localized components can be linearly combined to form a meaningful deformation gradient field, and can be used to reconstruct the mesh through a least squares optimization step. Our experiments show that the proposed method addresses the rotation problem associated with traditional deformation decomposition techniques, making it suitable to handle not only stretched deformations, but also articulated motions that involve large rotations.     

Learning 3D Deformation of Animals from 2D Images

Understanding how an animal can deform and articulate is essential for a realistic modification of its 3D model. In this paper, we show that such information can be learned from user‐clicked 2D images and a template 3D model of the target animal. We present a volumetric deformation framework that produces a set of new 3D models by deforming a template 3D model according to a set of user‐clicked images. Our framework is based on a novel locally‐bounded deformation energy, where every local region has its own stiffness value that bounds how much distortion is allowed at that location. We jointly learn the local stiffness bounds as we deform the template 3D mesh to match each user‐clicked image. We show that this seemingly complex task can be solved as a sequence of convex optimization problems. We demonstrate the effectiveness of our approach on cats and horses, which are highly deformable and articulated animals. Our framework produces new 3D models of animals that are significantly more plausible than methods without learned stiffness.     

Modeling and simulation of structural components in recursive closed-loop multibody systems

Passenger cars, transit buses, railroad vehicles, off-highway trucks, earth moving equipment and construction machinery contain structural and light-fabrications (SALF) components that are prone to excessive vibration due to rough terrains and work-cycle loads’ excitations. SALF components are typically modeled as flexible components in the multibody system allowing the analysts to predict elastic deformation and hence the stress levels under different loading conditions. Including SALF component in the multibody system typically generates closed-kinematic loops. This paper presents an approach for integrating SALF modeling capabilities as a flexible body in a general-purpose multibody dynamics solver that is based on joint-coordinates formulation with the ability to handle closed-kinematic loops. The spatial algebra notation is employed in deriving the spatial multibody dynamics equations of motion. The system kinematic topology matrix is used to project the Cartesian quantities into the joint subspace, leading to a condensed set of nonlinear equations with minimum number of generalized coordinates. The proposed flexible body formulation utilizes the component mode synthesis approach to reduce the large number of finite element degrees of freedom to a small set of generalized modal coordinates. The resulting reduced flexible body model has two main characteristics: the stiffness matrix is constant while the mass matrix depends on the elastic modal coordinates. A consistent set of pre-computed inertia shape integrals are identified and used to update the modal mass matrix at each time step. The implementation of the component mode synthesis approach in a closed-loop recursive multibody formulation is presented. The kinematic equations are modified to include the effect of the flexible body modal elastic coordinates. Also, modified constraint equations that include the effect of flexibility at the joint connections and the necessary details of the Jacobian matrix are presented. Baumgarte stabilization approach is used to stabilize the constraint equations without using iterative schemes. A sample results for flexible body impeded in a closed system will be presented to demonstrate the above mentioned approach.     

A model for compression and classification of face data structures

In this paper we present a 3-D model with physical properties which simplifies the analysis and the synthesis of deformable faces and solids. Our model presents three relevant particularities. First, it describes the external envelope of faces with 1-D finite elements assembled with a new 3-connected mesh topology. Second, the mesh deformations are analysed with a modal analysis. Because our model associates these two particularities, the number of rigid modes given by the modal analysis is equal to the number of 1-D finite elements, which is also the half of the number of Degrees of Freedom (DOF). This number of rigid modes is a basic characteristic of our model. The second half of modes constitutes the nonrigid modes. Third, we use these rigid modes and the first nonrigid mode to synthesize a mean face named a photo-fit identikit or class, around which we synthesize face varieties by action on secondary nonrigid modes. Our physical 3-D model allows compression of face data structures because a greater number of secondary nonrigid modes can be suppressed to define a class or its varieties, and because the synthesis of varieties does not need more information storage than their classes. Our physical 3-D model allows classification of face data structures because we can associate an objective measure to each synthesized face. We can measure the deformation between a variety and its photo-fit identikit.     

Example‐Based Retargeting of Human Motion to Arbitrary Mesh Models

We present a novel method for retargeting human motion to arbitrary 3D mesh models with as little user interaction as possible. Traditional motion‐retargeting systems try to preserve the original motion, while satisfying several motion constraints. Our method uses a few pose‐to‐pose examples provided by the user to extract the desired semantics behind the retargeting process while not limiting the transfer to being only literal. Thus, mesh models with different structures and/or motion semantics from humanoid skeletons become possible targets. Also considering the fact that most publicly available mesh models lack additional structure (e.g. skeleton), our method dispenses with the need for such a structure by means of a built‐in surface‐based deformation system. As deformation for animation purposes may require non‐rigid behaviour, we augment existing rigid deformation approaches to provide volume‐preserving and squash‐and‐stretch deformations. We demonstrate our approach on well‐known mesh models along with several publicly available motion‐capture sequences.     

Real‐Time Subspace Integration for Example‐Based Elastic Material

Example‐based material allows simulating complex material behaviors in an art‐directed way. This paper presents a method for fast subspace integration for example‐based elastic material, which is suitable for real‐time simulation in computer graphics. At the core of the method is the formulation of a new potential using example‐based Green strain tensors. By using this potential, the deformation can be attracted towards the example‐based deformation feature space, the example weights can be explicitly obtained and the internal force can be decomposed into the conventional one and an additional one induced by the examples. The real‐time subspace integration is then developed with subspace integration costs independent of geometric complexity, and both the reduced conventional internal force and additional one being cubic polynomials in reduced coordinates. Experiments demonstrate that our method can achieve real‐time simulation while providing comparable quality with the prior art.     

Real-Time Simulation of Thin Shells

This paper proposes a real-time simulation technique for thin shells undergoing large deformation. Shells are thin objects such as leaves and papers that can be abstracted as 2D structures. Development of a satisfactory physical model that runs in real-time but produces visually convincing animation of thin shells has been remaining a challenge in computer graphics. Rather than resorting to shell theory which involves the most complex formulations in continuum mechanics, we adopt the energy functions from the discrete shells proposed by Grinspun et al. [ [GHDS03] ]. For real-time integration of the governing equation, we develop a modal warping technique for shells. This new simulation framework results from making extensions to the original modal warping technique [ [CK05] ] which was developed for the simulation of 3D solids. We report experimental results, which show that the proposed method runs in real-time even for large meshes, and that it can simulate large bending and/or twisting deformations with acceptable realism.     

Gradient field based inhomogeneous volumetric mesh deformation for maxillofacial surgery simulation

This paper presents a novel inhomogeneous volumetric mesh deformation approach by gradient field manipulation, and uses it for maxillofacial surgery simulation. The study is inspired by the state-of-the-art surface deformation techniques based on differential representations. Working in the volumetric domain instead of on only the surface can preserve the volumetric details much better, avoid local self-intersections, and achieve better deformation propagation because of the internal mesh connections. By integrating the mesh cell material stiffness parameter into our new discrete volumetric Laplacian operator, it is very convenient to incorporate inhomogeneous materials into the deformation framework. In addition, the system matrix for solving the volumetric harmonic field to handle the local transformation problem is the same used for Poisson reconstruction equation, thus it requires solving essentially only one global linear system. The system is easy to use, and can accept explicit rotational constraints, or only translational constraints to drive the deformation. One typical maxillofacial surgery case was simulated by the new methodology with inhomogeneous material estimated directly from CT data, and compared to the commonly used finite element method (FEM) approach. The results demonstrated that the deformation methodology achieved good accuracy, as well as interactive performance. Therefore, the usage of our volumetric mesh deformation approach is relevant and suitable for daily clinical practice.     

Modal Locomotion: Animating Virtual Characters with Natural Vibrations

We present a general method to intuitively create a wide range of locomotion controllers for 3D legged characters. The key of our approach is the assumption that efficient locomotion can exploit the natural vibration modes of the body, where these modes are related to morphological parameters such as the shape, size, mass, and joint stiffness. The vibration modes are computed for a mechanical model of any 3D character with rigid bones, elastic joints, and additional constraints as desired. A small number of vibration modes can be selected with respect to their relevance to locomotion patterns and combined into a compact controller driven by very few parameters. We show that these controllers can be used in dynamic simulations of simple creatures, and for kinematic animations of more complex creatures of a variety of shapes and sizes.     

Compressed Manifold Modes for Mesh Processing

This paper introduces compressed eigenfunctions of the Laplace‐Beltrami operator on 3D manifold surfaces. They constitute a novel functional basis, called the compressed manifold basis, where each function has local support. We derive an algorithm, based on the alternating direction method of multipliers (ADMM), to compute this basis on a given triangulated mesh. We show that compressed manifold modes identify key shape features, yielding an intuitive understanding of the basis for a human observer, where a shape can be processed as a collection of parts. We evaluate compressed manifold modes for potential applications in shape matching and mesh abstraction. Our results show that this basis has distinct advantages over existing alternatives, indicating high potential for a wide range of use‐cases in mesh processing.     

Acceleration sensitivity of tuning fork gyroscopes: theoretical model,simulation and experimental verification

A two degrees of freedom (DOF) coupled model is investigated in this paper to analyze the acceleration sensitivity of MEMS tuning fork gyroscopes (TFG) and approaches of decreasing the acceleration sensitivity are presented. Since two tines of TFGs are asymmetric in the mass, stiffness and damping caused by the technological defects, there exists the coupled effect between two tines leading to the invalidity of a single DOF model. Therefore, a two DOFs model is established and the matrix perturbation technique is used to calculate the dynamic responses of the two tines by applying the common-mode acceleration. Our quantitative analysis reveals that the displacement difference is large in the in- and anti-phase modal frequencies between two tines, arising from the unsynchronized motion of two tines due to stiffness imbalance. The FEM simulations coincide with our theoretical calculations. Meanwhile, we take advantage of the experimental data from the other researches to verify our theoretical model and analytical expressions. Our results demonstrate that the acceleration sensitivity of TFGs can be reduced by increasing the coupled stiffness ratio, modal frequency and sense beams widths which are insensitive to technological dispersions.     

Visual Exploration of High‐Dimensional Data through Subspace Analysis and Dynamic Projections

We introduce a novel interactive framework for visualizing and exploring high‐dimensional datasets based on subspace analysis and dynamic projections. We assume the high‐dimensional dataset can be represented by a mixture of low‐dimensional linear subspaces with mixed dimensions, and provide a method to reliably estimate the intrinsic dimension and linear basis of each subspace extracted from the subspace clustering. Subsequently, we use these bases to define unique 2D linear projections as viewpoints from which to visualize the data. To understand the relationships among the different projections and to discover hidden patterns, we connect these projections through dynamic projections that create smooth animated transitions between pairs of projections. We introduce the view transition graph, which provides flexible navigation among these projections to facilitate an intuitive exploration. Finally, we provide detailed comparisons with related systems, and use real‐world examples to demonstrate the novelty and usability of our proposed framework.