We present an out-of-core multigrid for solving the Poisson equation defined over gigantic meshes. This enables gradient-domain operations on out-of-core meshes with irregular connectivity. Taking a streaming mesh and boundary constraints as input, our solver builds a multigrid hierarchy and refines the multigrid solution progressively by performing all operations as streaming computations. A set of rules are carefully designed to make neighboring multigrid nodes perform tasks cooperatively and efficiently. With a sublinear memory growth with respect to the number of mesh vertices, our approach handles meshes with 14M vertices using merely 84MB of memory, while an equivalent in-core multigrid implementation fails to fit into 2GB memory space.

This paper investigates how to maintain an efficient dynamic ordered set of bit strings, which is an important problem in the field of information search and information processing. Generally, a dynamic ordered set is required to support 5 essential operations including search, insertion, deletion, max-value retrieval and next-larger-value retrieval. Based on previous research fruits, we present an advanced data structure named rich binary tree (RBT), which follows both the binary-search-tree property and the digital-search-tree property. Also, every key K keeps the most significant difference bit (MSDB) between itself and the next larger value among K’s ancestors, as well as that between itself and the next smaller one among its ancestors. With the new data structure, we can maintain a dynamic ordered set in O(L) time. Since computers represent objects in binary mode, our method has a big potential in application. In fact, RBT can be viewed as a general-purpose data structure for problems concerning order, such as search, sorting and maintaining a priority queue. For example, when RBT is applied in sorting, we get a linear-time algorithm with regard to the key number and its performance is far better than quick-sort. What is more powerful than quick-sort is that RBT supports constant-time dynamic insertion/deletion.

In this paper we present an approach to enrich skeleton-driven animations with physically-based secondary deformation in real time. To achieve this goal, we propose a novel, surface-based deformable model that can interactively emulate the dynamics of both low-and high-frequency volumetric effects. Given a surface mesh and a few sample sequences of its physical behavior, a set of motion parameters of the material are learned during an off-line preprocessing step. The deformable model is then applicable to any given skeleton-driven animation of the surface mesh. Additionally, our dynamic skinning technique can be entirely implemented on GPUs and executed with great efficiency. Thus, with minimal changes to the conventional graphics pipeline, our approach can drastically enhance the visual experience of skeleton-driven animations by adding secondary deformation in real time.

In this paper, we present an image editing tool that allows the user to deform images using a sketch‐based interface. The user simply sketches a set of source curves in the input image, and also some target curves that the source curves should be deformed to. Then the moving least squares (MLS) deformation technique [ SMW06 ] is adapted to produce realistic deformations while satisfying the curves' positional constraints. We also propose a scheme to reduce image fold‐overs in MLS deformations. Our system has a very intuitive user interface, generates physically plausible deformations, and can be easily implemented on the GPU for real‐time performance.

We present mesh puppetry , a variational framework for detail-preserving mesh manipulation through a set of high-level, intuitive, and interactive design tools. Our approach builds upon traditional rigging by optimizing skeleton position and vertex weights in an integrated manner. New poses and animations are created by specifying a few desired constraints on vertex positions, balance of the character, length and rigidity preservation, joint limits, and/or self-collision avoidance. Our algorithm then adjusts the skeleton and solves for the deformed mesh simultaneously through a novel cascading optimization procedure, allowing realtime manipulation of meshes with 50 K + vertices for fast design of pleasing and realistic poses. We demonstrate the potential of our framework through an interactive deformation platform and various applications such as deformation transfer and motion retargeting.

This paper presents a novel interactive mesh deformation method that can achieve various dynamic material effects, including elastic membrane and cloth effects. In our framework, a mesh is encoded by some differential quantities based on edge length and dihedral angle; and the deformation is formulated as a least square problem for preserving the edge length and dihedral angle via the differential quantities. In order to obtain anisotropic material effects, we further propose an edge-weighting scheme based on a user-specified vector field. To avoid specifying the local transformations, we set up an iterative scheme for solving the deformation. At last, several examples are presented to show that our approach can interactively generate visually pleasing deformations. Copyright © 2006 John Wiley & Sons, Ltd.

In this paper we present a general framework for performing constrained mesh deformation tasks with gradient domain techniques. We present a gradient domain technique that works well with a wide variety of linear and nonlinear constraints. The constraints we introduce include the nonlinear volume constraint for volume preservation, the nonlinear skeleton constraint for maintaining the rigidity of limb segments of articulated figures, and the projection constraint for easy manipulation of the mesh without having to frequently switch between multiple viewpoints. To handle nonlinear constraints, we cast mesh deformation as a nonlinear energy minimization problem and solve the problem using an iterative algorithm. The main challenges in solving this nonlinear problem are the slow convergence and numerical instability of the iterative solver. To address these issues, we develop a subspace technique that builds a coarse control mesh around the original mesh and projects the deformation energy and constraints onto the control mesh vertices using the mean value interpolation. The energy minimization is then carried out in the subspace formed by the control mesh vertices. Running in this subspace, our energy minimization solver is both fast and stable and it provides interactive responses. We demonstrate our deformation constraints and subspace deformation technique with a variety of constrained deformation examples.

This paper presents a fast and stable technique for simulating deformable objects. Unlike in previous physically based methods, our potential energy of deformation is purely geometrically based. It is defined as the L-2 norm of the change of the differential coordinates. A key feature of this energy formulation is that the corresponding stiffness matrix is approximately constant, which enables fast and stable implicit integration and large deformations. Our algorithm can simulate various effects including solid, thin shell and plasticity. We also adopt two schemes to accelerate the simulation process: dimensionality reduction in frequency domain and adaptive rotation computation in spatial domain.

In this paper, we introduce a novel approach to mesh editing with the Poisson equation as the theoretical foundation. The most distinctive feature of this approach is that it modifies the original mesh geometry implicitly through gradient field manipulation. Our approach can produce desirable and pleasing results for both global and local editing operations, such as deformation, object merging, and smoothing. With the help from a few novel interactive tools, these operations can be performed conveniently with a small amount of user interaction. Our technique has three key components, a basic mesh solver based on the Poisson equation, a gradient field manipulation scheme using local transforms, and a generalized boundary condition representation based on local frames. Experimental results indicate that our framework can outperform previous related mesh editing techniques.