Rigidity Constraints for Large Mesh Deformation

It is a challenging problem of surface-based deformation to avoid apparent volumetric distortions around largely deformed areas. In this paper, we propose a new rigidity constraint for gradient domain mesh deformation to address this problem. Intuitively the proposed constraint can be regarded as several small cubes defined by the mesh vertices through mean value coordinates. The user interactively specifies the cubes in the regions which are prone to volumetric distortions, and the rigidity constraints ...     

Scale-aware shape manipulation

A novel representation of a triangular mesh surface using a set of scale-inva~iant measures is proposed. The measures consist of angles of the triangles （triangle angles） and dihedral angles along the edges （edge angles） which are scale and rigidity independent. The vertex coordinates for a mesh give its scale-invariant measures, unique up to scale, rotation, and translation. Based on the representation of mesh using scale-invariant measures, a two-step iterative deformation algorithm is proposed, which can arbitrarily edit the mesh through simple handles interaction. The algorithm can explicitly preserve the local geometric details as much as possible in different scales even under severe editing operations including rotation, scaling, and shearing. The efficiency and robustness of the proposed algorithm are demonstrated by examples.     

Un-thorough Delaunay Approach for Tetrahedral Mesh Generation

An integrated tetrahedrization algorithm in 3D domain which combines the Delaunay tetrahedral method with un-Delaunay tetrahedral method is described. The algorithm was developed by constructing Delaunay Tetrahedrons from a scattered point set, recovering boundaries using Delaunay and un-Delaunay method, inserting additional nodes in unsuitable tetrahedrons, optimizing tetrahedrons and smoothing the tetrahedral mesh with the 2D-3D Laplacian method. The algorithm has been applied to the injection molding CAE preprocessing.     

Spherical Parameterization of Marching Cubes IsoSurfaces Based upon Nearest Neighbor Coordinates

We present some new methods for parameterizing the triangle mesh surface (TMS) which result from the Marching Cubes (MC) algorithm. The methods apply to surfaces of genus zero and the parameter domain is a unit sphere. We take advantage of some special properties of the TMS resulting from the MC algorithm to obtain simple, computational efficient representations of the nearest neighbor coordinates and utilize these coordinates in the characterization of the parameterization by means of systems of equatio...     

Quasi-angle-preserving mesh deformation using the least-squares approach

We propose an angle-based mesh representation, which is invariant under translation, rotation, and uniform scaling, to encode the geometric details of a triangular mesh. Angle-based mesh representation consists of angle quantities defined on the mesh, from which the mesh can be reconstructed uniquely up to translation, rotation, and uniform scaling. The reconstruction process requires solving three sparse linear systems： the first system encodes the length of edges between vertices on the mesh, the second system encodes the relationship of local frames between two adjacent vertices on the mesh, and the third system defines the position of the vertices via the edge length and the local frames. From this angle-based mesh representation, we propose a quasi-angle-preserving mesh deformation system with the least-squares approach via detail-preserving mesh editing examples are presented to handle translation, rotation, and uniform scaling. Several demonstrate the effectiveness of the proposed method.     

Mesh Detail Editing by Filtering Differential Edge Coordinates

In this paper, we propose anovel geometricaldetail editing method for triangulatedmeshmodels based on filtering robust differential edge coordinates.Theintroduceddetail editing consists ofnot only feature-preserving denoising for removing scanner noises, but also interactive detail editing for weakening or enhancing some specific geometric details.Various detail editing results are obtainedby reconstructingthe mesh fromnew processed differential edge coordinates, which are filtered from the view of signal processing, in linear least square sense.Experimental results and comparisonswith other methodsdemonstrate that our method is effective and robust.     

Regional gradient observability for semilinear hyperbolic systems: HUM approach

The paper aims to extend the notion of regional observability of the gradient to the semilinear hyperbolic case, in order to reconstruct the gradient of the initial conditions in a subregion $\omega$ of the domain evolution $\varOmega$. We start with an asymptotically linear system, the approach is based on an extension of the Hilbert uniqueness method (HUM) and Schauder''s fixed point theorem. The analysis leads to an algorithm which is successfully numerically implemented and illustrated with examples and simulations.     

Contour detection improved by frequency domain filtering of gradient image

We propose an intermediate computational step,frequency domain filtering of gradient image,to improve contour detection performance of gradient-based edge detectors.This step is inspired by analyzing the spectrum distribution of object contours and texture edges in the frequency domain of gradient image.We illustrate the principle and efect of this step by adding it to the Canny edge detector.The resulting operator can selectively retain object contours and region boundaries,and meanwhile can dramatically reduce non-meaningful elements caused by textured background.We use several types of images to compare the proposed method and other related methods qualitatively and quantitatively.Experimental results show that the proposed method can efectively enhance the contour detection of Canny edge detector and achieves similar detection performance to two other related methods but runs faster.     

Automatic mesh generation on a regular background grid

This paper presents and automatic mesh generation procedure on a 2D domain based on a regular background grid.The idea is to devise a robust mesh generation scheme with equal emphasis on quality and efficiency,Instead of using a traditional regular rectangular grid,a mesh of equilateral triangles is employed to ensure triangular element of the best quality will be preserved in the interior of the domain.As for the boundary,it is to be generated by a node/segment insertion process.Nodes are inserted into the background mesh one by one following the sequence of the domain boundary.The local strcture of the mesh is modified based on the Delaunay criterion with the introduction of each node.Those boundary segments.which are not produced in the phase of node insertion,will be recovered through a systematic element swap produced in the phase of node insertion will be recovered through a systematic element swap process.Two theorems will be presented and proved to set up the theoretical basic of the boundary recovery part.Examples will be presented to demonstrate the robustness and the quality of the mesh generated by the proposed technique.     

Digital Differential Geometry Processing

The theory and methods of digital geometry processing has been a hot research area in computer graphics, as geometric models serves as the core data for 3D graphics applications. The purpose of this paper is to introduce some recent advances in digital geometry processing, particularly mesh fairing, surface parameterization and mesh editing, that heavily use differential geometry quantities. Some related concepts from differential geometry, such as normal, curvature, gradient, Laplacian and their counterparts on digital geometry are also reviewed for understanding the strength and weakness of various digital geometry processing methods.     

Non-iterative approach for global mesh optimization

This paper presents a global optimization operator for arbitrary meshes. The global optimization operator is composed of two main terms, one part is the global Laplacian operator of the mesh which keeps the fairness and another is the constraint condition which reserves the fidelity to the mesh. The global optimization operator is formulated as a quadratic optimization problem, which is easily solved by solving a sparse linear system. Our global mesh optimization approach can be effectively used in at least three applications: smoothing the noisy mesh, improving the simplified mesh, and geometric modeling with subdivision-connectivity. Many experimental results are presented to show the applicability and flexibility of the approach.     

Robust mesh editing using Laplacian coordinates

Shape deformation and editing are important for animation and game design. Laplacian surface based methods have been widely investigated and used in many works. In this paper we propose a robust mesh editing framework which improves traditional Laplacian surface editing. It consists of two procedures: skeleton based as-rigid-as-possible (ARAP) shape modeling and detail-preserving mesh optimization. Traditional ARAP shape modeling relies on the mesh quality. Degenerated mesh may adversely affect the deformation performance. A preprocessing step of mesh optimization can alleviate this problem. However, skinny triangles can still be generated during deformation, which adversely affect the editing performance. Thus our method performs Laplacian mesh deformation and optimization alternately in each iteration, which ensures mesh quality without noticeably increasing computational complexity or changing the shape details. This approach is more robust than those solely using Laplacian mesh deformation. An additional benefit is that the skeleton-based ARAP modeling can approximately preserve the volume of an object with large-scale deformations. The volume is roughly kept by leveraging the skeleton information and employing a carefully designed energy function to preserve the edge length. This method does not break the manifoldness of traditional ARAP methods or sacrifice speed. In our experiments, we show that (1) our method is robust even for degenerated meshes, (2) the deformation is natural in terms of recovering rotations, and (3) volumes are roughly kept even under large-scale deformations. The system achieves real time performance for surface meshes with 7k vertices.     

2D shape deformation using nonlinear least squares optimization

This paper presents a novel 2D shape deformation algorithm based on nonlinear least squares optimization. The algorithm aims to preserve two local shape properties: the Laplacian coordinates of the boundary curve and the local area of the shape interior, which are together represented in a non-quadratic energy function. An iterative Gauss–Newton method is used to minimize this nonlinear energy function. The result is an interactive shape deformation system that can achieve physically plausible results that are difficult to achieve with previous linear least squares methods. In addition to this algorithm that preserves local shape properties, we also introduce a scheme to preserve the global area of the shape, which is useful for deforming incompressible objects.     

Feature sensitive deformation for triangular mesh models

Shape deformation is a useful tool for shape modeling and animation in computer graphics. In this paper, we propose a novel surface deformation method based on a feature sensitive (FS) metric. Firstly, taking unit normal vectors into account, we derive a FS Laplacian operator, which is more sensitive to featured regions of mesh models than existing operators. Secondly, we use the 1‐ring tetrahedron in the dual mesh, a volumetric structure, to encode geometric details. To preserve the shape of the tetrahedron, we introduce linear tetrahedron constraints minimizing both the distortion of the base triangle and the change of the corresponding height. These ensure that geometric details are accurately preserved during deformation. The time complexity of our new method is similar to that of existing linear Laplacian methods. Examples are included to show that our FS deformation method better preserves mesh details, especially features, than existing Laplacian methods. Copyright © 2010 John Wiley & Sons, Ltd.     

Material-aware differential mesh deformation using sketching interface

In this paper, we present a material-aware mesh deformation method using a sketching interface. Guided by user-specified material properties, our method can deform the surface mesh in a non-uniform way, while previous deformation techniques are mainly designed for uniform materials. The non-uniform deformation is achieved by material-dependent gradient field manipulation and Poisson-based reconstruction. Compared with previous material-oblivious deformation techniques, our method supplies better control of the deformation process and can generate more realistic results. We propose a novel detail representation that transforms geometric details between successive surface levels as a combination of dihedral angles and barycentric coordinates. This detail representation is similarity-invariant and fully compatible with material properties. Based on these two methods, we implement a multi-resolution deformation tool, allowing the user to edit a mesh inside a hierarchy in a material-aware manner. We demonstrate the effectiveness and robustness of our methods by several examples with real-world data.     

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。     

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.