网格变形综述

网格变形作为一种几何模型交互编辑技术在几何建模和计算机动画中具有重要价值。近年来,保细节的网格变形特别是微分域网格变形一直得到国内外研究人员的高度关注。从骨骼变形、曲面变形、空间变形3个方面,结合近年来网格变形领域的最新研究进展,通过对各种典型的网格变形算法的算法思想、特点、局限性的描述和比较,提供该领域研究现状的系统综述。并对网格变形的研究趋势进行了展望。     

As-rigid-as-possible mesh deformation and its application in hexahedral mesh generation

This paper presents an efficient and stable as-rigid-as-possible mesh deformation algorithm for planar shape deformation and hexahedral mesh generation. The deformation algorithm aims to preserve two local geometric properties: scale-invariant intrinsic variables and elastic deformation energy, which are together represented in a quadric energy function. To preserve these properties, the position of each vertex is further adjusted by iteratively minimizing this quadric energy function to meet the position constraint of the controlling points. Experimental results show that the deformation algorithm is efficient, and can obtain physically plausible results, which have the same topology structure with the original mesh. Such a mesh deformation method is useful to project the source surface mesh onto the target surfaces in hexahedral mesh generation based on sweep method, and application results show that the proposed method is feasible to mesh projection not only between similar surface contours but also dissimilar surface contours.     

Robust edge-preserving surface mesh polycube deformation

Computational Visual Media - Polycube construction and deformation are essential problems in computer graphics. In this paper, we present a robust, simple, efficient, and automatic algorithm to...     

基于细分的网格模型骨架驱动变形技术

针对传统骨架驱动变形方法中模型细节特征不能得到有效保持的问题,提出一种基于细分的骨架驱动网格模型变形方法。首先,对网格模型待变形区域基于截交线进行局部骨架提取和控制网格构建,分别建立骨架与控制网格以及控制网格所对应细分曲面与待变形模型区域之间的关联关系;然后,将基本函数作用下的自由变形方法应用于骨架变形,通过骨架变形驱动控制网格变形,将变形前后控制网格所对应细分曲面的变化信息转为网格模型泊松梯度场的改变;最后,根据改变后梯度场重建网格模型。实例表明,该变形方法针对不同网格模型均可以得到较好的编辑效果,且细节信息在变形后都得到了有效保持。与传统骨架驱动变形方法相比,该方法除具备交互操作简单直观的优势外,同时能够更好保持变形模型几何细节特征,更为适合具有丰富几何细节的复杂模型的变形编辑。     

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.     

Preserving form features in interactive mesh deformation

Interactive mesh deformation that preserves differential properties is a promising technique for the design of mechanical parts such as automobile sheet-metal panels. However, existing methods lack the ability to manipulate the form features and hard constraints that are commonly used in engineering applications. In this paper, we propose a new deformation framework that precisely preserves the shapes of form features during deformation. Geometrical shapes are interactively deformed so that mean curvature normals are approximately preserved in a least-squares sense and positional constraints and form-feature constraints are precisely satisfied. In our system, the combination of soft and hard constraints is solved using the Lagrange multiplier method. We also show how to constrain the motion of a form feature on a plane or a straight line using linear constraints. The implemented system achieves a real-time response for constrained deformation.     

Volumetric subspace mesh deformation with structure preservation

Existing deformation techniques are oblivious to salient structures that often capture the essence of 3D meshes. Combining with gradient domain technique, we propose an alternative approach to preserve these structures in the volumetric subspace. Through a simple sketching interface, the structures of the input mesh are specified by the user. During deformations, these key structures are constrained to deform rigidly to maintain their original shapes, hence avoiding serious visual artifacts. However, this process leads to a nonlinear optimization problem. To guarantee fast convergence as well as numerical stability, we project the deformation energy onto a volumetric subspace which envelops the input mesh. Then the energy optimization is performed in this subspace to greatly facilitate the editing of large meshes. Massive experimental data demonstrate the effectiveness and efficiency of our algorithm. Copyright © 2012 John Wiley & Sons, Ltd.     

基于网格形变的立体图像内容重组

目的 近年来,随着数字摄影技术的飞速发展,图像增强技术越来越受到重视。图像构图作为图像增强中影响美学的重要因素,一直都是研究的热点。为此,从立体图像布局调整出发,提出一种基于Delaunay网格形变的立体图像内容重组方法。方法 首先将待重组的一对立体图像记为源图像,将用于重组规则确定的一幅图像记为参考图像;然后对源图像需要调整的目标、特征线和其他区域进行取点操作,建立Delaunay网格。将源图像的左图与参考图像进行模板匹配操作,得到源图像与参考图像在结构布局上的对应关系;最后利用网格形变的特性,移动和缩放目标对象,并对立体图像的深度进行自适应调整。结果 针对目标对象的移动、缩放和特征线调整几方面进行优化。当只涉及目标对象的移动或特征线调整时,立体图像视差保持不变;当目标对象缩放时,立体图像中目标对象的视差按照缩放比例变化而背景视差保持不变。实验结果表明,重组后的立体图像构图与参考图像一致且深度能自适应调整。与最新方法比较,本文方法在目标对象分割精度和图像语义保持方面具有优势。结论 根据网格形变相关理论,构建图像质量、布局匹配和视差适应3种能量项,实现了立体图像的内容重组。与现有需要提取和粘贴目标对象的重组方法不同,本文方法对目标对象的分割精度要求不高,不需要图像修复和混合技术,重组后的立体图像没有伪影和语义错误出现。用户可以通过参考图像来引导立体图像的布局调整,达到期望的图像增强效果。     

Interactive mesh deformation using equality-constrained least squares

Mesh deformation techniques that preserve the differential properties have been intensively studied. In this paper, we propose an equality-constrained least squares approach for stably deforming mesh models while approximately preserving mean curvature normals and strictly satisfying other constraints such as positional constraints. We solve the combination of hard and soft constraints by constructing a typical least squares system using QR decomposition. A well-known problem of hard constraints is over-constraints. We show that the equality-constrained least squares approach is useful for resolving such over-constrained situations. In our framework, the rotations of mean curvature normals are treated using the logarithms of unit quaternions in . During deformation, mean curvature normals can be rotated while preserving their magnitudes. In addition, we introduce a new modeling constraints called rigidity constraints and show that rigidity constraints can effectively preserve the shapes of feature regions during deformation. Our framework achieves good performance for interactive deformation of mesh models.     

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.     

四面体胞的尽可能刚性网格变形算法

提出一种基于四面体胞的尽可能刚性三角形网格变形算法。用户通过操作网格上的若干顶点以得到所需的模型变形结果。首先,算法对网格模型内部进行稀疏四面体化,以产生一个贴合模型表面的四面体胞集。在模型变形过程中,算法通过最小化相应的变形能量函数,以保持网格模型表面局部区域的刚性以及每个四面体胞的刚性,从而有效避免模型表面及其内部的扭曲。同时,针对大尺度编辑可能造成的模型局部塌陷,提出一种简单的四面体胞自适应剖分方法,根据模型局部体积的剧烈变化,自动剖分对应的四面体胞以增加模型内部的局部变形自由度,进而消除不正确的变形效果。此外,自适应的四面体胞剖分允许算法在初始时只需对网格模型进行稀疏的四面体化,而在变形过程中根据需要进一步提高四面体胞的局部稠密度,因而保证了算法的鲁棒性及其效率。实验结果表明,该变形算法可以有效保持模型的表面细节以及模型的内部体积,并能够有效避免模型形状在大尺度变形时的局部退化。     

适用于SBS网格变形的权重分配方法

提出一种适用于球面混合蒙皮（SBS）网格变形的权重分配算法,使用顶点在骨骼上的投影作为初始权重求解热平衡方程,将每一条骨骼控制的顶点进行聚类,对位于类边界上顶点相对于这条骨骼的权重衰减,对每个骨骼类的非边界顶点的权重基于邻域进行插值。该算法能够抑制肢体交接处权重过度分配的问题,并且使权重符合网格拓扑结构以及过渡平缓。实验结果表明,该算法计算的权重可以使SBS变形达到自然、平滑的效果。     

Differential coordinates for local mesh morphing and deformation

Published online: 14 February 2003     

Finite element mesh deformation with the skeleton-section template

To develop fast finite element (FE) adaptation methods for simulation-driven design optimization, we propose a radial basis functions (RBF) method with a skeleton-section template to globally and locally deform FE meshes of thin-walled beam structures.The skeleton-section template is automatically formulated from the input mesh and serves as a hierarchical parameterization for the FE meshes. With this hierarchical parameterization, both the global and the local geometries of a thin-walled beam can be processed in the same framework, which is of importance for designing engineering components. The curve skeleton of the mesh is constructed with Voronoi decomposition, while the cross-sections are extracted from the mesh based on the curve skeleton.The RBF method is employed to locally and globally deform the mesh model with the cross-sections and the skeleton, respectively. The RBF method solves the spatial deformation field given prescribed deformations at the cross-sections. At the local scale, the user modifies the cross-sections to deform a region of the surface mesh. At the global level, the skeleton is manipulated and its deformation is transferred to all cross-sections to induce the mesh deformation.In order to handle curved mesh models and attain flexible local deformations, the input mesh is embedded into its skeleton frame field using an anisotropic distance metric. In this way, even strip-like features along arbitrary directions can be created on the mesh model using only a few cross-sections as the deformation handles. In addition, form features can be rigidly preserved at both deformation levels.Numerical examples demonstrate that intuitive and qualified FE mesh deformations can be obtained with manipulation of the skeleton-section template.     

Automatic cage generation by improved OBBs for mesh deformation

In cage-based deformation, the most tedious task is to construct the coarse cage bounding a model. Currently, the coarse cage is constructed mainly by hand, and the construction usually takes several hours, even longer. Therefore, it is important to develop a convenient method to generate the coarse cage bounding a model. In this paper, we devise a method to construct the coarse cage automatically using the improved OBB tree, while allowing the users to modify the cage easily. Firstly, the OBB tree bounding the model is generated, where we propose an improved OBB slicing rule to make the generated OBBs close to the model it contains. Secondly, the OBBs are adjusted and merged into a whole entity by the boolean union operation. Finally, the outer surface of the entity is extracted as the coarse cage. Empirical results demonstrate the effectiveness and efficiency of the automatic coarse cage-generation method.     

基于局部刚性约束的微分网格变形算法

针对网格角色模型（人体或动物模型）的关节部位在变形中易出现扭曲或不自然体积改变的问题,结合网格刚性变形和微分变形的理论,提出了一种基于局部刚性约束的变形算法。在本算法中,首先采用距离场方法求取模型的骨架关节点,然后在关节点上插入刚性约束架,再用均值坐标将刚性约束架和模型绑定到一起,最后通过求解包含微分约束和局部刚性约束的能量方程得到变形结果。实验表明,本算法很好地解决了大规模角色模型变形过程中,关节部位出现失真的问题。     

骨架驱动的三维模型变形方法

为发展三维网格模型的变形技术,研究了多种三维模型变形算法,通过对骨架驱动变形算法的深入研究,针对现行算法多是以单一骨架驱动变形的不足,提出了一种新的基于多骨架点驱动的交互式局部变形方法.有效结合模型的骨架图结构,确定各骨架点对应的局部区域.并将骨架点拟合为二次Bézier曲线,通过交互式拖动任意骨架点计算与之相连的多骨架点的动态变化,实现模型局部区域的自然形变.实验结果表明了该算法的有效性和直观性.     

基于Kinect与网格几何变形的人脸表情动画

面部表情重建的实时性与重建效果的真实性是人脸表情动画的关键问题,提出一种基于Kinect人脸追踪和几何变形技术的面部表情快速重建新方法。使用微软的Kinect设备识别出表演者面部并记录其特征点数据,并利用捕捉到的特征点建立覆盖人脸的网格模型,从中选取变形使用的控制点数据,由于Kinect可以实时地自动追踪表演者面部,由此实现了利用三种不同变形算法对目标模型实时快速重建。实验结果表明,该方法简单易实施,不用在表演者面部做任何标定,可以自动地将人脸表情动作迁移到目标模型上,实现人脸表情快速重建,并且保证目标模型表情真实自然。     

Spectral 3D mesh segmentation with a novel single segmentation field

We present an automatic mesh segmentation framework that achieves 3D segmentation in two stages, hierarchical spectral analysis and isoline-based boundary detection. During the hierarchical spectral analysis stage, a novel segmentation field is defined to capture a concavity-aware decomposition of eigenvectors from a concavity-aware Laplacian. Specifically, a sufficient number of eigenvectors is first adaptively selected and simultaneously partitioned into sub-eigenvectors through spectral clustering. Next, on the sub-eigenvectors level, we evaluate the confidence of identifying a spectral-sensitive mesh boundary for each sub-eigenvector by two joint measures, namely, inner variations and part oscillations. The selection and combination of sub-eigenvectors are thereby formulated as an optimization problem to generate a single segmentation field. In the isoline-based boundary detection stage, the segmentation boundaries are recognized by a divide-merge algorithm and a cut score, which respectively filters and measures desirable isolines from the concise single segmentation field. Experimental results on the Princeton Segmentation Benchmark and a number of other complex meshes demonstrate the effectiveness of the proposed method, which is comparable to recent state-of-the-art algorithms.