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.     

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.     

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.     

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.     

Non-uniform deformation of an STL model satisfying error criteria

In this research, a method is presented for generating a deformed model satisfying given error criteria from an STL model in a triangular-mesh representation suitable for rapid prototyping (RP) processes. A deformed model is a non-uniformly modified shape from a base STL model. In developing a family product with various sizes such as a shoe, sometimes prototypes for all sizes should be made using an RP machine. Although an STL model is generated from a solid model, it is well known that creating a non-uniformly modified solid model from a base solid model is very difficult. Generally there are some gaps between surfaces after modification, and stitching the gaps is very difficult. To solve this problem, the authors explored the possibility of generating a deformed STL model directly from a base STL model. This research includes a data structure for modifying the STL model, checking the error of a modified edge compared with the exact non-uniformly scaled curve, checking the error of a modified facet compared with the exact non-uniformly scaled surface, and splitting a facet with an error greater than the allowable tolerance. Using the results of this research, the difficult work of creating solid models to build non-uniformly deformed STL models could be avoided.     

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。     

Inverse adaptation of a Hex-dominant mesh for large deformation finite element analysis

In the finite element analysis of metal forming processes, many mesh elements are usually deformed severely in the later stage of the analysis because of the corresponding large deformation of the geometry. Such highly distorted elements are undesirable in finite element analysis because they introduce error into the analysis results, and, in the worst case, inverted elements can cause the analysis to terminate prematurely. This paper proposes a new inverse-adaptation method that reduces or eliminates the number of inverted mesh elements created in the later stage of finite element analysis, thereby lessening the chances of early termination and improving the accuracy of the analysis results. By this method, a simple uniform mesh is created initially, and a pre-analysis is run in order to observe the deformation behavior of the elements. Next, an input hex-dominant mesh is generated in which each element is “inversely adapted”, or pre-deformed in such a way that it has approximately the opposite shape of the final shape that normal analysis would deform it into. Thus, when finite element analysis is performed, the analysis starts with an input mesh of inversely adapted elements whose shapes are not ideal. As the analysis continues, the element shape quality improves to almost ideal, and then, toward the final stage of analysis, degrades again, but much less than would be the case without the inverse adaptation. This method permits the analysis to run to the end, or to a further stage, with no inverted elements. Besides its pre-skewing the element shape, the proposed method is also capable of controlling the element size according to the equivalent plastic strain information collected from the pre-analysis. The proposed inverse adaptation can be repeated iteratively until reaching the final stage of deformation.     

Electronic sketching on a multi-platform context: A pilot study with developers

During the past 45 years there has been a recurrence of interest on supporting sketching at electronic devices and interactive surfaces, and despite being sketching recognition fairly well addressed on the literature, the adoption of electronic sketching as a design tool is still a challenge.The current popularization of touch screen devices allows designers to sketch using their device of preference, while the current multi-platform capabilities made possible by HTML5 allows sketching systems to run on many devices at the same time. Those two factors combined might pose new opportunities for researchers to explore how designers use sketching on flexible setups by combining heterogeneous sketching devices for design sessions.This may arise new possibilities in the field of prototyping user interfaces since, by using such multi-platform systems, designers would now be able of designing interfaces for multiple devices by producing and testing them on the device itself.This paper reports a pilot experiment conducted with 6 developers, grouped into pairs on design sessions using Gambit – a multi-platform sketching system that provides a lightweight approach for prototyping user interfaces for many devices at once. We performed a discourse analysis of the professionals based on recorded videos of interviews conducted during and after design sessions with the system and aggregated the data in order to investigate the main requirements for multi-platform sketching systems.     

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。     

A quantitative assessment of approaches to mesh generation for surgical simulation

In surgical simulation, it is common practice to use tetrahedral meshes as models for anatomy. These meshes are versatile, and can be used with a number of different physically based modelling schemes. A variety of mesh generators are available that can automatically create tetrahedral meshes from segmented anatomical volumes. Each mesh generation scheme offers its own set of unique attributes. However, few are readily available. When choosing a mesh generator for simulation, it is critical for it to output good-quality, patient-specific meshes that provide a good approximation of the shape or volume to be modelled. To keep computation time within the bounds required for real-time interaction, there is also a limit imposed on the number of elements in the mesh generated. To the authors knowledge, there has been little work directly assessing the suitability of mesh generators for surgical simulation. This paper seeks to address this issue by assessing the use of six mesh generators in a surgical simulation scenario, and examining how they affect simulation precision. This paper aims to perform these comparisons against high-resolution reference meshes, where we examine the precision of meshes from the same mesh generator at different levels of complexity.

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.     

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.     

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。     

3D sketching for aesthetic design using fully free-form deformation features

This paper addresses the designers’ activity and in particular the way designers express an object shape in 2D sketches through character lines and how these lines form a basis for sketching shapes in 3D. The tools currently available in commercial CAS/CAD systems to manipulate the digital models are still not sufficiently suited to support design. In this paper, the so-called fully free-form deformation features (δ-F⁴) are introduced as a modelling method to take into account the curve-oriented stylists’ way of working. Both the advantages of a free-form surface deformation method and a feature-based approach are merged to define these high-level modelling entities allowing for a direct manipulation of surfaces through a limited number of intuitive parameters. Such features incorporate several characteristics designed to handle the uncertainties and/or inconsistencies of the designer's input during a sketching activity. In addition, a δ-F⁴ classification is proposed to enable a fast access to the desired shape according to its semantics and characteristics.     

Hexahedral mesh smoothing via local element regularization and global mesh optimization

The quality of finite element meshes is one of the key factors that affect the accuracy and reliability of finite element analysis results. In order to improve the quality of hexahedral meshes, we present a novel hexahedral mesh smoothing algorithm which combines a local regularization for each hexahedral mesh, using dual element based geometric transformation, with a global optimization operator for all hexahedral meshes. The global optimization operator is composed of three main terms, including the volumetric Laplacian operator of hexahedral meshes and the geometric constraints of surface meshes which keep the volumetric details and the surface details, and another is the transformed node displacements condition which maintains the regularity of all elements. The global optimization operator is formulated as a quadratic optimization problem, which is easily solved by solving a sparse linear system. Several experimental results are presented to demonstrate that our method obtains higher quality results than other state-of-the-art approaches.     

Hexahedral mesh generation constraints

For finite element analyses within highly elastic and plastic structural domains, hexahedral meshes have historically offered some benefits over tetrahedral finite element meshes in terms of reduced error, smaller element counts, and improved reliability. However, hexahedral finite element mesh generation continues to be difficult to perform and automate, with hexahedral mesh generation taking several orders of magnitude longer than current tetrahedral mesh generators to complete. Thus, developing a better understanding of the underlying constraints that make hexahedral meshing difficult could result in dramatic reductions in the amount of time necessary to prepare a hexahedral finite element model for analysis. In this paper, we present a survey of constraints associated with hexahedral meshes (i.e., the conditions that must be satisfied to produce a hexahedral mesh). In presenting our formulation of these constraints, we will utilize the dual of a hexahedral mesh. We also discuss how incorporation of these constraints into existing hexahedral mesh generation algorithms could be utilized to extend the class of geometries to which these algorithms apply. We also describe a list of open problems in hexahedral mesh generation and give some context for future efforts in addressing these problems.     

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.     

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。     

Constrained space deformation techniques for design optimization

We present a novel shape deformation method for its use in design optimization tasks. Our space deformation technique based on moving least squares approximation improves upon existing approaches in crucial aspects: It offers the same level of modeling flexibility as surface-based deformations, but it is independent of the underlying geometry representation and therefore highly robust against defects in the input data. It overcomes the scalability limitations of existing space deformation techniques based on globally supported radial basis functions while providing the same high level of deformation quality. Finally, unlike existing space deformation approaches, our technique directly incorporates geometric constraints–such as preservation of critical feature lines, circular couplings, planar or cylindrical construction parts–into the deformation, thereby fostering the exploration of more favorable and producible shape variations during the design optimization process.     

Consistent mesh partitioning and skeletonisation using the shape diameter function

Mesh partitioning and skeletonisation are fundamental for many computer graphics and animation techniques. Because of the close link between an object’s skeleton and its boundary, these two problems are in many cases complementary. Any partitioning of the object can assist in the creation of a skeleton and any segmentation of the skeleton can infer a partitioning of the object. In this paper, we consider these two problems on a wide variety of meshes, and strive to construct partitioning and skeletons which remain consistent across a family of objects, not a single one. Such families can consist of either a single object in multiple poses and resolutions, or multiple objects which have a general common shape. To achieve consistency, we base our algorithms on a volume-based shape-function called the shape-diameter-function (SDF), which remains largely oblivious to pose changes of the same object and maintains similar values in analogue parts of different objects. The SDF is a scalar function defined on the mesh surface; however, it expresses a measure of the diameter of the object’s volume in the neighborhood of each point on the surface. Using the SDF we are able to process and manipulate families of objects which contain similarities using a simple and consistent algorithm: consistently partitioning and creating skeletons among multiple meshes.