L_p shape deformation

Shape deformation is a fundamental tool in geometric modeling.Existing methods consider preserving local details by minimizing some energy functional measuring local distortions in the L 2 norm.This strategy distributes distortions quite uniformly to all the vertices and penalizes outliers.However,there is no unique answer for a natural deformation as it depends on the nature of the objects.Inspired by recent sparse signal reconstruction work with non L 2 norm,we introduce general L p norms to shape deformation;the positive parameter p provides the user with a flexible control over the distribution of unavoidable distortions.Compared with the traditional L 2 norm,using smaller p,distortions tend to be distributed to a sparse set of vertices,typically in feature regions,thus making most areas less distorted and structures better preserved.On the other hand,using larger p tends to distribute distortions more evenly across the whole model.This flexibility is often desirable as it mimics objects made up with different materials.By specifying varying p over the shape,more flexible control can be achieved.We demonstrate the effectiveness of the proposed algorithm with various examples.     

Rigidity controllable as-rigid-as-possible shape deformation

Shape deformation is one of the fundamental techniques in geometric processing. One principle of deformation is to preserve the geometric details while distributing the necessary distortions uniformly. To achieve this, state-of-the-art techniques deform shapes in a locally as-rigid-as-possible (ARAP) manner. Existing ARAP deformation methods optimize rigid transformations in the 1-ring neighborhoods and maintain the consistency between adjacent pairs of rigid transformations by single overlapping edges. In this paper, we make one step further and propose to use larger local neighborhoods to enhance the consistency of adjacent rigid transformations. This is helpful to keep the geometric details better and distribute the distortions more uniformly. Moreover, the size of the expanded local neighborhoods provides an intuitive parameter to adjust physical stiffness. The larger the neighborhood is, the more rigid the material is. Based on these, we propose a novel rigidity controllable mesh deformation method where shape rigidity can be flexibly adjusted. The size of the local neighborhoods can be learned from datasets of deforming objects automatically or specified by the user, and may vary over the surface to simulate shapes composed of mixed materials. Various examples are provided to demonstrate the effectiveness of our method.     

Topology optimization of beam cross-section considering warping deformation

The beam cross-section optimization problems have been very important as beams are widely used as efficient load-carrying structural components. Most of the earlier investigations focus on the dimension and shape optimization or on the topology optimization along the axial direction. An important problem in beam section design is to find the location and direction of stiffeners, for the introduction of a stiffener in a closed beam section may result in a topologically different configuration from the original; the existing section shape optimization theory cannot be used. The purpose of this paper is to formulate a section topology optimization technique based on an anisotropic beam theory considering warping of sections and coupling among deformations. The formulation and corresponding solving method for the topology optimization of beam cross-sections are proposed. In formulating the topology optimization problem, the minimum averaged compliance of the beam is taken as objective, and the material density of every element is used as design variable. The schemes to determine the rigidity matrix of the cross-sections and the sensitivity analysis are presented. Several kinds of topologies of the cross-section under different load conditions are given, and the effect of load condition on the optimum topology is analyzed.     

Scalar-field-guided adaptive shape deformation and animation

In this paper, we propose a novel scalar-field-guided adaptive shape deformation (SFD) technique founded on PDE-based flow constraints and scalar fields of implicit functions. Scalar fields are used as embedding spaces. Upon deformation of the scalar field, a corresponding displacement/velocity field will be generated accordingly, which results in a shape deformation of the embedded object. In our system, the scalar field creation, sketching, and manipulation are both natural and intuitive. The embedded model is further enhanced with self-optimization capability. During the deformation we can also enforce various constraints on embedded models. In addition, this technique can be used to ease the animation design. Our experiments demonstrate that the new SFD technique is powerful, efficient, versatile, and intuitive for shape modeling and animation. This revised version was published online in February 2004 due to typesetting mistakes in the author correction process.     

Anisotropic deformation for local shape control

Computational Visual Media - We present a novel approach to mesh deformation that enables simple context sensitive manipulation of 3D geometry. The method is based on locally anisotropic...     

Topology and shape optimization of dissipative and hybrid mufflers

Structural and Multidisciplinary Optimization - This article presents a topology optimization (TO) method developed for maximizing the acoustic attenuation of a perforated dissipative muffler in...     

Diffusion-based non-uniform regularization for variational shape deformation

Regularization is a typical technique to correct the discontinuity artifacts at the control points in shape deformation. A regularizer with higher weights is required if the deformation is large, which will unfortunately distort the entire shape. In this work, we present a non-uniform regularization technique based on a shape-aware scalar field obtained from diffusion, which allows user to control the magnitude and range of the regularizer around specific control points. Experimental results show that shapes are deformed smoothly and no over-regularized artifact is observed with our non-uniform regularizer.     

Surface shape from the deformation of apparent contours

The spatiotemporal analysis of deforming silhouettes (apparent contours) is here extended using the mathematics of perspective projections and tools from differential geometry. Analysis of the image motion of a silhouette or apparent contour enables computation of local surface curvature along the corresponding contour generator on the surface, assuming viewer motion is known. To perform the analysis, a spatiotemporal parameterization of image-curve motion is needed, but is underconstrained (a manifestation of the well-known aperture problem). It is shown that an epipolar parameterization is most naturally matched to the recovery of surface curvature.One immediate facility afforded by the analysis is that surface patches can be reconstructed in the vicinity of contour generators. Once surface curvature is known, it is possible to discriminate extremal contours from other fixed curves in space. Furthermore, the known robustness of parallax as a cue to depth extends to the case of surface curvature. Its derivative—rate of parallax—is shown theoretically to be a curvature cue that is robust to uncertainties in the known viewer motion. This robustness has been confirmed in experiments.Finally, the power of the new analysis for robotics applications is demonstrated. Illustrations are given of an Adept robot, equipped with a CCD camera, circumnavigating curved obstacles. When further equipped with a suction gripper the robot manipulator can pick up an object by its curved surface, under visual guidance.     

3D anatomical shape atlas construction using mesh quality preserved deformable models

3D anatomical shape atlas construction has been extensively studied in medical image analysis research, owing to its importance in model-based image segmentation, longitudinal studies and populational statistical analysis, etc. Among multiple steps of 3D shape atlas construction, establishing anatomical correspondences across subjects, i.e., surface registration, is probably the most critical but challenging one. Adaptive focus deformable model (AFDM) [1] was proposed to tackle this problem by exploiting cross-scale geometry characteristics of 3D anatomy surfaces. Although the effectiveness of AFDM has been proved in various studies, its performance is highly dependent on the quality of 3D surface meshes, which often degrades along with the iterations of deformable surface registration (the process of correspondence matching). In this paper, we propose a new framework for 3D anatomical shape atlas construction. Our method aims to robustly establish correspondences across different subjects and simultaneously generate high-quality surface meshes without removing shape details. Mathematically, a new energy term is embedded into the original energy function of AFDM to preserve surface mesh qualities during deformable surface matching. More specifically, we employ the Laplacian representation to encode shape details and smoothness constraints. An expectation–maximization style algorithm is designed to optimize multiple energy terms alternatively until convergence. We demonstrate the performance of our method via a set of diverse applications, including a population of sparse cardiac MRI slices with 2D labels, 3D high resolution CT cardiac images and rodent brain MRIs with multiple structures. The constructed shape atlases exhibit good mesh qualities and preserve fine shape details. The constructed shape atlases can further benefit other research topics such as segmentation and statistical analysis.     

Topology and shape optimization of continuum structures using GA and BEM

In a previous study, the authors presented a shape optimization scheme for continuum structures by a genetic algorithm and a boundary element method. In this paper, the study is extended to topology and shape optimization problems of the continuum structures.Boundary profiles are expressed by spline functions. The chromosomes for the profiles are defined by a gene related to the topology (the number of internal boundaries) and genes related to the control points of the spline functions. The population is constructed by individuals with such chromosomes. The genetic opertors such as selection, crossover and mutation are applied to the population for searching the profile satisfying the design objectives. In the case of the objects with internal boundaries, intersection of the boundaries very often occurs and thus, the computational cost may become high. Therefore, we also discuss a scheme for increasing the computational efficiency in this case. Finally, the present scheme is applied to the topology and shape optimization of a plate in order to confirm its validity.     

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.     

Unsupervised cycle‐consistent deformation for shape matching

We propose a self‐supervised approach to deep surface deformation. Given a pair of shapes, our algorithm directly predicts a parametric transformation from one shape to the other respecting correspondences. Our insight is to use cycle‐consistency to define a notion of good correspondences in groups of objects and use it as a supervisory signal to train our network. Our method combines does not rely on a template, assume near isometric deformations or rely on point‐correspondence supervision. We demonstrate the efficacy of our approach by using it to transfer segmentation across shapes. We show, on Shapenet, that our approach is competitive with comparable state‐of‐the‐art methods when annotated training data is readily available, but outperforms them by a large margin in the few‐shot segmentation scenario.     

Surface deformation models for nonrigid 3D shape recovery

Three-dimensional detection and shape recovery of a nonrigid surface from video sequences require deformation models to effectively take advantage of potentially noisy image data. Here, we introduce an approach to creating such models for deformable 3D surfaces. We exploit the fact that the shape of an inextensible triangulated mesh can be parameterized in terms of a small subset of the angles between its facets. We use this set of angles to create a representative set of potential shapes, which we feed to a simple dimensionality reduction technique to produce low-dimensional 3D deformation models. We show that these models can be used to accurately model a wide range of deforming 3D surfaces from video sequences acquired under realistic conditions.     

SMA在星载天线上的热变形控制研究

为了保证星载大型可展开桁架天线在轨运行时能可靠的工作,就必须对其进行在轨热变形控制.通过使用ANSYS软件对可展开天线加入NiNi形状记忆合金丝且在轨道的不同位置点的情况进行了计算,得出了天线反射面的均方根误差.通过研究可以发现,在周边桁架天线中嵌入SMA后减小了天线反射面的均方根误差,从而达到了保证天线型面精度的目的.     

基于粒子系统和形状匹配的实时无网格变形仿真

介绍了一种基于粒子系统和形状匹配的无网格变形算法。该算法将模型的每个顶点当成一个粒子,一个模型对应一个粒子系统,通过粒子系统控制物体外形。同时,每个粒子都对应一个目标位置,粒子与其目标位置之间存在弹力,能将粒子拉向目标位置,使得变形后的物体能够恢复原来的形状。目标位置可以通过粒子系统未变形时的静止状态与当前变形状态之间的形状匹配来计算。该算法简单,易于实现,且不需要复杂的数据结构。实验结果表明该算法稳定,具有实时性,可以有效地应用于三维游戏中。