基于区域分割的三维自由曲面相似性评价算法

为了在工程应用中检索已有的三维CAD模型,以便重用相应零件的设计信息,节省设计和加工成本,提出一种基于曲面分割技术的CAD自由曲面相似性评价算法.依据曲面的曲率将自由曲面分割成具有相对固定曲率特征的不同区域;对每个分割得到的区域用一个7维向量表达其形状的几何特征和拓扑特征,一个自由曲面形状特征即可通过各分割区域所对应的7维向量组成的向量组表达;将该向量组作为自由曲面的形状描述子,2个自由曲面的相似性可通过相对应的形状描述子间的相似性表达.在评价2个曲面形状描述子的相似性时,将描述子中的每个向量看成是一个带有属性的节点,2个形状描述子所对应的2组属性节点可看成是一个二分图,2组属性节点间相应节点距离看成是二分图的权值,并利用赋权二分图最优匹配的算法求出2组属性节点的相似性,实现2个自由曲面之间的相似性评价.实验结果表明,该算法是有效、可行的.     

Smooth surfaces from rational bilinear patches

Smooth freeform skins from simple panels constitute a challenging topic arising in contemporary architecture. We contribute to this problem area by showing how to approximate a negatively curved surface by smoothly joined rational bilinear patches. The approximation problem is solved with help of a new computational approach to the hyperbolic nets of Huhnen-Venedey and Rörig and optimization algorithms based on it. We also discuss its limits which lie in the topology of the input surface. Finally, freeform deformations based on Darboux transformations are used to generate smooth surfaces from smoothly joined Darboux cyclide patches; in this way we eliminate the restriction to surfaces with negative Gaussian curvature.     

三维CAD曲面模型距离-曲率形状分布检索算法

产品三维CAD模型检索对实现产品设计信息的有效重用具有重要意义和作用.针对在工程应用中存在大量含有曲面的产品,提出一种基于距离-曲率形状分布的三维CAD曲面模型检索算法.首先在模型表面随机取点,计算出所取点的曲率以及该点到模型质心的距离;然后以模型质心为球心,统计处在不同半径球壳间所取随机点的曲率分布,分别以球壳半径和曲率为坐标轴构建距离-曲率平面网格,并统计每个网格中随机点出现的频次,从而形成距离-曲率矩阵;最后利用特定的规则计算矩阵的相似值,用该值衡量2个模型的相似程度,实现模型的相似性检索.实验结果表明,文中算法的检索性能比传统的形状分布算法有较大提高,尤其适用于自由曲面模型的检索.     

具有规整曲率线网的光滑曲面设计

为了设计具有规整曲率线网且无脐点的光滑曲面,提出一种曲面交互设计算法。 采用 Bézier 曲面片光滑拼接构成的复合曲面作为表达形式,通过交替曲率线网的优化和曲面细 分得到自由形状的设计曲面,所得曲面具有规整曲率线网而且没有脐点。以此复合 Bézier 曲面 为基础,通过圆纹样条曲面优化算法得到结构规整的圆纹样条曲面,同时也能得到圆锥曲面条 模型以及曲面多层支撑结构等自由建筑曲面设计中有重要应用的几何结构。     

Surface Fairing towards Regular Principal Curvature Line Networks

Freeform surfaces whose principal curvature line network is regularly distributed, are essential to many real applications like CAD modeling, architecture design, and industrial fabrication. However, most designed surfaces do not hold this nice property because it is hard to enforce such constraints in the design process. In this paper, we present a novel method for surface fairing which takes a regular distribution of the principal curvature line network on a surface as an objective. Our method first removes the high‐frequency signals from the curvature tensor field of an input freeform surface by a novel rolling guidance tensor filter, which results in a more regular and smooth curvature tensor field, then deforms the input surface to match the smoothed field as much as possible. As an application, we solve the problem of approximating freeform surfaces with regular principal curvature line networks, discretized by quadrilateral meshes. By introducing the circular or conical conditions on the quadrilateral mesh to guarantee the existence of discrete principal curvature line networks, and minimizing the approximate error to the original surface and improving the fairness of the quad mesh, we obtain a regular discrete principal curvature line network that approximates the original surface. We evaluate the efficacy of our method on various freeform surfaces and demonstrate the superiority of the rolling guidance tensor filter over other tensor smoothing techniques. We also utilize our method to generate high‐quality circular/conical meshes for architecture design and cyclide spline surfaces for CAD modeling.     

基于曲度特征的三维模型检索算法

针对如何提高复杂曲面的三维模型的检索精度的问题,提出了一种基于曲度特征的三维模型检索算法。首先,在模型表面选取随机采样点,计算点所在局部曲面的高斯曲率和平均曲率,通过高斯曲率和平均曲率求出随机点的曲度值,曲度值表明了曲面的凹凸属性。然后,以模型的质心为球心,以随机点与质心距离和曲度值为坐标轴建立坐标系,统计出一定距离范围内曲度值分布的概率,构建距离与曲度的分布矩阵,以此分布矩阵作为三维模型特征描述符。该特征描述符具有旋转不变性和平移不变性,能够很好地反映复杂曲面的几何特征。最后,通过比较分布矩阵给出不同模型间的相似度。实验结果表明,该方法相比形状分布算法的检索性能有较大提高,尤其适用于具有复杂曲面的三维模型检索。     

高斯曲率约束的MRG骨架提取优化算法

三维模型的骨架保持了模型的拓扑特性,并被广泛应用于模型相似性比较、计算机动画及压缩等领域.根据多分辨率Reeb图的原理,提出了一种基于离散高斯曲率约束的骨架提取优化算法.通过计算网格顶点的离散高斯曲牢判断曲面局部凸凹特性,以获取模型表面的双曲极值点作为约束点;并依据约束点及其邻域的μ函数值产生的分裂线进行区域细分,获得子连通区域、确定关节点、形成优化的骨架结构.实验结果表明,该算法有效地突出了模型的拓扑分支特征以及模型表面的细节,提高了骨架提取的精度和效率.     

The Alignment of Objects with Smooth Surfaces

This paper examines the recognition of rigid objects bounded by smooth surfaces, using an alignment approach. The projected image of such an object changes during rotation in a manner that is generally difficult to predict. An approach to this problem is suggested, using the 3D surface curvature at the points along the silhouette. The curvature information requires a single number for each point along the object′s silhouette, the radial curvature at the point. We have implemented this method and tested it on images of complex 3D objects. Models of the viewed objects were acquired using three images of each object. The implemented scheme was found to give accurate predictions of the objects′ appearances for large transformations. Using this method, a small number of (viewer-centered) models can be used to predict the new appearance of an object from any given viewpoint.     

Improving three-dimensional point reconstruction from image correspondences using surface curvatures

Recovering three-dimensional (3D) points from image correspondences is an important and fundamental task in computer vision. Traditionally, the task is completed by triangulation whose accuracy has its limitation in some applications. In this paper, we present a framework that incorporates surface characteristics such as Gaussian and mean curvatures into 3D point reconstruction to enhance the reconstruction accuracy. A Gaussian and mean curvature estimation scheme suitable to the proposed framework is also introduced in this paper. Based on this estimation scheme and the proposed framework, the 3D point recovery from image correspondences is formulated as an optimization problem with the surface curvatures modeled as soft constraints. To analyze the performance of proposed 3D reconstruction approach, we generated some synthetic data, including the points on the surfaces of a plane, a cylinder and a sphere, to test the approach. The experimental results demonstrated that the proposed framework can indeed improve the accuracy of 3D point reconstruction. Some real-image data were also tested and the results also confirm this point.     

红血球图像表面曲率的计算方法

提出一种基于阴影恢复技术的细胞图像表面各点的曲率计算方法,利用边界轮廓提取技术分离由扫描电镜SEM得到的红血球亮度图像,对单个细胞从跟踪得到的中心点开始进行区域生长,其每个像素点的亮度变化信息决定了与之相对应的高度场深度,阴影恢复技术可以将这种变化的亮度转化为不同的深度,从而得到像素的三维数据点。通过最小二乘法对三维点进行曲面拟合得到分段连续光滑的细胞表面,其形状特征由平均曲率与高斯曲率来表示。结果表明,该方法具有很强的实用性和应用价值。     

An algorithm for calculating the similarity measures of surfaces represented as point clouds

The problem of estimating the similarity of surfaces represented as point clouds is studied. An approach is suggested to the comparison of such surfaces based on the surface approximation by piecewise-linear functions of two variables in the Delaunay triangulations. The approach is based on the developed algorithm for comparison of the functions of two variables specified on various irregular sets of points. Possible applications of this algorithm were considered such as the problems of 3D portraits comparison, e.g., problems of estimation of facial asymmetry and dynamics of lower jaw movements on the basis of a 3D video sequence of models. The performed experiments confirmed the correctness, validity, and computational efficiency of the proposed algorithm.     

Generating subdivision surfaces from profile curves

The construction of freeform models has always been a challenging task. A popular approach is to edit a primitive object such that its projections conform to a set of given planar curves. This process is tedious and relies very much on the skill and experience of the designer in editing 3D shapes. This paper describes an intuitive approach for the modeling of freeform objects based on planar profile curves. A freeform surface defined by a set of orthogonal planar curves is created by blending a corresponding set of sweep surfaces. Each of the sweep surfaces is obtained by sweeping a planar curve about a computed axis. A Catmull-Clark subdivision surface interpolating a set of data points on the object surface is then constructed. Since the curve points lying on the computed axis of the sweep will become extraordinary vertices of the subdivision surface, a mesh refinement process is applied to adjust the mesh topology of the surface around the axis points. In order to maintain characteristic features of the surface defined with the planar curves, sharp features on the surface are located and are retained in the mesh refinement process. This provides an intuitive approach for constructing freeform objects with regular mesh topology using planar profile curves.     

3D CAD model retrieval with perturbed Laplacian spectra

This paper presents a novel approach to the 3D CAD model retrieval, whereby the 3D models are treated and matched as undirected graphs. While there is much success made in the matching of graphs based on their spectral decomposition, most of these approaches consider smooth surfaces and are not suitable for CAD models because of their complex topology and singular structure. In the proposed approach, the models are simplified based on the piecewise flat properties of the surfaces first, and a perturbed Laplacian spectrum approach is then applied to characterize the shape. These spectral values are used as samples for spectral distribution estimation. The perturbed spectral distributions of different models are then compared by their KL-divergence for model retrieval. The proposed approach is tested with models from known 3D CAD database for verification.     

Detection and reconstruction of freeform sweeps

We study the difficult problem of deciding if parts of a freeform surface can be generated, or approximately generated, by the motion of a planar profile through space. While this task is basic for understanding the geometry of shapes as well as highly relevant for manufacturing and building construction, previous approaches were confined to special cases like kinematic surfaces or “moulding” surfaces. The general case remained unsolved so far. We approach this problem by a combination of local and global methods: curve analysis with regard to “movability”, curve comparison by common substring search in curvature plots, an exhaustive search through all planar cuts enhanced by quick rejection procedures, the ordering of candidate profiles and finally, global optimization. The main applications of our method are digital reconstruction of CAD models exhibiting sweep patches, and aiding in manufacturing freeform surfaces by pointing out those parts which can be approximated by sweeps.     

Splat representation of parametric surfaces

Point and splat-based representations have become a suitable technique both for modeling and rendering complex 3D shapes. Converting other kinds of models as parametric surfaces to splat-based representations will allow to mix surface and splat-based models and to take advantage of the existing point-based rendering methods. In this work, we present an approach to convert a parametric surface into a splat-based representation. It works in parametric space, performs an adaptive sampling based on the surface curvature and a given error tolerance and uses power Voronoi diagrams. The goal is to approximate the surface with an optimized set of elliptical splats.     

面向层析测量反求工程的自由曲面轮廓集分割技术

轮廓集的分割分为粗略分割和精化两个阶段．粗略分割是指从其他层上抽取和种子轮廓最相似的轮廓，提出了基于轮廓串匹配的优化方法；在精化阶段，提出了基于转角映射的特征连接点辨识技术，用来调整粗略分割轮廓段的两端点．实例表明，文中算法解决了自由曲面轮廓集精确分割的问题，为进一步实现三维特征参数识别和CAD模型重构打下了基础．     

G2 quasi-developable Bezier surface interpolation of two space curves

Surface development is used in many manufacturing planning operations, e.g., for garments, ships and automobiles. However, most freeform surfaces used in design are not developable, and therefore the developed patterns are not isometric to the original design surface. In some domains, the CAD model is created by interpolating two given space curves. In this paper, we propose a method to obtain a G² quasi-developable Bezier surface interpolating two arbitrary space curves. The given curves are first split into a number of piecewise Bezier curves and elemental Bezier patches each of which passes through four splitting points are constructed. All neighboring elemental patches are G² connected and they are assembled optimally in terms of the degree of developability (the integral Gaussian curvature). Experiments show that the final composite Bezier surface is superior to a lofted one which is defined regardless of the final surface developability.     

Region-based toolpath generation for robotic milling of freeform surfaces with stiffness optimization

Because of industrial robots’ relatively low stiffness, many research efforts have been performed to improve the robot stiffness by optimizing the robot posture. For freeform surfaces with large curvature, however, the expected high stiffness posture may undergo excessive changes that exceed the robot joint speed limit. Therefore, the stiffness optimization may not achieve the expected results in actual machining owing to the limitation of robot kinematics and conventional toolpath pattern. To address this problem, a region-based toolpath generation method is proposed to improve robot stiffness in this study for robotic milling of freeform surfaces. To provide the possibility of higher stiffness robot posture, not only the redundant degree of freedom (DOF) of the robot but also the orientation of tool axis during machining is optimized. Under the influence of surface curvature and position, the change of high stiffness posture has regionality. A surface subdivision method is proposed to divide the surface into multiple sub-regions, so that actual robot posture with better stiffness can be obtained. For each sub-region, the feed direction of toolpath is optimized to further enhance robot stiffness. Simulations and experimental studies are conducted, and show that the proposed toolpath generation method can improve the robot stiffness in freeform surface machining.     

Volumetric feature recognition for machining components with freeform surfaces

This paper describes a procedure for the extraction of features of a part containing a combination of 2.5D features and freeform surfaces. This work invokes a previous algorithm that was designed to recognize machining features from 2.5D parts destined to be machined on a 3-axis milling machine. The essence of that algorithm was a volume decomposition based on a recursive descent into the part, yielding a feature graph that captured both the geometry and the spatial relationships of the features. This work augments the previous algorithm with the ability to handle a limited class of components having freeform surfaces. Freeform features are defined similar to the 2.5D features as comprising a planar contour, but substituting a bottom freeform surface for the depth. Covering faces, defined as projection of the freeform surface on the faces of the bounding box of the surface, are used as equivalent planar faces for performing the recursive descent. Inter-feature open edges are used to signal the relationship between the freeform feature and other neighboring features. Examples of molds and components that were machined using the proposed algorithms are also presented.     

基于语义参数的三维复杂模型变形方法研究

针对含有自由曲面的三维模型不易变形的问题,提出一种基于语义参数的三维复杂模型变形方法,旨在实现三维模型的快速设计。该方法利用变形控制点作为模型变形的基本元素,通过设置语义参数实现层次化变形：以变形控制点带动分组部件变形,以分组部件促进三维模型整体变形。首先,采用Hausdorff测距法和均值聚类法,将已分组的电动车的自由曲面替换成二次曲面;然后,根据变形控制点间及与部件顶点的关系,计算各分组部件内部和外部的约束条件;最后,编辑修改定义在变形控制点上的语义参数,实现模型自定义变形。以电动车三维模型验证实验,结果表明,本方法支持用户通过修改少量语义参数对模型变形,有效提升三维模型个性化设计的效率。