Signed algebraic level sets on NURBS surfaces and implicit Boolean compositions for isogeometric CAD–CAE integration

Boundary-representation (B-rep) geometrical models, often mathematically represented using Non-Uniform Rational B-Spline (NURBS) surfaces, are the starting point for complex downstream product life-cycle evaluations including Computer-Aided Engineering (CAE). Boolean operations during B-rep model generation require surface intersection computations to describe the composed entity. However, for parametric NURBS surfaces, intersection operations are non-trivial and typically carried out numerically. The numerical intersection computations introduce challenges relating to the accuracy of the resulting representation, efficiency with which the computation is carried out, and robustness of the result to small variations in geometry. Often, for downstream CAE evaluations, an implicit, procedural knowledge of the Boolean operations between the composed objects that can resolve point containment queries (exact to the original NURBS bounding surfaces) maybe sufficient during quadrature. However, common point containment queries on B-rep models are numerical, iterative and relatively expensive. Thus, the first goal of the present paper is to describe a purely algebraic, and therefore non-iterative, approach to carrying out point containment queries on complex B-rep models built using low-degree NURBS surfaces. For CAE operations, the boundary representation of B-rep solids is, in general, not convenient and as a result, the B-rep model is converted to a meshed volumetric approximation. The major challenges to such a conversion include capturing the geometric features accurately when constructing the secondary (meshed) representation, apart from the efficiency of carrying out such a mesh generation step repeatedly as the geometric shape evolves. Thus, an ideal analysis procedure would operate directly on B-rep CAD models, without needing a secondary mesh, and would procedurally unify the geometric operations during CAD as well as CAE stages. Therefore, the second and broader goal of the present paper is to demonstrate CAD–CAE integration using signed algebraic level set operations directly on B-rep models by embedding or immersing the bounding surfaces within a discretized domain while preserving the geometric accuracy of the surfaces exact to the original NURBS representation during analysis.     

Automatic surface repairing,defeaturing and meshing algorithms based on an extended B-rep

This paper presents an extended surface boundary representation (B-rep), where each topology entity can have dual geometric representations to accommodate various defects (e.g., gaps and overlaps) commonly present in CAD models. Keeping a uniform B-rep and the unsuppressed geometry data enables the use of various existing repairing, defeaturing and meshing algorithms to process CAD models with small gaps and overlaps on surface boundaries. The continuous geometry of the input model remains untouched in the repairing, defeaturing and meshing process, and the output mesh is loyal to this geometry. Such feature is often desirable in numerical simulations that require meshes with high geometry fidelity.     

Feature suppression based CAD mesh model simplification

Dynamic simulation and high quality FEA mesh generation need the CAD mesh model to be simplified, that is, suppressing the detailed features on the mesh without any changes to the rest. However, the traditional mesh simplification methods for graphical models can not satisfy the requirements of CAD mesh simplification. In this paper, we develop a feature suppression based CAD mesh model simplification framework. First, the CAD mesh model is segmented by an improved watershed segmentation algorithm, constructing the region-level representation required by feature recognition. Second, the form features needing to be suppressed are extracted using a feature recognition method with user defined feature facility based on the region-level representation, establishing the feature-level representation. Third, every recognized feature is suppressed using the most suitable one of the three methods, i.e. planar Delaunay triangulation, Poisson equation based method, and the method for blend features, thus simplifying the CAD mesh model. Our method provides an effective way to make CAD mesh model simplification meet the requirements of engineering applications. Several experimental results are presented to show the superiority and effectivity of our approach.     

Recognition of virtual loops on 3D CAD models based on the B-rep model

Loops are critical elements in boundary representation (B-rep) models because they link all edges corresponding to a face. Loops can be used in feature recognition for identifying depressions or protrusions. In real 3D CAD models, however, features typically lie across multiple faces, which is beyond the data structure of current B-rep models. This study presents a virtual loop concept to account for all loop types used in CAD models, and develops algorithms for recognizing them. In accordance with the complexity of the recognition algorithm, this study defines three types of loop: single, virtual, and multivirtual. A single loop is the current loop recorded in the B-rep model. A virtual loop lies across faces that are at least G¹ continuous. Finally, a multivirtual loop lies across faces that are either G⁰ or G¹ continuous. The proposed loop structure provides a more complete data structure for recognizing various types of features in feature-recognition modules. Several realistic CAD models are presented to confirm the feasibility of the proposed loop-recognition and feature-recognition methods.     

Extension of surface reconstruction algorithm to the global stitching and repairing of STL models

In the design of complex parts involving free-form or sculptured surfaces, the design is usually represented by a B-rep model. But in production involving rapid prototyping (RP) or solid machining, the B-rep model is often converted to the popular STL model. Due to defects such as topological and geometric errors in the B-rep model, the resulting STL model may contain gaps, overlaps, and inconsistent orientations. This paper presents the extension of a surface reconstruction algorithm to the global stitching of STL models for RP and solid machining applications. The model to be stitched may come from the digitization of physical objects by 3D laser scanners, or the triangulation of trimmed surfaces of a B-rep model. Systematic procedures have been developed for each of these two different but equally important cases. The result shows that the proposed method can robustly and effectively solve the global stitching problem for very complex STL models.     

Cyclides in pure blending II

In this the second of a two part paper, we continue our study of pure blends between natural quadrics using both Dupin ring cyclides and parabolic cyclides. Note, we make a distinction between blends and joins. If and only if conditions for the existence of cyclide blends and constructive proofs of their correctness are given in each quadric/quadric case. Easily implementable tests are given for these conditions. The relationship of the existence of cyclide blends to the common inscribed sphere condition is examined. Finally, an example that contains at least one of each type of cyclide blend is presented.     

Feature-based reverse modeling strategies

We presented two integrated solution schemes, sectional feature based strategy and surface feature based strategy, for modeling industrial components from point cloud to surfaces without using triangulation. For the sectional feature based strategy, slicing, curve feature recognition and constrained fitting are introduced. This strategy emphasizes the advanced feature architecture patterns from 2D to 3D in reverse engineering. The surface feature based strategy relies on differential geometric attributes estimation and diverse feature extraction techniques. The methods and algorithms such as attributes estimation based on 4D Shepard surface, symmetry plane extraction, quadric surface recognition and optimization, extruded and rotational surface extraction, and blend feature extraction with probability and statistic theory are proposed. The reliable three-dimensional feature fabricated the valid substratum of B-rep model faultlessly. All the algorithms are implemented in RE-SOFT, a reverse engineering software developed by Zhejiang University. The proposed strategies can be used to capture the original design intention accurately and to complete the reverse modeling process conveniently. Typical industrial components are used to illustrate the validation of our feature-based strategies.     

Evolving pattern recognition systems

A hybrid evolutionary learning algorithm is presented that synthesizes a complete multiclass pattern recognition system. The approach uses a multifaceted representation that evolves layers of processing to perform feature extraction from raw input data, select cooperative sets of feature detectors, and assemble a linear classifier that uses the detectors' responses to label targets. The hybrid algorithm, called hybrid evolutionary learning for pattern recognition (HELPR), blends elements of evolutionary programming, genetic programming, and genetic algorithms to perform a search for an effective set of feature detectors. Individual detectors are represented as expressions composed of morphological and arithmetic operations. Starting with a few small random expressions, HELPR expands the number and complexity of the features to produce a recognition system that achieves high accuracy. Results are presented that demonstrate the performance of HELPR-generated recognition systems applied to the task of classification of high-range resolution radar signals.     

在任意拓扑三角形网格上的光滑样条曲面

介绍了一种在控制三角形网格上创建光滑样条曲面的算法,该控制网格能够刻画具有或没有边界的任意自由曲面.生成的曲面有一个4次参数多项式表示并且被表示成一个切平面连续的三角形Bézier片网.曲面对网格的逼近程度受到一个混合比控制,当混合比为0时,产生的曲面插值网格.该算法是一种局部方法,简单且效率高,适合于外形设计.     

Biquartic C-surface splines over irregular meshes

C¹-surface splines define tangent continuous surfaces from control points in the manner of tensor-product (B-)splines, but allow a wider class of control meshes capable of outlining arbitrary free-form surfaces with or without boundary. In particular, irregular meshes with non-quadrilateral cells and more or fewer than four cells meeting at a point can be input and are treated in the same conceptual frame work as tensor-product B-splines; that is, the mesh points serve as control points of a smooth piecewise polynomial surface representation that is local and evaluates by averaging. Biquartic surface splines extend and complement the definition of C¹-surface splines in a previous paper (Peters, J SLAM J. Numer. Anal. Vol 32 No 2 (1993) 645–666) improving continuity and shape properties in the case where the user chooses to model entirely with four-sided patches. While tangent continuity is guaranteed, it is shown that no polynomial, symmetry-preserving construction with adjustable blends can guarantee its surfaces to lie in the local convex hull of the control mesh for very sharp blends where three patches join. Biquartic C¹-surface splines do as well as possible by guaranteeing the property whenever more than three patches join and whenever the blend exceeds a certain small threshold.     

基于集成RBF神经网络的小类别手写体汉字识别系统

该文介绍了RBF神经网络的模型,讨论了RBF网络分类器的机理和特点,提出了一种集成RBF神经网络并应用于小类别手写体汉字识别系统的设计,采用了组合重心分解网格特征方法来提取汉字特征,设计了遗传进化隐层节点自生成算法用于RBF的训练。实验表明该小类别手写体汉字识别系统有很高的识别率,具有一定的实用推广价值。     

Application of mortar elements to diffuse-interface methods

An adaptive 2D mesh refinement technique based on mortar spectral elements applied to diffuse-interface methods is presented. The refinement algorithm tracks the movement of the 2D diffuse-interface and subsequently refines the mesh locally at that interface, while coarsening the mesh in the rest of the computational domain, based on error estimators. Convergence of the method is validated using a Gaussian distribution problem and results are presented for a Cahn–Hilliard diffuse-interface model applied to capture the transient dynamics of polymer blends.     

Real-Time GPU Silhouette Refinement using Adaptively Blended Bézier Patches

We present an algorithm for detecting and extracting the silhouette edges of a triangle mesh in real time using Graphical Processing Units (GPUs). We also propose a tessellation strategy for visualizing the mesh with smooth silhouettes through a continuous blend between Bézier patches with varying level of detail. Furthermore, we show how our techniques can be integrated with displacement and normal mapping. We give details on our GPU implementation and provide a performance analysis with respect to mesh size.     

相交过渡的识别与抑制算法

通过分析相交过渡识别与抑制的难点,提出一种简单高效的相交过渡识别与抑制算法.该算法基于过渡抑制前后尖边的去留状态预测模型的拓扑变化,实现相交过渡的识别与抑制:对过渡面的尖边进行分类,将其分为删除边、保留边和分割保留边3类;基于分类结果,将含有保留边的过渡识别为相交过渡;根据相交过渡中尖边所对应的过渡抑制后的拓扑变化重构过渡周围面边界,实现相交过渡抑制.实验结果表明,文中算法能快速、有效地简化相交过渡,具有较高的效率和较强的鲁棒性.     

用C-C细分法和流形方法构造G2连续的自由型曲面

通过改进Cotrina等利用流形方法构造n边曲面片的算法,以C-C细分网格奇异点的5一环作为控制网构造出了带有均匀三次B样条边界的n边曲面片,使得该曲面片和C-C细分曲面G^2拼接．在此基础上,讨论了C-C细分曲面中n边域的构造和填充,从而为基于任意拓扑网格构造低次G^2连续曲面的问题给出了一个有效的解决方案,实现了用流形方法构造的曲面和C-C细分曲面的融合．最后,给出了几个具体算例．     

Direct (Re)Meshing for Efficient Surface Processing

We propose a novel surface remeshing algorithm. While many remeshing algorithms are based on global parametrization or local mesh optimization, our algorithm is closely related to surface reconstruction techniques and it requires no explicit parameterization. Our approach is based on the advancing‐front paradigm, and it can be used to both incrementally remesh the complete surface, or simply to remesh a portion of it with a high‐quality mesh. It is accurate, fast, robust, and suitable for use with interactive mesh processing applications that require local remeshing. We show a number of applications, including matching the resolution of meshes when doing Boolean operations such as unions and intersections. We also show how to adapt the algorithm to blend and merge mixed‐mode objects — for example, to compute the union of a point‐set surface and a triangle mesh.     

基于PSO的路牌识别模型黑盒对抗攻击方法

随着深度学习在计算机视觉领域的广泛应用，人脸认证、车牌识别、路牌识别等也随之呈现商业化应用趋势，因此针对深度学习模型的安全性研究至关重要.已有的研究发现深度学习模型易受精心制作的包含微小扰动的对抗样本攻击，输出完全错误的识别结果.针对深度模型的对抗攻击是致命的，但同时也能帮助研究人员发现模型漏洞并采取进一步改进措施.基于该思想，本文针对自动驾驶场景中的基于深度学习的路牌识别模型，提出一种基于粒子群优化的黑盒物理攻击方法（black-box physical attack via PSO，BPA-PSO），BPA-PSO在未知模型结构的前提下，不仅可以实现对深度模型的黑盒攻击，还能使得实际物理场景中的路牌识别模型失效.通过在电子空间的数字图像场景、物理空间的实验室及户外路况等场景下的大量实验，验证了本文提出的BPA-PSO算法的攻击有效性，可发现模型漏洞，进一步提高深度学习的应用安全性.最后，文章对BPA-PSO算法存在的问题进行分析，对未来的研究可能面临的挑战进行了展望.     

Construction and optimization of CSG representations

Boundary representations (B-reps) and constructive solid geometry (CSG) are widely used representation schemes for solids. While the problem of computing a B-rep from a CSG representation is relatively well understood, the inverse problem of B-rep to CSG conversion has not been addressed in general. The ability to perform B-rep to CSG conversion has important implications for the architecture of solid modelling systems and, in addition, is of considerable theoretical interest.

The paper presents a general approach to B-rep to CSG conversion based on a partition of Euclidean space by surfaces induced from a B-rep, and on the well known fact that closed regular sets and regularized set operations form a Boolean algebra. It is shown that the conversion problem is well defined, and that the solution results in a CSG representation that is unique for a fixed set of halfspaces that serve as a ‘basis’ for the representation. The ‘basis’ set contains halfspaces induced from a B-rep plus additional non-unique separating halfspaces.

An important characteristic of B-rep to CSG conversion is the size of a resulting CSG representation. We consider minimization of CSG representations in some detail and suggest new minimization techniques.

While many important geometric and combinatorial issues remain open, a companion paper shows that the proposed approach to B-rep to CSG conversion and minimization is effective in E², In E³, an experimental system currently converts natural-quadric B-reps in PARASOLID to efficient CSG representations in PADL-2.     

Euclidean distance transform for binary images on reconfigurable mesh-connected computers.

The distance calculation in an image is a basic operation in computer vision, pattern recognition, and robotics. Several parallel algorithms have been proposed for calculating the Euclidean distance transform (EDT). Recently, Chen and Chuang proposed a parallel algorithm for computing the EDT on mesh-connected SIMD computers (1995). For an nxn image, their algorithm runs in O(n) time on a two-dimensional (2-D) nxn mesh-connected processor array. In this paper, we propose a more efficient parallel algorithm for computing the EDT on a reconfigurable mesh model. For the same problem, our algorithm runs in O(log(2)n) time on a 2-D nxn reconfigurable mesh. Since a reconfigurable mesh uses the same amount of VLSI area as a plain mesh of the same size does when implemented in VLSI, our algorithm improves the result in [3] significantly.     

Recognition of simple and complex interacting non-orthogonal features

Feature recognition systems that deal with non-orthogonal features are seldom reported. This paper addresses this gap in the research by presenting a neural network-based feature recognition system to deal with non-orthogonal interacting features. The system accesses the B-rep data of a solid model, and searches for the feature volumes, using a cross-sectional layer method. The volumes are then transformed into 2D patterns of edges and vertices, using the conventions of ‘crosses and dots’ and ‘solid and dashed lines’. These feature patterns are later translated into input matrices for the recognition by a multilayer feedforward neural network.