B-rep Model Research Articles

Variational B-rep model analysis for direct modeling using geometric perturbation

Abstract The very recent CAD paradigm of direct modeling gives rise to the need of processing 3D geometric constraint systems defined on boundary representation (B-rep) models. The major issue of processing such variational B-rep models (in the STEP format) is that free motions of a well-constrained model involve more than just rigid-body motions. The fundamental difficulty lies in having a systematic description of what pattern these free motions follow. This paper proposes a geometric perturbation method to study these free motions. This method is a generalization of the witness method, allowing it to directly deal with variational B-rep models represented by the STEP format. This generalization is essentially achieved by using a direct, geometric representation of the free motions, and then expressing the free motions in terms of composites of several basis motions. To demonstrate the effectiveness of the proposed method, a series of comparisons and case studies are presented. Highlights A new method to analyze geometric constraint systems for direct modeling. A generalization of the witness configuration method. A new method to characterize the constraint states of variational B-rep models.

Fillets, rounds, grooves and sharp edges segmentation from 3D scanned surfaces

Fillets, rounds, chamfers and grooves are secondary features which are typically present in real manufactured mechanical components to satisfy some manufacturing and functional requirements. Despite the broad array of research conducted on feature recognition, the investigation of secondary features is a relatively new topic. All of the pertinent studies have been focusedonly on the recognition of secondary features from B-Rep models. The recognition and segmentation of secondary features from a discrete model is a non-trivial problem due to the same geometric descriptors that may be applied to both primary and secondary features. Moreover, although in real-world mechanical parts primary features are planes, cylinders or cones, the secondary features may be non-analytical and complex-shaped geometries. Further sources of uncertainty are the measurement errors and non-ideal geometries of the real objects to which the method is applied.To overcome these problems, a new and original method to segment secondary features of tessellated geometric models is proposed. The method is based on the analysis of geometric-differential properties and provides specific strategies that reduce its sensitivity to all of the above-mentioned uncertainties without affecting its selectivity. The proposed method, described in detail in this paper, is tested in some very critical cases, and the results are presented and discussed.

Fast pose estimation for texture-less objects based on B-Rep model

Widespread industrial products, which are usually texture-less, are mainly represented with 3D boundary representation (B-Rep) model for designing and manufacturing, hence the pose estimation of texture-less object based on B-Rep model is worthy of much studying in industrial inspection. In view of such facts that surfaces are much crucial both to construction of B-Rep model and to recognition of real object, the edges of the visible surfaces in each aspect view of B-Rep model are computed and the edges in a search image containing real B-Rep objects are extracted with modified Hough algorithm. Secondly, the two edge sets are converted into the metric space for comparison, where each edge is expressed with the tetrad of edge length, angle of middle point, angle of perpendicular axis, and length of perpendicular axis. In that way, the pose of real B-Rep object in a search image is estimated by comparing the edge set of every aspect view with the edge set of the search image with the bipartite graph matching algorithm. The corresponding experiment was taken with some products in national design reservoir (NDR), and it verified the effectiveness of the texture-less pose estimation approach based on B-Rep model.

Research on Shape Feature Recognition of B-Rep Model Based on Wavelet Transform

B-Rep (Boundary Representation) CAD model is widely used in the representation of manufactured product in computer, and it is a kind of real 3D structure with invisible part relative to 2.5D mesh model, so the shape feature recognition of B-Rep model is worth of much studying. We present one approach of shape feature recognition of B-Rep model based on the wavelet transform of surface boundary and region; it is inspired by the neuropsychology view that surface is the key visual features and by the systematology method that an object is recognized by decomposing and grouping its similar parts. Surface elements of B-Rep model are extracted from the neutral STEP (Standard for Exchange of Product Model Data) file; the curvatures of surface boundary and region were decomposed by wavelet transform, and then the coefficient statistics of same scale were as the surface feature vector. Similar surfaces of B-Rep model were clustered as a bin with the sum of perimeters and the mean vector, and all bins constituting a histogram are finally as the feature vector of B-Rep model. Thus B-Rep models are compared and retrieved using the EMD (Earth Mover’s Distance) of histogram. Our approach was evaluated by retrieval experiment with NDR (National Design Reservoir), and the result indicated its highly competent performance.

Identification of Similar and Complementary Subparts in B-Rep Mechanical Models

Content-based retrieval is particularly important for exploiting company model databases and online catalogs. To allow the identification of reusable part models possibly fitting with the product under development, methods for the similarity assessment between shapes should be provided in terms of both global and partial shape matching. In this perspective, this paper proposes a method directly working on B-rep models for 3D model retrieval, which does not require any model conversion to triangular meshes and in addition to global and partial matching allows the identification of components that may likely be assembled with a given model.

Rapid B-rep model preprocessing for immersogeometric analysis using analytic surfaces

Computational fluid dynamics (CFD) simulations of flow over complex objects have been performed traditionally using fluid-domain meshes that conform to the shape of the object. However, creating shape conforming meshes for complicated geometries such as automobiles require extensive geometry preprocessing. This process is usually tedious and requires modifying the geometry, including specialized operations such as defeaturing and filling of small gaps. Hsu et al. (2016) developed a novel immersogeometric fluid-flow method that does not require the generation of a boundary-fitted mesh for the fluid domain. However, their method used the NURBS parameterization of the surfaces for generating the surface quadrature points to enforce the boundary conditions, which required the B-rep model to be converted completely to NURBS before analysis can be performed. This conversion usually leads to poorly parameterized NURBS surfaces and can lead to poorly trimmed or missing surface features. In addition, converting simple geometries such as cylinders to NURBS imposes a performance penalty since these geometries have to be dealt with as rational splines. As a result, the geometry has to be inspected again after conversion to ensure analysis compatibility and can increase the computational cost. In this work, we have extended the immersogeometric method to generate surface quadrature points directly using analytic surfaces. We have developed quadrature rules for all four kinds of analytic surfaces: planes, cones, spheres, and tori. We have also developed methods for performing adaptive quadrature on trimmed analytic surfaces. Since analytic surfaces have frequently been used for constructing solid models, this method is also faster to generate quadrature points on real-world geometries than using only NURBS surfaces. To assess the accuracy of the proposed method, we perform simulations of a benchmark problem of flow over a torpedo shape made of analytic surfaces and compare those to immersogeometric simulations of the same model with NURBS surfaces. We also compare the results of our immersogeometric method with those obtained using boundary-fitted CFD of a tessellated torpedo shape, and quantities of interest such as drag coefficient are in good agreement. Finally, we demonstrate the effectiveness of our immersogeometric method for high-fidelity industrial scale simulations by performing an aerodynamic analysis of a truck that has a large percentage of analytic surfaces. Using analytic surfaces over NURBS avoids unnecessary surface type conversion and significantly reduces model-preprocessing time, while providing the same accuracy for the aerodynamic quantities of interest.

Automatic synchronization of a feature model with direct editing based on cellular model

ABSTRACTAs the de-facto standard in modern CAD systems, feature-based modeling is widely used in industry. Direct modeling, in contrast, is an emerging technology which allows users to promptly and directly edit B-rep models. To exert the powers of both technologies in a single design session and enable the communication between them, we propose a method that automatically converts direct modeling operations into feature model modification operations. We sequentially adopt three synchronization strategies - feature parameter modification, feature order adjustment and feature add/remove - to preserve the original design semantics of the feature model as much as possible. With a series of experiments, we demonstrate that the proposed method can fuse direct modeling and feature-based modeling in a natural and efficient way.

Research on Shape Feature Recognition of Boundary Representation CAD Model

B-Rep (Boundary Representation) CAD model is being widely used in representation of industrial product, so its feature recognition has acquired widespread research interests in computer vision and 3D model retrieval fields. We present one approach of feature recognition based on the idea of human visual mechanism. Surfaces as the visual shape features, and solids as well as shells as the topological relations, were extracted from the neutral STEP (Standard for Exchange of Product Model Data) files of B-Rep model. Towards three surface types of NURBS, analytical and poly loop, the properties of surface boundary and region are established based on curvature and other geometric index. So B-Rep CAD model is characterized as the hierarchical tree with solid layer, shell layer and surface layer for object recognition and retrieval, and the corresponding experiments verified the effectiveness of the method of shape feature recognition.

STEP-based feature recognition from solid models having non-planar surfaces

To enhance the interoperability of different CAD systems, 3D B-rep models should be represented in a neutral file format. Standard for exchange of product model data (STEP) is a neutral format that supports the representation of product model data from its geometrical and topological information to life cycle data. In this work, STEP-based feature recognition (FR) system is developed, which is capable of recognising the features having non-planar surfaces from solid models represented in STEP AP203 format. The considered non-planar surfaces are elementary (cylindrical, conical, spherical, toroidal) and advanced surfaces (i.e. B-spline and swept surfaces). The STEP AP203 file is accessed through Java Standard Data Access Interface (JSDAI). The recognition of considered non-uniform elementary and advanced surface features is performed by exploring the geometry and topological representation schema of the surfaces in STEP AP203 file in two phases. In the first phase, the surface and the edge-level geometrical and topological information of the considered object is extracted. In the second phase, the features with non-planar surfaces are recognised and presented as per the data needed for STEP AP224 format. Since the FR system uses STEP AP203 file as input, after recognising features, there is minimum chance of losing information from CAD model to feature representation. The developed FR system is demonstrated with a blow moulding die, which is having different non-planar elementary and advanced surfaces. The output information of the developed FR system is useful for downstream application such as automatic generation of STEP-NC programs.

Generation Method and Application of Product-Oriented Medial Axis

Abstract In this paper, the generation method of the medial axis in the arbitrary quadrilateral surface is proposed. It can provide a solution for the simplification of the complex fillet feature and the generation of the mesh in the model. By using the locus method associated with moving Frenet frame, we realize the simple and fast algorithm for generating the medial axis. As for the engineering problem, B-rep 3D solid models with clear boundary definition are mostly applied; the information of vertex, side and surface of the model, which is clearly stored in the model file, can be used to simplify the traditional locus method for generating the medial axis, in order to reduce the amount of data required by the generation. In this paper, we use the clear boundary information in the B-rep model as the condition for generating the medial axis and the characteristics of the bisector to eliminate the calculation of the branch points, reducing the factors affecting the accuracy of the medial axis. In order to ensure the accuracy of the medial axis, the density of the insertion points can be used for control.

Automatic small chamfer feature recognition from B-rep models for analysis

The recognition and suppression of small feature from B-rep models play an important role in effectively generating the qualified mesh for analysis. This paper presents the ruled-based algorithm for recognizing two types of small chamfers automatically from manifold B-rep models from the viewpoint of finite element analysis (FEA). The algorithm firstly transforms the input B-rep model into an aggregation of the faces. Then, each face is judged to be a chamfer feature or not based on matching conditions. At last, the chamfers with larger physical sizes than a threshold value are excluded. The innovations of this algorithm lie in the related recognition conditions and unique procedures for calculating the chamfer physical size. Several comprehensive examples are given to demonstrate the validity and applicability of the algorithm.

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.

A topological enabled three-dimensional model based on constructive solid geometry and boundary representation

Ordinary triangular mesh model can be constructed from discrete point cloud. However, this kind of model contains large amount of data. It is not only difficult to split, but also lacks topological relation information. We proposed a CSG---BRep (Constructive Solid Geometry--Boundary Representation) topological model to overcome these problems. CSG---BRep model can record topological relationship of 3D model in great detail. We first introduced aspects of the topological model: location, orientation and sub-shape. Then we proposed two algorithms to access topological structure. We also proposed algorithms for performing Boolean operation on CSG---BRep models. Finally, we demonstrated CSG---BRep construction using LIDAR point cloud as a data source. We would show that, compared to ordinary triangular mesh model, CSG---BRep model is composable and can effectively reduce data volume. In addition, CSG---BRep model has detailed topological relation information, allowing further querying and analysis of 3D spatial topological information.

EXTENSION OF RCC TOPOLOGICAL RELATIONS FOR 3D COMPLEX OBJECTS COMPONENTS EXTRACTED FROM 3D LIDAR POINT CLOUDS

Abstract. Topological relations are fundamental for qualitative description, querying and analysis of a 3D scene. Although topological relations for 2D objects have been extensively studied and implemented in GIS applications, their direct extension to 3D is very challenging and they cannot be directly applied to represent relations between components of complex 3D objects represented by 3D B-Rep models in R3. Herein we present an extended Region Connection Calculus (RCC) model to express and formalize topological relations between planar regions for creating 3D model represented by Boundary Representation model in R3. We proposed a new dimension extended 9-Intersection model to represent the basic relations among components of a complex object, including disjoint, meet and intersect. The last element in 3*3 matrix records the details of connection through the common parts of two regions and the intersecting line of two planes. Additionally, this model can deal with the case of planar regions with holes. Finally, the geometric information is transformed into a list of strings consisting of topological relations between two planar regions and detailed connection information. The experiments show that the proposed approach helps to identify topological relations of planar segments of point cloud automatically.

EXTENSION OF RCC TOPOLOGICAL RELATIONS FOR 3D COMPLEX OBJECTS COMPONENTS EXTRACTED FROM 3D LIDAR POINT CLOUDS

Topological relations are fundamental for qualitative description, querying and analysis of a 3D scene. Although topological relations for 2D objects have been extensively studied and implemented in GIS applications, their direct extension to 3D is very challenging and they cannot be directly applied to represent relations between components of complex 3D objects represented by 3D B-Rep models in <i>R</i><sup>3</sup>. Herein we present an extended Region Connection Calculus (RCC) model to express and formalize topological relations between planar regions for creating 3D model represented by Boundary Representation model in <i>R</i><sup>3</sup>. We proposed a new dimension extended 9-Intersection model to represent the basic relations among components of a complex object, including disjoint, meet and intersect. The last element in 3*3 matrix records the details of connection through the common parts of two regions and the intersecting line of two planes. Additionally, this model can deal with the case of planar regions with holes. Finally, the geometric information is transformed into a list of strings consisting of topological relations between two planar regions and detailed connection information. The experiments show that the proposed approach helps to identify topological relations of planar segments of point cloud automatically.

Small blend suppression from B-rep models in computer-aided engineering analysis

In mechanical design, small blending is a common operation used to improve the strength and aesthetics of the workpiece. In blending operations, certain smooth faces are added to the boundary representation (B-rep) model to smooth sharp edges and vertices. These faces are termed ‘blend faces.’ However, they may affect the quality of analysis; these faces should be meshed with tiny meshes, which may result in an increase in computational time and reduced accuracy of simulation results. Hence, small blend suppression is an approach for improving the quality of generated meshes. Blend suppression is a technique for reverting a blended computer-aided design model to its original unblended status. This study proposes a blend suppression algorithm for removing blend faces in computer-aided engineering (CAE) analysis. The proposed algorithm operates as follows: (1) edge blend faces and vertex blend faces are grouped individually, (2) new geometric data are computed, (3) new elements are added to the data structure of the B-rep model, (4) all data related to blend faces are deleted, and (5) all topological data in the B-rep model are updated. Several examples are presented in this paper to demonstrate the feasibility of the proposed method for blend suppression as well as its advantage in improving the quality of meshes in CAE analysis.

Isogeometric analysis-suitable trivariate NURBS models from standard B-Rep models

This paper presents an effective method to automatically construct trivariate spline models of complicated geometry and arbitrary topology required for NURBS-based isogeometric analysis. The input is a triangulation of the solid model’s boundary. The boundary surface is decomposed into a set of cuboids in two steps: pants decomposition and cuboid decomposition. The novelty of our method is the pants-to-cuboids decomposition algorithm. The algorithm is completely automatic and very robust even for low-quality and noisy meshes. The set of cuboids composes a generalized polycube approximating very roughly the input model’s geometry while faithfully replicating its topology. Due to its regular structure, the polycube is suitable for serving as the parametric domain for the tensor-product spline representation. Based on a discrete harmonic mapping between the cuboids’ boundary and the polycube’s boundary, surface and volume parameterizations are generated in order to fit the trivariate splines. The efficiency and the robustness of the proposed approach are illustrated by several examples.

Incremental reconstruction of planar B-Rep models from multiple point clouds

Boundary representation (B-Rep) models are surface representations containing geometric and topological information that are used in many fields such as reverse engineering, simulation and optimiza...

Towards a declarative modeling approach built on top of a CAD modeler

ABSTRACTToday’s CAD modelers are very efficient in processing 3D shapes of CAD models by means of B-Rep modeling operators such as pad, pocket, shaft, groove, hole, fillet and so on. At a lower description level, those modeling operators are based on Euler operators acting directly on the faces, edges and vertices of the B-Rep models. Using such a top-down approach, the designers do not have to work on low-level geometric entities, but rather manipulate so-called structural and detail features to shape directly the CAD models. However, there is still a gap between the shapes the designers have in mind and the way they have to decompose them in a succession of modeling steps. This paper proposes a new declarative modeling approach to design industrial shapes allowing the designers to interact with a CAD software at a more conceptual level. The designers enter a high-level description of the expected shapes that is then transformed through scripts into traditional CAD operators successively called to create...

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.