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

Recently, concurrent engineering (CE) has become one of the major conceptual approaches in reducing product developing time. Design for manufacturing (DFM) and design for assembly (DFA) are two of the major areas in CE. Several researchers have integrated a CAD/CAM system and a knowledge-based system to implement DFA and DFM concepts. However, the incompatibility of the data representation methods between CAD/CAM and knowledge-based systems is the major issue in this integration method. In this paper, an approach is proposed to find the minimum wall thickness of a part from its boundary representation (B-Rep) model. These data can then be directly utilized by a knowledge-based system to analyse the manufacturability of thin wall parts such as injection moulded or diecast parts.

Shape recognition of the 3D shapes in computer-aided design (CAD) can help automate the product modelling and reduce the time to develop a new product. In this paper, in order to recognize partial shapes of 3D CAD models such as bolts and fillets, we propose a shape recognition method based on graph-neural-networks, which learns geometrical and topological information from data of annotated 3D CAD models. By using the graph of face adjacencies of the BRep model as input to the learning model, it is possible to predict recognition target directly from the BRep models. We applied this method to machine part data and verified its effectiveness. We demonstrate that our method can classify the BRep models in FabWave dataset with higher accuracy than the methods based on the point clouds.

The line structure is an efficient form of representation and modeling for LiDAR point clouds, while the Line Structure Construction (LSC) method aims to extract complete and coherent line structures from complex 3D point clouds, thereby providing a foundation for geometric modeling, scene understanding, and downstream applications. However, traditional LSC methods often fall short in preserving both the geometric integrity and topological connectivity of line structures derived from such datasets. To address this issue, we propose the Geometry and Topology Preservable Line Structure Construction (GTP-LSC) method, based on the Encoding and Extracting Framework (EEF). First, in the encoding phase, point cloud features related to line structures are mapped into a high-dimensional feature space. A 3D U-Net is then employed to compute Subsets with Structure feature of Line (SSL) from the dense, unstructured, and noisy indoor LiDAR point cloud data. Next, in the extraction phase, the SSL is transformed into a 3D field enriched with line features. Initially extracted line structures are then constructed based on Morse theory, effectively preserving the topological relationships. In the final step, these line structures are optimized using RANdom SAmple Consensus (RANSAC) and Constructive Solid Geometry (CSG) to ensure geometric completeness. This step also facilitates the generation of complex entities, enabling an accurate and comprehensive representation of both geometric and topological aspects of the line structures. Experiments were conducted using the Indoor Laser Scanning Dataset, focusing on the parking garage (D1), the corridor (D2), and the multi-room structure (D3). The results demonstrated that the proposed GTP-LSC method outperformed existing approaches in terms of both geometric integrity and topological connectivity. To evaluate the performance of different LSC methods, the IoU Buffer Ratio (IBR) was used to measure the overlap between the actual and constructed line structures. The proposed method achieved IBR scores of 92.5% (D1), 94.2% (D2), and 90.8% (D3) for these scenes. Additionally, Precision, Recall, and F-Score were calculated to further assess the LSC results. The F-Score of the proposed method was 0.89 (D1), 0.92 (D2), and 0.89 (D3), demonstrating superior performance in both visual analysis and quantitative results compared to other methods.

Face area evaluation algorithm for solids

Current reverse engineering systems can generate boundary representation (B-rep) models from 3D range data. Such models suffer from inaccuracies caused by noise in the input data and algorithms. The quality of reverse engineered geometric models can be improved by finding candidate shape regularities in such a model, and constraining the model to meet a suitable subset of them, in a post-processing step called beautification. This paper discusses algorithms to detect such approximate regularities in terms of similarities between feature objects describing properties of faces, edges and vertices, and small groups of these elements in a B-rep model with only planar, spherical, cylindrical, conical and toroidal faces. For each group of similar feature objects they also seek special feature objects which may represent the group, e.g. an integer value which approximates the radius of similar cylinders. Experiments show that the regularities found by the algorithms include the desired regularities as well as spurious regularities, which can be limited by an appropriate choice of tolerances.

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.

: Described is a set of algorithms for efficiently rendering a CSG- defined objective directly into a frame buffer without converting first to a boundary representation. The method requires only that the frame buffer contain sufficient memory to hold two color values, two z values, and three one-bit flags. The algorithm first converts the CSG tree to a normalized form that is analogous to the sum-of-products form for boolean switching functions. Expanding on results previously reported the authors, introduce 1) an improved algorithm for converting a CSG expression to sum-of-products form, 2) a technique for minimizing the tree using don't care conditions based on geometry, 3) the dynamic interleaving of the above two algorithms, allowing very efficient rendering for most CSG objects, 4) a method for extending the technique to non- convex primitives, and 5) an implementation of these ideas in an interactive CSG design system on Pixelplanes 4. In this system the designer directly manipulates the CSG structure while continuously viewing the color rendering of the object under design. It is believed these algorithms will attain similar speeds on many of the next generation high-performance graphics system that have frame buffers with many bits per pixel.

Fetuses are extremely radiosensitive and the protection of pregnant females against ionizing radiation is of particular interest in many health and medical physics applications. Existing models of pregnant females relied on simplified anatomical shapes or partial-body images of low resolutions. This paper reviews two general types of solid geometry modeling: constructive solid geometry (CSG) and boundary representation (BREP). It presents in detail a project to adopt the BREP modeling approach to systematically design whole-body radiation dosimetry models: a pregnant female and her fetus at the ends of three gestational periods of 3, 6 and 9 months. Based on previously published CT images of a 7-month pregnant female, the VIP-Man model and mesh organ models, this new set of pregnant female models was constructed using 3D surface modeling technologies instead of voxels. The organ masses were adjusted to agree with the reference data provided by the International Commission on Radiological Protection (ICRP) and previously published papers within 0.5%. The models were then voxelized for the purpose of performing dose calculations in identically implemented EGS4 and MCNPX Monte Carlo codes. The agreements of the fetal doses obtained from these two codes for this set of models were found to be within 2% for the majority of the external photon irradiation geometries of AP, PA, LAT, ROT and ISO at various energies. It is concluded that the so-called RPI-P3, RPI-P6 and RPI-P9 models have been reliably defined for Monte Carlo calculations. The paper also discusses the needs for future research and the possibility for the BREP method to become a major tool in the anatomical modeling for radiation dosimetry.For more information on this article, see medicalphysicsweb.org

Abstract. A Digital Surface Model (DSM) is a crucial spatial geographic information data used to describe the shape of the earth’s surface in Geographic Information Systems (GIS). DSM is the core data used in terrain analysis in GIS. A regular grid DSM is generally generated by interpolating a large number of discrete point clouds. This paper proposes a method of using a hierarchical weighted strategy to fit a regular grid DSM with discrete points. This method uses a pyramid hierarchical strategy to refine the target regular grid from one grid with finer parameters of 3*3, until the nth level (the interval of the grid is equal to the expected interval), and then gradually places the discrete point cloud into the corresponding grid by weighted averaging, and uses the result of this level as the initial value of the next level. This algorithm can avoid the problem of low efficiency in retrieving a large number of discrete point clouds, and the indirect interpolation method not considering the contribution of distant neighboring point clouds. The operation of point cloud data is a stream operation, which does not require consideration of the topological information of point clouds, and has simple operation and no additional memory consumption. It is especially suitable for the production of regular grid DSM with massive point clouds. To verify the effectiveness of this method, the article selected six typical terrain data such as high mountains, mountains, hills, plains, urban areas, and lakes for experiments. The results show that compared with the construct-TIN method for producing DSM, this method has very good processing accuracy and processing efficiency.

CAD models serve as the fundamental carriers for representing geometric structures and design logic. Understanding the underlying construction logic of complex shapes facilitates the reuse, editing, and optimization of designs. Constructive Solid Geometry (CSG) offers a viable approach for shape parsing by representing complex geometries through combinations of simple primitives. This paper proposes a novel method for parsing 3D CAD shapes based on CSG representations. Leveraging quadric surfaces as the fundamental modeling primitives, our approach employs a dual-branch architecture— “composition–subtraction”—to construct target 3D shapes via Boolean operations. Each branch receives either voxel grids or point clouds as input and uses an auto-encoder to extract shape features, which are then used to predict a set of intermediate shapes. The final reconstruction is obtained through set difference operations. To enhance the model’s expressive capacity under a fixed Boolean operation sequence, we introduce rotation parameters and dual primitive designs. Moreover, we adopt a staged training framework that progressively guides the model from learning approximate signed distance functions to precise structural modeling. A regularization loss is incorporated to promote geometric diversity and plausibility of the primitives. After training, we further propose a post-processing strategy based on signed distance influence to remove redundant primitives, resulting in more compact and interpretable CSG sequences. Experimental comparisons on the ABC dataset demonstrate that our method reduces the 3D chamfer distance and edge chamfer distance by 72.1% and 31.1%, respectively, and improves the normal vector consistency by 9.48%, compared to SECAD-Net, and achieves better results in visual metrics.

The topological and geometric information in B-rep models is essential for various applications, including feature recognition, design verification, and automatic tool path generation. In particular, representing surfaces using an analytic format offers advantages for utilizing geometric information such as surface type, axis of rotation, and radius. Models composed solely of NURBS surfaces often have limitations in extracting this type of information. To address this issue, this study proposes a method for identifying and replacing NURBS surfaces that can be represented analytically. In the first step, the feasibility of substituting a NURBS surface with an analytic surface is determined by examining the characteristics of its isocurves. In the second step, an equivalent analytic surface is created and used to replace the existing NURBS surface. To validate the proposed method, surface replacement experiments were conducted on multiple test cases. The results showed that, among 10 176 NURBS surfaces identified for possible analytic replacement across 37 B-rep models, 9 163 surfaces were successfully substituted in a stable manner. In addition, an experiment comparing feature recognition in the pre- and post-replacement models was conducted. As a result, none of the 12 design features were recognized in the pre-replacement model, whereas all were correctly detected afterward, confirming that the replacement process significantly enhances feature recognition accuracy.

In boundary representation (B-rep) reconstruction for computer aided design (CAD) applications, it is still challenging with existing methods to distinguish primitives in the smoothly blended regions reasonably. Thus, intensive manual post-processing is always required for correcting the primitives and their neighboring relationships to obtain a valid B-rep solid, seriously preventing the efficiency. In this paper, we address these challenges by presenting two novel techniques. The first is to robustly extract primitives by iteratively estimating the probability distribution of the noise to eliminate outliers. The second is to present intersection-aware constraints, like tangency and collinearity constraints, to correctly obtain intersections between primitives, which have not been explored in existing methods to our knowledge. Therefore, we can effectively extract primitives, especially those blended smoothly, and obtain high-quality relationships between them. As a result, a valid B-rep model can be constructed without a lot of manual post-processing on topology correction, while not with existing methods. As a benefit, with our constructed B-rep models, their corresponding meshes can be intuitively and conveniently edited, which is quite useful in CAD applications. Experimental results show that our proposed B-rep construction method outperforms both classical and recent learning-based methods in terms of reconstruction efficiency and accuracy.

The concept of feature was introduced because of need to integrate the design and the manufacturing activities. Therefore, the generation of features usually occurs after design completion. However, in recent product development approaches such as concurrent engineering (CE), features need to be generated during design evolution. This paper presents an incremental feature generation (IFG) and feature modification (FM) approach applicable during design evolution, defined by constructive solid geometry (CSG) and boundary representation (B-rep). In IFG, a classified boundary component, obtained from boundary evaluation, is defined as a protrusion or depression (P/D) according to Boolean operation and convexity analysis. The existing features are then updated in accordance with feature interactions in the FM. The FM involves feature existence analysis and modification procedures. The modification procedures are; 1) decide whether the remaining part of an existing feature is valid for a feature definition, 2) update it as a new feature and 3) define the feature relationship. In the IFG approach, the geometry of the current design step is automatically isolated by Boolean operation and defined as a protrusion or depression (P/D) without convexity calculation of topological entities such as edges or face sets. The above procedures are performed through tracing Boolean operations and convexity checking of an intersection edge loop generated during design evolution.

We present faceton, a geometric modeling primitive designed for building architectural models, using a six degrees of freedom (DoF) input device in a virtual environment (VE). A faceton is given as an oriented point floating in the air and defines a plane of infinite extent passing through the point. The polygonal mesh model is constructed by taking the intersection of the planes associated with the facetons. With the simple drag-and-drop and group interaction of faceton, users can easily create 3D architecture models in the VE. The faceton primitive and its interaction reduce the overhead associated with standard polygonal mesh modeling in VE, where users have to manually specify vertexes and edges which could be far away. The faceton representation is inspired by the research on boundary representations (B-rep) and constructive solid geometry (CSG), but it is driven by a novel adaptive bounding algorithm and is specifically designed for the 3D modeling activities in an immersive virtual environment.

This paper proposes a 3D inclusion test which enables processing very large datasets in a limited amount of time. Each point in the dataset is provided with a label according to its location relative to a polyhedron. These 3D objects can be modeled in a number of ways, related to its purpose or application in which it is used. The two representation types considered in this paper are the Boundary Representation (B-Rep) and the Constructive Solid Geometry (CSG). In order to be able to process a large amount of points in a relative limited amount of time, a preprocessing phase is essential prior to performing a sequence of operations. In this initial step, the space is subdivided into a 3D array of voxels. The voxelization procedure deviates slightly between the two representation types, but the general principle remains the same. This subdivision allows fast retrieval of the status (inside/outside) of a very large amount of points in space.