An Intelligent Analysis Method for 3D CAD Shapes Based on CSG

This paper presents a unified differentiable boolean operator for implicit solid shape modeling using Constructive Solid Geometry (CSG). Traditional CSG relies on min, max operators to perform boolean operations on implicit shapes. But because these boolean operators are discontinuous and discrete in the choice of operations, this makes optimization over the CSG representation challenging. Drawing inspiration from fuzzy logic, we present a unified boolean operator that outputs a continuous function and is differentiable with respect to operator types. This enables optimization of both the primitives and the boolean operations employed in CSG with continuous optimization techniques, such as gradient descent. We further demonstrate that such a continuous boolean operator allows the modeling of both sharp mechanical objects and smooth organic shapes with the same framework. Our proposed boolean operator opens up new possibilities for future research toward fully continuous CSG optimization.

Structural topology optimization using multi-objective genetic algorithm with constructive solid geometry representation

Robust event-driven particle tracking in complex geometries

Set operation evaluation is an important component of Geometric Modeling System (GMS). Input data can be a CSG (Constructive Solid Geometry) representation with solid primitives approximated by polyhedra. This representation is a powerful tool for solid object description. Output data will be the unique resulting polyhedral object which provides an efficient data structure in display field. With no use of spatial coherency, computational complexity of set operation is quadratic. In this paper, we are introducing a new space subdivision scheme called Boolean Octree which performs set operations on polyhedra in an efficient way. This structure aims at limiting set operation evaluation in a ‘minimal space of calculation’ where primitive boundaries intersect each other and where resulting evaluation participates in the construction of the final resulting object. Boolean Octree computes set operations in a local level providing a linear complexity for geometric calculations. During space subdivision, Boolean Octree has a global view on local CSG tree (projection of the CSG tree in local space) taking into account simplifications of the boolean expression, avoiding evaluation and subdivision for the object parts out of the ‘minimal space of calculation’.

Introduction T HE technique for associating design variables with mesh data is the most crucial factor in three-dimensional shape optimization. Previously, work in three-dimensional shape optimization involved specifying design variables by associating parameters directly with grid points on an existing mesh. For realistic problems this can be a very tedious (and errorprone) process. In the past, shape optimization capabilities have been developed based on a variety of design/analysis capabilities ranging from associating parameters with a mesh created manually to associating parameters with control points of a mapped mesh generator. Special techniques have also been developed to properly move internal grid points during sensitivity calculations. More recently, a capability based on constructive solid geometry (CSG) has been developed, but CSG representations are not particularly suitable for design optimization. A new optimization approach is demonstrated in this Note that uses a new, fully automatic mesh generation capability. The design model is developed based on design-oriented geometric primitives that represent recognizable features of a part and can be assembled into complete solid models that are defined in terms of a small set of design parameters.

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.

The generation of 3-D solid objects, and more generally solid geometric modelling, is very important in Computer Aided Design (CAD). An important role is played by the Constructive Solid Geometry (CSG) representation scheme. In CSG, objects are described by trees of Boolean operations on half-spaces or boundaries of primitive solids. The study of techniques to speed up the rendering of scenes modelled with the CSG scheme is an attractive field of research; in this paper we propose a new algorithm which reduces the computational complexity for ray casting approaches. Our strategy identifies a set of areas on the plane of view where the rays starting from the observer have to be traced; for each zone, only a portion of the entire CSG tree has to be considered for intersection tests, instead of the whole database of the primitive objects. A comparison of our algorithm with a ray caster that adopts bounding volume hierarchies and with a freeware ray tracer called POV-Ray shows that, for the examples considered, we may reduce the intersection tests to one third of those performed when standard optimizations are adopted.

A feature-based topological optimization for structure design

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.

Solid modeling is the technique for representing and manipulating a complete description of physical objects. Valid representations of solid are developed base on a mathematical description of rigid object. A valid solid representation scheme provides sufficient information for geometric operations on objects, e.g. Boolean operations, collision detection. The description here introduces the Fundamental concepts in solid modeling are introduced. Characteristics of a solid representation scheme are discussed. Two popular solid representation schemes, the constructive solid geometry and the boundary representation schemes, are described. The fundamental algorithms for solid modeling, point membership classification, and Boolean operations, are also discussed. Validity of the boundary representation scheme, the Euler operators, as well as the Winged‐edge data structure for the implementation of boundary representation scheme are also presented.

The Constructive Solid Geometry (CSG) allows modelers to create models by using Boolean operations to combine different types of basic solids. CSG has been adopted by lots of numerical simulation codes as geometric description. In the research of reactor numerical simulation, Monte Carlo (MC) is a common method for neutronics analysis, which needs to calculate the intersections between the random flight paths of neutrons and the geometry. A lot of widely used MC codes (such as Geant4, MCNP) use CSG to describe geometry. The prerequisite to run MC code is to do geometric modeling, which however in many MC codes, is finished by manually writing text files, it is very hard to view the model and it is inefficient to build. In this work, a MC modeling tool (JLAMT) based on UG software is used to build the benchmark model. The tool supplies geometric modeling functions, physical parameter setting functions, and other assistant tools. With a flexible GUI, it helps users to achieve quick modeling.

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.

Abstract. As-built BIM reconstruction supports building digitalization, enabling efficient management and maintenance of existing buildings. Manual reconstruction from point clouds is both error-prone and cost-intensive, while automatic reconstruction remains challenging despite recent advancements. This paper explores the use of Constructive Solid Geometry (CSG) for automatically reconstructing IFC-compatible models from indoor point clouds of existing buildings. The proposed approach starts with segmented point clouds corresponding to rooms, doors, and windows, then CSG operations are used to reconstruct key building components as solids, including slabs, walls, doors, windows, and interior spaces. These solids are subsequently converted into corresponding IFC entities. The method is evaluated using two case studies, achieving a centimetre-level accuracy and a runtime of approximately 9 seconds per case study. The proposed method provides a promising ability to advance the Scan-to-BIM pipeline, as it enables accurate reconstruction of building components while preserving topological relationships during an efficient runtime.

Terrestrial laser scanning (TLS) is an important part of urban reconstruction and terrain surveying. In TLS applications, 4-point congruent set (4PCS) technology is widely used for the global registration of point clouds. However, TLS point clouds usually enjoy enormous data and uneven density. Obtaining the congruent set of tuples in a large point cloud scene can be challenging. To address this concern, we propose a registration method based on the voxel grid of the point cloud in this paper. First, we establish a voxel grid structure and index structure for the point cloud and eliminate uneven point cloud density. Then, based on the point cloud distribution in the voxel grid, keypoints are calculated to represent the entire point cloud. Fast query of voxel grids is used to restrict the selection of calculation points and filter out 4-point tuples on the same surface to reduce ambiguity in building registration. Finally, the voxel grid is used in our proposed approach to perform random queries of the array. Using different indoor and outdoor data to compare our proposed approach with other 4-point congruent set methods, according to the experimental results, in terms of registration efficiency, the proposed method is more than 50% higher than K4PCS and 78% higher than Super4PCS.

The advancement of deep learning technology has been concentrating on deploying end-to-end solutions using high dimensional data, such as images. Recently, a number of methods have been proposed for reconstructing 3D objects using deep learning. One such technique is the method that involves recovering 3D objects as voxel grids using one or multiple images. However, there has been very little work directed towards the generation of 3D objects represented by a set of points, i.e. point cloud, from voxel grids which are ambiguous and coarse. The development of a deep learning model that generates point clouds with details from coarse voxel grids has numerous benefits to quality of life. For example, design professionals can use this model to generate detailed 3D point clouds using a sketched and coarse voxel to enable their creativities. This paper presents an algorithm to generate point clouds from voxel grids. The algorithm explicitly loads 3D objects into voxels without projection operations and associated information loss. To obtain a comprehensive understanding of the voxel grid, the grid is analyzed through various angles, as inspired by how humans observe 3D objects. The features from various angles are passed into a GRU layer to extract patterns across views, which will then be passed to a channel-wise convolutional layer and graph convolution to generated the predicted point cloud. The experimental result of the algorithm indicates that the algorithm is capable of generating high-quality point clouds by understanding the semantic features of the voxel grid.