Solid Modeling

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.

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 Cartesian grid generation method is developed in this study. Two kinds of solid modeling methods, CSG and STL models, are used for complicated solid modeling. The staircase boundary approximation is implemented to handle irregular geometries and the computational domain is discretized using a regular Cartesian grid. Using the edge-based integral slice algorithm, the models are sliced with a set of parallel planes to generate 2D slices information. The scan line filling technique is used to achieve grid generation after slicing. Two grid generation examples with a CSG model and a STL model are given to test the capability of the grid generation method. For grid displaying, a method is proposed to remove the hidden surfaces fasten based on the topology of orthogonal hexahedral grids. The parallelization of grid displaying is achieved by employing multi-threaded parallel technique. Parallel test results show that the parallel algorithm has the absolute advantage on speed compared to the serial algorithm.

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 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.

Constructive non-regularized geometry

A new collision detection method for CSG-represented objects in virtual manufacturing

Interpretation of engineering drawings as solid models: Comput.-Aided Eng. J. Vol 5 No 2 (1988) pp 67–78

Accelerated robust Boolean operations based on hybrid representations

This work presents the role of 3D visualization and analysis of monuments and archaeological sites in producing useful data regarding their preservation condition. The progress made in 3D digitization technologies, in combination with the development of new data processing algorithms, has enabled reliable and highly detailed digitization of the characteristics of different parts of the monuments. Due to both the effects of nature and human intervention, monuments and sites all over the world have undergone changes over time. The use of analog documentation data can help significantly towards this direction. In this work, we use as a case study a luxurious residential complex in the Athenian Agora, known as the Omega House. We use a retrospective 3D model, created with photographs taken in the late 60’s and early 70’s, in comparison with a 3D model made with contemporary digital photos, taken in 2017. All models are georeferenced. The old model is derived using analog terrestrial photographs and aerial photos taken by a blimp. The new one is created by terrestrial digital photographs in combination with images taken by an unmanned aerial vehicle, commonly known as a drone. The 3D models have been divided into smaller parts so that we can analyze them with greater accuracy separately, and then the whole models were compared as well. The Constructive Solid Geometry (CSG) modelling scheme is used and Boolean operations are applied to find the difference and intersection of the models. The comparison that is carried out in the current work elaborates on legacy data usefulness and their utility for monitoring the Omega House condition. The type of investigation proposed in this work proves that legacy data can be repurposed and can attain a new role through change detection techniques.

A feature-based topological optimization for structure design

Robust event-driven particle tracking in complex geometries

This paper describes a fast algorithm for the volume conversion and rendering of CSG models constructed from both geometric and volumetric primitives. Using 3D texture mapping and frame buffer pixel operations, the algorithm can interactively generate a binary volume of the CSG model. The result can be used for volume rendering and other applications. Boolean operations are implicitly computed by a Point-Classification Map, and implemented by a hardware assisted frame buffer pixel map. The algorithm can be applied to any regions of interest of the model, thus provides a multi-resolution rendering solution through dynamic voxelization of the viewing regions. Since no pre-processing is required for any change of the CSG tree, it can be used as an effective rendering tool in a volumetric CSG modeling environment.

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 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.