Face area evaluation algorithm for solids

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.

: 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.

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.

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

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.

Octree reinforced thin-shell rapid prototyping

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.

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.

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’.

This paper proposes a model-based building reconstruction method. Modeled by Constructive Solid Geometry (CSG), buildings are reconstructed part by part by fitting each parameterized CSG primitive to the corresponding edge pixels of aerial images. The shape and pose parameters associated to a primitive provide a link between perception (images) and prior knowledge (primitive) of a building part, so that the fitting method proceeds to determine the shape and pose parameters so as to fit a primitive with the corresponding images. Having all of the building parts been uniquely represented by parametric primitives, a building can be reconstructed by using CSG Boolean set operators to combine the building parts. Consequently, a building is represented by a CSG-tree in which each node links two branches of combined parts. This paper demonstrates 10 examples of extracting various buildings. The process time for each primitive is about 20 sec and the successful rate of model-image fitting is about 90%.

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.

Additive Manufacturing (AM) based Printed Electronics (PE) is an emerging technique where electronic components and interconnects are printed directly on substrates using a layered technique. The direct printing of the electronic components allows large scale and ultra-thin components to be printed on a wide variety of substrates including glass, silicon and plastic. These attributes make AM based Printed Electronics an invaluable manufacturing technique in the area of electronic sensors and sensor networks where thin, flexible and rugged form factors are very important. However, currently this technology is a labor intensive and manual process with the machine operator using his experience and judgment to slice the CAD file of the part to create 2D layers at different levels. This manual process increases the overall production time as well as the cost of the product and also results in inconsistent quality of parts. A major challenge faced by existing AM based Printed Electronics users for automating this process is the lack of a standard input file format that can be used by different PE machines for producing the components in layers. To leverage the capabilities of both AM and PE processes, a new file format based on the Constructive Solid Geometry (CSG) technique is proposed in this research paper. This file format data will not only include CAD data in the form of CSG primitives and Boolean representation but will also include manufacturing information related to the AM based PE process. The manufacturing information embedded within this new format will include data about the location of the different electronic components such as interconnects, resistors, capacitors, inductors, transistors, memory and substrate, and the materials required for the different components part. Different circuit board components will be represented as primitives or a combination of primitives obtained using CSG technique. In addition to the new file format, a slicing algorithm will also be developed which can be used to create the layers automatically using user inputs. The proposed file format and the slicing algorithm will be explained with the help of a case study.

This paper extends the verification and validation of MCNP6’s unstructured mesh (UM) features for neutron transport capabilities by comparing code and experimental results for two different sets of experiments. The first set of experiments comprises time-of-flight spectrum measurements of spheres pulsed by 14-MeV neutrons performed by Lawrence Livermore National Laboratory in the early 1970s. The second set of experiments comprises spontaneous fission neutron attenuation measurements in relatively simple geometries with varying shield thicknesses performed by Ueki et al. in the early 1990s. First, traditional constructive solid geometry (CSG) models are analyzed to ensure agreement with experimental values and to form a basis of comparison with UM results. For the pulsed sphere experiments, a series of UM calculations is performed using first-order tetrahedral elements with various levels of mesh refinement. For the Ueki experiments, purely CSG, purely UM, and hybrid CSG/UM calculations are performed using first- and second-order tetrahedral and hexahedral elements. In the purely UM cases, two different meshing algorithms are used to specify the first-order tetrahedral mesh. The pulsed sphere calculated and experimental time-of-flight spectra agree with p-values >0.999 when compared using χ2 goodness-of-fit tests. Furthermore, the UM results show discrepancies with the experimental values comparable to the CSG cases. The Ueki neutron attenuation calculated values using track-length and point detector tallies agree with the experimental values within 1σ with a single exception that agrees well within 2σ. As such, we conclude that the results for the CSG and UM calculations agree among themselves and with the experimental quantities when considering the associated statistical uncertainties.

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.