Constructive Solid Geometry Models Research Articles

Point containment algorithms for constructive solid geometry with unbounded primitives

We present several algorithms for evaluating point containment in constructive solid geometry (CSG) trees with unbounded primitives. Three algorithms are presented based on postfix, prefix, and infix notations of the CSG binary expression tree. We show that prefix and infix notations enable short-circuiting logic, which reduces the number of primitives that must be checked during point containment. To evaluate the performance of the algorithms, each algorithm was implemented in the OpenMC Monte Carlo particle transport code, which relies on CSG to represent solid bodies through which subatomic particles travel. Two sets of tests were carried out. First, the execution time to generate a rasterized image of a 2D slice of three CSG models of varying complexity was measured. Use of both prefix and infix notations offered significant speedup over the postfix notation that has traditionally been used in particle transport codes, with infix resulting in a 6× reduction in execution time relative to postfix for a model of a tokamak fusion device. We then measured the execution time of neutron transport simulations of the same three models using each of the algorithms. The results and performance improvements reveal the same trends as for the rasterization test, with a 5.52× overall speedup using the infix notation relative to the original postfix notation in OpenMC for the tokamak model.

CAD and constructive solid geometry modeling of the Molten Salt Reactor Experiment with OpenMC

In this study, we present a detailed comparison of two independently developed models of the Molten Salt Reactor Experiment (MSRE) for Monte Carlo particle transport simulations: the constructive solid geometry (CSG) model that was developed in support of the MSRE benchmark in the International Handbook of Evaluated Reactor Physics Benchmark Experiments, and a CAD model that was developed by Copenhagen Atomics. The original Serpent reference CSG model was first converted to OpenMC’s input format so that it could be systematically compared to the CAD model, which was already available as an OpenMC model, using the same Monte Carlo code. Results from simulations using the Serpent and OpenMC CSG models showed that keff agreed within 10 pcm while the flux distribution in space and energy generally agreed within 0.1%. Larger differences were observed between the OpenMC CAD and CSG models; notably, the keff computed for the CAD model was 1.00872, which is more than 1% lower than the value for the CSG model and much closer to experiment. Several areas of the reactor that were modeled differently in the CSG and CAD models were discussed and, in several cases, their impact on keff was quantified. Lastly, we compared the computational performance and memory usage between the CAD and CSG models. Simulation of the CSG model was found to be 1.4–2.3× faster than simulation of the CAD model based on the Embree ray tracer while using 4× less memory, highlighting the need for continued improvements in the CAD-based particle transport ecosystem. Finally, major performance degradation was observed for CAD-based simulations when using the MOAB ray tracer.

Improved algorithm of finding the next volume in direct CAD method for fusion neutronics analysis

The magnetic confinement fusion device, Tokamak, has a complex 3D geometry structure. As a result, the fusion neutronics geometry modeling process will be time-consuming and labor-intensive. Some researchers have improved modeling methods by using CAD (Computer Aided Design) models, but there is still a need to convert CAD models to CSG (Constructive Solid Geometry) or pre-process CAD models. Based on the existing direct CAD Monte Carlo approach, this paper creates a new algorithm for finding the next volume, which greatly simplifies or even omits the preprocessing process. By forming a grouping bounding box acceleration algorithm, the improved finding next volume performance is adequate to ensure precision and computation speed for complex 3D models. The results are verified by comparing them with a commercial Monte Carlo code, cosRMC, and an example of neutron fluence per particle on real CAD models of the HL-3 first wall and divertor shows a better applicability of this new algorithm.

Investigation of discretization uncertainty in Monte Carlo neutron transport simulations of the Molten Salt Fast Reactor (MSFR)

In the present work, an assessment of the Neutronic Benchmark of the Molten Salt Fast Reactor (MSFR) was performed using mesh based Monte Carlo Neutron Transport (MCNT) calculations with numerical uncertainty quantification due to discretization in neutronic parameters. Calculations with Constructive Solid Geometry (CSG) models where made as a baseline for the developed mesh based models. The numerical uncertainty given by the mesh utilization is evaluated using an extended version of the Grid Convergence Index (GCI). The fuel salt reprocessing is evaluated regarding a constant reprocessing rate. The fuel salt inventory variation with time for the developed models (CSG and meshed) is presented. The differences caused by the discretization procedure are noticeable, which shows that mesh based MCNT require careful mesh sensitivity evaluation and further validation.

A Survey of Methods for Converting Unstructured Data to CSG Models

The goal of this document is to survey existing methods for recovering or extracting CSG (Constructive Solid Geometry) representations from unstructured data such as 3D point-clouds or polygon meshes. We review and discuss related topics such as the segmentation and fitting of the input data. We cover techniques from solid modeling for the conversion of a polyhedron to a CSG expression and for the conversion of a B-rep to a CSG expression. We look at approaches coming from program synthesis, evolutionary techniques (such as genetic programming or genetic algorithm), and deep learning. Finally, we conclude our survey with a discussion of techniques for the generation of computer programs involving higher-level constructs, representations, and operations for representing solids.

An unstructured mesh based neutronics optimization workflow

We have developed a fully automated workflow to optimize the neutronics performance of the Second Target Station (STS) at the Oak Ridge National Laboratory’s Spallation Neutron Source. The optimization workflow starts with the parametrized solid CAD engineering models and converts them into the unstructured mesh (UM) models for the neutronics calculations with MCNP6.2. Calculations are executed and their results are loaded into the Dakota optimization toolkit. Dakota analyzes the results and proposes new geometry parameters for the next design iteration. The cycle repeats until the optimal parameters are found. The automated CAD to MCNP conversion, the use of high-fidelity UM models, and the use of modern optimizer are the key elements that advance the entire optimization workflow in comparison with the original workflow. The original workflow was based on a simplified constructive solid geometry (CSG) modeling with MCNPX, mcnp_pstudy tool, and an in-house optimizer. To demonstrate the new workflow, we present a case of neutronics optimization of the moderator–reflector assembly (MRA). Apart from the MRA, the workflow can optimize other major STS components, such as the spallation target, neutron beamlines, radiation shielding, and various accelerator components. Importantly, the new workflow opens the door to the advanced multi-physics multi-parameter optimization and has the potential for use in other nuclear physics and accelerator applications.

Layered CAD/CSG geometry for spatially complex radiation transport scenarios

Many spatially complex fission, fusion, and national security Monte Carlo (MC) radiation transport scenarios involve combining computer-aided design (CAD) models with constructive solid geometry (CSG) models. A layered geometry method has been implemented in the Shift MC code to address this need. With layered geometry, multiple CAD and/or CSG models can be clipped, translated, rotated, and placed in overlapping layers to form transport-ready geometries. The utility of this method is demonstrated with two problems: (1) a fixed-source simulation with a layered geometry consisting of a LiDAR-generated CAD model of the Combined Arms Collective Training Facility urban environment overlaid with CSG models of a mock hotel and a detector apparatus, and (2) a k-eigenvalue calculation using a layered geometry model of the Transformational Challenge Reactor consisting of CAD fuel elements placed in a CSG core. Tallied particle flux distributions match expectations, but tracking robustness must be improved prior to general-purpose use.

Hybrid unstructured mesh geometry model of the next-generation spallation neutron source at LANSCE

We have developed a hybrid Unstructured Mesh (UM)/Constructive Solid Geometry (CSG) model of the next-generation spallation neutron target-moderator-reflector-shield (TMRS) assembly Mark-IV at the Los Alamos Neutron Science Center (LANSCE) to perform MCNP neutronics calculations in support of the engineering design process. The hybrid model consists of an essential component of the new TMRS—the upper target—built as UM and the rest of the model that resembles the original TMRS Mark-III built as CSG. The UM model for the neutronics analysis as well as the model for the subsequent engineering analyses such as structural stress and fluid dynamics are automatically converted from the identical computer aided design (CAD) model. Such an automatic conversion is highly time-efficient and preserves a great level of detail of the original model. In addition, only a relatively small UM portion of our model (0.003 m3) is embedded into the surrounding CSG universe (314 m3), enabling a more efficient MCNP calculation due to the reduced requirements on computer memory and shorter computation time in comparison with a fully extended UM model. Our MCNP calculations focus on the neutronics performance and energy deposition in the upper target. They employ high-energy nuclear physics models, tabular data, and scattering kernels, use an 800 MeV proton beam as a source, tally secondary fast and thermal neutrons with point detectors, and apply mesh tallies and elemental edit outputs to score energy deposition from all particles, i.e., neutrons, photons, protons, and charged pions. Because the use of UM marks a major departure from our original method based entirely on the traditional CSG modeling with MCNPX 2.7.0, we validate the new hybrid UM/CSG model against the legacy CSG model. We found a good agreement between the two models, which demonstrates that MCNP6.2 with UM/CSG hybrids can solve complex neutronics problems at large accelerator facilities, including spallation neutron sources.

Research of Visual Conversion Technology for Reactor Core Monte Carlo Model Based on CSG

In order to improve the efficiency of 3D visualization analysis of the core Monte Carlo fine transport calculation model (MC calculation model), on the basis of fully investigating the current development status of the MC calculation model 3D visualization tools, and by analyzing the characteristics of different types of geometric models and the description methods of constructive solid geometry (CSG) models, this paper proposed an automatic 3D visualization converting method for the core fine MC calculation model, and conducted a deep study on the key technologies such as the conversion from CSG model to boundary representation (BREP) model, the mesh discretization of BREP model and the optimization of conversion efficiency for CSG model. The test results show that the proposed method can meet the engineering requirements in terms of function and efficiency.

Constructing 3D CSG Models from 3D Raw Point Clouds

AbstractThe Constructive Solid Geometry (CSG) tree, encoding the generative process of an object by a recursive compositional structure of bounded primitives, constitutes an important structural representation of 3D objects. Therefore, automatically recovering such a compositional structure from the raw point cloud of an object represents a high‐level reverse engineering problem, finding applications from structure and functionality analysis to creative redesign. We propose an effective method to construct CSG models and trees directly over raw point clouds. Specifically, a large number of hypothetical bounded primitive candidates are first extracted from raw scans, followed by a carefully designed pruning strategy. We then choose to approximate the target CSG model by the combination of a subset of these candidates with corresponding Boolean operations using a binary optimization technique, from which the corresponding CSG tree can be derived. Our method attempts to consider the minimal description length concept in the point cloud analysis setting, where the objective function is designed to minimize the construction error and complexity simultaneously. We demonstrate the effectiveness and robustness of our method with extensive experiments on real scan data with various complexities and styles.

HCSG

Constructive Solid Geometry models solids as boolean combinations of base primitives. It is one of the classical modeling approaches in Computer Graphics. With the advent of 3D printing, it has received a renewed interest: CSG affords for the robust definition of solids, and fits well with parametric modeling, affording for easy customization of existing designs. However, the interactive display and manipulation of CSG models is challenging: Ideally, CSG has to be performed between a variety of solid representations (meshes, implicit solids, voxels) and the renderer has to provide immediate feedback during parameter exploration. The end result has to be prepared for fabrication, which involves robustly extracting cross-sections of the model. In this work we propose a novel screen space technique for the rendering, interactive modeling and direct fabrication of parametric CSG models. It builds upon spatial hashing techniques to efficiently evaluate CSG expressions, checking whether each interval along a view ray is solid in constant time, using constant local shader memory. In addition, the scene is rendered progressively, from front to back, bounding memory usage. We describe how the hash encoding the CSG is constructed on the fly during visualization, and analyze performance on a variety of 3d models.

Point-based tool representations for modeling complex tool shapes and runout for the simulation of process forces and chatter vibrations

Geometric physically-based simulation systems can be used for analyzing and optimizing complex milling processes, for example in the automotive or aerospace industry, where the surface quality and process efficiency are limited due to chatter vibrations. Process simulations using tool models based on the constructive solid geometry (CSG) technique allow the analysis of process forces, tool deflections, and surface location errors resulting from five-axis machining operations. However, modeling complex tool shapes and effects like runout is difficult using CSG models due to the increasing complexity of the shape descriptions. Therefore, a point-based method for modeling the rotating tool considering its deflections is presented in this paper. With this method, tools with complex shapes and runout can be simulated in an efficient and flexible way. The new modeling approach is applied to exemplary milling processes and the simulation results are validated based on machining experiments.

Interactive vizualization of constructive solid geometry scenes on graphic processors

A ray-tracing algorithm for interactive visualization of very large and structurally complicated scenes presented in the constructive solid geometry (CSG) form is suggested. The algorithm is capable of visualizing such scenes in real time by using a graphic processor. As primitives, classical shapes and objects represented in an analytical form (in particular, second-order surfaces and implicit functions) are used. Unlike other similar algorithms, our algorithm produces the final image in a single pass and has no constraints on the maximum number of primitives and on the CSG tree depth. The key feature of the algorithm is a method for optimizing CSG models, which converts the input tree to an equivalent spatially coherent and well-balanced form (a completely balanced equivalent tree may not exist). The performance of visualization after applying the optimization technique is shown to depend on only the computational resource of the GPU (in contrast to multi-pass algorithms whose performance is restricted by memory capacity). It has been shown experimentally that our algorithm is capable of rendering CSG models consisting of more than a million CSG primitives with the tree depth up to 24.

CAD-Based Monte Carlo Neutron Transport KSTAR Analysis for KSTAR

The Monte Carlo (MC) neutron transport analysis for a complex nuclear system such as fusion facility may require accurate modeling of its complicated geometry. In order to take advantage of modeling capability of the computer aided design (CAD) system for the MC neutronics analysis, the Seoul National University MC code, McCARD, has been augmented with a CAD-based geometry processing module by imbedding the OpenCASCADE CAD kernel. In the developed module, the CAD geometry data are internally converted to the constructive solid geometry model with help of the CAD kernel. An efficient cell-searching algorithm is devised for the void space treatment. The performance of the CAD-based McCARD calculations are tested for the Korea Superconducting Tokamak Advanced Research device by comparing with results of the conventional MC calculations using a text-based geometry input.

Evaluation of Pulsed Sphere Time-of-Flight and Neutron Attenuation Experimental Benchmarks Using MCNP6’s Unstructured Mesh Capabilities

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.

Evaluation of the Kobayashi Analytical Benchmark Using MCNP6’s Unstructured Mesh Capabilities

This paper provides results for calculations performed using MCNP6’s unstructured mesh (UM) capabilities based on the three problems described in the Kobayashi benchmark suite. These calculations are performed to provide a comprehensive and consistent basis for the verification and validation of MCNP6’s constructive solid geometry (CSG) and UM neutron transport capabilities relative to a well-known analytic benchmark. First, preexisting MCNP5 CSG models are updated and reexecuted to form a basis of comparison with UM for both the consistency of the numeric results and speed of execution. Next, a series of UM calculations is performed using first- and second-order tetrahedral and hexahedral elements with mesh generated using Abaqus. In addition, a different first-order tetrahedral mesh is generated with Attila4MC in order to investigate the effect on the results. When executed, the results for both CSG and UM agree among themselves and with the benchmark quantities within reasonable statistical fluctuations (at worst, the results agree within 2σ or 10% but generally within 1σ or 5%) and recognizing from historical work that improved agreement is possible with additional variance-reduction effort. As expected, for the simple geometries herein, we find the CSG calculations completing approximately ten times faster than the comparable fastest UM calculations. We find minor speed differences (~1%) between multigroup and continuous-energy nuclear data and significant speed differences (factor ~100) between different element types. As such, the timing results support the recommendation that users run with the simplest UM element type that adequately represents the problem geometry, ideally first-order hexahedra, and with the most convenient nuclear data energy treatment.

MCR2S unstructured mesh capabilities for use in shutdown dose rate analysis

As nuclear fusion progresses towards a sustainable energy source and the power of tokamak devices increases, a greater understanding of the radiation fields will be required. As well as on-load radiation fields, off-load or shutdown radiation field are an important consideration for the safety and economic viability of a commercial fusion reactor. Previously codes such as MCR2S have been written in order to predict the shutdown dose rates within, and in regions surrounding, a fusion reactor. MCR2S utilises a constructive solid geometry (CSG) model and a superimposed structured mesh to calculate 3-D maps of the shutdown dose rate. A new approach to MCR2S calculations is proposed and implemented using a single unstructured mesh to replace both the CSG model and the superimposed structured mesh.This new MCR2S approach has been demonstrated on three models of increasing complexity. These models were: a sphere, the ITER computational shutdown dose rate benchmark and the DEMO computational shutdown dose rate benchmark. In each case the results were compared to MCR2S calculations performed using MCR2S with CSG geometry and a superimposed structured mesh. It was concluded that the results from the unstructured mesh implementation of MCR2S compared well to the CSG structured mesh calculations. It was found that the resolution of the unstructured mesh can significantly affect the results of the calculations, and therefore it is important to finely mesh components with streaming paths or significantly contribute to the dose rate in the areas of interest. Although computationally more expensive it was found that there are some clear advantages when using unstructured meshes with MCR2S calculations which are outlined in this paper.

Optimal Spatial Subdivision method for improving geometry navigation performance in Monte Carlo particle transport simulation

Geometry navigation is one of the key aspects of dominating Monte Carlo particle transport simulation performance for large-scale whole reactor models. In such cases, spatial subdivision is an easily-established and high-potential method to improve the run-time performance. In this study, a dedicated method, named Optimal Spatial Subdivision, is proposed for generating numerically optimal spatial grid models, which are demonstrated to be more efficient for geometry navigation than traditional Constructive Solid Geometry (CSG) models. The method uses a recursive subdivision algorithm to subdivide a CSG model into non-overlapping grids, which are labeled as totally or partially occupied, or not occupied at all, by CSG objects. The most important point is that, at each stage of subdivision, a conception of quality factor based on a cost estimation function is derived to evaluate the qualities of the subdivision schemes. Only the scheme with optimal quality factor will be chosen as the final subdivision strategy for generating the grid model. Eventually, the model built with the optimal quality factor will be efficient for Monte Carlo particle transport simulation. The method has been implemented and integrated into the Super Monte Carlo program SuperMC developed by FDS Team. Testing cases were used to highlight the performance gains that could be achieved. Results showed that Monte Carlo simulation runtime could be reduced significantly when using the new method, even as cases reached whole reactor core model sizes.

Isogeometric analysis for CSG models

The IGA (Isogeometric Analysis) was developed as a bridge between CAD and CAE with its highly precise geometry representation. However, IGA can only do little with the models that CAD systems generated in CSG (Constructive Solid Geometry) manner, because the trimmed domain exists. This paper presents a method named Constructive Solid Isogeometric Analysis (CSIGA) to work for CSG models that are composed of primitive solids with union, subtraction and intersection operators. First, this work decomposes the CSG models into several primitive solids represented by NURBS separately, then cuts the primitives with their adjacent ones to produce a set of trimmed tri-variable NURBS primitives, and finally uses Boolean operators to compose them. As to the single trimmed solid, an integration scheme is presented. Meanwhile, a combination scheme has been developed to deal with the union of multiple trimmed solids by using a mortar method. The formulation is verified by applying the isogeometric analysis on several solids which have theoretical solutions such as elliptic cylinder and combined brick, and some tests on multiple trimmed solids are done, too. It is shown that the CSIGA method can deal with CSG models efficiently.

Simulation of grinding processes using finite element analysis and geometric simulation of individual grains

The wear-resistance of sheet metal forming tools can be increased by thermally sprayed coatings. However, without further treatment, the high roughness of the coatings leads to poor qualities of the deep drawn sheet surfaces. In order to increase the surface quality of deep drawing tools, grinding on machining centers is a suitable solution. Due to the varying engagement situations of the grinding tools on free-formed surfaces, the process forces vary as well, resulting in inaccuracies of the ground surface shape. The grinding process can be optimized by means of a simulative prediction of the occurring forces. In this paper, a geometric-kinematic simulation coupled with a finite element analysis is presented. Considering the influence of individual grains, an additional approximation to the resulting topography of the ground surface is possible. By using constructive solid geometry and dexel modeling techniques, multiple grains can be simulated with the geometric-kinematic approach simultaneously. The process forces are predicted with the finite element method based on an elasto-plastic material model. Single grain engagement experiments were conducted to validate the simulation results.