Constructive Solid Geometry Research Articles

Methodology, applications and performance of the CAD-based geometry type in the serpent 2 Monte Carlo code

The Serpent 2 Monte Carlo code features a CAD-based geometry option for the modeling of complicated and irregular systems. The methodology is based on the STL data format, which is commonly used for computer graphics and 3D printing, and supported by a wide range of software tools. The methodology has been available for several years, but not described in complete detail. This paper presents the geometry routine with its advantages, limitations and known flaws. A brief overview on practical applications and a workflow example involving neutron and photon transport calculations for a spent nuclear fuel storage rack are provided for discussion. It is concluded that the CAD-based geometry type is a convenient option for various neutron and radiation transport problems, and does not suffer from significant deterioration in computational efficiency compared to conventional CSG models. It is also noted, however, that taking full advantage of the methodology requires some level of understanding on the software tools, the STL data format and the Serpent geometry routine to avoid the most common pitfalls.

Construction of IGA-suitable Volume Parametric Models by the Segmentation–Mapping–Merging Mechanism of Design Features

Volumetric parameterization is the key and bottleneck issue in the current research of constructing complex models for isogeometric analysis(IGA). Many researchers used reconstruction methods to convert the models presented in the boundary form such as B-rep, constructive solid geometry(CSG) or the finite element(FE) meshes. In these methods, recognition and understanding of topology is a difficult and unavoidable issue. What is more, the reconstruction methods are not compatible with the current modeling methods and processes adopted in the prevailing CAD software. In this paper, a method is proposed to construct the complex volume parametric models based on the Segmentation–Mapping–Merging mechanism of the design features. The semantic feature network is obtained by the interactive input or the feature elements extracted from existing CAD models, which allows great geometric flexibility. Then the semantic feature network is partitioned into the geometric feature networks and the complete feature networks under the constraints of volume parametric modeling. Each complete feature network is constructed as a volume parametric patch by volume parametric mapping. Finally, the volume parametric patches are merged into a whole model and are adjusted to be suitable for IGA. Some complex shapes including the mechanical parts, free-form models are presented to verify the effectiveness, availability and robustness of our method. • A platform of integration design based on volumetric parameterization is put forward. • A modeling mechanism called segmentation–mapping–merging for the volume parametric patches is studied. • The proposed method is realized and verified on the complex three-dimensional models.

Hardware-Accelerated Ray Tracing of CAD-Based Geometry for Monte Carlo Radiation Transport

Monte Carlo radiation transport (MCRT) methods have been used to simulate radiation environments for many decades by tracking individual particles through a model to accumulate statistical information. MCRT geometry is historically formed using the constructive solid geometry (CSG). Recently, significant work has been performed to support simulations using computer-aided design (CAD)-based tessellated surfaces to support highly complex geometries. Ray tracing acceleration data structures from the rendering and visualization community are applied to accelerate particle tracking in CAD-based models. Despite these efforts, CSG representations provide the superior performance in surface intersection operations during particle flight. Concurrently, pseudo Monte Carlo methods have become prevalent in rendering applications to support more realistic models for scattering media, motivating innovations that are advantageous for MCRT simulations. The authors’ work extends these innovations by employing Intel’s Embree ray tracing kernel within a geometry toolkit for Monte Carlo to improve the simulation performance using CAD-based models by factors of 1.5 to 2.

Interactive Editing of Voxel-Based Signed Distance Fields

Signed distance functions computed in discrete form from given RGB-D data as regular voxel grids can represent manifold shapes as the zero crossing of a trivariate function; the corresponding meshes can be derived by the Marching Cubes algorithm. However, 3D models automatically reconstructed in this way often contain irrelevant objects or artifacts, such as holes or noise, due to erroneous scan data and error-prone reconstruction processes. This paper presents an approach for interactive editing of signed distance functions, derived from RGB-D data in the form of regular voxel grids, that enables the manual refinement and enhancement of reconstructed 3D geometry. To this end, we combine concepts known from constructive solid geometry, where complex models are created from simple base shapes, with the voxel-based representation of geometry reconstructed from real-world scans. Our approach can be implemented entirely on GPU to enable real-time interaction. Further, we present how to implement high-level operators, such as copy, move, and unification.

Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks

In this paper, we introduce a new approach based on distance fields to exactly impose boundary conditions in physics-informed deep neural networks. The challenges in satisfying Dirichlet boundary conditions in meshfree and particle methods are well-known. This issue is also pertinent in the development of physics informed neural networks (PINN) for the solution of partial differential equations. We introduce geometry-aware trial functions in artificial neural networks to improve the training in deep learning for partial differential equations. To this end, we use concepts from constructive solid geometry (R-functions) and generalized barycentric coordinates (mean value potential fields) to construct ϕ(x), an approximate distance function to the boundary of a domain in Rd. To exactly impose homogeneous Dirichlet boundary conditions, the trial function is taken as ϕ(x) multiplied by the PINN approximation, and its generalization via transfinite interpolation is used to a priori satisfy inhomogeneous Dirichlet (essential), Neumann (natural), and Robin boundary conditions on complex geometries. In doing so, we eliminate modeling error associated with the satisfaction of boundary conditions in a collocation method and ensure that kinematic admissibility is met pointwise in a Ritz method. With this new ansatz, the training for the neural network is simplified: sole contribution to the loss function is from the residual error at interior collocation points where the governing equation is required to be satisfied. Numerical solutions are computed using strong form collocation and Ritz minimization. To convey the main ideas and to assess the accuracy of the approach, we present numerical solutions for linear and nonlinear boundary-value problems over convex and nonconvex polygonal domains as well as over domains with curved boundaries. Benchmark problems in one dimension for linear elasticity, advection-diffusion, and beam bending; and in two dimensions for the steady-state heat equation, Laplace equation, biharmonic equation (Kirchhoff plate bending), and the nonlinear Eikonal equation are considered. The construction of approximate distance functions using R-functions extends to higher dimensions, and we showcase its use by solving a Poisson problem with homogeneous Dirichlet boundary conditions over the four-dimensional hypercube. The proposed approach consistently outperforms a standard PINN-based collocation method, which underscores the importance of exactly (a priori) satisfying the boundary condition when constructing a loss function in PINN. This study provides a pathway for meshfree analysis to be conducted on the exact geometry without domain discretization.

Sampling from Quadric‐Based CSG Surfaces

AbstractWe present an efficient method to create samples directly on surfaces defined by constructive solid geometry (CSG) trees or graphs. The generated samples can be used for visualization or as an approximation to the actual surface with strong guarantees. We chose to use quadric surfaces as CSG primitives as they can model classical primitives such as planes, cubes, spheres, cylinders, and ellipsoids, but also certain saddle surfaces. More importantly, they are closed under affine transformations, a desirable property for a modeling system. We also propose a rendering method that performs local quadric ray‐tracing and clipping to achieve pixel‐perfect accuracy and hole‐free rendering.

Raymarching Distance Fields with CUDA

Raymarching is a technique for rendering implicit surfaces using signed distance fields. It has been known and used since the 1980s for rendering fractals and CSG (constructive solid geometry) surfaces, but has rarely been used for commercial rendering applications such as film and 3D games. Raymarching was first used for photorealistic rendering in the mid 2000s by demoscene developers and hobbyist graphics programmers, receiving little to no attention from the academic community and professional graphics engineers. In the present work, we explain why the use of Simple and Fast Multimedia Library (SFML) by nearly all existing approaches leads to a number of inefficiencies, and hence set out to develop a CUDA oriented approach instead. We next show that the usual data handling pipeline leads to further unnecessary data flow overheads and therefore propose a novel pipeline structure that eliminates much of redundancy in the manner in which data are processed and passed. We proceed to introduce a series of data structures which were designed with the specific aim of exploiting the pipeline’s strengths in terms of efficiency while achieving a high degree of photorealism, as well as the accompanying models and optimizations that ultimately result in an engine which is capable of photorealistic and real-time rendering on complex scenes and arbitrary objects. Lastly, the effectiveness of our framework is demonstrated in a series of experiments which compare our engine both in terms of visual fidelity and computational efficiency with the leading commercial and open source solutions, namely Unreal Engine and Blender.

Extracting datums to reconstruct CSG models from 2D engineering sketches of polyhedral shapes

Our goal is to automatically generate CAD 3D models from 2D sketches as part of a design chain where models should be procedural, containing features arranged in a model tree and linked to suitable datums. Current procedural models capture much about the design intent and are easy to edit, but must be created from scratch during the detailed design state—given conceptual sketches as used by designers in the early part of the design process, current sketch-based modeling approaches only output explicit models. Thus, we describe an approach to extract high-level information directly from 2D engineering wireframe sketches and use it to complete a CSG feature tree, which serves as a model tree for a procedural 3D CAD model.Our method extracts procedural model information directly from 2D sketches in the form of a set of features, plus a set of datums and relationships between these features. We detect and analyze features of 2D sketches in isolation, and define the CSG feature tree by the parent–child relationships between features, and combine this information to obtain a complete and consistent CSG feature tree that can be transferred to a 3D modeler, which reconstructs the model. This paper focuses on how to extract the feature datums and the extrusion operation from an input 2D sketch.

Propagating Geometry Information to Finite Element Computations

The traditional workflow in continuum mechanics simulations is that a geometry description —for example obtained using Constructive Solid Geometry (CSG) or Computer Aided Design (CAD) tools—forms the input for a mesh generator. The mesh is then used as the sole input for the finite element, finite volume, and finite difference solver, which at this point no longer has access to the original, “underlying” geometry. However, many modern techniques—for example, adaptive mesh refinement and the use of higher order geometry approximation methods—really do need information about the underlying geometry to realize their full potential. We have undertaken an exhaustive study of where typical finite element codes use geometry information, with the goal of determining what information geometry tools would have to provide. Our study shows that nearly all geometry-related needs inside the simulators can be satisfied by just two “primitives”: elementary queries posed by the simulation software to the geometry description. We then show that it is possible to provide these primitives in all of the frequently used ways in which geometries are described in common industrial workflows, and illustrate our solutions using a number of examples.

Boundary-sampled halfspaces

We present a novel representation of solid models for shape design. Like Constructive Solid Geometry (CSG), the solid shape is constructed from a set of halfspaces without the need for an explicit boundary structure. Instead of using Boolean expressions as in CSG, the shape is defined by sparsely placed samples on the boundary of each halfspace. This representation, called Boundary-Sampled Halfspaces (BSH), affords greater agility and expressiveness than CSG while simplifying the reverse engineering process. We discuss theoretical properties of the representation and present practical algorithms for boundary extraction and conversion from other representations. Our algorithms are demonstrated on both 2D and 3D examples.

Swept volumes via spacetime numerical continuation

Given a solid 3D shape and a trajectory of it over time, we compute its swept volume - the union of all points contained within the shape at some moment in time. We consider the representation of the input and output as implicit functions, and lift the problem to 4D spacetime, where we show the problem gains a continuous structure which avoids expensive global searches. We exploit this structure via a continuation method which marches and reconstructs the zero level set of the swept volume, using the temporal dimension to avoid erroneous solutions. We show that, compared to other methods, our approach is not restricted to a limited class of shapes or trajectories, is extremely robust, and its asymptotic complexity is an order lower than standards used in the industry, enabling its use in applications such as modeling, constructive solid geometry, and path planning.

Real-time pre-rectification of aberrations for 3D light-field display based on a constructed virtual lens and ray path tracing

Aberrations caused by optical lens refraction in a light-field display (LFD) are minimized based on real-time pre-rectification. A virtual optical lens with the high precision surface is developed the constructive solid geometry under minimum primitives to rectify the sampling rays, and the virtual lens exhibits the same response to different incident ray wavelengths as the real lens in the LFD optical domain. In addition, assembly misalignment is taken into consideration during the partitioning of the elemental image array so that all the elemental images and the covering lenses can be precisely aligned. After rectifying the sampling rays with the constructed virtual lens, the rays are launched in parallel in the GPU, and path tracing is conducted to shade the element image array. The proposed approach ensures the consistency of the integral photography and LFD processes, which minimize the distortion and increasing the depth of field for three-dimensional (3D) images. Experimental results verify the feasibility of our proposed method. The structural similarity index is improved by 0.1, and 3D images at different depths are correctly expressed. Only three primitives are introduced to the system as a whole, meaning that the extra computation has little impact on the rendering efficiency. Consequently, the real-time generation of 3D light-field images is possible.

MATLAB PDE toolbox for 2-D and 3-D neutron diffusion simulations

This research extends MATLAB PDE Toolbox to model nuclear reactors by solving the 2-D and 3-D multigroup neutron diffusion equations using the finite element method. The developed scripts can simulate reactors with rectangular and hexagonal lattices and have the potential to handle complex core configurations, benefitting from the constructive solid geometry. The meshing subroutine decomposes the domain into unstructured triangular or tetrahedral elements that are either linear or quadratic. With many versatile MATLAB functions, data analysis and visualization can be accomplished within the same software environment. The proposed toolbox provides a graphical user interface for novices and simple models and a programmatic workflow for experienced users and complex problems. Multiple benchmark tests show that the developed framework produces accurate results with acceptable computation speed. The developed MATLAB reactor simulation engine is license friendly and readily accessible by researchers and students, making it an ideal research and educational tool.

Efficient interactions for reconstructing complex buildings via joint photometric and geometric saliency segmentation

The reconstruction of level-of-detail 2 (LOD-2) buildings has drawn considerable attention over the past two decades. Since completely automatic reconstruction approaches still face many difficulties in industry solutions, efficient and robust interactive modeling tools are of huge demand. This paper proposes an interactive LOD-2 modeling approach that can generate boundary-precise and topology-correct building models efficiently from Digital Surface Model (DSM) and Digital Orthophoto Map (DOM) data. Click-based saliency segmentation is first adopted to extract the outline of building primitives, where both photometric and geometric information are unified. Those outlines decompose the complex-shaped buildings into predefined primitive types. The primitives are then further enriched with other semantic key points, which are essential for inferring the primitives’ shapes and positions. Finally, the models can be built based on the constructive solid geometry and assembly of partial primitives into complex buildings. The order of the primitives can be irrelevant, and the sketches and semantic key points do not necessarily be perfect. Users only need very few and simple operators to generate the integral models, mostly several clicks on a 2D platform. Experimental results on various dataset demonstrate the proposed approach can minimize the amount of interaction while maintaining the ability to deal with various roof types. The integral model quality indices at pixel and object level achieve the precision of 92.3% and 82.5%, accordingly.

Development and benchmarking of the Weight Window Mesh function for OpenMC

OpenMC is a community-driven open-source Monte Carlo neutron and photon transport simulation code. It supports geometry modeling using constructive solid geometry, and is capable of performing fixed source particle transport simulation based on continuous-energy and group-wise nuclear cross-section data. The lack of variance reduction technique is one of the main drawbacks of this code, which prevent its use for deep penetration shielding calculations. In this work, a commonly used variance reduction technique – using the Weight Window Mesh (WWM) function has been developed and benchmarked for OpenMC. This enables OpenMC to use any WWM file produced for the MCNP code. For benchmarking, two deep penetration shielding cases, a sphere simulation model and the thickest shielding cases in the TIARA high energy neutron shielding experiment has been employed, using the WWM produced by the ADVANTG code. In addition, the OpenMC WWM function has also been applied on the IFMIF-DONES Test Cell global neutron flux distribution calculations. The successful benchmarking and application demonstrate ability of the newly developed OpenMC WWM function for applications in general purposes deep penetration shielding calculations.

A constructive solid geometry-based generative design method for additive manufacturing

The unique capability of additive manufacturing (AM) to deal with complex geometries drives the traditional topological optimization and lightweight design to a new paradigm. However, AM constraints are still hard to integrate into the optimization procedure, and the multiple conflict design objectives are difficult to handle when making decisions. In addition, the computation cost is usually high. To solve these problems, this paper proposes a new generative design method with a manufacturing validation so that the designer’s decision-making is more efficient. This method first uses a CSG (constructive solid geometry)-based technique to generate and represent topology geometries with smooth boundaries and parametric control. Then, a genetic algorithm is used to operate the CSG geometries in order to search for optimal solutions. Finally, a set of finite optimal non-dominated design solutions on the Pareto front are located and presented for the designer’s further decision making. The proposed method can generate a large quantity of qualified optimal alternative solutions with smooth geometric boundaries but the computation cost is less. It is promising to design qualified solutions, especially for lightweight structure design, in AM. Several demonstration examples and comparison case studies with existing methods in literature are presented at the end of this paper to show the advantages.

Application of MCNP unstructured mesh in the design process of the ITER EC-UL M3 mirror

Finite element analysis (FEA) is widely used in engineering to accurately model physical systems. FEA enables multi-physics investigations to be undertaken efficiently and increases the cohesiveness of interdisciplinary engineering assessments. Thanks to the recent implementation of the FEA Unstructured Mesh capability (UM) into MCNP6, radiation transport is now able to contribute more effectively to such multi-physics investigations. Furthermore, the use of UM in MCNP allows complicated components to be modelled more accurately since it does not have the geometrical limitations of the alternate Constructive Solid Geometry method (CSG), leading to more accurate simulations and inherent results. The ITER Electron Cyclotron-Upper Launcher (EC-UL) M3 Mirror is a complex component currently under design that had required various engineering assessments that utilise FEA such as mechanical and thermohydraulic. Therefore, this neutronics assessment took advantage of the UM capability of MCNP6.2 to be consistent with the other assessments. The peak volumetric nuclear heating for this component was found to be 3.76 ± 22.0 % W/cm3 by this method. The total integral nuclear heating was found to be 6595.1 ± 0.6 W, an increase of 9.3 % on the previous design but with a slightly different deposition distribution. Crucially, the total integral nuclear heating of the CuCrZr reflector was determined to be 142.92 ± 0.07 W, a decrease of 69 % from the previous mirror design allowing the fulfilment of the mechanical code and standards.

Voxel-Based Geometry Reconstruction for Repairing and Remanufacturing of Metallic Components Via Additive Manufacturing

In the component repair process using additive manufacturing (AM) technique, reconstructing the repair volume is essential to generate the repair tool path and guide the AM system to deposit correct geometry on the worn parts. In this study, a novel repair volume reconstruction methodology based on voxel modeling was introduced. At first, the stereolithography (STL) models of the nominal and damaged components were acquired either from computer-aided design (CAD) modeling or through robot-aided 3D scanning. The pre-machining approach was introduced to guarantee the defective zone is accessible to repair tools. The damaged models were aligned with the nominal models by best-fitting their common convex-hull centroids. After that, these STL models were converted to voxel models using the Marching Cube algorithm. The accuracy of the transferred voxel models was investigated by comparing them with the exact geometry. Boolean operations algorithm based on constructive solid geometry was proposed to extract the repair volume by comparing the nominal and damaged voxel models. The Boolean operations can output both the repair volume that is missing from the damaged parts which should be restored by AM and the excess geometry which should be removed by subtractive machining. The proposed approach was implemented on three CAD models and three scanned models. The repair volumes for these damaged parts were successfully reconstructed. Three components were repaired via the directed energy deposition AM process. Finally, the bonding performance between the deposited layers and base parts was evaluated via tensile testing.

HEXAGONAL PWR-CORE MODELING AND SIMULATION WITH APPLICATION OF NECP-BAMBOO

In this paper, the modeling and simulation of the PWRs loaded with hexagonal fuel assemblies has been implemented with the NECP-Bamboo code. NECP-Bamboo, consisting of a 2D lattice code named Bamboo-Lattice and a 3D steady-state core code named Bamboo-Core, was primitively designed for the PWRs loaded with the rectangular fuel assemblies. As the capability extension for PWRs with hexagonal fuel assemblies, four aspects of improvement have been implemented in NECP-Bamboo. Firstly, the Constructive Solid Geometry (CSG) has been implemented in Bamboo-Lattice for the lattice modeling. Secondly, the explicit modeling of the reflector assembly has been applied to provide more reliable few-group constants, compared with the conventional 1D model for the reflector assembly. Thirdly, the assembly-homogenization capability has been extended to the hexagonal assembly. Fourthly, the diffusion solver in Bamboo-Core based on the Variational Nodal Method (VNM) has been extended to handle hexagonal geometry. With application of the capability-extended NECP-Bamboo, the modeling and simulations for the VVER-1000 benchmark loaded with MOX fuel has been implemented. It can be observed that the numerical results provided by NECP-Bamboo can agree well with corresponding results by the Monte-Carlo code.

RESONANCE CALCULATION BASED ON THE GLOBAL-LOCAL METHOD FOR THE COMPLEX GEOMETRY PROBLEMS

With the development of nuclear reactor, new complicated designs introduce some challenges for the resonance method in the NECP-X code, which is called as the Global-Local method. There are two limitations of the present NECP-X. One is the geometry modeling limitation, and the other one is that the Global-Local resonance method can only deal with the cylindrical fuel rods in the current version. Therefore, some fuels like plate, annular fuels cannot be calculated in the NECP-X code because of these limitations. To overcome above issues, the constructive solid geometry (CSG) method is developed to model the complex problem, and the capability of constructing and solving the equivalent 1D plate and 1D annual fuel pin based on the framework of Global-Local method, is developed. A set of tests are calculated, including multi-annular fuel problems and plate fuel problems. The results show good accuracy of the new developed resonance self-shielding method.