Boundary Representation Research Articles

On the Local Boundary Representations of Locally $$C^*$$-Algebras

On the Local Boundary Representations of Locally $$C^*$$-Algebras

A Hybrid Recognition Framework for Highly Interacting Machining Features Based on Primitive Decomposition, Learning and Reconstruction

For the highly interacting machining features, Layered Projection Decomposition Method presents inferior recognition efficiency and accuracy, due to its high-cost 3D projection and failures in determining projection faces for internal occluded faces. To address these issues, we propose a potential hybrid recognition framework. We first introduce a straightforward adjacent projection wire (APW) over UV wires, automatically restoring the full projection wires from highly interacting features. Building on APWs, an efficient hybrid boundary representation and its corresponding unambiguous primitive definitions are proposed by combing with graph-based boundary representations. Subsequently, we design an efficient primitive decomposition method by introducing primitive boundary matching to decide the initial projection faces, and introducing iterative projection boundary expansion to complete the full primitives from occluded faces. Moreover, we establish an efficient Graph Neural Network to learn the distinguishable distributions over the decomposed primitives. Specifically, an Adjacency Attention Unit is proposed to automatically perceive the influence weight of adjacent nodes, leading to more discriminative self-adaptive shape embedding for efficient primitive recognition. Finally, we summarize convenient reconstruction rules to correct the wrong predictions of feature faces with indistinguishable adjacent relationships. To evaluate the effectiveness of the proposed recognition framework, CAD models of complex aircraft structural parts are collected to present a challenging machining feature dataset. Extensive numerical experiments demonstrate that the proposed hybrid recognition framework enables significant improvements over the state-of-the-art machining feature recognition techniques.

Relational descriptors for retrieving design features in a B-rep model using the similarity-based retrieval approach

Design features refer to local shapes or regions within a part that perform specific functions such as fastening and force transmission. These design features must be identified from product design results to conduct design verification, manufacturing evaluation, and process planning. Design features are formed by combining various form features, which poses a challenge when using existing methods to retrieve individual features. Therefore, this study introduced a relational descriptor that describes the relational characteristics between topological elements to retrieve design features in boundary representation (B-rep) models. In addition, a method to retrieve design features by combining the relational descriptor with shape descriptors was proposed. Experiments were performed to identify specific design features to validate the proposed method. The experimental results successfully retrieved all the design features included in the B-rep model.

An automatic generation approach of process model based on feature knowledge and geometric modeling

Traditional process planning applies knowledge to convert design information within the part model into process information. This information is then displayed by manually drawing two-dimensional (2D) process cards from multiple views, illustrating the geometric design and the process details. However, this method has revealed several issues, including poor efficiency, information misinterpretation, and the potential for manual drawing errors. This traditional approach hampers the integration of manufacturing information across engineering software. It exacerbates the digital divide between computer-aided design (CAD), computer-aided process planning (CAPP), and computer-aided manufacturing (CAM). To address these issues, this study proposes an automated approach for creating three-dimensional (3D) process models based on feature knowledge and geometric modeling. The 3-axis milling features are recognized as the machining objects from the boundary representation (B-Rep) part model. Geometric and parameter knowledge for modeling is derived from the machining step. In the proposed approach, two geometric modeling methods are investigated to construct feature state volumes (FSVs). The first method utilizes FSV modeling to simulate the shape of unmachined features before rough machining, while the second method utilizes FSV modeling to construct the shape of machined features before finishing machining. The case studies illustrate that the proposed approach can construct FSVs for various machining states and autonomously generate process models. In digital manufacturing, this approach assists process planners in intuitively evaluating the reasonableness of process routes. Additionally, it provides the essential driving geometry required for the autonomous generation of tool paths.

From CAD to representations suitable for isogeometric analysis: a complete pipeline

AbstractNext generation CAD/CAE systems shall integrate design and analysis procedures as a means to simplify workflows, boost performance, and speed up time to market. In the present paper we demonstrate a proof of concept of such a unification using subdivision surfaces and the enabling technology of isogeometric analysis. In particular, we present a complete pipeline to convert CAD models into smooth $$G^1$$ G 1 spline representations, which are suitable for isogeometric analysis. Starting from a CAD boundary representation of a mechanical object, we perform an automatic control cage extraction by means of quadrangular faces, such that its limit Catmull-Clark subdivision surface approximates accurately the input model. We then compute a basis of the $$G^1$$ G 1 spline space over the quad mesh in order to carry out least squares fitting over a point cloud, acquired by sampling the original CAD geometry. The resulting surface is a collection of Bézier patches with $$G^1$$ G 1 regularity. Finally, we use the basis functions to perform isogeometric analysis simulations of realistic PDEs on the reconstructed $$G^1$$ G 1 model. The quality of the construction is demonstrated via several numerical examples performed on a collection of CAD objects presenting various challenging realistic shapes.

Implementation of PMDL and DRM in OpenSees for Soil-Structure Interaction Analysis

It is widely acknowledged that the effects of soil-structure interaction (SSI) can have substantial implications during periods of intense seismic activity; therefore, accurate quantification of these effects is of paramount importance in the design of earthquake-resistant structures. The analysis of SSI is typically conducted using either direct or substructure methods. Both of these approaches involve the use of numerical models with truncated or reduced-order computational domains. To ensure effective truncation, it is crucial to employ boundary representations that are capable of perfectly absorbing outgoing waves and allowing for the consistent application of input motions. At present, such capabilities are not widely available to researchers and practicing engineers. In order to address this issue, this study implemented the Domain Reduction Method (DRM) and Perfectly Matched Discrete Layers (PMDLs) in OpenSees. The accuracy and stability of these implementations were verified through the use of vertical and inclined incident SV waves in a two-dimensional problem. In terms of computational efficiency, PMDLs require a shorter analysis time (e.g., with PMDLs, the analysis concluded in 35 min as compared to 250 min with extended domain method) and less computational power (one processor for PMDLs against 20 processors for the extended domain method) thus offering a balance between accuracy and efficiency. Furthermore, illustrative examples of the aforementioned implemented features are presented, namely the response analysis of single-cell and double-cell tunnels exposed to plane waves inclined at an angle.

Extended B‐spline‐based implicit material point method for saturated porous media

AbstractThe large deformation and fluidization process of a solid–fluid mixture includes significant changes to the temporal scale of the phenomena and the shape and properties of the mixed material. This paper presents an extended B‐spline (EBS)‐based implicit material point method (EBS‐MPM) for the coupled hydromechanical analysis of saturated porous media to enhance the overall versatility of MPM in addressing such diverse phenomena. The proposed method accurately represents phenomena such as high‐speed motion in both the quasi‐static and dynamic states by employing a full formulation of coupled hydromechanical modeling. The weak imposition of boundary conditions based on Nitsche's method allows representing the boundary conditions independent of the relative position of the particles and computational grid. In addition, it enables dynamic changes in the boundary domain based on the deformation. The robustness of this boundary representation is reinforced using EBS basis functions, which prevent the degradation of the condition number of the system matrices regardless of the position of the boundary domain with respect to the computational grid. Furthermore, a stabilization method based on a variational multiscale method (VMS) approach is employed to provide the flexibility in choosing arbitrary basis functions for spatial discretization, facilitating the effective construction of EBS. Numerical examples including comparisons between a full formulation and a simplified formulation are presented to demonstrate the performance of the developed method under various boundary conditions and loading states across different time scales.

Parallel isogeometric boundary element analysis with T-splines on CUDA

We present a framework for parallel isogeometric boundary element analysis (BEA) of elastic solids on CUDA. To deal with traction discontinuities, we propose a BEA model that supports multiple nodes and semi-discontinuous elements. The multiplicity of a node is defined by the number of regions containing any element influenced by the node. A region is a group of connected elements delimited by a closed crease curve. The default shape function of an element is determined by a linear operator applied to a set of basis functions. A BEA model is supposed to be generated from a watertight boundary representation of a solid. In this paper, we employ bicubic analysis-suitable T-splines. In this case, the shape of an element is defined by its Bézier extraction operator applied to the tensor product of Bernstein polynomials of degree 3. We describe the data structures of the BEA model and the main algorithms of the analysis pipeline on CUDA. In particular, we describe two strategies for parallel assembling of the linear system of equations. We also introduce a novel approach for inside integration based on the subdivision of the singular region in triangles with constant aspect ratio. In the T-splines context, we extend the Bézier extraction to handle unstructured T-meshes with crease edges. Moreover, we propose a scheme for embedding the influence of linked tangency handles on the shape of an element directly into the Bézier extraction operator. Such an embedding enables the removal of the corresponding nodes from the BEA model and the application of an alternative collocation method we discuss in the paper. We present several experiments to evaluate the accuracy and efficiency of the proposed framework. The results demonstrate that the GPU can be advantageously employed for parallelizing T-spline-based isogeometric analysis using boundary elements, achieving a speedup of up to 29x compared to the sequential code on a current laptop. We make the BEA code available in a prototype in MATLAB with a graphical interface that allows users to apply boundary conditions and visualize analysis results on the boundary.

Multimodal Image Confidence: A Novel Method for Tumor and Organ Boundary Representation

BackgroundThe ambiguous boundaries of tumors and organs at risk (OARs) seen in medical images pose challenges in treatment planning and other tasks in radiotherapy. MethodsThis study introduces an innovative analytical algorithm, Multi-Modal Image Confidence (MMC), which exploits the collective strengths of complementary multi-modal medical images to determine a confidence measure for each voxel belonging to the region of interest (ROI). MMC facilitates the creation of modality-specific ROI-enhanced images, enabling a detailed representation of the ROI's boundaries and internal features. By employing an interpretable mathematical model that propagates voxel confidence based on inter-voxel correlations, MMC avoids the need for model training, distinguishing it from deep learning (DL)-based methods. ResultsThe performance of the proposed algorithm was qualitatively and quantitatively evaluated using 156 nasopharyngeal carcinoma cases and 1251 glioma cases. Qualitative assessments underscored the accuracy of MMC and ROI-enhanced images in estimating lesion boundaries and capturing internal tumor characteristics. Quantitative analyses revealed strong agreement between MMC and manual delineations. ConclusionThis paper introduces a novel analytical algorithm to identify and depict ROI boundaries based on complementary multi-modal 3D medical images. The applicability of the proposed method can extend to both targets and OARs at diverse anatomical sites across multiple image modalities, amplifying its potential for augmenting radiotherapy-related tasks.

Topology Optimization with Explicit Components Considering Stress Constraints

Topology optimization focuses on the conceptual design of structures, characterized by a large optimization space and a significant impact on structural performance, and has been widely applied in industrial fields such as aviation and aerospace. However, most topology optimization methods prioritize structural stiffness and often overlook stress levels, which are critical factors in engineering design. In recent years, explicit topology optimization methods have been extensively developed due to their ability to produce clear boundaries and their compatibility with CAD/CAE systems. Nevertheless, research on incorporating stress constraints within the explicit topology optimization framework remains scarce. This paper is dedicated to investigating stress constraints within the explicit topology optimization framework. Due to the clear boundaries and absence of intermediate density elements in the explicit topology optimization framework, this approach avoids the challenge of stress calculation for intermediate density elements encountered in the traditional density method. This provides a natural advantage in solving topology optimization problems considering stress constraints, resulting in more accurate stress calculations. Compared with existing approaches, this paper proposes a novel component topology description function that enhances the deformability of components, improving the representation of geometric boundaries. The lower-bound Kreisselmeier–Steinhauser aggregation function is employed to manage the stress constraint, reducing the solution scale and computational burden. The effectiveness of the proposed method is demonstrated through two classic examples of topology optimization.

The Visual Scene Network and Hippocampus Represent Spatial Boundary Structures for Temporal Episodic Memory Organization.

Crossing a spatial boundary such as a doorway plays an important role in the temporal organization of episodic memory. However, despite the wealth of evidence showing that visual boundary structures in scenes affect our representation of space, no studies have tested the possibility that they also function as event boundaries even without active navigation. In this study, we used a nonnavigational scene-based memory task that required participants to remember a sequence of objects moving to various baskets in a scene. In the boundary condition, there was a freestanding boundary in the middle of the room, low enough to see the rest of the room beyond it. We found that the additional boundary within the scene was sufficient to trigger a larger response in the cortical visual scene network, the hippocampus, and their coordinated activity. These results suggest that active navigation across a spatial boundary such as a doorway into another room is not necessary to form an event boundary and that a visual representation of boundaries is sufficient to influence the organization of a hippocampal episodic memory.

Print No Border

As borders gradually open up once again, the consequences of the first two years of the COVID-19 pandemic are casting light on the renewed importance of regional and national borders. This is also true of European national borders – which had already been tested by the intensification of migratory flows and populist impulses – now in the process of becoming unwilling symbols of the restrictions ushered in by the pandemic. Closed for months, or at the very least made difficult to get through by health-related restrictions, the internal EU national borders that European peoples were coming to think of as a thing of the past were, quite suddenly, extremely concrete once again. This is a process that has been brought even more dramatically to the fore by the tragedy of the war in Ukraine. From the starting point of these premises, the Print no border project explored the border and frontier concepts via xylographic practice, juxtaposing, stratifying, and comparing the geographical representation of boundaries with images borrowed from nature and the man-made elements that boundaries cut through.

Split-and-Fit: Learning B-Reps via Structure-Aware Voronoi Partitioning

We introduce a novel method for acquiring boundary representations (B-Reps) of 3D CAD models which involves a two-step process: it first applies a spatial partitioning , referred to as the "split", followed by a "fit" operation to derive a single primitive within each partition. Specifically, our partitioning aims to produce the classical Voronoi diagram of the set of ground-truth (GT) B-Rep primitives. In contrast to prior B-Rep constructions which were bottom-up, either via direct primitive fitting or point clustering, our Split-and-Fit approach is top-down and structure-aware , since a Voronoi partition explicitly reveals both the number of and the connections between the primitives. We design a neural network to predict the Voronoi diagram from an input point cloud or distance field via a binary classification. We show that our network, coined NVD-Net for neural Voronoi diagrams, can effectively learn Voronoi partitions for CAD models from training data and exhibits superior generalization capabilities. Extensive experiments and evaluation demonstrate that the resulting B-Reps, consisting of parametric surfaces, curves, and vertices, are more plausible than those obtained by existing alternatives, with significant improvements in reconstruction quality. Code will be released on https://github.com/yilinliu77/NVDNet.

BrepGen: A B-rep Generative Diffusion Model with Structured Latent Geometry

This paper presents BrepGen , a diffusion-based generative approach that directly outputs a Boundary representation (B-rep) Computer-Aided Design (CAD) model. BrepGen represents a B-rep model as a novel structured latent geometry in a hierarchical tree. With the root node representing a whole CAD solid, each element of a B-rep model (i.e., a face, an edge, or a vertex) progressively turns into a child-node from top to bottom. B-rep geometry information goes into the nodes as the global bounding box of each primitive along with a latent code describing the local geometric shape. The B-rep topology information is implicitly represented by node duplication. When two faces share an edge, the edge curve will appear twice in the tree, and a T-junction vertex with three incident edges appears six times in the tree with identical node features. Starting from the root and progressing to the leaf, BrepGen employs Transformer-based diffusion models to sequentially denoise node features while duplicated nodes are detected and merged, recovering the B-Rep topology information. Extensive experiments show that BrepGen advances the task of CAD B-rep generation, surpassing existing methods on various benchmarks. Results on our newly collected furniture dataset further showcase its exceptional capability in generating complicated geometry. While previous methods were limited to generating simple prismatic shapes, BrepGen incorporates free-form and doubly-curved surfaces for the first time. Additional applications of BrepGen include CAD autocomplete and design interpolation. The code, pretrained models, and dataset are available at https://github.com/samxuxiang/BrepGen.

Intelligent toy tracking trajectory design based on mobile cloud terminal deployment and depth-first search algorithm.

The popularization of intelligent toys enriches the lives of the general public. To provide the public with a better toy experience, we propose the intelligent toy tracking method by the mobile cloud terminal deployment and depth-first search algorithm. Firstly, we construct a toy detection model via Transformer, which realizes the positioning of toys in the image through the refined region adaptive boundary representation. Then, using these detected continuous frames, we improve the toy tracking based on a depth-first search. Long-short-term memory (LSTM) constructs the continuous frame tracking structure, and the depth-first search mechanism is embedded to realize the accurate tracking of multiple targets in continuous frames. Finally, to realize the terminal marginalization of the proposed method, this chapter proposes a lightweight model deployment method based on mobile cloud terminals to realize the maintenance of the optimal machine state of intelligent toys. The experiment proves that our proposed target method can reach the world-leading level and obtain the mAP value of 0.858. Our tracking method can also perform excellently with a MOTA value of 0.916.

Ensemble Kalman inversion based on level set method for inverse elastic scattering problem

Abstract We consider an ensemble Kalman inversion scheme for inverse elastic scattering problems in which the unknown quantity is the shape of the scatterer. Assume that the scatterer is a piecewise constant function with known value inside inhomogeneities. The level set method is described as an implicit representation of the scatterer boundary, with Gaussian random fields serving as prior to provide information on the level set functions. The ensemble Kalman filter method is then employed based on the level set functions to reconstruct the shape of the scatterer. We demonstrate the effectiveness of the proposed method using several numerical examples.

Speech prosody enhances the neural processing of syntax

Human language relies on the correct processing of syntactic information, as it is essential for successful communication between speakers. As an abstract level of language, syntax has often been studied separately from the physical form of the speech signal, thus often masking the interactions that can promote better syntactic processing in the human brain. However, behavioral and neural evidence from adults suggests the idea that prosody and syntax interact, and studies in infants support the notion that prosody assists language learning. Here we analyze a MEG dataset to investigate how acoustic cues, specifically prosody, interact with syntactic representations in the brains of native English speakers. More specifically, to examine whether prosody enhances the cortical encoding of syntactic representations, we decode syntactic phrase boundaries directly from brain activity, and evaluate possible modulations of this decoding by the prosodic boundaries. Our findings demonstrate that the presence of prosodic boundaries improves the neural representation of phrase boundaries, indicating the facilitative role of prosodic cues in processing abstract linguistic features. This work has implications for interactive models of how the brain processes different linguistic features. Future research is needed to establish the neural underpinnings of prosody-syntax interactions in languages with different typological characteristics.

A novel immersed boundary approach for irregular topography with acoustic wave equations

Irregular terrain has a pronounced effect on the propagation of seismic and acoustic wavefields but is not straightforwardly reconciled with structured finite-difference (FD) methods used to model such phenomena. Accurate wavefield simulation is paramount in subsurface imaging applications such as reverse time migration and full-waveform inversion, requiring suitable topography handling. Methods currently detailed in the literature generally are limited in scope application-wise or nontrivial to apply to real-world geometries. A general immersed boundary treatment capable of imposing a range of boundary conditions in a relatively equation-agnostic manner has been developed, alongside a framework implementing this approach to complement emerging code-generation paradigms. The approach is distinguished by the use of N-dimensional Taylor-series extrapolants constrained by boundary conditions imposed at some suitably distributed set of surface points. The extrapolation process is encapsulated in modified derivative stencils applied in the vicinity of the boundary, using hyperspherical support regions. This method ensures boundary representation is consistent with the FD discretization. Furthermore, high-dimensional and vector boundary conditions can be applied without approximation prior to discretization. A consistent methodology can thus be applied across free and rigid surfaces with first- and second-order acoustic wave equation formulations. Application to both equations is demonstrated, and numerical examples based on analytic and real-world topography implementing free and rigid surfaces in 2D and 3D are presented. Numerical examples and convergence tests demonstrate the accuracy of boundary treatments devised by the prescribed approach, their suitability to practical applications, and the feasibility of automatically generating treatments to suit each case.

Topology optimization of anisotropic structure for arbitrary objective functionals with exact free boundary representation

A new approach to performing sensitivity analysis of arbitrary objective functionals for anisotropic elasticity is proposed in this work. Three different objective functionals have been considered, and good agreement is achieved between derived topological derivatives and numerical ones. Following the verification of topological derivatives, structural topology optimizations for selected anisotropic problems are conducted. To efficiently achieve the exact free boundary representation, our Finite Element Method (FEM)-based optimization comprises two loops. In the initial loop, a fixed and coarse mesh is employed to solve the anisotropic problem and update the level-set function. Once this loop concludes, the second loop reconstructs the material domain, ensuring an exact boundary representation. The convergence of the second loop is facilitated by (1) utilizing topological derivatives instead of explicit derivatives of ϕ (similar to density derivatives) and (2) imposing the exact volume constraint on the Reaction-Diffusion Equation (RDE)-based level-set method. Moreover, we introduce a scheme to prevent structural breakdown, allowing for the standalone implementation of Loop 2 always with exact free boundary representation. The previously proposed algorithm for the exact volume constraint has been generalized to accommodate inequalities, resulting in an acceleration of the equivalent optimization process.

Adaptive recognition of machining features in sheet metal parts based on a graph class-incremental learning strategy

The integration of computer-aided design (CAD), computer-aided process planning (CAPP), and computer-aided manufacturing (CAM) systems is significantly enhanced by employing deep learning-based automatic feature recognition (AFR) methods. These methods outperform traditional, rule-based approaches, particularly in handling the complexities of intersecting features. However, existing deep learning-based AFR methods face two major challenges. The initial challenge stems from the frequent utilization of voxelized or point-cloud representations of CAD models, resulting in the unfortunate loss of valuable geometric and topological information inherent in original Boundary representation (B-Rep) models. The second challenge involves the limitation of supervised deep learning methods in identifying machining features that are not present in the predefined dataset. This constraint renders them suboptimal for the continually evolving datasets of real industrial scenarios. To address the first challenge, this study introduces a graph-structured language, Multidimensional Attributed Face-Edge Graph (maFEG), crafted to encapsulate the intricate geometric and topological details of CAD models. Furthermore, a graph neural network, Sheet-metalNet, is proposed for the efficient learning and interpretation of maFEGs. To tackle the second challenge, a three-component incremental learning strategy is proposed: an initial phase of pre-training and fine-tuning, a prototype sampling-based replay, and a stage employing knowledge distillation for parameter regularization. The effectiveness of Sheet-metalNet and its complementary incremental learning strategy is evaluated using the open-source MFCAD++ dataset and the newly created SMCAD dataset. Experimental results show that Sheet-metalNet surpasses state-of-the-art AFR methods in machining feature recognition accuracy. Moreover, Sheet-metalNet demonstrates adaptability to dynamic dataset changes, maintaining high performance when encountering newly introduced features, thanks to its innovative incremental learning strategy.