Boundary representation (B-rep) is the de facto standard for CAD model representation in modern industrial design. The intricate coupling between geometric and topological elements in B-rep structures has forced existing generative methods to rely on cascaded multi-stage networks, resulting in error accumulation and computational inefficiency. We present BrepGPT, a single-stage autoregressive framework for B-rep generation. Our key innovation lies in the Voronoi Half-Patch (VHP) representation, which decomposes B-reps into unified local units by assigning geometry to nearest half-edges and sampling their next pointers. Unlike hierarchical representations that require multiple distinct encodings for different structural levels, our VHP representation facilitates unifying geometric attributes and topological relations in a single, coherent format. We further leverage dual VQ-VAEs to encode both vertex topology and Voronoi Half-Patches into vertex-based tokens, achieving a more compact sequential encoding. A decoder-only Transformer is then trained to autoregressively predict these tokens, which are subsequently mapped to vertex-based features and decoded into complete B-rep models. Experiments demonstrate that BrepGPT achieves state-of-the-art performance in unconditional B-rep generation. The framework also exhibits versatility in various applications, including conditional generation from category labels, point clouds, text descriptions, and images, as well as B-rep autocompletion and interpolation.

Supercapacitors are at the forefront of energy storage innovation, excelling in power density, rapid charge-discharge cycles, and operational lifespan. Despite these advantages, their relatively low energy density and storage capacity remain significant barriers to widespread adoption and replacement of conventional energy storage systems. Addressing this challenge requires an efficient approach to explore and optimize complex electrode and electrolyte designs – an area where computational modeling proves indispensable. Computation methods enable systematic exploration of design spaces that are experimentally infeasible or costly to investigate, providing a deeper understanding of the interplay between material properties and electrochemical performance. This study introduces a diffuse-interface model, which offers a continuous representation of phase boundaries to simplify simulations of multiphase electrochemical systems. The model incorporates essential phenomena such as faradaic reactions and double-layer capacitance by employing indicator functions that delineate distinct phases within the system. By integrating key electrochemical equations such as Butler-Volmer kinetics, the model simulates charge distribution and electrostatic potential, with validation achieved through cyclic voltammetry (CV) curves.Building on this foundation, the model's capabilities were extended to optimize porous electrode microstructures using the phase-field framework. The Cahn–Hilliard equation was employed to simulate phase separation, enabling the generation of porous electrode structures. Supercapacitors with optimized microstructures demonstrated improved charge storage and power density, validating the proposed methodology's effectiveness in linking microstructural properties to electrochemical behaviour. This comprehensive analysis underscores the importance of tailoring electrode designs to achieve balanced performance metrics, including high energy density and power density. In addition to enhancing supercapacitor performance, this research provides a robust computational framework that can be adapted to study a wide range of energy storage devices. By incorporating the generation of electrode and electrolyte microstructures within the phase-field model, this approach facilitates a deeper understanding of the interplay between morphology and electrochemical processes. The diffuse-interface model offers significant adaptability, enabling its application in designing advanced supercapacitors and extending its utility to other battery technologies. The insights gained through this research lay the groundwork for the development of next-generation energy storage devices with unprecedented performance, contributing to a sustainable energy future.

Skin cancer remains a major public health concern due to its high morbidity and mortality rates. While automatic segmentation techniques have improved diagnostic accuracy, they continue to face challenges such as artefacts, small lesion detection, and poor contrast between lesions and surrounding tissue. To overcome these limitations, we propose WA-NET, a novel skin lesion segmentation network that integrates a Boundary Refinement module (BRM) and an Enhanced Wavelet Transform (EWT) module. The BRM employs independent edge detection branches to enhance boundary representation, particularly in low-contrast regions. The EWT module adaptively fuses multi-scale, multi-directional sub-band features in the frequency domain to better capture texture and structural details. Furthermore, a composite loss function combining binary cross-entropy, Dice loss, and edge-supervised loss is introduced to improve both global segmentation accuracy and local boundary precision. WA-NET achieves state-of-the-art performance on three benchmark datasets—ISIC2017 (DSC: 0.9395, SE: 0.9357, ACC: 0.9573), ISIC2018 (DSC: 0.9458, SE: 0.9460, ACC: 0.9610), and PH2 (DSC: 0.9517, SE: 0.9593, ACC: 0.9638)—demonstrating strong robustness and superior boundary segmentation under challenging imaging conditions.

This review paper surveys the application of Maxwell’s equations to simulate light propagation in the human eye, using discontinuous Galerkin methods for spatial discretisation. Understanding this process is crucial for medical imaging and the early diagnosis of eye diseases. Case studies involving corneal opacity, diabetic macular edema, and retinal elasticity demonstrate the importance of simulating this phenomenon considering realistic geometries and material properties. Specifically, these simulations provide valuable insight into how structural changes in the cornea and retina affect light scattering and transparency, offering a useful tool for non-invasive diagnosis. Curved anatomical features, such as structures of the eye, require accurate boundary representation to avoid loss of order of convergence of the numerical schemes. Highorder discontinuous Galerkin method combined with a polynomial reconstruction technique enable an appropriate enforcement of boundary conditions without relying on curved meshes.

Reverse engineering (RE) is increasingly recognized as a vital methodology for reconstructing mechanical components, particularly in high-value sectors such as aerospace, transportation, and energy, where technical documentation is often missing or outdated. This study presents a systematic review that investigates the application, challenges, and future directions of RE in mechanical component reconstruction. Adopting the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) framework, 68 peer-reviewed studies were identified, screened, and synthesized. The review highlights RE applications in restoration, redesign, internal geometry modeling, and simulation-driven performance assessment, leveraging technologies such as 3D scanning, CAD modeling, and finite element analysis. However, persistent challenges remain across five domains: product complexity, tolerance and dimensional variations, scanning limitations, integration barriers, and human-material-process dependencies, which hinder automation, accuracy, and manufacturability. Future research opportunities include the automated conversion of point cloud data into editable boundary representation (B-rep) models and AI-driven approaches for feature recognition, geometry reconstruction, and the generation of simulation-ready models. Additionally, advancements in scanning techniques to capture hidden or internal features more effectively are crucial. Overall, this review provides a comprehensive synthesis of current practices and challenges while proposing pathways to advance RE in industrial applications, fostering greater automation, accuracy, and integration in digital manufacturing workflows.

In stress-dependent topology optimization (TO), the design structure is highly dependent on stress constraints, and significant stress concentration is prone to occur near structural discontinuities and rigid constraints. Therefore, this paper proposes a TO method for level-set structures, incorporating a subregional P-norm stress constraint. The level set method is independent of the physical model and may delineate the border with greater clarity while precisely defining the stress of the boundary element, so circumventing the ambiguity associated with the variable density method’s boundary representation. Firstly, the structural topology optimization (STO) model with stress penalty is established by employing P-norm stress as a constraint and volume fraction as the objective function, integrated with the parametric level set approach. Secondly, a sensitivity analysis utilizing shape derivatives is conducted, and the TO problem is addressed using the moving asymptote approach, achieving STO with volume minimization under a stress constraint. The P-norm subregional stress-constrained topology optimization method exhibits enhanced stability and a more uniform structure in areas of stress concentration, as evidenced by two engineering cases.

Service area boundaries are the geographic delineation of a community water system’s (CWS) customer base. Lack of consistent and precise service area boundaries may affect how measures of water quality are geospatially assigned in academic or regulatory work, potentially hindering our ability to locate and accurately characterize disparities in drinking water provision. Though it is generally understood that more accurate boundaries would improve the analytical precision of drinking water quality analyses, it is unclear how the choice of boundary representations would impact conclusions of empirical analyses or the potential magnitude of bias. This paper aims to fill this gap by summarizing a set of novel drinking water quality metrics for arsenic, bacterial detection, disinfection byproduct formation, lead, nitrates, PFAS, and health-based violations of the Safe Drinking Water Act. We compare these drinking water measures across service area assignment methods including the use of county served, zip codes served, the EPIC/SimpleLab dataset, boundaries created by the U.S. Geologic Survey, and a national data layer produced by EPA’s Office of Research and Development. Conclusions regarding the presence of a disparity depend on the service area boundary selected for at least one demographic group for six of seven drinking water quality measures in this analysis. This paper helps to motivate the importance of producing, maintaining, and updating a high-quality, nationally consistent geodatabase of drinking water system service areas.

Accurate segmentation of colorectal polyps is crucial for the early screening and clinical diagnosis of colorectal cancer. However, the diverse morphology of polyps, significant variations in scale, and unstable quality of endoscopic imaging pose serious challenges for existing algorithms in achieving precise boundary segmentation. To address these issues, this study proposes a novel polyp segmentation algorithm, GDCA-Net, which is developed based on the You Only Look Once version 12 segmentation model (YOLOv12-seg). GDCA-Net introduces several architectural innovations. First, a Gather-and-Distribute (GD) mechanism is incorporated to optimize multi-scale feature fusion, while Alterable Kernel Convolution (AKConv) is integrated to enhance the modeling of complex geometric structures. Second, the Convolution and Attention Fusion Module (CAF) and Context-Mixing dynamic convolution (ContMix) modules are designed to strengthen long-range dependency modeling and multi-scale feature extraction for polyp boundary representation. Finally, a Wise Intersection over Union–based (Wise-IoU) loss function is introduced to accelerate model convergence and improve robustness to low-quality samples. Experiments conducted on the PolypDB, Kvasir-SEG, and CVC-ClinicDB datasets demonstrate the superior performance of GDCA-Net in polyp segmentation tasks. On the most challenging PolypDB dataset, GDCA-Net achieved a mean Average Precision at 50% IoU threshold (mAP50) of 85.9% and an F1-score (F1) of 85.5%, representing improvements of 2.2% and 0.7% over YOLOv12-seg, respectively. Moreover, on the Kvasir-SEG dataset, GDCA-Net achieved a leading F1 score of 94.9%. These results clearly demonstrate that GDCA-Net possesses strong performance and generalization capabilities in handling polyps of varying sizes, shapes, and imaging qualities.

Abstract We present a data-driven, differentiable neural network model designed to learn the temperature field, its gradient, and the cooling rate, while implicitly representing the melt pool boundary as a level set in laser powder bed fusion. The physics-guided model combines fully connected feed-forward neural networks with Fourier feature encoding of the spatial coordinates and laser position. Notably, our differentiable model allows for the computation of temperature derivatives with respect to position, time, and process parameters using autodifferentiation. Moreover, the implicit neural representation of the melt pool boundary as a level set enables the inference of the solidification rate and the rate of change in melt pool geometry relative to process parameters. The model is trained to learn the top view of the temperature field and its spatiotemporal derivatives during a single-track laser powder bed fusion process, as a function of three process parameters, using data from high-fidelity thermo-fluid simulations. The model accuracy is evaluated and compared to a state-of-the-art convolutional neural network model, demonstrating strong generalization ability and close agreement with high-fidelity data.

Accurate spatial information of cropland is crucial for precision agricultural management and ensuring national food security. High-resolution remote sensing imagery combined with deep learning algorithms provides a promising approach for extracting detailed cropland information. However, due to the diverse morphological characteristics of croplands across different agricultural landscapes, existing deep learning methods encounter challenges in precise boundary localization. The advancement of large-scale vision models has led to the emergence of the Segment Anything Model (SAM), which has demonstrated remarkable performance on natural images and attracted considerable attention in the field of remote sensing image segmentation. However, when applied to high-resolution cropland extraction, SAM faces limitations in semantic expressiveness and cross-domain adaptability. To address these issues, this study proposes a dual-branch framework integrating SAM and a semantically aware network (SAM-SANet) for high-resolution cropland extraction. Specifically, a semantically aware branch based on a semantic segmentation network is applied to identify cropland areas, complemented by a boundary-constrained SAM branch that directs the model’s attention to boundary information and enhances cropland extraction performance. Additionally, a boundary-aware feature fusion module and a prompt generation and selection module are incorporated into the SAM branch for precise cropland boundary localization. The former aggregates multi-scale edge information to enhance boundary representation, while the latter generates prompts with high relevance to the boundary. To evaluate the effectiveness of the proposed approach, we construct three cropland datasets named GID-CD, JY-CD and QX-CD. Experimental results on these datasets demonstrated that SAM-SANet achieved mIoU scores of 87.58%, 91.17% and 71.39%, along with mF1 scores of 93.54%, 95.35% and 82.21%, respectively. Comparative experiments with mainstream semantic segmentation models further confirmed the superior performance of SAM-SANet in high-resolution cropland extraction.

ABSTRACT Semantic segmentation of cropland is essential for extracting crop distribution from satellite remote sensing (RS) images. However, the dynamic temporal patterns caused by crop rotations and the heterogeneous spatial characteristics of cropland hinder high-precision segmentation, leading to boundary ambiguity, intra-class variability across crop growth stages and occlusion from clouds or shadows. To address these challenges, we propose STFE, a spatiotemporal feature-enhanced network for cropland segmentation in remote sensing time-series images. STFE integrates spatial and temporal features through three key designs. First, an edge-guided spatial attention (EGSA) module enhances boundary representation, improving delineation of irregular parcels. Second, a progressive feature enhancement (PFE) strategy progressively fuses multi-scale features, strengthening spatial representation. Third, for temporal feature extraction, we incorporate a differential awareness attention (DAA) module, built on ConvLSTM, dynamically aggregates temporal information, enabling robust modeling of crop rotations and seasonal variations. Experimental on three benchmark datasets – PASTIS, ZueriCrop, and DNETHOR – confirm the effectiveness of STFE, achieving a mean IoU gain of 3.2% over the best baseline. By effectively leveraging spatiotemporal cues, STFE provides a reliable and scalable solution for monitoring cropland dynamics, supporting sustainable agriculture and informed decision-making.

ABSTRACT A modeling framework was implemented to streamline the generation of hydrodynamic pluvial flood models from geospatial data. The geoprocessing methods were specifically tailored towards the parametrization of Nature-based Solutions (NBS) in urban environments. Model entities are collected and processed into a boundary representation (BRep) via a coverage discretization technique that makes use of a novel concept: polygonal coverages. Necessary spatial relationships between model entities were formally defined and enforced to guarantee valid coverages. Model domains are triangulated by supplying the generated BRep to the Gmsh mesh engine. Simulation was performed via static coupling of the STORM hydrological engine and TELEMAC-2D finite-volume solver. An urban-planning model, simulating a flood event with and without NBS, was presented to demonstrate the framework capabilities: generating valid models and quantifying the mitigation effects in terms of inundation depths and water velocities.

Class imbalance remains a significant challenge in machine learning, leading to biased models that favor the majority class while failing to accurately classify minority instances. Traditional oversampling methods, such as Synthetic Minority Over-sampling Technique (SMOTE) and its variants, often struggle with class overlap, poor decision boundary representation, and noise accumulation. To address these limitations, this study introduces ClusterDEBO, a novel hybrid oversampling method that integrates K-Means clustering with differential evolution (DE) to generate synthetic samples in a more structured and adaptive manner. The proposed method first partitions the minority class into clusters using the silhouette score to determine the optimal number of clusters. Within each cluster, DE-based mutation and crossover operations are applied to generate diverse and well-distributed synthetic samples while preserving the underlying data distribution. Additionally, a selective sampling and noise reduction mechanism is employed to filter out low-impact synthetic samples based on their contribution to classification performance. The effectiveness of ClusterDEBO is evaluated on 44 benchmark datasets using k-Nearest Neighbors (kNN), decision tree (DT), and support vector machines (SVM) as classifiers. The results demonstrate that ClusterDEBO consistently outperforms existing oversampling techniques, leading to improved class separability and enhanced classifier robustness. Moreover, statistical validation using the Friedman test confirms the significance of the improvements, ensuring that the observed gains are not due to random variations. The findings highlight the potential of cluster-assisted differential evolution as a powerful strategy for handling imbalanced datasets.

ABSTRACT According to CityGML, 3D models at different Levels of Details (LoDs) are defined to meet the geometric requirements of various applications. Following this principle, this paper introduces a concept of LoDs for the 3D modeling of Buddhist statues. The procedure consists of four steps: (1) inventory of applications, (2) analysis of geometric requirements in applications, (3) determination of the number of LoDs, and (4) design of geometric representations of each LoD. Based on 60 application scenarios, we proposed four LoDs for Buddhist statue modeling. LoD1 is defined as 2D symbols for geospatial analysis, LoD2 uses convex hull geometry for GIS applications, LoD3 is represented by coarse solid boundary representation of primary components for applications such as conservation and transportation, and LoD4 models detailed geometries for every small component to support various types of archeology calculations. The key feature of the proposed LoD concept is the integration of semantic information, which serves as fundamental data for interoperability in computer-aided applications. Based on the proposed LoD in this paper, a CityGML Application Domain Extension (ADE) can be developed for the 3D digital modeling of Buddhist statues or even figure sculptures more broadly. The procedure developed in this paper could be generally used to design LoDs for other types of features in context with their application needs. Although this study focuses on Buddhist statues, the proposed LoD framework is adaptable to other sculptural traditions that require semantic-aware modeling, thereby enabling broad applicability across different cultural heritage domains.

Distinguishing our body from the external world is crucial for self-perception and environmental interaction. Yet, the accuracy with which we perceive this boundary remains underexplored. Here, we developed a psychophysical protocol to assess how accurately individuals perceive their body boundaries. Participants were asked whether the midpoint between two tactile stimuli was inside or outside their perceived body boundary. Three-dimensional scans provided objective anatomical boundaries, allowing psychometric functions to be fitted. Results revealed remarkable overall precision, often within millimetres, in localizing body boundaries across multiple body regions. However, accuracy varied: while palm boundaries were localized nearly perfectly, stimuli along the wrist boundaries were frequently misjudged as extending beyond their true anatomical limit, revealing a systematic perceptual bias. Perceptual judgements adapted to changes in posture, but accuracy declined when the detailed local three-dimensional structure was omitted, indicating that proprioceptive cues are combined with detailed local body models. Finally, participants whose anatomy deviated from the average tended to align their responses with a typical body model rather than their unique physiology, suggesting that top-down processes influence boundary judgements. Our findings suggest that body boundary representation combines detailed three-dimensional body models with proprioceptive feedback into an integrated perceptual model of the anatomical body.

Segmentation of skin lesions in dermoscopic images is critical for the accurate diagnosis of skin cancers, particularly malignant melanoma, yet it is hindered by irregular lesion shapes, blurred boundaries, low contrast, and artifacts, such as hair interference. Conventional deep learning methods, typically based on UNet or Transformer architectures, often face limitations in regard to fully exploiting lesion features and incur high computational costs, compromising precise lesion delineation. To overcome these challenges, we propose SGNet, a structure-guided network, integrating a hybrid CNN-Mamba framework for robust skin lesion segmentation. The SGNet employs the Visual Mamba (VMamba) encoder to efficiently extract multi-scale features, followed by the Dual-Domain Boundary Enhancer (DDBE), which refines boundary representations and suppresses noise through spatial and frequency-domain processing. The Semantic-Texture Fusion Unit (STFU) adaptively integrates low-level texture with high-level semantic features, while the Structure-Aware Guidance Module (SAGM) generates coarse segmentation maps to provide global structural guidance. The Guided Multi-Scale Refiner (GMSR) further optimizes boundary details through a multi-scale semantic attention mechanism. Comprehensive experiments based on the ISIC2017, ISIC2018, and PH2 datasets demonstrate SGNet's superior performance, with average improvements of 3.30% in terms of the mean Intersection over Union (mIoU) value and 1.77% in regard to the Dice Similarity Coefficient (DSC) compared to state-of-the-art methods. Ablation studies confirm the effectiveness of each component, highlighting SGNet's exceptional accuracy and robust generalization for computer-aided dermatological diagnosis.

We introduce a novel representation for learning and generating Computer-Aided Design (CAD) models in the form of boundary representations (B-Reps). Our representation unifies the continuous geometric properties of B-Rep primitives in different orders (e.g., surfaces and curves) and their discrete topological relations in a holistic latent (HoLa) space. This is based on the simple observation that the topological connection between two surfaces is intrinsically tied to the geometry of their intersecting curve. Such a prior allows us to reformulate topology learning in B-Reps as a geometric reconstruction problem in Euclidean space. Specifically, we eliminate the presence of curves, vertices, and all the topological connections in the latent space by learning to distinguish and derive curve geometries from a pair of surface primitives via a neural intersection network. To this end, our holistic latent space is only defined on surfaces but encodes a full B-Rep model, including the geometry of surfaces, curves, vertices, and their topological relations. Our compact and holistic latent space facilitates the design of a first diffusion-based generator to take on a large variety of inputs including point clouds, single/multi-view images, 2D sketches, and text prompts. Our method significantly reduces ambiguities, redundancies, and incoherences among the generated B-Rep primitives, as well as training complexities inherent in prior multi-step B-Rep learning pipelines, while achieving greatly improved validity rate over current state of the art: 82% vs. ≈50%.

Boolean operations for Boundary Representation (B-Rep) models are among the most commonly used functions in Computer Aided Design (CAD) systems. They are also one of the most delicate soft modules, with challenges arising from complex algorithmic flows and efficiency and accuracy issues, especially in extreme cases. Common issues encountered in processing complex models include low efficiency, missing results, and non-watertightness. In this paper, we propose a novel algorithm for efficient and accurate Boolean operations on B-Rep models. This is achieved by establishing a bijective mapping between B-Rep models and the corresponding triangle meshes with controllable approximation error, thus mapping B-Rep Boolean operations to mesh Boolean operations. By using conservative intersection detection on the mesh to locate all surface intersection curves and carefully handling degeneration and topology errors, we ensure that the results are consistently watertight and correct. We demonstrate the superior efficiency of the proposed method using the open-source geometry engine OCCT, the commercial engine ACIS, and the commercial software Rhino as benchmarks.

ABSTRACTAccurate and robust modeling of large deformation three‐dimensional contact interaction is an important area of engineering, but it is also challenging from a computational mechanics perspective. This is particularly the case when there is significant interpenetration and evolution of the contact surfaces, such as the case of a relatively rigid body interacting with a highly deformable body. This paper provides a new three‐dimensional large deformation contact approach where the Material Point Method (MPM) is used to represent the deformable material. A new contact detection approach is introduced that checks the interaction of the vertices of the domains associated with each material point with the discretized rigid body. This provides a general and consistent approach without requiring the reconstruction of an additional boundary representation of the deformable body. A new energy‐consistent material point domain updating approach is also introduced that maintains stable simulations under large deformations. The dynamic governing equations allow the trajectory of the rigid body to evolve based on the interaction with the deformable body, and the governing equations are solved within an efficient implicit framework. The performance of the new contact approach is demonstrated on a number of benchmark problems with analytical solutions. The method is also applied to the specific case of soil‐structure interaction, using geotechnical centrifuge experimental data that confirms the veracity of the proposed approach.

This paper presents a medical image analysis application designed to facilitate advanced edge detection and fuzzy processing techniques within an intuitive, modular graphical user interface. Key functionalities include classical edge detection, Ant Colony Optimization (ACO)-based edge extraction, and fuzzy edge generation, which offer improved boundary representation in images where uncertainty and soft transitions are prevalent. One of the main novelties in contrast to the initial innovative Medical Image Analyzer, iMIA, is the fact that the system includes fuzzy C-means clustering to support tissue classification and unsupervised segmentation based on pixel intensity distribution. The application also features an interactive zooming and panning module with the option to overlay edge detection results. As another novelty, fuzzy performance metrics were added, including fuzzy false negatives, fuzzy false positives, fuzzy true positives, and the fuzzy index, offering a more comprehensive and uncertainty-aware evaluation of edge detection accuracy. The application executable file is provided at no cost for the purposes of evaluation and testing.