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Search Results (1,049)

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Keywords = geometry reconstruction

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21 pages, 2514 KB  
Article
Identification and Characterization of Creep-Capable Faults Using Advanced HVSR Processing: Implications for Seismic Microzonation (Etna, Italy)
by Sabrina Grassi, Claudia Pirrotta, Sebastiano Imposa, Gabriele Quattrocchi and Gabriele Morreale
Geosciences 2026, 16(7), 248; https://doi.org/10.3390/geosciences16070248 (registering DOI) - 24 Jun 2026
Abstract
The southeastern flank of Mt. Etna is affected by the presence of active faults capable of adapting to deformation through both seismic slip and aseismic creep, posing challenges for seismic microzonation and for land-use planning. Structural surveys in the urban area of San [...] Read more.
The southeastern flank of Mt. Etna is affected by the presence of active faults capable of adapting to deformation through both seismic slip and aseismic creep, posing challenges for seismic microzonation and for land-use planning. Structural surveys in the urban area of San Gregorio di Catania revealed a ~1 km long, N–S trending secondary fracture zone with an extensional component, inducing progressive damage to buildings and infrastructure. To characterize this scarcely visible structure, passive seismic single-station surveys processed with Horizontal-to-Vertical Spectral Ratio (HVSR) tecnique were integrated with Multichannel Analysis of Surface Waves (MASW). The HVSR data enabled the mapping of the spatial distribution of resonance frequencies, tracking an anomalous trend in the seismic bedrock geometry and depth directly correlatable with the presence of the secondary fracture zone. Directional analyses exhibit systematic preferential orientations of resonance peaks near the fracture corridor, confirming a rigorous structural control and a tectonic origin for the recorded anomalies. Furthermore, reconstructed 2D impedance contrast sections show distinct discontinuities and a local westward dislocation of the main seismo-stratigraphic interface across the deformation zone. The lack of correlated instrumental seismicity supports the interpretation that the displacement is primary accommodated via aseismic fault creep. Methodologically, these findings demonstrate that the passive seismic method provides a highly effective, non-invasive approach for identifying hard-to-detect tectonic structures that remain unobliterated by dense urbanization. Ultimately, these results offer critical, actionable constraints for seismic microzonation and urban land-use setback zoning. Full article
21 pages, 8895 KB  
Article
Registration Quality and the Limits of Statistical Shape Modeling Evaluation in Transtibial Residual Limb Modeling: A Cross-Sectional Shape Representation Framework
by Shinichiro Kon, Yukio Agarie, Hironori Suda, Hiroshi Otsuka, Kengo Ohnishi, Akihiko Hanahusa, Motoki Takagi and Shinichiro Yamamoto
Prosthesis 2026, 8(7), 65; https://doi.org/10.3390/prosthesis8070065 (registering DOI) - 23 Jun 2026
Abstract
Background/Objectives: Statistical shape modeling (SSM) is used to describe transtibial residual-limb morphology for prosthetic socket design, simulation, and future structural testing. However, conventional intrinsic metrics such as compactness, generality, and specificity may not directly reflect geometric fidelity to the original shape. This [...] Read more.
Background/Objectives: Statistical shape modeling (SSM) is used to describe transtibial residual-limb morphology for prosthetic socket design, simulation, and future structural testing. However, conventional intrinsic metrics such as compactness, generality, and specificity may not directly reflect geometric fidelity to the original shape. This study examined the relationship between geometric fidelity and SSM evaluation and assessed a cross-sectional shape representation framework for transtibial residual limbs. Methods: Residual-limb surfaces were acquired from 62 adults with unilateral transtibial amputation using a structured-light 3D scanner while preserving habitual limb posture. Two surface-based registration methods, non-rigid iterative closest point and Bayesian coherent point drift, were compared with a cross-sectional representation in which proximal and distal regions were sectioned separately and reconstructed by strip triangulation. Geometric fidelity to the original mesh was quantified using average symmetric surface distance (ASSD). SSM performance was evaluated using compactness, generality, and specificity. Results: The optimal cross-sectional configuration was 60 sections × 72 points. The proposed method showed the best geometric fidelity (ASSD, 1.30 ± 0.14 mm), followed by Bayesian coherent point drift (1.33 ± 0.14 mm) and non-rigid iterative closest point (1.48 ± 0.48 mm). Compactness was highest for the proposed method, reaching 95% cumulative variance in four modes, compared with five and seven modes, respectively, for the two surface-based methods. In geometry-space evaluation, the proposed method showed the lowest specificity error, while differences in generality were statistically significant but small in magnitude. Conclusions: Intrinsic SSM metrics alone were insufficient to judge registration quality in transtibial residual-limb modeling. The cross-sectional representation preserved the original surface geometry more faithfully than the evaluated surface-based methods while maintaining competitive SSM performance. Full article
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16 pages, 2336 KB  
Article
Numerical Study on Thermodynamic Performance of Shell-and-Tube and Compact Printed-Circuit Heat Exchangers for Aero-Engine Lubricating Oil System
by Huiqing Jiang, Guangle Li, Qian Huang, Wang Li and Yaguo Lyu
Energies 2026, 19(12), 2941; https://doi.org/10.3390/en19122941 (registering DOI) - 22 Jun 2026
Viewed by 132
Abstract
To address the continuously increasing thermal load of aero-engines, fuel/lubricating oil heat exchangers are evolving toward higher heat transfer efficiency, lower flow resistance, and lighter weight. This paper numerically compares the thermo-hydraulic performance of a conventional shell-and-tube heat exchanger (STHE) and three typical [...] Read more.
To address the continuously increasing thermal load of aero-engines, fuel/lubricating oil heat exchangers are evolving toward higher heat transfer efficiency, lower flow resistance, and lighter weight. This paper numerically compares the thermo-hydraulic performance of a conventional shell-and-tube heat exchanger (STHE) and three typical types of printed-circuit heat exchangers (PCHEs) for aero-engine applications. The three PCHE configurations fall into two categories based on their flow channel geometries: continuous-rib structures (straight and Z channels) and a discontinuous-rib structure (airfoil channel). All models are established under identical core volume and equivalent diameter to ensure a fair comparison. The results show that the airfoil-channel PCHE achieves the best overall performance. Compared with the STHE, it increases the heat transfer rate by 63%, reduces flow resistance by 76%, expands heat transfer area by 125%, and reduces operating weight by 60%. Flow field analysis reveals that the airfoil channel enables efficient heat transfer without excessive flow resistance through three key mechanisms: leading-edge impingement, periodic boundary layer reconstruction, and uniform flow mixing. This study provides an important reference for the selection and optimization of high-efficiency compact heat exchangers in aero-engines. Full article
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33 pages, 57220 KB  
Article
Agri-DETR: An Efficient Visual Obstacle Detection Framework for Intelligent Agricultural Machinery in Unstructured Field Environments
by Hao Fan, Jintao Xi, Xi Chen and Bingyu Sun
Agriculture 2026, 16(12), 1361; https://doi.org/10.3390/agriculture16121361 (registering DOI) - 22 Jun 2026
Viewed by 106
Abstract
Object detection in unstructured agricultural environments remains challenging due to large scale variations, complex backgrounds, irregular obstacle shapes, and limited computational resources. To address these challenges, this paper proposes Agri-DETR, an efficient end-to-end detection framework based on the Real-Time Detection Transformer (RT-DETR), with [...] Read more.
Object detection in unstructured agricultural environments remains challenging due to large scale variations, complex backgrounds, irregular obstacle shapes, and limited computational resources. To address these challenges, this paper proposes Agri-DETR, an efficient end-to-end detection framework based on the Real-Time Detection Transformer (RT-DETR), with coordinated improvements in feature perception, multi-scale representation, spatial reconstruction, and bounding box regression. Specifically, a lightweight backbone with a high-resolution feature branch is introduced to enhance the representation of small and fine-grained targets. A large selective feature fusion module is designed to strengthen multi-scale contextual modeling and improve feature discrimination under complex backgrounds. In addition, an attention-enhanced dynamic upsampling module refines high-resolution feature reconstruction, while a scale–shape–geometry-aware Intersection over Union (SSGIoU) loss improves localization stability for irregular and elongated objects. Experimental results show that Agri-DETR achieves 66.0% Average Precision (AP) on the self-constructed Agricultural Obstacle Dataset (AO-Dataset), outperforming representative detectors while reducing the parameter count by approximately 25% compared with RT-DETR-R18 baseline. In particular, small-object AP increases by 1.4%, demonstrating improved detection capability for small obstacles. Cross-dataset evaluation on COCO2017 further shows that Agri-DETR achieves 48.3% AP, demonstrating favorable generalization capability beyond the agricultural domain. These results indicate that Agri-DETR achieves an effective balance among detection accuracy, model complexity, and practical efficiency, making it a promising solution for real-world agricultural obstacle detection. Full article
(This article belongs to the Section Agricultural Technology)
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30 pages, 86356 KB  
Article
Geometric Principles of Stereo Vision: A Quantitative Evaluation and Physical Validation of the Classical Pipeline
by Angel Fernando Ceballos-Espinoza, David Balderas-Silva, Alfredo Diaz-Lara and Rita Q. Fuentes-Aguilar
Appl. Sci. 2026, 16(12), 6212; https://doi.org/10.3390/app16126212 (registering DOI) - 19 Jun 2026
Viewed by 106
Abstract
Stereo vision is essential for passive three-dimensional perception in resource-constrained applications that require low power consumption, predictable latency, and explainable geometry. Although deep learning architectures dominate recent benchmarks, the classical block-matching pipeline remains a foundational approach. Optimizing this pipeline involves navigating complex trade-offs [...] Read more.
Stereo vision is essential for passive three-dimensional perception in resource-constrained applications that require low power consumption, predictable latency, and explainable geometry. Although deep learning architectures dominate recent benchmarks, the classical block-matching pipeline remains a foundational approach. Optimizing this pipeline involves navigating complex trade-offs among matching robustness, map density, and computational efficiency. This study systematically surveys and physically validates the classical stereo framework. After revisiting geometric first principles, three matching costs (SAD, NCC, ZNCC) are benchmarked alongside Sobel preprocessing and structural refinements, with subsequent validation using a calibrated consumer webcam rig. Middlebury benchmarks (2001–2021) indicate that while SAD fails under complex radiometric distortion, NCC consistently achieves superior quantitative metrics, incurring only a 1.2-fold computational overhead. Extending the disparity search range improves foreground localization, while block size imposes a trade-off between resolving the aperture problem and preserving fine geometric detail. To bridge theoretical analysis and practical deployment, the pipeline is validated using a custom-calibrated consumer stereo rig. The optimized Sobel-NCC architecture is then evaluated for real-time edge deployment on constrained hardware (NVIDIA Jetson Nano) and narrow-baseline sensors (OAK-D SR) in the context of agricultural robotic manipulation. By prioritizing metric precision over dense prediction, the classical pipeline reconstructs target surfaces with approximately 1 cm depth accuracy at 21 frames per second. These results demonstrate that optimized local algorithms offer deterministic and reliable geometric foundations for real-time edge-computed robotics. Although neural networks are essential for dense reconstructions in ill-posed regions, the foundational principles established here remain indispensable for advanced stereo vision system deployment. Full article
(This article belongs to the Section Robotics and Automation)
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22 pages, 32128 KB  
Article
Atomistic Mechanisms of Silicone Rubber Degradation Under Coupled Temperature–Humidity–Electric Field Conditions
by Yiheng Zhou, Zhijun An, Yixin He, Cong Qian, Qiuhua Zhou, Wentian Zeng, Xinhan Qiao and Wenyu Ye
Polymers 2026, 18(12), 1530; https://doi.org/10.3390/polym18121530 (registering DOI) - 19 Jun 2026
Viewed by 283
Abstract
Silicone rubber is an important external insulating material for composite bushings, composite insulators, and other power equipment. During long-term service, it is inevitably exposed to coupled environmental and electrical stresses, such as elevated temperature, moisture ingress, strong electric fields, and partial discharge, which [...] Read more.
Silicone rubber is an important external insulating material for composite bushings, composite insulators, and other power equipment. During long-term service, it is inevitably exposed to coupled environmental and electrical stresses, such as elevated temperature, moisture ingress, strong electric fields, and partial discharge, which may lead to hydrophobicity loss, surface chalking, crack propagation, and particle shedding. To reveal the microscopic degradation mechanism of silicone rubber under complex operating conditions, a molecular model of methyl vinyl silicone rubber was constructed using Materials Studio. A stable silicone rubber molecular structure was obtained through crosslinking, geometry optimization, and ensemble relaxation. Subsequently, a reactive molecular dynamics simulation system under coupled temperature–humidity–electric field conditions was established using LAMMPS and the ReaxFF reactive force field. Different temperature gradients, electric field intensities, and aging–recovery stages were designed to investigate the degradation behavior of silicone rubber. The evolution of the maximum carbon content, maximum silicon content, carbon-containing decomposition products, and typical small-molecule products, including H2, H2O, CH4, C2H2, C2H4, and C2H6, was statistically analyzed. In addition, atomic trajectory tracking was performed to clarify the processes of methyl group detachment, Si-O bond cleavage, water molecule participation, and molecular chain reconstruction. The results show that high temperature mainly promotes methyl group detachment from side chains and fracture of the siloxane main chain, while a strong electric field accelerates the decomposition process and induces the transformation of long siloxane chains into shorter chains. Water molecules can react with broken siloxane chains to form hydroxyl-containing structures, making the structural degradation partially irreversible. The degradation process of silicone rubber under coupled temperature–humidity–electric field stress can be summarized as side-chain detachment, main-chain scission, water-assisted reactions, free-radical recombination, and local molecular aggregation. This study provides a molecular-level theoretical basis for aging mechanism analysis, condition assessment, and lifetime prediction of composite external insulating materials. Full article
(This article belongs to the Section Polymer Analysis and Characterization)
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18 pages, 6858 KB  
Article
Three-Dimensional Scanning-Based Discrete Element Modeling, Contact Parameter Calibration, and Validation of Sugar Beet Roots
by Wang Qian, Xingbang Guo, Shenying Wang, Shengshi Xie, Yang Hao and Xin Guo
Appl. Sci. 2026, 16(12), 6194; https://doi.org/10.3390/app16126194 (registering DOI) - 18 Jun 2026
Viewed by 117
Abstract
To enhance the fidelity of the DEM representation of sugar beet roots, the root geometry was reconstructed from three-dimensional scanning data and represented in EDEM2024 as a multi-sphere clump. The Hertz–Mindlin (no slip) model was used to describe particle contact behavior. The root–Q235 [...] Read more.
To enhance the fidelity of the DEM representation of sugar beet roots, the root geometry was reconstructed from three-dimensional scanning data and represented in EDEM2024 as a multi-sphere clump. The Hertz–Mindlin (no slip) model was used to describe particle contact behavior. The root–Q235 steel contact parameters were determined by drop-rebound, inclined-plane sliding, and inclined-plane rolling experiments. For root–root interactions, the parameters were further refined through cylinder-lifting repose-angle simulations combined with the steepest-ascent method and a three-factor quadratic orthogonal rotatable regression scheme. The optimized inter-root restitution coefficient, static friction coefficient, and rolling friction coefficient were 0.534, 0.728, and 0.080, respectively. With this parameter set, the deviation between the simulated and measured angles of repose was 0.86%, and the error obtained in the independent validation test was 1.5%. These results demonstrate that the proposed DEM model and calibrated parameter set can accurately represent the motion and contact behavior of sugar beet roots. Full article
(This article belongs to the Section Agricultural Science and Technology)
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24 pages, 50831 KB  
Article
Conservation Beyond Geometry: Hybrid 3D Documentation and Digital Restoration of a Byzantine Leather Bag from Rhodes
by Eleftheria Iakovaki, Markos Konstantakis, Georgios Koutsouflakis, Ekaterini Malea and Dimitrios Makris
Heritage 2026, 9(6), 238; https://doi.org/10.3390/heritage9060238 - 18 Jun 2026
Viewed by 106
Abstract
The documentation and reconstruction of fragile underwater organic artifacts remain among the most challenging tasks in digital heritage practice. This study presents a conservation-first, contact-minimizing protocol applied to a rare Byzantine leather bag recovered from the commercial port of Rhodes, Greece. Due to [...] Read more.
The documentation and reconstruction of fragile underwater organic artifacts remain among the most challenging tasks in digital heritage practice. This study presents a conservation-first, contact-minimizing protocol applied to a rare Byzantine leather bag recovered from the commercial port of Rhodes, Greece. Due to its incomplete preservation and structural instability, exclusively non-invasive methodologies were employed. High-resolution close-range photogrammetry and structured-light 3D scanning were integrated to capture both micro-topographic detail and metrically stable geometry. Quantitative deviation analysis (nearest-neighbor cloud-to-mesh distances) indicated that most geometric differences remain below 0.5 mm. The resulting models were processed through controlled mesh optimization, UV remapping, and conservation-oriented digital completion workflows. In addition, radiance field visualization techniques such as Gaussian Splatting were explored as complementary visualization approaches for incomplete geometries. These methods were evaluated primarily in terms of visual continuity and interpretative support rather than as reconstruction tools. The study demonstrates that the integration of photogrammetry, structured-light scanning, and Gaussian Splatting can significantly enhance the documentation and visualization of fragile underwater organic heritage. At the same time, it highlights the necessity of methodological transparency and ethical framing when incorporating probabilistic reconstructions into conservation workflows. Full article
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32 pages, 27890 KB  
Article
Serverless 3D Reconstruction and Spatial Anchoring for Cloud-Native Infrastructure Inspection
by Youssef Arhrib, Flor Alvarez-Taboada and Hakim Boulaassal
Buildings 2026, 16(12), 2433; https://doi.org/10.3390/buildings16122433 - 18 Jun 2026
Viewed by 262
Abstract
While infrastructure asset management increasingly relies on high-resolution drone imagery, existing workflows suffer from fragmented information management and dependence on costly local processing infrastructure. This paper addresses these limitations by using a cloud-native spatial intelligence hub that converts raw inspection imagery into an [...] Read more.
While infrastructure asset management increasingly relies on high-resolution drone imagery, existing workflows suffer from fragmented information management and dependence on costly local processing infrastructure. This paper addresses these limitations by using a cloud-native spatial intelligence hub that converts raw inspection imagery into an interactive and queryable three-dimensional information layer. The system integrates a timeout-resilient orchestration layer for photogrammetry pipelines, a multi-user three-dimensional environment for collaborative review, and a PostGIS-backed spatial database that stores defects as georeferenced anchors. We further introduce a spatial anchoring workflow mapping three-dimensional interactions to world coordinates, retrieving context-relevant images via frustum-based visibility scoring. Evaluated on real inspection datasets, the serverless architecture achieved end-to-end reconstruction in under one hour with sub-25 ms query latency. Results indicate that acquisition geometry, particularly oblique convergent viewpoints, is a stronger predictor of reconstruction complexity than image count. This work establishes a reproducible reference architecture, enabling a transition from file-centric documentation to traceable, spatially indexed evidence management for infrastructure Digital Twins. Full article
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25 pages, 8924 KB  
Article
3D Localization of Heat Sources Using LiDAR–Thermal Data Fusion and Multisensor Calibration
by Rafał Gasz, Mateusz Pluskota and Krzysztof Schwierz
Sensors 2026, 26(12), 3876; https://doi.org/10.3390/s26123876 - 18 Jun 2026
Viewed by 259
Abstract
Integration of LiDAR and thermal sensing has become increasingly important in robotics, infrastructure diagnostics, environmental monitoring, and autonomous perception systems. LiDAR sensors provide accurate three-dimensional geometric information but do not directly capture thermal properties of observed objects, whereas thermal cameras provide temperature distributions [...] Read more.
Integration of LiDAR and thermal sensing has become increasingly important in robotics, infrastructure diagnostics, environmental monitoring, and autonomous perception systems. LiDAR sensors provide accurate three-dimensional geometric information but do not directly capture thermal properties of observed objects, whereas thermal cameras provide temperature distributions without explicit spatial structure. Fusion of both sensing modalities enables thermally augmented 3D scene reconstruction and spatial localization of temperature anomalies. This paper presents a practical LiDAR–thermal fusion framework for three-dimensional localization of heat sources using an Ouster OS1 LiDAR sensor and a FLIR A70 thermal camera. The proposed framework includes intrinsic thermal-camera calibration, extrinsic LiDAR–thermal calibration, multimodal data synchronization, projection of LiDAR points onto the thermal image plane, and assignment of temperature values to spatial points. Additionally, a dedicated thermally distinguishable calibration target is proposed to enable reliable multimodal feature extraction under low-contrast LWIR imaging conditions. The developed framework was experimentally validated using real radiometric thermal data and LiDAR point clouds acquired under laboratory conditions. Quantitative evaluation demonstrated reprojection errors below 1 pixel and a mean hottest-point localisation error of approximately 4.1 cm at a distance of 12.3 m. The results confirm that accurate spatial localisation of thermal anomalies can be achieved using a geometry-based multimodal fusion approach without relying on computationally expensive learning-based methods. The proposed framework emphasises practical deployment, deterministic calibration, and applicability in scenarios where limited training data or constrained computational resources make learning-based approaches difficult to apply. The proposed system may be applied to building energy diagnostics, industrial inspection, technical infrastructure monitoring, and robotic perception systems that require reliable spatial localisation of heat sources under real measurement conditions. Full article
(This article belongs to the Collection 3D Imaging and Sensing System)
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17 pages, 6801 KB  
Article
Accelerating Buckling Load Factor Prediction in Timber Frame Walls Using an Encoder–Decoder Surrogate Model
by Jannik Sobisch, Julian Ziegler, Cristoph Dijoux, Felix Schmidt-Kleespies, Alexander Stahr and Mirco Fuchs
Buildings 2026, 16(12), 2424; https://doi.org/10.3390/buildings16122424 - 18 Jun 2026
Viewed by 264
Abstract
In structural engineering, the iterative optimisation of complex timber wall components is fundamentally limited by the prohibitive computational costs of non-linear Finite Element Analysis (FEA). To overcome this bottleneck, this study introduces a highly efficient machine learning-based surrogate model utilising a convolutional encoder–decoder [...] Read more.
In structural engineering, the iterative optimisation of complex timber wall components is fundamentally limited by the prohibitive computational costs of non-linear Finite Element Analysis (FEA). To overcome this bottleneck, this study introduces a highly efficient machine learning-based surrogate model utilising a convolutional encoder–decoder architecture to predict the global buckling load factor (BLF) directly from structural topology. We evaluate three distinct modeling strategies: a Direct prediction model, a Sequential model, and a multitask Dual-Loss model designed to simultaneously predict the BLF and reconstruct spatial tensile stress fields. Experimental results demonstrate that both the Direct and Dual-Loss approaches achieve near-perfect predictive accuracy on in-distribution data, yielding a coefficient of determination (R2) of approximately 0.996. Crucially, these surrogates accelerate inference times by a factor of roughly 12,800 compared to traditional iterative solvers, reducing evaluation times from hours to mere seconds. Furthermore, the models exhibit exceptional robustness and extrapolative capability under rigorous out-of-distribution testing. The models maintain high predictive fidelity when subjected to cross-dataset distributional shifts (R2 0.94) and when evaluating intentionally low-performing, highly vulnerable configurations (R20.967). Extensive validation on structurally disjoint, hold-out wall geometries confirms the models’ ability to generalise to entirely unseen topologies without introducing systematic bias (R2>0.95). By successfully internalising the underlying physical principles of load redistribution, this surrogate framework provides a reliable, computationally inexpensive foundation for enabling real-time, autonomous generative design and structural optimisation. Full article
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33 pages, 1587 KB  
Article
Optimized M-Hermite Interpolation for Geometrically and Physically Consistent Airfoil Reconstruction
by Bihter Das, Gülden Altay Suroğlu and Mehmet Bektas
Mathematics 2026, 14(12), 2180; https://doi.org/10.3390/math14122180 - 17 Jun 2026
Viewed by 111
Abstract
Accurate airfoil reconstruction is crucial for aerodynamic analysis, geometric modeling, and computational design applications. This study proposes an optimized M-Hermite interpolation framework for high-accuracy airfoil reconstruction and geometric preservation. Unlike classical Hermite interpolation, the proposed framework integrates a truncated M-derivative formulation through M-inspired [...] Read more.
Accurate airfoil reconstruction is crucial for aerodynamic analysis, geometric modeling, and computational design applications. This study proposes an optimized M-Hermite interpolation framework for high-accuracy airfoil reconstruction and geometric preservation. Unlike classical Hermite interpolation, the proposed framework integrates a truncated M-derivative formulation through M-inspired parameter-dependent scaling into the interpolation structure, enabling adaptive local geometric control via fractional parameters α and β. Additionally, a tangential scaling coefficient is incorporated to improve curvature adaptation and reconstruction stability in critical geometric regions. The proposed framework is evaluated using 11 reference airfoil geometries and compared with widely used interpolation methods, including Cubic Spline, B-Spline, Bézier, Catmull-Rom, Classical Hermite, and unoptimized M-Hermite interpolation. Reconstruction performance was assessed using both global and local geometric validation metrics, including RMSE, MAE, maximum error, Hausdorff distance, leading-edge RMSE, trailing-edge RMSE, thickness retention error, and curvature retention error. Experimental results demonstrated that the optimized M-Hermite framework achieved the best overall reconstruction performance and geometric consistency across the evaluated airfoil families. The proposed framework improved reconstruction accuracy, particularly in high-curvature leading-edge regions, while preserving geometrically relevant shape descriptors known to influence aerodynamic behavior, including thickness distribution, camber-line consistency, and curvature structure. Optimization analyses further revealed that reconstruction performance is strongly dependent on geometry-adaptive parameter configurations, particularly the β parameter, which governs local geometric behavior. These findings demonstrate that the proposed optimized M-Hermite framework provides an adaptive and computationally efficient interpolation strategy for accurate airfoil reconstruction and geometric shape preservation applications. Full article
(This article belongs to the Special Issue Advances in Fractional Calculus for Modeling and Applications)
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34 pages, 23099 KB  
Article
Integrated Borehole Interpretation and BIM-Based Three-Dimensional Geological Modeling for Gas Control in Underground Coal Mining
by Yuantian Sun, Md Habibullah, Arifuggaman Arif, Shang Wang, Md. Sadickuzzaman and Feiyu Zhang
Appl. Sci. 2026, 16(12), 6142; https://doi.org/10.3390/app16126142 - 17 Jun 2026
Viewed by 247
Abstract
Accurate characterization of underground geological conditions is essential for gas control, geological hazard assessment, and safe coal mining operations. However, conventional geological interpretation methods often suffer from limited spatial accuracy due to borehole deviation, sparse geological control, and insufficient integration of multi-source borehole [...] Read more.
Accurate characterization of underground geological conditions is essential for gas control, geological hazard assessment, and safe coal mining operations. However, conventional geological interpretation methods often suffer from limited spatial accuracy due to borehole deviation, sparse geological control, and insufficient integration of multi-source borehole data. To address these limitations, this study proposes an integrated geological characterization framework combining resistivity-based image logging, borehole trajectory correction, and BIM-based three-dimensional geological modeling using 135 gas extraction boreholes from the Coal Seam 15-21050 working face of Pingdingshan No. 8 Coal Mine, China. Multi-parameter logging data, including natural gamma, apparent resistivity, natural potential, and borehole image observations, were used to identify coal seam lithology, stratigraphic interfaces, and structural characteristics. Borehole trajectory analysis revealed systematic deviation patterns controlled by borehole inclination, lithological heterogeneity, and drilling conditions, highlighting the necessity of trajectory correction for accurate spatial positioning. Trajectory-corrected borehole coordinates were subsequently integrated into a BIM-based three-dimensional geological reconstruction workflow using spatial interpolation methods. The resulting model successfully reproduced coal seam geometry, interburden distribution, and localized concealed structural anomalies. Coal Seam 15 exhibited thicknesses ranging from 2.69 to 3.47 m, while Coal Seam 16–17 ranged from 1.51 to 2.38 m. The proposed workflow improved the reliability of geological interpretation and the accuracy of spatial characterization, providing an effective technical basis for gas drainage optimization, geological hazard assessment, and intelligent underground coal mining. Full article
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20 pages, 564 KB  
Article
A Line-Integral Representation of Gravitational Lensing by Black Holes
by İzzet Sakallı
Universe 2026, 12(6), 180; https://doi.org/10.3390/universe12060180 - 16 Jun 2026
Viewed by 126
Abstract
We present a path-based curvature representation of the gravitational bending of light in black-hole (BH) spacetimes. The bending angle is written as a one-dimensional line integral of the optical Gaussian curvature Kopt along the photon trajectory, weighted by a geometric kernel [...] Read more.
We present a path-based curvature representation of the gravitational bending of light in black-hole (BH) spacetimes. The bending angle is written as a one-dimensional line integral of the optical Gaussian curvature Kopt along the photon trajectory, weighted by a geometric kernel W(r,b). This representation sits within the Gibbons–Werner Gauss–Bonnet (GB) optical-geometry family rather than alongside it: the kernel is fixed by a co-area reduction of the GB surface integral along an undeflected reference path, and the single new computational object is the resulting radial integral together with its cumulative, directly plottable reading of how the deflection builds up along the ray. With the lever-arm choice W=r2b2, the integral reproduces α^=4M/b for every static, asymptotically flat metric (Theorem 1) and evaluates in closed form for Schwarzschild, Reissner–Nordström (RN), and equatorial Kerr. The representation becomes reliable at a large impact parameter; at the small impact parameters relevant to horizon-scale imaging, it is not numerically competitive with the standard expansions, a limitation we quantify. Beyond leading order the kernel must import information from the bent geodesic, after which the scheme reconstructs the known perturbative series; the second-order mismatch in the lever-arm result therefore measures, rather than hides, the deformation of the photon path away from the straight-line reference. Finite source–observer distances enter through the Ono–Ishihara–Asada (OIA) construction, and a winding-sum continuation outlines the route toward the strong-deflection regime, whose closed-form reduction is left to future work. Full article
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19 pages, 7247 KB  
Article
Digital Integration Through Parametric Geometry Governance: A Framework for Design-to-Manufacturing in Prefabricated Timber Construction
by Sasindu Samarawickrama, Tharaka Gunawardena, Priyan Mendis and Ding Wen Bao
Appl. Sci. 2026, 16(12), 6091; https://doi.org/10.3390/app16126091 - 16 Jun 2026
Viewed by 118
Abstract
Prefabricated timber construction relies on coordinated digital processes that integrate architectural design, structural engineering, and manufacturing requirements. However, current industry practices are highly fragmented, with models often reconstructed across different software platforms, and collaboration is mainly focused on exchanging files and document-based approvals. [...] Read more.
Prefabricated timber construction relies on coordinated digital processes that integrate architectural design, structural engineering, and manufacturing requirements. However, current industry practices are highly fragmented, with models often reconstructed across different software platforms, and collaboration is mainly focused on exchanging files and document-based approvals. These issues lead to geometric misalignments, delayed coordination of manufacturing limitations, and inefficient design-to-manufacturing workflows. This study introduces a parametric geometry-based integration framework aimed at enhancing digital continuity throughout the design, engineering, and manufacturing stages of prefabricated timber buildings. The framework offers a rule-based parametric system where geometry is governed by specific relationships and constraints, enabling the development of discipline-specific models from a unified computational source. A model was created using Rhinoceros and Grasshopper to generate a parametric timber module and to test cross-platform compatibility with structural analysis software (Dlubal) and manufacturing detailing software (Cadwork). The results show that parameter-driven geometry can be integrated across platforms, supporting reduced primary geometry re-authoring and improved cross-platform coordination within the proof-of-concept workflow. The framework extends technical validation by shifting parametric modelling from merely a generative design tool to a comprehensive infrastructure that supports industrialised timber workflows. The proposed approach provides a practical solution to enhance design-to-manufacturing integration in prefabricated construction, while maintaining modelling flexibility specific to each discipline. Full article
(This article belongs to the Section Civil Engineering)
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