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This study presents strategies for the three fundamental origami operations of grasping, bending, and folding using a novel robot hand and simple motions. These operations are executed using a simple geometric model and without any visual feedback or physical modeling not to restrict the motions. With a few applications in the field of paper manipulation, the electroadhesion technology is employed to perform single hand grasping. Bending is realized by a single hand utilizing the elasticity of origami and friction. Folding is performed by holding an origami with more than two points to fix it at any moment for preciseness. In addition to the design of hardware and motions, operations are demonstrated with general criteria for the crease precision evaluation. [ABSTRACT FROM AUTHOR]

Due to the increase in the frequency and intensity of natural disasters such as heavy rainfall events, the evaluation of the vulnerability of the built environment is becoming increasingly important. Evaluation techniques for each separate building often require detailed geometric models of the supporting structures and time-consuming simulations. One possibility to overcome this problem is to categorize the buildings in a first step and use representative building models for each category. This paper presents a semi-automated approach for categorizing buildings and creating parametric models for the respective building categories. Using these models, the buildings of a category can be collectively examined for their vulnerability to various impacts. First, this paper introduces open geodata that can be used for this process. For the categorization of the buildings, the collected data is further processed to extract additional information such as building age classes or floor plan geometries of the buildings. This results in a data set, with the help of which the buildings can be categorized. However, information about the load-bearing structure is often missing in the different data sources. By including information on typical construction methods that are associated with the previously determined characteristics (age, floor plan geometry, usage), representative models can be created for individual building categories. In this study, the approach was tested in a selected reference area in Berlin. The results indicate that the presented approach is a promising first step towards deriving geometrical models from open geodata that can be used to evaluate the vulnerability of buildings. [ABSTRACT FROM AUTHOR]

In this paper, we present an enhanced version of the two-scale numerical homogenization with application to asphalt concrete modeling in the elastic range. We modified the method of effective material parameters tensor assessment for analysis based on the representative volume element (RVE). As the method was tested on asphalt concrete, we also present two possible approaches to geometrical modeling of its internal microstructure. Selected numerical tests were performed to verify the proposed approach. The main novelties of this study, i.e. higher order approximation at the macroscale and modification of boundary conditions at the level of RVE analysis, improved the efficiency of our methodology by error reduction. Practically, we obtained a reduction of NDOF up to 3 orders of magnitude (comparing to full-scale and homogenized analysis) that was accompanied with the introduced error of order of several percent (measured in L2 norm). [ABSTRACT FROM AUTHOR]

The paper explores enhancing the mechanical behavior of stochastic lattice structures through a semi-controlled design approach. By leveraging the Gibson-Ashby model and predefined geometric routines, the study aims to optimize the mechanical response of lattice structures under compressive stress. Transitioning from stochastic to semi-controlled tessellation using Rhinoceros 7 software enables more predictable deformation behavior. Design parameters such as node formation, strut thickness, and lattice generation patterns are correlated with relative density to regulate stiffness and strength. Experimental validation using Acrylic Styrene Acrylonitrile (ASA) filament demonstrates the effectiveness of the proposed design model. The research emphasizes the importance of understanding internal mechanics by introducing a novel design approach to control geometry and topology arrangement in shaping lattice properties. By introducing a semi-controlled mechanism, the study seeks to improve the reliability and uniformity of mechanical responses in lattice structures. The findings highlighted the benefits of semi-controlled design approaches in achieving tailored mechanical properties. Specimens were compression tested in quasi-static uniaxial loading and showed that structures created with parabolic distribution dimensioned by h p = 0.5 h v originated the most reliable and most vital mechanical response compared with other design models, including typical Voronoi distribution. The improved mechanical response in between proposed design models constantly progressed by about 15% on average consecutively, starting from the parabolic distribution dimensioned by h p = 1.0 h v as the weakest ranked, up to the best one, dimensioned by h p = 0.5 h v , even better than the typical Voronoi distribution. The proposed design model has introduced an entirely novel approach that significantly enhances the product's volume tessellation using routines that guarantee the validity of geometric and topologic entities. Uniaxial compression tests on lattice blocks highlighted the effect of the proposed approach on the mechanical properties of these structures, having shown particularly crucial repeatability and stability. Overall, the paper contributes to advancing the field of lightweight lattice structures through the novel design methodology and material characterization. [ABSTRACT FROM AUTHOR]

Rapid mapping demands efficient methods for a fast extraction of information from satellite data while minimizing data requirements. This paper explores the potential of deep learning for the generation of high-resolution urban elevation data from Synthetic Aperture Radar (SAR) imagery. In order to mitigate occlusion effects caused by the side-looking nature of SAR remote sensing, two SAR images from opposing aspects are leveraged and processed in an end-to-end deep neural network. The presented approach is the first of its kind to implicitly handle the transition from the SAR-specific slant range geometry to a ground-based mapping geometry within the model architecture. Comparative experiments demonstrate the superiority of the dual-aspect fusion over single-image methods in terms of reconstruction quality and geolocation accuracy. Notably, the model exhibits robust performance across diverse acquisition modes and geometries, showcasing its generalizability and suitability for height mapping applications. The study's findings underscore the potential of deep learning-driven SAR techniques in generating high-quality urban surface models efficiently and economically. [ABSTRACT FROM AUTHOR]

This paper complicates the classic security dilemma by considering the notions of ontological security and relational deterrence. It studies how the ontological security dilemma has emerged between the US, China, and Taiwan from the relational perspective and how these spiral chains will further develop in the future. The paper incurs the literature on relational analysis to expound on how different ontological security concerns allude to relational deterrence between the three actors. Taiwan's separatism is more of a threat to China's relational self than to physical security because the separatist does not belong to any already agreed relationship. A geometric model and a few simulations yield three unconventional findings. 1) The less advantaged the US military is over China, the less likely armed unification will occur. 2) The US anti-Chinese tendency is irrelevant in determining the probability of armed unification. 3) What may escalate the spiral are China's anti-Taiwan independence and Taiwan's anti-unification. Case sensitivity indicates the ontological sensibilities of a security dilemma. [ABSTRACT FROM AUTHOR]

This paper introduces the methods of teaching subjects of drawing geometry and 3D modeling used in the High Aviation Academy in Belgrade. These courses are attended in the first year of basic vocational studies of the Department of Aeronautical Mechanical Engineering. The paper will present the objectives of studying subjects, learning outcomes, auditory exercises, as well as learning through the work of students. [ABSTRACT FROM AUTHOR]

Defined digital Facilities' Management (FM) systems will contribute to the realisation of the United Nations' Sustainable Development Goal (SDG) 11. Of the available digital FM systems, Building Information Modelling (BIM) for FM, herein referred to as BIM-FM, is the least developed. Where BIM-FM varies from existing digital FM tools is its advanced 3D visualisation capabilities. A semi-structured literature review is undertaken to assess the current implementation of BIM-FM and identify opportunities to engender its increased adoption. This paper is part of an ongoing piece of research aimed at defining a standard methodology for the application of BIM to historically significant structures, otherwise known as Historic BIM (HBIM). Two existing approaches to BIM-FM, current and developing, are outlined. The potential value BIM-FM can provide according to the literature is discussed but there exists minimal practical evidence to justify these claims. Barriers to its adoption are discussed, with a key underlying barrier found to be a lack of defined user requirements. Consequently, functional, modelling and information requirements established within the literature are identified, and existing attempts at realising the requirements are discussed. Six information categories and two functional requirements are identified. It is theorised that the tendency to utilise simplified geometric models for FM is primarily due to software and practical limitations as opposed to actual end user needs, and it is suggested that this should be investigated further in future work. Attempts at realising BIM-FM user requirements using other advanced technologies, primarily Digital Twins, are investigated and found to be an area of increasing commonality. A new conception of BIM-FM is proposed. [ABSTRACT FROM AUTHOR]

In the current era of urban construction, smart city management, and digital twinning, three-dimensional reconstruction of urban buildings is particularly important. Traditional methods have limitations in reconstructing complex geometric scenes, while new methods such as Nerf focus on using implicit MLP to represent the geometric space of the model, but suffer from slow training and rendering speeds. To address this issue, this paper proposes the use of 3D Gaussian scatter points for three-dimensional reconstruction of urban buildings, improving training speed and reconstruction quality through optimized and accelerated rendering algorithms. This method demonstrates high efficiency and editability, providing a new solution for urban building reconstruction. [ABSTRACT FROM AUTHOR]

Numerous studies have extensively examined the correlation between convex structures and covering rough set models. However, limited attention has been devoted to investigating the relationship between convex structures and rough set models based on relations. In this paper, we aim to integrate convex geometry with rough sets based on relations. Firstly, a novel class of binary relation known as quasi-atomic relation is introduced. We show that each ordinal convex geometry can be reformulated by rough sets based on quasi-atomic relations. Subsequently, we illustrate that any convex geometry can be embedded in an ordinal convex geometry using the rough set approach. Secondly, we develop a new model called the multi-valued rough set model which serves as a valuable tool for investigating convex geometry. A novel representation of any convex geometry is provided by multi-valued rough sets based on the family of quasi-atomic relations. Furthermore, we demonstrate that any convex geometry can be decomposed into a union of ordinal convex geometries. Lastly, We develop a method to determine whether an element belongs to a convex closure of a given set. In addition, we incorporate terminologies from rough set theory into the study of convex geometry by defining concepts such as rough convex sets and degree of convexity which are utilized to analyze the structure of convex geometry. In summary, this paper offers an efficient method to integrate rough sets with convex geometry, which extends the theory and application of rough sets. [ABSTRACT FROM AUTHOR]

Parallel seam welding (PSW) is the most commonly employed encapsulation technology to ensure hermetic sealing and to safeguard sensitive electronic components. However, the PSW process is complicated by the presence of multiphysical phenomena and nonlinear contact problems, making the analysis of the dynamics of the PSW process highly challenging. This paper proposes a multiphysics simulation model based on direct coupling, enabling the concurrent coupling of the electric field, temperature field, and structural field to facilitate the analysis of the thermal and electrical dynamics within the PSW process. First, this paper conducts an in-depth theoretical analysis of thermal and electrical contact interactions at all contact interfaces within the PSW process, taking into account material properties related to temperature. Second, the acquired data are integrated into a geometric model encompassing electrode wheels and ceramic packaging components, facilitating a strongly coupled multiphysics simulation. Finally, the experimental results show that the simulated weld area deviates by approximately 6.5% from the actual values, and the highest component temperature in the model exhibits an approximate 10.8% difference from the actual values, thus validating the accuracy of the model. This directly coupled multiphysics simulation model provides essentially a powerful tool for analyzing the dynamic processes in the PSW process. [ABSTRACT FROM AUTHOR]

This paper presents an efficient algorithm for voxelizing the surface of triangular meshes in a single compute pass. The algorithm uses parallel equidistant lines to traverse the interior of triangles, minimizing costly memory operations and avoiding visiting the same voxels multiple times. By detecting and visiting only the voxels in each line operation, the proposed method achieves better performance results. This method incorporates a gap detection step, targeting areas where scanline‐based voxelization methods might fail. By selectively addressing these gaps, our method attains superior performance outcomes. Additionally, the algorithm is written entirely in a single compute GLSL shader, which makes it highly portable and vendor independent. Its simplicity also makes it easy to adapt and extend for various applications. The paper compares the results of this algorithm with other modern methods, comprehensibly comparing the time performance and resources used. Additionally, we introduce a novel metric, the ‘Slope Consistency Value’, which quantifies triangle orientation's impact on voxelization accuracy for scanline‐based approaches. The results show that the proposed solution outperforms existing, modern ones and obtains better results, especially in densely populated scenes with homogeneous triangle sizes and at higher resolutions. [ABSTRACT FROM AUTHOR]

The deterministic methods are efficient for solving the neutron transport equation (NTE), but suffer from discretization errors. The increasingly complex geometric models make spatial discretization errors the primary source of discretization errors. Considering that spatial discretization errors come from inaccurate geometric shape descriptions and low-accuracy numerical schemes, this paper develops a Discontinuous Galerkin Finite Element Method for the NTE on unstructured polygonal meshes to reduce spatial discretization errors. In this method, the physical modal basis is adopted to handle the polygonal mesh and to achieve high-order accuracy in a uniform and efficient way. The numerical results of various fixed-source and k-eigenvalue benchmarks demonstrate that the method developed in this paper can give accurate solutions on polygonal meshes with high convergence rates. [ABSTRACT FROM AUTHOR]

Six-dimensional object pose estimation is a fundamental problem in the field of computer vision. Recently, category-level object pose estimation methods based on 3D-GC have made significant breakthroughs due to advancements in 3D-GC. However, current methods often fail to capture long-range dependencies, which are crucial for modeling complex and occluded object shapes. Additionally, discerning detailed differences between different objects is essential. Some existing methods utilize self-attention mechanisms or Transformer encoder–decoder structures to address the lack of long-range dependencies, but they only focus on first-order information of features, failing to explore more complex information and neglecting detailed differences between objects. In this paper, we propose SAPENet, which follows the 3D-GC architecture but replaces the 3D-GC in the encoder part with HS-layer to extract features and incorporates statistical attention to compute higher-order statistical information. Additionally, three sub-modules are designed for pose regression, point cloud reconstruction, and bounding box voting. The pose regression module also integrates statistical attention to leverage higher-order statistical information for modeling geometric relationships and aiding regression. Experiments demonstrate that our method achieves outstanding performance, attaining an mAP of 49.5 on the 5°2 cm metric, which is 3.4 higher than the baseline model. Our method achieves state-of-the-art (SOTA) performance on the REAL275 dataset. [ABSTRACT FROM AUTHOR]

Micro-Computed Tomography (µCT) systems are used for examining the internal structures of various objects, such as material samples, manufactured parts, and natural objects. Resolving fine details or performing accurate geometric measurements in the voxel data critically depends on the precise calibration of the µCT systems geometry. This paper presents a calibration method for µCT systems using projections of a calibration phantom, where the coordinates of the phantom are initially unknown. The approach involves detecting and tracking steel ball bearings and adjusting the unknown system geometry parameters using non-linear least squares optimization. Multiple geometric models are tested to verify their suitability for a self-calibration approach. The implementation is tested using a calibration phantom captured at different magnifications. The results demonstrate the system's capability to determine the geometry model parameters with a remaining error on the detector between 0.27 px and 0.18 px. Systematic errors that remain after calibration, as well as changing parameters due to system instabilities, are investigated. The source code of this work is published to enable further research. [ABSTRACT FROM AUTHOR]

An effective formula for the shape-sensitivity analysis of electromagnetic scattering is presented in this paper. First, based on the boundary element method, a new electromagnetic scattering formula is derived by combining the traditional electromagnetic scattering formula with the non-uniform rational B-spline (NURBS) curve, and the geometric model is represented by NURBS, which ensures the geometric accuracy, avoids the heavy grid division in the optimization process, and realizes the fast calculation of high-fidelity numerical solutions. Second, by deducing the sensitivity variables, the electromagnetic scattering equation of shape optimization is obtained, which can provide reliable data references for shape optimization. Finally, the effectiveness and accuracy of the algorithm are demonstrated by an example, and the sensitivity data of some examples are given. [ABSTRACT FROM AUTHOR]

With the development of simulation technology, more and more manufacturers have begun to use the digital twin to design workshops and factories. For these design scenarios under real-time interaction requirements with an excessive amount of model data, if the rendering is stuck, it will reduce the work efficiency. It is a key enabling technology to simplify and switch the geometry models with different resolutions, according to the distance of the viewpoint or the motion state to reduce the computational complexity. Existing model simplification methods emphasize the universality and efficiency under various scenarios, while the simplification performance in the 3D geometry models of industrial mechanisms is poor. This paper proposes a rapid simplification approach to the 3D geometry model of mechanisms in the digital twins-driven manufacturing system design context. A novel Vertex Saliency-oriented Classified Edge Collapse (VS-CEC) algorithm is proposed to simplify the shape feature of the 3D geometry model of mechanisms. It especially emphasizes solving the sharp shape preservation issues in the mechanical design scenario rather than a universal things design scenario. A vertex saliency factor is defined and integrated with the region boundary information obtained from the processing of detailed features to ensure visual fidelity as well as shape preservation such as sharp edges. Experiments show that this approach reduces the data model complexity more reasonably to speed up the rendering. It ensures that the digital twin model interacts quickly with the physical manufacturing system, and thus realizes the low-latency visual effect of cyber-physical synchronization. [ABSTRACT FROM AUTHOR]

Semantic segmentation of point clouds, aiming to assign each point a semantic category, is critical to 3D scene understanding. Although significant advances in recent years, most of the existing methods still suffer from either the object-level misclassification or the boundary-level ambiguity. In this paper, we present a robust semantic segmentation network by deeply exploring the geometry of point clouds, dubbed GeoSegNet. Our GeoSegNet consists of a multi-geometry-based encoder and a boundary-guided decoder. In the encoder, we develop a new residual geometry module from multi-geometry perspectives to extract object-level features. In the decoder, we introduce a contrastive boundary learning module to enhance the geometric representation of boundary points. Benefiting from the geometric encoder–decoder modeling, GeoSegNet infers the segmentation of objects effectively while making the intersections (boundaries) of two or more objects clear. GeoSegNet achieves a significant performance with 64.9% mIoU on the challenging S3DIS dataset (Area 5) and 70.2% mIoU on S3DIS sixfold. Experiments show obvious improvements of GeoSegNet over its competitors in terms of the overall segmentation accuracy and object boundary clearness. Code is available at https://github.com/Chen-yuiyui/GeoSegNet. [ABSTRACT FROM AUTHOR]

Pressure ulcers are a frequent issue involving localized damage to the skin and underlying tissues, commonly arising from prolonged hospitalization and immobilization. This paper introduces a mathematical model designed to elucidate the mechanics behind pressure ulcer formation, aiming to predict its occurrence and assist in its prevention. Utilizing differential geometry and elasticity theory, the model represents human skin and simulates its deformation under pressure. Additionally, a system of ordinary differential equations is employed to predict the outcomes of these deformations, estimating the cellular death rate in skin tissues and underlying layers. The model also incorporates changes in blood flow resulting from alterations in skin geometry. This comprehensive approach provides new insights into the optimal bed surfaces required to prevent pressure ulcers and offers a general predictive method to aid healthcare personnel in making informed decisions for at-risk patients. Compared to existing models in the literature, our model delivers a more thorough prediction method that aligns well with current data. It can forecast the time required for an immobilized individual to develop an ulcer in various body parts, considering different initial health conditions and treatment strategies. [ABSTRACT FROM AUTHOR]

This paper explores the problem of automated robot program generation from limited historical data when neither accurate geometric environmental models nor online vision feedback are available. The Program Reuse Framework (PRF) is developed, which uses expert-defined motion classes, a novel data structure introduced in this work, to learn affordances, workspaces, and skills from historical data. Historical data comprise raw robot joint trajectories and descriptions of the robot task being completed. Given new tasks, motion classes are then used again to formulate an optimization problem capable of generating new open-loop, skill-based programs to complete the tasks. To cope with a lack of geometric models, a technique to learn safe workspaces from demonstrations is developed, allowing the risk of new programs to be estimated before execution. A new learnable motion primitive for redundant manipulators is introduced, called a redundancy dynamical movement primitive, which enables new end-effector goals to be reached while mimicking the whole-arm behavior of a demonstration. A mobile manipulator part transportation task is used throughout to illustrate each step of the framework. [ABSTRACT FROM AUTHOR]

The Geometric Algebra Fulcrum Library (GA-FuL) version 1.0 is introduced in this paper as a comprehensive computational library for geometric algebra (GA) and Clifford algebra (CA), in addition to other classical algebras. As a sophisticated software system, GA-FuL is useful for practical applications requiring numerical or symbolic prototyping, optimized code generation, and geometric visualization. A comprehensive overview of the GA-FuL design is provided, including its core design intentions, data-driven programming characteristics, and extensible layered design. The library is capable of representing and manipulating sparse multivectors of any dimension, scalar kind, or metric signature, including conformal and projective geometric algebras. Several practical and illustrative use cases of the library are provided to highlight its potential for mathematical, scientific, and engineering applications. The metaprogramming code optimization capabilities of GA-FuL are found to be unique among other software systems. This allows for the automated production of highly efficient code, based on powerful geometric modeling formulations provided by geometric algebra. [ABSTRACT FROM AUTHOR]

The efficient and accurate calculation of neutron flux distribution is essential for evaluating the safety of nuclear facilities and the surrounding environment. While traditional numerical simulation methods such as the discrete ordinates (SN) method and Monte Carlo method have demonstrated excellent performance in terms of accuracy, their complex solving process incurs significant computational costs. This paper explores a data-driven and efficient method for obtaining neutron flux distribution based on deep learning, specifically targeting shielding problems with constant geometry and varying material cross-sections in practical engineering. The proposed method bypasses the intricate numerical transport calculation process of the discrete ordinates method by constructing a surrogate model that captures the correlation between transport characteristics and neutron flux from data characteristics. Simulations were carried out using Kobayashi-1 and Kobayashi-2 geometric models for shielding problems with constant geometry and varying material cross-sections. A series of validations have proved that the data-driven surrogate model demonstrates high generalization ability and reliability, while reducing the time required to obtain neutron flux distribution to 0.1 s without compromising on calculation accuracy compared to the discrete ordinates method. [ABSTRACT FROM AUTHOR]

In recent years, there has been extensive research and application of unsupervised monocular depth estimation methods for intelligent vehicles. However, a major limitation of most existing approaches is their inability to predict absolute depth values in physical units, as they generally suffer from the scale problem. Furthermore, most research efforts have focused on ground vehicles, neglecting the potential application of these methods to unmanned aerial vehicles (UAVs). To address these gaps, this paper proposes a novel absolute depth estimation method specifically designed for flight scenes using a monocular vision sensor, in which a geometry-based scale recovery algorithm serves as a post-processing stage of relative depth estimation results with scale consistency. By exploiting the feature correspondence between successive images and using the pose data provided by equipped navigation sensors, the scale factor between relative and absolute scales is calculated according to a multi-view geometry model, and then absolute depth maps are generated by pixel-wise multiplication of relative depth maps with the scale factor. As a result, the unsupervised monocular depth estimation technology is extended from relative depth estimation in semi-structured scenes to absolute depth estimation in unstructured scenes. Experiments on the publicly available Mid-Air dataset and customized data demonstrate the effectiveness of our method in different cases and settings, as well as its robustness to navigation sensor noise. The proposed method only requires UAVs to be equipped with monocular camera and common navigation sensors, and the obtained absolute depth information can be directly used for downstream tasks, which is significant for this kind of vehicle that has rarely been explored in previous depth estimation studies. [ABSTRACT FROM AUTHOR]

Tilt-to-length (TTL) coupling noise arises from angular misalignments of interfering beams in optical path length (OPL) measurements and significantly impacts the accuracy of interferometry measurement systems. This paper focuses on geometric TTL coupling in a test mass (TM) interferometer and examines how an imaging system influences TTL noise suppression. First, the analytical expression of the geometric TTL coupling in a TM interferometer with alignment errors is derived and confirmed through numerical simulation. Subsequently, an imaging system is incorporated into the geometric model and the corresponding analytical expressions are obtained under two common conjugate relationships. Nevertheless, the TTL coupling remains beyond the requirement of TM interferometer, as the residual TTL coupled with alignment errors persists even with the imaging system. Therefore, an optimal position of the imaging system capable of eliminating the second-order term of the TTL coupling is determined. Meanwhile, the first-order term can be mitigated through in-orbit calibrations. These findings offer valuable guidance for the design and adjustment of imaging systems in space-borne gravitational wave detection missions, which require high-precision laser interferometry. [ABSTRACT FROM AUTHOR]

Point cloud acquisition systems now enable the capture of geometric models enriched with additional attribute data, providing a deeper semantic understanding of the measured environments. However, visualizing complex spatiotemporal point clouds remains computationally challenging. This paper presents a fusion methodology that aggregates points from different instants into unified clouds with reduced redundancy while preserving time-varying information. The static 3D structure is condensed using a voxel approach, while temporal attributes are propagated across the merged data. The resulting point cloud is optimized and rendered interactively in a virtual reality (VR) application. This platform allows for intuitive exploration, visualization, and analysis of the merged clouds. Users can examine thermographic properties using color maps and study graphical temperature trends. The potential of VR for insightful interrogation of point clouds enriched with multiple properties is highlighted by the system. [ABSTRACT FROM AUTHOR]

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Historical aerial images constitute an invaluable heritage that requires meticulous recovery and preservation. Interest in this task has been shown at the international level, where several congresses have been held to analyse orthophotographs production techniques, as well as the state of the art of preservation and dissemination of historical material. Innovative image orthorectification models, such as Structure for Motion and Multi-View Stereo, derived from classical photogrammetric methods such as collinearity equations, Direct Linear Transformation and Rational Function Model, have shown excellent results in the creation of 3D models from images captured by mobile devices and unmanned aerial vehicles (UAVs). These advances open up a new line of research for its application in historical flights, characterised by unsuitable flight and conservation conditions, with geometries away from the conventional geometric model and the absence of orientation parameters. On the basis of the papers presented at the EuroSDR congresses in 2019 and 2022, and using SfM and MVS algorithmic programmes, research on the processes of orthorectification of historical images has been deepened, particularly in the processing of large volumes of data. The methodology was applied to what is potentially the largest block of data to date, comprising over 4,000 images covering an area of over 40,000 square kilometres corresponding to the A-series flight, carried out by the US Army Map Service between 1945 and 1946. This technical process represents a significant step towards the accurate correction of valuable historical aerial imagery, contributing to architectural study, urban planning, property organisation, and historical heritage conservation. [ABSTRACT FROM AUTHOR]

Existing galvanometer-based laser-scanning systems are challenging to apply in multi-scale 3D reconstruction because of the difficulty in achieving a balance between a high reconstruction accuracy and a wide reconstruction range. This paper presents a novel method that synchronizes laser scanning by switching the field-of-view (FOV) of a camera using multi-galvanometers. Beyond the advanced hardware setup, we establish a comprehensive geometric model of the system by modeling dynamic camera, dynamic laser, and their combined interaction. Furthermore, since existing calibration methods mainly focus on either dynamic lasers or dynamic cameras and have certain limitations, we propose a novel high-precision and flexible calibration method by constructing an error model and minimizing the objective function. The performance of the proposed method was evaluated by scanning standard components. The results show that the proposed 3D reconstruction system achieves an accuracy of 0.3 mm when the measurement range is extended to 1100 mm × 1300 mm × 650 mm. This demonstrates that for meter-scale reconstruction ranges, a sub-millimeter measurement accuracy is achieved, indicating that the proposed method realizes multi-scale 3D reconstruction and simultaneously allows for high-precision and wide-range 3D reconstruction in industrial applications. [ABSTRACT FROM AUTHOR]

This paper surveys the presentation of astronomical knowledge in two encyclopedic writings of Isidore of Seville, Etymologies and On the Nature of Things, as a transformative episode in the history of early medieval astronomy. In the section De Astronomia in Etymologies, Book III, Isidore provides a (re)formulation of the field of astronomy as follows: (1) he narrows and defines its scope under a Christian framework, demarcating it from astrology labelled 'superstitious' from the view of faith; and (2) he applies a characteristic etymological approach instead of mathematical calculations and geometrical models, changing the study of astronomy from an investigative enterprise into a text-based, hermeneutic learning. Sometimes this is at the expense of mathematical knowledge left available to him by earlier Latin authors. In the treatment of the seven planets in On the Nature of Things, Isidore more evidently imposes Christian themes on the basis of an Aristotelian--Ptolemaic cosmology, declaring the authority of scriptural assertions over 'pagan' natural philosophy on the structure of the heavens, and demonstrating the orderliness of the world as divine creation by a schema of concentric spheres. Through the works of Isidore, what took place was not simply the loss and decline of Greek and Hellenistic astronomy, but rather a conscious and methodological transformation of this area of knowledge, which was to become typical for medieval Latin encyclopedias, subsuming late Antique legacies of learning under the newly formed Christian world-picture and social realities. [ABSTRACT FROM AUTHOR]

This paper presents an adaptive slicing method for Hermite non-planar tessellated surfaces models to improve the geometric accuracy of Rapid Prototyping (RP). Based on the bending characteristics of Hermite curved triangles, a slicing method for a complete Hermite surface model, including the grouping, the construction of the topological relationships, and the calculation of the intersection contours, was employed. The adaptive layering method considering the normal vector at the vertexes of the Hermite curved triangles was employed to grain the variable thickness of all layers of the Hermite surface model. The classical Stanford bunny model illustrates the significant improvement in the accuracy of the proposed method compared to the traditional method. [ABSTRACT FROM AUTHOR]

Due to their complex aerodynamics, helicopters may enter different dangerous aerodynamic conditions under certain adverse circumstances. In this paper, we examine one such phenomenon—the Vortex Ring State (VRS). We present a simulation of the formation and evolution of a vortex ring around a helicopter's main rotor. The calculations were carried out by solving Navier–Stokes equations using the Ansys CFX code. The simulations modeled a real helicopter using the rotor wing concept, assuming that only the main rotor blade's geometry was modeled. A sensitivity study assessed the impact of the calculation domain and mesh size on main rotor thrust and required moment parameters. Simulations were conducted to determine the VRS region by observing the transition of the helicopter from a level flight, with the main rotor blades held at a fixed pitch position, to a gradual increase in vertical descent. The VRS region was compared with experimental results obtained from other authors, revealing sufficient coincidences. The main characteristics of the identified region were then described. [ABSTRACT FROM AUTHOR]

This paper introduces the fractional Heston-type (fHt) model as a stochastic system comprising the stock price process modeled by a geometric Brownian motion. In this model, the infinitesimal return volatility is characterized by the square of a singular stochastic equation driven by a fractional Brownian motion with a Hurst parameter H ∈ (0 , 1) . We establish the Malliavin differentiability of the fHt model and derive an expression for the expected payoff function, revealing potential discontinuities. Simulation experiments are conducted to illustrate the dynamics of the stock price process and option prices. [ABSTRACT FROM AUTHOR]

This paper presents an exoskeleton mechanism designed to assist the locomotion of individuals with disabilities. The model is a walking biped mechanism developed within our research team, consisting of two identical kinematic chains driven by a single motor. The mechanism is modeled using SolidWorks for kinematic analysis and 3D printing purposes. Kinematic analysis is performed using Altair Inspire program to validate the functionality of the geometric model. Finally, 3D printing is performed to obtain a prototype of the robotic system, thus benefiting from the advantages of 3D printing technology, especially obtaining the component parts at a lower cost price compared to classical processing technology. [ABSTRACT FROM AUTHOR]

In the territory of the former Yugoslavia, in the post-war period, numerous monumental sculptures, also referred to as "spomeniks" (monuments), were erected at various points, often in natural settings, to commemorate the People's Liberation War. Our focus in this paper is on one of them, the monument to the Kosmaj Partisan Detachment on mountain Kosmaj, near Belgrade. We examine the historical context in which the monument was created, directing the emphasis of the work towards the geometrical analysis of this object. We delve into the geometric elements of the monument, utilizing photogrammetry and descriptive geometry procedures. Through 'reverse engineering' based on the point cloud model and its orthogonal projections, we provide its idealized dimensions and plan. [ABSTRACT FROM AUTHOR]

Cellular thin-shell structures are widely applied in ultralightweight designs due to their high bearing capacity and strength-to-weight ratio. In this paper, a full-scale isogeometric topology optimization (ITO) method based on Kirchhoff-Love shells for designing cellular tshin-shell structures with excellent damage tolerance ability is proposed. This method utilizes high-order continuous nonuniform rational B-splines (NURBS) as basis functions for Kirchhoff-Love shell elements. The geometric and analysis models of thin shells are unified by isogeometric analysis (IGA) to avoid geometric approximation error and improve computational accuracy. The topological configurations of thin-shell structures are described by constructing the effective density field on the controlmesh. Local volume constraints are imposed in the proximity of each control point to obtain bone-like cellular structures. To facilitate numerical implementation, the p-norm function is used to aggregate local volume constraints into an equivalent global constraint. Several numerical examples are provided to demonstrate the effectiveness of the proposed method. After simulation and comparative analysis, the results indicate that the cellular thin-shell structures optimized by the proposed method exhibit great load-carrying behavior and high damage robustness. [ABSTRACT FROM AUTHOR]

The proper scheduling of track maintenance and renewal operations is dependent on the accuracy of predictive maintenance outputs which, in turn, rely on the appropriate modelling of the track geometry degradation process. This paper explores the incidence and representativeness of the alerts generated due to local defects of track geometry and the modelling of their degradation rates between consecutive tamping operations. A software tool was developed and used to process track inspection data collected over 12 years of operation of the main Portuguese line (Lisbon-Porto) on a total of 727 km of single-track lines where speeds vary between 30 and 220 km/h. Linear regressions are found to be suitable to model the degradation rates of local defects of longitudinal levelling, alignment and twist in the vast majority of cases, although 20–30% of the time degradation patterns prove to be non-linear even in the short term. The local defects of alignment degrade more rapidly and trigger 80% of the unplanned maintenance needs. Modelling the evolution of local defects, and not only the standard deviation on sections 200 m long, allows us to anticipate unplanned maintenance and tackle unavailability costs. [ABSTRACT FROM AUTHOR]

Outliers significantly impact the accuracy of geometric model fitting. Previous approaches to handling outliers have involved threshold selection and scale estimation. However, many scale estimators assume that the inlier distribution follows a Gaussian model, which often does not accurately represent cases in geometric model fitting. Outliers, defined as points with large residuals to all true models, exhibit similar characteristics to high values in quantized residual preferences, thus causing outliers to cluster away from inliers in quantized residual preference space. In this paper, we leverage this consensus among outliers in quantized residual preference space by extending energy minimization to combine model error and spatial smoothness for outlier detection. The outlier detection process based on energy minimization follows an alternate sampling and labeling framework. Subsequently, an ordinary energy minimization method is employed to optimize inlier labels, thereby following the alternate sampling and labeling framework. Experimental results demonstrate that the energy minimization-based outlier detection method effectively identifies most outliers in the data. Additionally, the proposed energy minimization-based inlier segmentation accurately segments inliers into different models. Overall, the performance of the proposed method surpasses that of most state-of-the-art methods. [ABSTRACT FROM AUTHOR]

This paper explores a historical innovation created by Henry Muncaster: a stationary steam engine featuring a single-cylinder horizontal design with a crosshead trunk guide. Through the application of engineering graphics techniques, we have elucidated the functioning of this invention by developing a 3D CAD model based on the original drawings published in Model Engineer magazine in 1957. However, the geometric modeling process faced challenges due to missing and erroneous dimensions for several components. Consequently, dimensional, geometric, and movement constraints were applied to ensure the coherence and functionality of the 3D CAD model, alongside conducting an interference analysis. Ultimately, the proper alignment of the cylinder and crosshead was ascertained, which is crucial for maintaining uniform forces and motions within the steam engine. This alignment is pivotal for achieving balanced operation, minimizing vibrations, and enhancing the overall efficiency of the invention. [ABSTRACT FROM AUTHOR]

In this paper, we examine q-Bernstein-Bézier surfaces in Minkowski space- R13 with q as the shape parameter. These surfaces, a generalization of Bézier surfaces, have applications in mathematics, computer-aided geometric design, and computer graphics for the surface formation and modeling. We analyze the timelike and spacelike cases of q-Bernstein-Bézier surfaces using known boundary control points. The mean curvature and Gaussian curvature of these q-Bernstein-Bézier surfaces are computed by finding the respective fundamental coefficients. We also investigate the shape operator dependency for timelike and spacelike q-Bernstein-Bézier surfaces in Minkowski space- R13 , and provide biquadratic and bicubic q-Bernstein-Bézier surfaces as illustrative examples for different values of the shape controlling parameter q. [ABSTRACT FROM AUTHOR]

Patient-specific 3D models of the human mandible are finding increasing utility in medical fields such as oral and maxillofacial surgery, orthodontics, dentistry, and forensic sciences. The efficient creation of personalized 3D bone models poses a key challenge in these applications. Existing solutions often rely on 3D statistical models of human bone, offering advantages in rapid bone geometry adaptation and flexibility by capturing a range of anatomical variations, but also a disadvantage in terms of reduced precision in representing specific shapes. Considering this, the proposed parametric model allows for precise manipulation using morphometric parameters acquired from medical images. This paper highlights the significance of employing the parametric model in the creation of a personalized bone model, exemplified through a case study targeting mandibular prognathism reconstruction. A personalized model is described as 3D point cloud determined through the utilization of series of parametric functions, determined by the application of geometrical morphometrics, morphology properties, and artificial neural networks in the input dataset of human mandible samples. With 95.05% of the personalized model's surface area displaying deviations within −1.00–1.00 mm relative to the input polygonal model, and a maximum deviation of 2.52 mm, this research accentuates the benefits of the parametric approach, particularly in the preoperative planning of mandibular deformity surgeries. [ABSTRACT FROM AUTHOR]

This paper presents an experimental investigation conducted to determine the influence of parameters such as the ambient temperature, pollution level, and substrate material on the formation of dry bands on polluted layers. To investigate these parameters, we applied a simplified insulator geometry, developed in our previous work, to experimentally control the complex process of dry band formation on a polluted surface. The simple geometry of the experimental model enabled the use of Plexiglas, RTV, and glass as construction substrate materials. RTV and glass were used to simulate a composite and ceramic insulator surface, respectively. Moreover, an electrooptic (EO) probe enabled the measurement of the axial E-field evolution at the surface of the dry band during dry band formation. The results indicated that the substrate material, ambient temperature, and pollution level substantially influence dry band formation. The effects of the first two parameters are directly associated with heat transfer phenomena in the substrate material and at the ambient air/substrate interface. The effect of the third parameter is associated with absorption and evaporation of the pollution layer. In addition, the appearance of the dry band can be clearly identified by a rapid increase in both the pollution layer resistance and the axial E-field in the dry band area. The value of the axial E-field is influenced primarily by the width of the dry band and by the pollution layer resistance, which is directly dependent on the humidification duration. Finally, because most of the results obtained herein were in accordance with those in the literature, we conclude that the proposed experimental model may provide an effective and inexpensive testing method for developing new materials and solutions for improving the dielectric performance of insulators used in polluted environments. Similarly, the simple geometry of the experimental model and the ability to easily control the experimental parameters may enable this tool to validate the results of various numerical models in studies of the thermoelectrical behavior of polluted insulators. [ABSTRACT FROM AUTHOR]

• A fully digital methodology for pottery sherd analysis is proposed. • The method consists of two main parts: 3D acquisition and geometric model processing. • 3D acquisition method is based on the structure for motion technologies. • The processing implements elements of archeologists' knowledge to analyze sherds. • The method was applied to 133 Phoenician amphorae sherds excavated at Tell el-Burak. • The results show the potential for objectively analyzing large amounts of sherds. • New morphological features are introduced for fragments classification. Over the last few years, significant interest has been addressed in developing computer-based methods to document and analyze fragments of ceramics sherds in archaeology. This is because traditional manual processes do not allow for an objective, repeatable, and reproducible analysis of the large quantities of material needed to fully understand and explain human practices in various cultural contexts, such as the economy, daily life, and the material expression of religious beliefs. In that context, this paper proposes a fully digital methodology resulting from the constitution of an international research group coming from different scientific backgrounds: archaeologists with specific skills and experience in fast 3D geometry acquisition methods and researchers who developed and published the only available computer-based process for recognizing the geometric and morphological sherds features analyzed by archaeologists. The proposed methodology consists of two main parts: 1. 3D acquisition of sherds with the construction of the discrete 3D manifold model based on the Structure for Motion technologies; 2. recognition, segmentation, and dimensional characterization of morphological and geometrical features based on the codification and algorithmic implementation of the knowledge used by the archeologists in the traditional method. The method was applied to analyze a set of 133 sherds excavated at Tell el-Burak (Lebanon) to obtain, through the analysis of the namely Phoenician carinated-shoulder amphorae, new insights into the economic organization of the Phoenician homeland. The method demonstrated the potential for objectively, repeatedly, and reproducibly analyzing large quantities of sherds. Furthermore, it allowed studying sherds by generating new high-level knowledge from those acquired from 3D models; in particular, this paper introduces new morphological features that help the archaeologist classify fragments from an analysis of the rim's shape. [ABSTRACT FROM AUTHOR]

Thermo-elastic systems have a wide range of applications in various engineering fields. Traditional single-objective topology optimization (TO) design of thermos-elastic structures is difficult to achieve the combined optimum of multiple properties, and the non-periodic TO design of results are complex and difficult to fabricate. This paper introduces a multi-objective TO formulation based on density for designing thermo-elastic structures with periodic constraints, aiming to overcome the aforementioned issues. This paper assesses two competing weighted objective functions, the first function corresponds to structural and thermal compliance, while the second pertains to regional temperature and global stress. To solve the optimization issue, we utilize the p-norm function with a modified coefficient for evaluating the maximum temperature and stress values. Additionally, the adjoint variable method is employed to evaluate the sensitivity of various objectives, while the method of moving asymptotes (MMA) is used to update the design variables. Then the influence of different weight coefficients and subregion numbers regarding thermos-elastic coupled analysis is demonstrated through numerical examples. The results show that the complexity of the subregion features decreases as the number of subregions increases, and that changing both the number of subregions and the weighting coefficients results in changes in the overall structural performance. Finally, the geometric model is reconstructed using the TO results, and the structural performance is validated through the simulation of the reconstructed model. The results indicate that the TO results obtained by the method of this paper have predefined performance. [ABSTRACT FROM AUTHOR]

The evaluation of the structural behaviour of a masonry Venetian church with a pointed barrel vault is presented in this paper through an analysis following the necessary steps of a monument study. With a detailed geometric model and material estimation, the finite-element method is used to investigate the influence of specific structural parts of the structure, like masonry buttresses and wall connections, on the structural behaviour. The operational modal analysis is used to identify the structure dynamically. The comparison of the eigenfrequencies, which are estimated by in situ measurements and finite-element modal analysis, is used to perform a model identification. The response spectrum analysis, the static analysis after the subsistence of some parts following strengthening proposals, and the transient analysis of specific seismic excitations are used for the evaluation of the structural behaviour. The purpose of the work is to highlight the need for an interdisciplinary approach to the study of a monumental complex structure, regardless of its scale. The coexistence of structural elements of different stiffnesses, such as vaults, elongated walls, buttresses, transverse walls with pediment and belfry, as well as the concha, affects the mechanical behaviour and the pathology of the structure, which is difficult to study with simplifying models. From the analysis, it is concluded that subsidence problems, combined with seismic actions, lead to the cracking of the masonry, while the existence of buttresses limits the extension of the damage and contributes to the stabilization of the structure. [ABSTRACT FROM AUTHOR]

This paper addresses the design of beam position monitor (BPM) devices suitable for fourth-generation diffraction-limited X-ray storage rings. Detailed investigations of the electromagnetic (EM) phenomena occurring inside the component under various working conditions are carried out by considering different BPM EM models defined by their geometry and materials. Moving from a theoretical characterization of the common round geometry, rhomboidal structures are studied through a careful numerical analysis relying on advanced computer-aided tools. Several critical elements, such as wakefields, pick-up signal extraction, and trapped and propagating modes, are explored from the simulation point of view and from the experimental one, by deploying a manufactured microwave test bench, which is employed to measure the radio frequency behavior of a BPM prototype built at Elettra Sincrotrone Trieste. The aim of the proposed study is to identify a satisfactory tradeoff between achievable performance and practical realizability for BPM devices operating in last-generation light sources. [ABSTRACT FROM AUTHOR]

This paper presents a 3D ray-tracing model using geometrical optics and the uniform theory of diffraction in radio channel characterizations of macrocellular environments. On the basis of the environmental information obtained from a digitized map, the model is effectively applied. A technique considering multiple reflections and diffractions through the ray path classification is utilized in this model. Ray paths belonging to each ray category are determined using different methods. The proposed model is justified (the prediction accuracy of the model is better than 6.5 dB) with measurement data for the two scenarios and can provide reliable theory as a basis for radio wave propagation prediction and network planning in urban macrocellular environments. [ABSTRACT FROM AUTHOR]

Monitoring joystick operations in power wheelchairs (PWCs) is promising for investigating user-wheelchair interaction and providing quantitative measures to assess the user's driving performance. In this paper, an add-on measurement system, Power Wheelchair Maneuvering Logger (PWhML), is developed to provide an easy-to-implement and cost-effective solution for monitoring the user's joystick operations in PWCs. The proposed system uses two compact inertial measurement units (IMUs), which are respectively attached to the joystick and wheelchair armrest for movement sensing. A coordinate transformation-based method is proposed to estimate the joystick operating angles using the acceleration data measured by the attached IMUs. The accuracy of the proposed method was thoroughly evaluated under different conditions. The evaluation trials in a stationary PWC reported a mean absolute error (MAE) of 0.59° in the forward/backward direction and 0.64° in the leftward/rightward direction, validating the established geometry model for coordinate transformation. The subsequent driving experiments on outdoor test courses demonstrated the effectiveness and robustness of the proposed method in various terrain conditions (MAE of less than 3°). A clustering analysis based on the t-distributed stochastic neighborhood embedding method correctly categorized different driving activities using the joystick operating angles measured by PWhML. These results indicate that integrating the developed PWhML into PWCs can facilitate a quantitative measurement of the user's driving behavior, providing valuable insights to identify careless operation patterns and help PWC users to improve driving performance. [ABSTRACT FROM AUTHOR]

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