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The thin-walled tubular deployable composite boom (DCB) can realize folding and deploying functions, and it has a good application prospect in space field. This paper investigates the folding behaviour of the tubular DCB by analytical modeling. Based on the Archimedes' helix, the geometrical model of the DCB was established. By combining equilibrium equation and energy principle, an analytical model to predicted the folding moment versus rotational displacement of the DCB was presented. The failure indices in the equal-sense and opposite-sense folding processes were calculated utilizing Tsai‐Hill and maximum stress criteria. Analytical results agreed well with experimental and numerical results. At last, the influence of geometric parameters (i.e., radius, central angle and thickness of cross-section) on the folding behaviour of the DCB was further studied using the analytical model. [Display omitted] • An analytical model is presented to predict the folding behaviour of the deployable composite boom (DCB). • Failure indices are calculated using two criteria in equal-sense and opposite-sense folding processes. • The analytical model is validated against experimental and numerical results, showing good prediction accuracy. • Geometric parameters (radius, central angle, and thickness) significantly affect the folding behavior of the DCB. [ABSTRACT FROM AUTHOR]

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]

The ability to glide through an arboreal habitat has been acquired by several mammals, amphibians, snakes, lizards, and even invertebrates. Lizards of the genus Draco possess specialized morphological structures for gliding, including a patagium, throat lappets, and modified hindlimbs. Despite being among the most specialized reptilian gliders, it is currently unknown how Draco is able to maneuver effectively during flight. Here, we present a new computational method for characterizing the role of tail control on Draco glide distance and stability. We first modeled Draco flight dynamics as a function of gravitational, lift, and drag forces. Lift and drag estimates were derived from wind tunnel experiments of 3D printed models based on photos of Draco during gliding. Initial modeling leveraged the known mass and planar surface area of the Draco to estimate lift and drag coefficients. We developed a simplified, 3D simulation for Draco gliding, calculating longitudinal and lateral position and a pitch angle of the lizard with respect to a cartesian coordinate frame. We used PID control to model the lizards' tail adjustment to maintain an angle of attack. Our model suggests an active tail improves both glide distance and stability in Draco. These results provide insight toward the biomechanics of Draco ; however, future in vivo studies are needed to provide a complete picture for gliding mechanics of this genus. Our approach enables the replication and modification of existing gliders to better understand their performance and mechanics. This can be applied to extinct species, but also as a way of exploring the biomimetic potential of different morphological features. [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 traditional diamond cutting, the cutting force is usually large and it will affect tool life and machining quality. Elliptical vibration cutting (EVC) as one of the ultra-precision machining technologies has a lot of advantages, such as reduces cutting force, extend tool life and so on. It’s difficult to predict the transient cutting force of EVC due to its unique elliptical motion trajectory. Study on chip formation will helpfully to predict cutting force. The geometric feature of chip has important effects on cutting force, however, few scholars have studied the chip formation. In order to investigate the time-varying cutting force of EVC, the geometric feature model of chip is established based on analysis of chip formation, and the effects of cutting parameters on the geometric feature of chip are analyzed. To predict transient force quickly and effectively, the geometric feature of chip is introduced into the cutting force model. The calculated results show that the error between the predicted cutting force in this paper and that in the literature is less than 2%, which proves its feasibility. [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]

Fault geometry is a primary control on hanging wall deformation. In order to examine their geometrical relationships, a positive inversion analogue experiment was conducted using a rigid fault surface of listric geometry. The hanging wall deformation observed on a representative vertical section was examined with conventional 2D geometric models, and was restored to its pre-inversion phase with two techniques. These results suggest that the deformation can be best approximated by inclined simple shearing (ISS). The ISS model can determine the inclination of the apparent shear plane and the amount of apparent horizontal shortening, which is equivalent to that calculated with the conventional depth-to-detachment method. This estimated apparent shortening was generally smaller than the actual amount of the experiments, probably due to tectonic compaction. [Copyright &y& Elsevier]

Recently, microfluidic paper‐based analytical devices (μPADs) have outstripped polymeric microfluidic devices in the ease of fabrication and simplicity. Surface tension‐based fluid motion in the paper's porous structure has made the paper a suitable substrate for multiple biological assays by directing fluid into multiple assay zones. The widespread assumption in most works for modeling wicking in a paper is that the paper is a combination of capillaries with the same diameter equal to the effective pore diameter. Although assuming paper as a bundle of capillaries gives a good insight into pressure force that drives the fluid inside the paper, there are some difficulties using the effective pore radius. The effective pore radius is totally different from the average geometrical pore radius which makes it impossible to predict wicking in μPADs based on geometrical parameters. In this article, we introduce different analytical and numerical models to investigate the possibility of determining the permeability of the paper, based on geometrical parameters rather than effective parameters. The lattice Boltzmann method is used for numerical simulations. The permeability of each of the proposed models was compared with the experimental permeability. Results indicated that assuming paper as a combination of capillaries and annuluses leads to accurate results that totally depend on average geometrical values rather than effective values. This paves the way for prediction of the fluid wicking only by considering average geometrical pore and fiber diameters. [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]

Most of the kinematic calibration methods of parallel mechanisms only consider the geometric error of the mechanism, and the calibration effect is poor. To improve the calibration effect, this paper takes the 3-PTT (3-prismatic hook hook) parallel mechanism as the research object and proposes a kinematics calibration method based on the normalized representation model of the geometric error and non-geometric error of the mechanism. First, the degree of freedom of the mechanism is analyzed, its kinematics positive and negative solutions are solved, and its singularity is analyzed. Secondly, a normalized characterization method of mechanism geometric errors and non-geometric errors is proposed, and an error model without redundant parameters is constructed. The end motion error of the machine is measured by laser tracker, and the objective function is constructed. The genetic algorithm is designed to solve the minimum value of the objective function, and the normalized error of the mechanism is identified. By comparing with the recent methods, the better identification performance of the algorithm in this paper is verified. Finally, the kinematics model was corrected according to the identification results. After the calibration was completed, the movement errors of the end of the mechanism along each coordinate axis were reduced by more than 99 %. Compared with other calibration methods, the better calibration performance of the method in this paper is verified. [ABSTRACT FROM AUTHOR]

Abstract: We formalize paper fold (origami) by graph rewriting. Origami construction is abstractly described by a rewriting system , where is the set of abstract origamis and is a binary relation on , that models fold. An abstract origami is a structure , where is a set of faces constituting an origami, and and are binary relations on , each representing adjacency and superposition relations between the faces. We then address representation and transformation of abstract origamis and further reasoning about the construction for computational purposes. We present a labeled hypergraph of origami and define fold as algebraic graph transformation. The algebraic graph-theoretic formalism enables us to reason about origami in two separate domains of discourse, i.e. pure combinatorial domain where symbolic computation plays the main role and geometrical domain . We detail the program language for the algebraic graph rewriting and graph rewriting algorithms for the fold, and show how fold is expressed by a set of graph rewrite rules. [Copyright &y& Elsevier]

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]

Due to the numerous objects with regular structures in indoor environments, identifying and modeling the regular objects in scenes aids indoor robots in sensing unknown environments. Typically, point cloud preprocessing can obtain highly complete object segmentation results in scenes which can be utilized as the objects for geometric analysis and modeling, thus ensuring modeling accuracy and speed. However, due to the lack of a complete object model, it is not possible to recognize and model segmented objects through matching methods. To achieve a greater understanding of scene point clouds, this paper proposes a direct geometric modeling algorithm based on segmentation results, which focuses on extracting regular geometries in the scene, rather than objects with geometric details or combinations of multiple primitives. This paper suggests using simpler geometric models to describe the corresponding point cloud data. By fully utilizing the surface structure information of segmented objects, the paper analyzes the types of faces and their relationships to classify regular geometric objects into two categories: planar and curved. Different types of geometric objects are fitted using random sampling consistency algorithms with type classification results as prior knowledge, and segmented results are modeled through a combination of size information associated with directed bounding boxes. For indoor scenes with occlusion and stacking, utilizing a higher-level semantic expression can effectively simplify the scene, complete scene abstraction and structural modeling, and aid indoor robots' understanding and further operation in unknown environments. [ABSTRACT FROM AUTHOR]

Overhead transmission lines are important lifelines in power systems, and the research and application of their intelligent patrol technology is one of the key technologies for building smart grids. The main reason for the low detection performance of fittings is the wide range of some fittings' scale and large geometric changes. In this paper, we propose a fittings detection method based on multi-scale geometric transformation and attention-masking mechanism. Firstly, we design a multi-view geometric transformation enhancement strategy, which models geometric transformation as a combination of multiple homomorphic images to obtain image features from multiple views. Then, we introduce an efficient multiscale feature fusion method to improve the detection performance of the model for targets with different scales. Finally, we introduce an attention-masking mechanism to reduce the computational burden of model-learning multiscale features, thereby further improving model performance. In this paper, experiments have been conducted on different datasets, and the experimental results show that the proposed method greatly improves the detection accuracy of transmission line fittings. [ABSTRACT FROM AUTHOR]

This letter from the editor introduces Vol. 25(3) of the Nexus Network Journal: Architecture and Mathematics. The research in this issue addresses three interconnected themes, the first of which is the use of projective geometry to model vision or light. The second is about the geometric tiling and construction of surfaces and the final theme, which is also the most extensive, involves the geometric and parametric generation of architectural forms. The twelve research contributions in this issue examine architectural cases from the third century (BCE) to the twentieth century (CE) and building types from commercial and domestic designs to Christian and Islamic religious structures. The issue concludes with a conference report on Bridges Aalto 2022. [ABSTRACT FROM AUTHOR]

Image registration is the basis for the joint interpretation of synthetic aperture radar (SAR) and optical images. However, the significant nonlinear radiation difference (NRD) and the geometric imaging model difference render the registration quite challenging. To solve this problem, both traditional and deep learning methods are used to extract structural information with dense descriptions of the images, but they ignore that structural information of the image pair is coupled and often process images separately. In this paper, a deep learning-based registration method with a co-attention matching module (CAMM) for SAR and optical images is proposed, which integrates structural feature maps of the image pair to extract keypoints of a single image. First, joint feature detection and description are carried out densely in both images, for which the features are robust to radiation and geometric variation. Then, a CAMM is used to integrate both images' structural features and generate the final keypoint feature maps so that the extracted keypoints are more distinctive and repeatable, which is beneficial to global registration. Finally, considering the difference in the imaging mechanism between SAR and optical images, this paper proposes a new sampling strategy that selects positive samples from the ground-truth position's neighborhood and augments negative samples by randomly sampling distractors in the corresponding image, which makes positive samples more accurate and negative samples more abundant. The experimental results show that the proposed method can significantly improve the accuracy of SAR–optical image registration. Compared to the existing conventional and deep learning methods, the proposed method yields a detector with better repeatability and a descriptor with stronger modality-invariant feature representation. [ABSTRACT FROM AUTHOR]

A reasonable geometric transformation model is the key to image registration. When the relative motion direction between the line-scan camera and the object is strictly parallel to the planar object, it is possible to align the image by using the eight-parameter geometric transformation model of the line-scan image. However, it will be invalid when the relative motion direction is arbitrary. Therefore, a new general geometric transformation model of line-scan images is proposed for line-scan image registration in this paper. Considering the different initial poses and motion directions of the line-scan camera, the proposed model is established based on the imaging model of the line-scan camera. In order to acquire line-scan images to verify the proposed model, a line-scan image acquisition system was built. The method based on feature points is used to register the line-scan images. The experimental results show that the proposed geometric transformation model can align the line-scan image collected under arbitrary relative motion direction, not just the parallel case. Besides, the statistical errors of the image feature point coordinates are the best performance after registration. The accuracy of the registration results is better than that of other existing geometric transformation models, which verifies the correctness and generality of the geometric transformation model of the line-scan camera proposed in this paper. [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]

Nowadays the robot manipulation skills are usually learned by human demonstration via trajectory-level learning, which somewhat lacks robustness and generalization. In this paper, we propose a novel contact state level learning method for robot manipulation skill acquisition via human demonstration. The robot-environment contact states are described via environment dynamics modelling and geometric constraints modelling for flexible contact and rigid contact cases, respectively. During human demonstration process, the robot-environment interaction force, the robot position, and velocity data are collected. After that, the environment dynamics and geometric constraints modelling methods are presented to determine the contact state changes during the robot manipulation process. Then the robot manipulator learns the contact state information rather than specific manipulation trajectory. On this basis, the manipulation control law using active exploration method is presented to control the robot during the button pressing process and peg-hole-insertion process, respectively. Finally, the performance of the presented methodology has been verified via experimental studies. Note to Practitioners—Intelligent robots will become the right assistants of human beings in the future, especially in various areas of manipulation occasions. The important premise of realizing this vision is that the robots should have certain ability of manipulation skill learning. A lot of research has been carried out in this field, many of which are focusing on trajectory level manipulation skill learning and reproduction. Other than the trajectory level learning, human beings can learn many other higher levels of manipulation skills, such as the contact state level and semantic level learning, which makes the learning results more robust and general. In this paper, the contact state estimation and learning method via environment dynamics and geometric constraints modelling is presented to learn the robot manipulation skill based on the contact state transition conditions. In this way, the robot needs less data in the skill learning process, and the trajectory level learning is avoided. After learning the contact state level manipulation skill, the lower trajectory level command is autonomously generated. Experiments on button pressing and peg-hole-insertion tasks by KUKA iiwa robot have obtained very good results. Other than the button pressing and peg-hole-insertion tasks, the presented methodology can be applied to many other manipulation tasks, as long as there are contact state changes in the manipulation process. The work of this paper lays a foundation for the robot learning of higher-level manipulation skills. [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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The applications and understanding of Land-use Regulations (LuR) are more communicable when they are linked to the digital representation of the physical world. In order to support issuing a planning permit and move towards the establishment of automated planning permit checks, this paper investigates how LuRs related to a planning permit process can be modelled in 3D called 3D CityLuR. 3D CityLuR serves as a 3D model for representing LuRs' legal extents on a city scale. It is formed based on multiple geometric modelling approaches representing LuRs, which can provide a better cognitive understanding of LuRs and subsequently facilitate LuR automatic checks. To this purpose, according to LuRs' descriptions and characteristics explained in related planning documents, key parameters representing LuRs' extent are identified (e.g. maximum distance in overlooking or maximum allowed height in building height regulations). Accordingly, to automatically model each LuR, a geometric modelling approach (e.g. Boundary Representation (B-Rep), CSG, and extrusion) that best fits with the identified key parameters is proposed. In addition, to combine 3D CityLuR with an integrated BIM-GIS environment, the level of information need in terms of geometries and semantics is specified. Finally, the paper results in a showcase for five LuRs including building height, energy efficiency protection, overshadowing open space, overlooking, and noise impacts regulations. The showcase is a proof of concept for determining how these LuRs can be modelled in 3D and combined with 3D city models based on the selected geometric modelling approaches, identified parameters, and level of information need. [ABSTRACT FROM AUTHOR]