Search Results (91)

A geodesic or geodetic line on a sphere is called the orthodrome. Research has shown that the orthodrome can be defined in a large number of ways. This article provides an overview of various definitions of the orthodrome. We recall the definitions of the orthodrome according to the greats of geodesy, such as Bessel and Helmert. We derive the equation of the orthodrome in the geographic coordinate system and in the Cartesian spatial coordinate system. A geodesic on a surface is a curve for which the geodetic curvature is zero at every point. Equivalent expressions of this statement are that at every point of this curve, the principal normal vector is collinear with the normal to the surface, i.e., it is a curve whose binormal at every point is perpendicular to the normal to the surface, and that it is a curve whose osculation plane contains the normal to the surface at every point. In this case, the well-known Clairaut equation of the geodesic in geodesy appears naturally. It is found that this equation can be written in several different forms. Although differential equations for geodesics can be found in the literature, they are solved in this article, first, by taking the sphere as a special case of any surface, and then as a special case of a surface of rotation. At the end of this article, we apply calculus of variations to determine the equation of the orthodrome on the sphere, first in the Bessel way, and then by applying the Euler–Lagrange equation. Overall, this paper elaborates a dozen different approaches to orthodrome definitions. Full article

Digital twin models utilising point cloud data have received significant attention for efficient bridge maintenance and performance assessment. There are some studies that show finite element (FE) models from point cloud data. While most of those approaches focus on modelling by solid elements, modelling of some civil structures, such as bridges, requires various uses of beam and shell elements. This study proposes a systematic approach for constructing shell element FE models from point cloud data of thin-walled structural members. The proposed methodology involves k-means clustering for point cloud segmentation into individual plates, principal component analysis for neutral plane estimation, and edge detection based on normal vector variations for geometric structure determination. Validation experiments using point cloud data of a steel corner specimen revealed dimensional errors up to 5 mm and angular errors up to 6°, but static load analysis demonstrated good accuracy with maximum displacement errors within 3.8% and maximum stress errors within 7.7% compared to nominal models. Additionally, the influence of point cloud data quality on FE model geometry and analysis results was evaluated based on geometric accuracy and point cloud density metrics, revealing that significant variations in density within the same surface lead to reduced neutral plane estimation accuracy. Furthermore, toward practical application to actual bridge structures, on-site measurements and quality evaluation of point cloud data from a steel plate girder bridge were conducted. The results showed that thickness errors in the bridge data reached up to 2 mm, while surface deviation RMSE ranged from 3 to 5 mm. This research contributes to establishing practical FE modelling procedures from point cloud data and providing a model validation framework that ensures appropriate abstraction in structural analysis. Full article

When facing geometrically similar environments such as subway tunnels, Scan-Map registration is highly dependent on the correct initial value of the pose, otherwise mismatching is prone to occur, which limits the application of SLAM (Simultaneous Localization and Mapping) in tunnels. We propose a novel coarse-to-fine registration strategy that includes geometric feature extraction and a keyframe-based pose optimization model. The method involves initial feature point set acquisition through point distance calculations, followed by the extraction of line and plane features, and convex hull features based on the normal vector’s change rate. Coarse registration is achieved through rotation and translation using three types of feature sets, with the resulting pose serving as the initial value for fine registration via Point-Plane ICP. The algorithm’s accuracy and efficiency are validated using Innovusion lidar scans of a subway tunnel, achieving a single-frame point cloud registration accuracy of 3 cm within 0.7 s, significantly improving upon traditional registration algorithms. The study concludes that the proposed method effectively enhances SLAM’s applicability in challenging tunnel environments, ensuring high registration accuracy and efficiency. Full article

This paper investigates the performance of a five-phase silicon carbide (SiC)-based current-source converter (CSC) integrated with a Doubly Fed Induction Generator (DFIG) for wind energy applications. The study explores both healthy and faulty operation, focusing on system behavior under transient conditions and various load scenarios in stand-alone mode. A novel five-phase space vector PWM strategy in dual coordinate planes is introduced, which enables stable control during normal and open-phase fault conditions. Experimental results demonstrate improved stator voltage and current quality, particularly in terms of reduced Total Harmonic Distortion (THD), compared to traditional voltage-source converter-based systems. Furthermore, the system maintains operational stability under a single-phase open fault, despite increased oscillations in stator quantities. The results highlight the potential of five-phase CSC-DFIG systems as a robust and efficient alternative for wind power plants, particularly in configurations involving long cable connections and requiring low generator losses. Future work will focus on enhancing fault-tolerant capabilities and expanding control strategies for improved performance under different operating conditions. Full article

LiDAR point clouds of reflective targets often contain significant noise, which severely impacts the feature extraction accuracy and performance of object detection algorithms. These challenges present substantial obstacles to point cloud processing and its applications. In this paper, we propose a Unified Denoising Framework (UDF) aimed at removing noise and restoring the geometry of reflective targets. The proposed method consists of three steps: veiling effect denoising using an improved pass-through filter, range anomalies correction through M-estimator Sample Consensus (MSAC) plane fitting and ray projection, and blooming effect denoising based on an adaptive error ellipse. The parameters of the error ellipse are automatically determined using the divergence angle of the laser beam, blooming factors, and the normal vector along the boundary of the point cloud. The proposed method was validated on a self-constructed traffic sign point cloud dataset. The experimental results showed that the method achieved a mean square error (MSE) of 0.15 cm², a mean city-block distance (MCD) of 0.05 cm, and relative height and width errors of 1.92% and 1.91%, respectively. Compared to five representative algorithms, the proposed method demonstrated superior performance in both denoising accuracy and the restoration of target geometric features. Full article

The thermomechanical effects on aircraft structures in flight are compared between fair weather and a lightning storm based on a model problem, namely, equations of anisothermal unsteady piezoelectromagnetism are solved in the particular case of a parallel-sided slab assuming (i) steady conditions and spatial dependence only on the coordinate orthogonal to the slab; (ii) the displacement vector orthogonal to the slab; (iii) the magnetic field orthogonal to the electric field, with both in the plane parallel to the sides of the slab. The exact analytical solution is obtained in the linear approximation for the displacement vector, electric and magnetic fields and temperature as function of the coordinate normal to the slab, taking into account heating by the Joule effect of Ohmic electric currents and Fourier thermal conduction. These specify the strain and stress tensors, the electric current and the heat flux. The material properties involved include the mass density, dielectric permittivity, magnetic permeability, elastic stiffness tensor, electromagnetic coupling and thermal stress tensors, pyroelectric and pyromagnetic vectors and piezoelectric and piezomagnetic tensors. The analytic results of the theory are simplified assuming (i) isotropic material properties; (ii) a steady state independent of time. The profiles as a function of the coordinate normal to the slab of the electric and magnetic fields, temperature and heat flux and displacement, strain and stress are obtained in these conditions. Full article

The Mw 7.0 Dingri earthquake, which occurred on 7 January 2025, occurred at the southern end of the Xainza-Dinggyê Fault Zone within the South Tibet Rift (STR) system, in the Dengmecuo graben. It is the largest normal-faulting event in the region recorded by modern instruments. Using Sentinel-1A and Lutan SAR data combined with strong-motion records, we derived the coseismic surface deformation and slip distribution. InSAR interferograms and displacement vectors confirm a typical normal-faulting pattern. The slip model, based on an elastic half-space assumption, identifies the Dengmecuo Fault as the source fault, with an average strike of ~187° and a dip of ~55°. The rupture was concentrated within the upper 10 km, with a maximum slip of 4–5 m at ~5 km depth, extending to the surface with ~3 m vertical displacement. Partial rupture (≤2 m) in the southern segment (5–10 km depth) did not reach the surface, likely due to lacustrine deposits or possible post-seismic stress release. The rupture bottom intersects the fault plane of the South Tibet Detachment System (STDS), suggesting a restraining effect on coseismic rupture propagation. Considering stress transfer along the Main Himalayan Thrust (MHT), we propose that the 2025 Dingri earthquake is closely associated with stress transfer following the 2015 Gorkha earthquake in the lower Himalayas. Full article

We describe a method to calibrate angular positioning errors of a rotation stage using a laser tracker (LT), a plane mirror mounted on the stage, and stationary registration nests placed around the stage. Our technique involves determining the direction of the normal vector to the plane of the mirror at each angular step by performing two LT measurements—one directly to a stationary spherically mounted retroreflector (SMR), and another to the same SMR by bouncing the laser off a mirror mounted on the rotation stage. Because the angular range that can be measured from a single LT station is limited by the angle of incidence on the mirror, multiple LT stations are necessary to cover the full 360°, hence the need for stationary registration nests to tie the LT data into a common coordinate frame. We compare this technique against a direct approach involving a rigid bar with two SMRs mounted on the rotation stage so that we can measure the direction of the line joining the SMRs at each angular position using the LT and, therefore, the angle between positions. Through experiments, we demonstrate that our mirror-based approach provides errors on the order of ±0.5″, smaller than the ±1.5″ for the direct approach, when compared against a reference instrument with accuracy better than 0.3″. Through simulations, we estimate the uncertainty in our mirror-based angle measurements to be 0.4″ (k = 2). Placing the LT close to and the SMR away from the rotation stage results in lower uncertainty for our mirror-based angle measurements. Full article

With the growing adoption of Unmanned Aerial Vehicles (UAVs) in industrial and commercial sectors, the limitations of traditional under-actuated multirotors are becoming increasingly evident, particularly in manipulation tasks. Limited control over the thrust vector direction of the propellers, coupled with its interdependence on the vehicle’s roll, pitch, and yaw moments, significantly restricts manipulation capabilities. To address these challenges, this work presents a control framework for multirotor UAVs equipped with thrust-vectoring components, enabling enhanced control over the direction of lateral forces. The framework supports various actuator configurations by integrating fixed vertical propellers with horizontally mounted thrust-vectoring components. It is capable of handling horizontal thruster setups that generate forces in all directions along the x- and y-axes. Alternatively, it accommodates constrained configurations where the vehicle is limited to generating force in a single direction along either the x- or y-axis. The supported UAVs can follow transmitter commands, setpoints, or predefined trajectories, while the flight controller autonomously manages the propellers and thrusters to achieve the desired motion. Moment evaluations were conducted to assess the torsional capabilities of the vehicles by varying the angles of the thrusters during torsional tasks. The results demonstrate comparable torsional magnitudes to previously studied thrust-vectoring UAVs. Simulations with vehicles of varying inertia and dimensions showed that, even with large horizontal thruster offsets, the vehicles followed desired trajectories while maintaining stable horizontal orientation and smaller attitude variations compared to normal flight. Similar performance was observed with positive and negative vertical offsets, demonstrating the framework’s tolerance for thrusters outside the horizontal plane. Full article

The study of the process of laser action on powder materials requires the construction of mathematical models of the interaction of laser radiation with powder particles that take into account the features of energy supply and are applicable in a wide range of beam parameters and properties of the particle material. A model of the interaction of pulsed or pulse-periodic laser radiation with a spherical metal particle is developed. To find the temperature distribution in the particle volume, the non-stationary three-dimensional heat conductivity equation with a source term that takes into account the action of laser radiation is solved. In the plane normal to the direction of propagation of laser radiation, the change in the radiation intensity obeys the Gaussian law. It is possible to take into account changes in the intensity of laser radiation in space due to its absorption by the environment. To accelerate numerical calculations, a computational algorithm is used based on the use of vectorized data structures and parallel implementation of operations on general-purpose graphics accelerators. The features of the software implementation of the method for solving a system of difference equations that arises as a result of finite-volume discretization of the heat conductivity equation with implicit scheme by the iterative method are presented. The model developed describes the heating and melting of a spherical metal particle exposed by multi-pulsed laser radiation. The implementation of the computational algorithm developed is based on the use of vectorized data structures and GPU resources. The model and calculation results are of interest for constructing a two-phase flow model describing the interaction of test particles with laser radiation on the scale of the entire calculation domain. Such a model is implemented using a discrete-trajectory approach to modeling the motion and heat exchange of a dispersed admixture. Full article

Objectives: This study aims to define three-dimensional (3D) parameters for the inclination of the distal radius joint surface. The goal is to develop standardized parameters for fracture reduction through comprehensive 3D evaluations of the joint surfaces. Methods: We analyzed 112 CT scans of unaffected wrists (56 males and 56 females) to construct 3D models of the distal radius. Using 3D coordinates, the normal vectors and angles were calculated based on three reference points on the distal radius joint surface. These normal vector components were then converted into unit vector components A, B, and C for the x, y, and z axes, respectively. Additionally, the angles of these unit vectors were assessed in the xy, yz, and xz planes. The 3D measurements were compared between males and females and against traditional two-dimensional (2D) parameters such as palmar tilt and radial inclination. Results: For males, the unit vector components were as follows: A: −0.14 ± 0.09, B: −0.92 ± 0.02, and C: −0.36 ± 0.07; for females, A: −0.21 ± 0.08, B: −0.90 ± 0.03, and C: −0.36 ± 0.05. Significant differences were found between males and females for the A and B vector components (representing the palmar–dorsal and proximal–distal axes, p < 0.01). The angles of the unit vectors in the xy, yz, and xz planes were 8.9 ± 5.4°/12.9 ± 5.0°, 21.3 ± 4.1°/22.1 ± 3.2°, and 22.2 ± 14.8°/28.8 ± 10.1° for males and females, respectively. There were significant differences between males and females in the angles of the xy and xz planes (sagittal and axial planes, p < 0.01). Strong correlations were observed between the xy-plane vectors and palmar tilt (r = 0.96), as well as between the yz-plane vectors and radial inclination (r = 0.88). Conclusions: This study evaluated the 3D inclination of the distal radius joint surface, revealing significant gender differences. This method, which also allows for the assessment of rotational alignment—difficult with conventional techniques—is expected to be a key 3D parameter in treating distal radius fractures. Full article

To address the complex and space-constrained characteristics of underground coal mine roadways, this study proposes an electromagnetic wave reflection model based on the mirror image method. A U-shaped roadway model was designed and a relay node was established at the center of the roadway to simplify calculations. The point normal vector method was used to calculate the equations and boundary ranges of eight reflection planes. The valid reflection paths were determined by calculating the mirror points, counting the number of reflection lines, and evaluating their validity. The sensitivity of the number of valid reflection lines to the positions of the transmitting and receiving points relative to the corners was determined, and the reflected field strength at the receiving point was calculated. Its sensitivity to variables such as the distance between the relay node and the receiving point, antenna transmitting frequency, relative dielectric constant of the roadway walls, and width of the U-shaped roadway was studied. The simulation results showed that the number of valid reflection lines decreased with increasing distance from the transmitting and receiving points to the corners. The horizontal position of the transmitting point has a higher effect on the number of effective reflection lines than the vertical position, while the transmitting and receiving points are favorable for electromagnetic wave propagation when they are located in the center of the roadway. As the distance between the relay node and the receiving point increases, the reflection field strength attenuation at the receiving point will decrease with a larger roadway width, a smaller relative permittivity of the roadway walls, and a lower transmitting frequency of the antenna. Full article

Gear skiving is a highly productive method for manufacturing gears, especially internal gears. Circular arc internal gears are important parts of Rotary Vector (RV) reducers and harmonic reducers. This study presents the implementation of the gear skiving technique using a cylindrical tool to enhance the precision and efficiency of machining circular arc internal gears. By establishing the mathematical model for skiving a circular arc internal gear based on the conjugation theory of two surfaces, the barrel-shaped conjugate surface was solved by deducing gear meshing equations. A design method is proposed for a cylindrical skiving tool by utilizing the barrel-shaped conjugate surface with an off-center tool position along the axis. The cutting edge of the tool rake face was then obtained through cubic spline interpolation from the conjugate surface. The influence of the tool rake face offsets on the cutting rake angle and clearance angle is also discussed by defining the normal cutting plane of the tool. The correctness of the proposed cylindrical skiving tool was validated through simulation and actual skiving experiments. The experimental results demonstrated that the tooth profile error of the gear fell within ±0.004 mm, thereby satisfying the accuracy requirement for pin wheel housing gears. These research findings can contribute to advancements in novel cylindrical skiving tools. Full article

In response to the issues of slow convergence and the tendency to fall into local optima in traditional iterative closest point (ICP) point cloud registration algorithms, this study presents a fast registration algorithm for laser point clouds based on 3D scale-invariant feature transform (3D-SIFT) feature extraction. First, feature points are preliminarily extracted using a normal vector threshold; then, more high-quality feature points are extracted using the 3D-SIFT algorithm, effectively reducing the number of point cloud registrations. Based on the extracted feature points, a coarse registration of the point cloud is performed using the fast point feature histogram (FPFH) descriptor combined with the sample consensus initial alignment (SAC-IA) algorithm, followed by fine registration using the point-to-plane ICP algorithm with a symmetric target function. The experimental results show that this algorithm significantly improved the registration efficiency. Compared with the traditional SAC−IA+ICP algorithm, the registration accuracy of this algorithm increased by 29.55% in experiments on a public dataset, and the registration time was reduced by 81.01%. In experiments on actual collected data, the registration accuracy increased by 41.72%, and the registration time was reduced by 67.65%. The algorithm presented in this paper maintains a high registration accuracy while greatly reducing the registration speed. Full article

Existing methods for 3D local feature description often struggle to achieve a good balance between distinctiveness, robustness, and computational efficiency. To address this challenge, a novel 3D local feature descriptor named Histograms of Projected Normal Vector Distribution (HPNVD) is proposed. The HPNVD descriptor consists of two main components. First, a local reference frame (LRF) is constructed based on the covariance matrix and neighborhood projection to achieve invariance to rigid transformations. Then, the local surface normals are projected onto three coordinate planes within the LRF, which allows for effective encoding of the local shape information. The projection planes are further divided into multiple regions, and a histogram is computed for each plane to generate the final HPNVD descriptor. Experimental results demonstrate that the proposed HPNVD descriptor outperforms state-of-the-art methods in terms of descriptiveness and robustness, while maintaining compact storage and computational efficiency. Moreover, the HPNVD-based point cloud registration algorithm shows excellent performance, further validating the effectiveness of the descriptor. Full article