Local Coordinate System Research Articles

A proposed method for mathematical quantitative description of fractures from borehole wall images

Fractures from borehole wall images are different from those from surface outcrop in trace pattern, distribution pattern, parameters description and so on. Focus on the geometric parameters of fractures from borehole images, a method for mathematical quantitative description of these fractures is proposed. The fracture from borehole images is described into a point in spatial coordinate system, and this point is defined Fracture Feature Point. The key parameters including dip direction, dip angle and position depth of fractures from borehole wall images are converted into coordinates of fractures feature points. The related calculation equations are deduced in local coordinate system and spatial coordinate system. Furtherly, the space distribution regularities of the fractures based on the distribution characteristics of fracture feature points are summarized. Typical application in multiple boreholes of this description method is studied and an analysis method for any two fractures’ connectivity is established based on Fracture Feature Point. The results of an engineering example research show that the method is effective in fractures connectivity analysis. The mathematical quantitative description method of fractures from borehole wall images will provide new ideas of the research on deep rock mass structure.

Statistical relationship between soot volume fraction, temperature, primary particle diameter and OH radicals along transects normal to the local reaction zone in a turbulent flame

We present a new method to extract experimental data from simultaneous planar images in turbulent sooting flames, to derive transects of key species based on local coordinates that are aligned normal to the instantaneous, fluctuating reaction zone. Such statistics represent a milestone in the assessment of turbulent sooting flames, because they are one-dimensional and based on local coordinates conditioned on the distribution of soot sheets, in contrast to previous statistics, which are typically Eulerian and single point in nature. The local coordinate system was determined from instantaneous images of soot volume fraction (fv) based on a varying threshold and the local reaction zone was identified by further referring OH images. Quantitative experimental data of fv, temperature (T) and primary particle diameter (Dp), together with qualitative OH intensities, were extracted along the direction normal to the local reaction zone from simultaneous images of the four parameters. These results were measured in a pre-vaporized toluene diffusion flame (Reynolds number = 10,000) using advanced laser-based techniques. Statistical data were combined together and used to generate the profiles for these four parameters with high accuracy and level of resolution that is not possible using previous statistics methods based on Eulerian coordinates. These new kind results showed that the spatial relationship between fv, T and OH remains broadly similar anywhere in the flame, while the profiles of Dp significantly shift away from those of the other three parameters with the increase in the height of the flame. The mean values of fv, Dp and T also show a clear relationship as a function of the height, even though the trends of mean fv and Dp along the height are different from that of T, also suggesting a strong relationship exists between soot and temperature in the local reaction zone.

Frequency-domain elastic-wave modeling for polygonal topography using rotated average-derivative difference operators

Modeling of seismic wave propagation in areas with irregular topography is an important topic in the field of seismic exploration. As a popular numerical method for seismic modeling, the finite difference method is nontrivial to consider the irregular free surface. There have been extensive studies on the time-domain finite difference simulations with irregular topography; however, the frequency-domain finite difference simulation considering irregular topography is relatively less studied. The average-derivative approach is an optimal numerical simulation scheme in the frequency domain, which can produce accurate modeling results at a relatively low computational cost. Nevertheless, this approach can only deal with the modeling problems with a flat free surface. To address this issue, we design a new frequency-domain finite difference scheme by introducing the polygonal representation of topography into the average-derivative method. The irregular topography is represented by line segments with various slopes. An extension of the conventional average-derivative difference operator in the local rotated coordinate system is used for formulating the spatial derivatives aligned with the topographic line segments. As a result, new average-derivative difference schemes are obtained for irregular topography. In this way, the average-derivative optimal method is generalized to the model with irregular topography. Numerical examples show the effectiveness of the presented method.

Three-dimensional alignment changes of the shoulder girdle between the supine and standing positions

BackgroundAlthough humans spend most of their day in a standing or sitting position, it is difficult to accurately evaluate the alignment of the shoulder girdle during daily activity, and its alignment changes between positions. The purpose of this study was to evaluate the 3-dimensional alignment of the shoulder girdle in the supine and standing positions by computed tomography (CT) and to assess the alignment changes of the shoulder girdle between these two positions.MethodsCT scans of both shoulders of 100 healthy volunteers were prospectively taken in both supine and standing positions on the same day. The local 3-dimensional coordinate systems of the thorax, clavicle, and scapula were defined from the specific bony landmarks, and 3-dimensional angular rotations and positions of the clavicle and scapula were calculated. Differences in rotations and positions of the clavicle and scapula were evaluated between the supine and standing positions.ResultsCompared with the supine position, the clavicle showed significantly less elevation and greater retraction, and the scapula showed significantly less upward rotation, anterior tilting, and internal rotation in the standing position. Compared with the supine position, the clavicle center was located more inferiorly, posteriorly, and laterally, and the scapula center was located more inferiorly, posteriorly, and medially in the standing position.ConclusionsThe present study showed that angular rotations and positions of the clavicle and scapula change significantly with position due to the effect of gravity.

A Mathematical Model of the Dynamic Interaction of a Locomotive’s Wheelset and Track

The interaction of the wheel and the rail is the physical basis for the movement of rolling stock on railways. In order to reduce the wear rate of wheel sets and rails, it is necessary to create a mathematical model for the interaction of the “wheel-rail” pair, on which one could look at various methods to reduce catastrophic wear. Currently widely used mathematical algorithms with many degrees of freedom of dynamic interaction of a pair of “wheelset rolling stock – railway track” have a number of disadvantages that affect the accuracy of the calculation results. It is necessary to first build the dynamic equations of dynamics in a basic fixed coordinate system, and then introduce a transformation into local coordinate systems. The algorithm proposed by the authors for constructing dynamic equations, taking into account the inclination and elevation of the outer rail over the inner rail, and the speed of the portable movement of the center of mass of the wheelset, allows to avoid all kinds of errors. In this paper, we describe an algorithm for constructing dynamic equations describing the joint motion of a wheel pair and a rail track, as well as an algorithm for solving the dynamic contact problem. The equations of translational and rotational dynamics of a wheel pair of a railway rolling stock (locomotive), the equations of motion of interacting bodies and communications are constructed. Based on the described mathematical algorithms, programs have been developed for calculating the forces of dynamic interaction in the wheel – rail system.

Distributed Rigidity Recovery in Distance-Based Formations Using Configuration Lattice

This article addresses the rigidity recovery problem of a formation controlled over an undirected sensing framework after a link is broken. In the formation control problem, mobile agents are controlled individually such that all interagent distances remain unchanged. The control law used by each agent is designed based on the relative positions of that agent to its neighbors, sensed in its local coordinate system. When the sensing graph is rigid, it has been shown that one can design a distributed control law to guarantee the stability of the formation. However, obtaining sensing measurements is a challenge in the formation control, since these systems are always subjected to sensing constraints, such as line-of-sight requirements and power limitations. This clearly affects the rigidity of the sensing graph, thus affecting the formation. This article proposes an online distributed algorithm based on the lattice of configurations to recover the distance-based controlled formation when a failure in a sensing link causes the network to lose its rigidity. The approach is to recover the rigidity of subframeworks of the formation, i.e., the subframework established by each node and its neighbors within the sensing range, by adding new sensing links locally so as to ensure a rigid formation. This article also proposes a multilayer rigidity recovery technique using a combination of sensing and communication networks, when the lattice of configurations fails due to a lack of neighbors for an agent. An upper bound is established on the delay in this indirect distance-measuring approach, which guarantees the tolerance of the formation against link failures. Simulations on a sample formation support the theoretical results.

Cervical spine intervertebral kinematics estimated from inverse kinematics and compared to dynamic X-ray data

Interpretation of shoulder motion across studies has been complicated due to the use of numerous scapular coordinate systems in the literature. Currently, there are no simple means by which to compare scapular kinematics between coordinate system definitions when data from only one coordinate system is known.How do scapular kinematics vary based on the choice of coordinate system and can average rotation matrices be used to accurately convert kinematics between scapular local coordinate systems?Average rotation matrices derived from anatomic landmarks of 51 cadaver scapulae (29 M/22 F; 59 ± 13 yrs; 26R/25 L; 171 ± 11 cm; 70 ± 19 kg; 23.7 ± 5.5 kg/m2) were generated between three common scapular coordinate systems. Absolute angle of rotation was used to determine if anatomical variability within the cadaver population influenced the matrices. To quantify the predictive capability to convert kinematics between the three coordinate systems, the average rotation matrices were applied to scapulothoracic motion data collected from 19 human subjects (10 M/9 F; 43 ± 17 yrs; 19R; 173 ± 9 cm; 71 ± 16 kg; 23.6 ± 4.5 kg/m2) using biplane fluoroscopy. Root mean squared error (RMSE) was used to compare kinematics from an original coordinate system to the kinematics expressed in each alternative coordinate system.The choice of scapular coordinate system resulted in mean differences in scapulothoracic rotation of up to 23°, with overall different shapes and/or magnitudes of the curves. A single average rotation matrix between any two coordinate systems achieved accurate conversion of scapulothoracic kinematics to within 4° of RMSE of the known solution. The average rotation matrices were independent of sex, side, decomposition sequence, and motion.Scapulothoracic kinematic representations vary in shape and magnitude based solely on the choice of local coordinate system. The results of this study enhance interpretability and reproducibility in expressing scapulothoracic motion data between laboratories by providing a simple means to convert data between common coordinate systems. This is necessitated by the variety of available motion analysis techniques and their respective scapular landmark definitions.

New design modifications of the supporting ring for a large deployable space reflector

Though theoretical and experimental studies of the design of large deployable antenna reflectors have already been carried out for quite a long time, the results obtained in this area of research still attract a lively interest and have good application prospects. In the present paper, two novel design modifications are described for the symmetric (i.e. with circular apertures) radio telescopes. The novelty consists in that improved stiffness and stability have been obtained by combining two conical pantograph systems and thus getting the whole hinged-bar structure consisting of cylindrical and sliding hinges only. Three FE models of the supporting ring structure are constructed and compared with one another using the NASTRAN FEA software. The degrees of freedom of hinges are simulated in local coordinate systems. A static, modal and buckling analysis had been done to investigate, strength and stiffness characteristics.

GEO-LOCATING HISTORICAL SURVEY DATA AND IMAGES – A CASE STUDY FOR THE CANNING RIVER, PERTH, WESTERN AUSTRALIA

Abstract. The aim of this project is to create the required framework to allow the transformation of the Canning River location survey data captured by Dr. J. A. Ludwig Preiss from 1841 into today’s maps and to utilise visualisation techniques to analyse the results. The original survey data includes distances and bearing observations as well as 14 historical maps. Firstly, the old survey data (includes distances and angles measurements) is plotted into a local coordinates system using modern surveying software (MAGNET Office). Then, common points (unchanged locations) are identified by comparison with the plotted and the current paths of the river. A similarity and affine transformation are used to find transformation parameters that allow to geo-locate the plotted river into the current geodetic datum (MGA94). The calculated Root Mean Squared Errors (RMSE) are 21.7 m and 21.1 m obtained by geo-locating the common points using similarity and affine transformation, respectively. For geo-referencing the historical maps, the similarity, projective and Thin Plate Spline (TPS) transformations have been applied. It has been found that one point of interest (referred to as Nairn’s house), which was drawn in one of the historical maps, still exists today (now known as Maddington Homestead). The distances from the actual position of Nairn’s house to its position in the georeferenced maps using similarity, projective and TPS are 11.8 m, 13 m, and 14 m respectively. All the gained information and map details are utilised in creating a dynamic visualisation suitable for comparing the generated map and historical map with modern aerial imaging and DTM data.

Coupled three-dimensional discrete element–finite difference simulation of dynamic compaction

Discrete element method has been widely adopted to simulate processes that are challenging to continuum-based approaches. However, its computational efficiency can be greatly compromised when large number of particles are required to model regions of less interest to researchers. Due to this, the application of DEM to boundary value problems has been limited. This paper introduces a three-dimensional discrete element–finite difference coupling method, in which the discrete–continuum interactions are modeled in local coordinate systems where the force and displacement compatibilities between the coupled subdomains are considered. The method is validated using a model dynamic compaction test on sand. The comparison between the numerical and physical test results shows that the coupling method can effectively simulate the dynamic compaction process. The responses of the DEM model show that dynamic stress propagation (compaction mechanism) and tamper penetration (bearing capacity mechanism) play very different roles in soil deformations. Under impact loading, the soil undergoes a transient weakening process induced by dynamic stress propagation, which makes the soil easier to densify under bearing capacity mechanism. The distribution of tamping energy between the two mechanisms can influence the compaction efficiency, and allocating higher compaction energy to bearing capacity mechanism could improve the efficiency of dynamic compaction.

Deep Learning Based Autonomous Vehicle Super Resolution DOA Estimation for Safety Driving

In this paper, a novel system architecture including a massive multi-input multi-output (MIMO) or a reconfigurable intelligent surface (RIS) and multiple autonomous vehicles is considered in vehicle location systems. The location parameters of autonomous vehicles can be estimated based on the deep unfolding technique, which is a recent advance of deep learning. Traditional vehicle location methods such as the global position system (GPS) can only locate the target vehicles with relatively low accuracy. The super resolution cannot be achieved when two vehicles are too close, which means that the safety incidents exist when autonomous vehicles are deployed in future intelligent transportation systems (ITS). Different from the existing massive MIMO or RIS equipped with a regular array such as uniform rectangular array (URA) and uniform circular array (UCA), we exploit a massive MIMO or a RIS equipped with a conformal array extended from traditional regular array. First, the rotation from the global coordinate system to the local coordinate system is achieved based on geometric algebra. Second, 2D-DOA estimation of autonomous vehicles is modeled as a novel block sparse recovery problem. Third, the deep network architecture SBLNet is implemented to learn the nonlinear characteristic from the DOAs of autonomous vehicles and the data received by massive MIMOs or RISs. The 2D-DOA and polarization parameters can be estimated based on SBLNet with relatively low computational complexity. Simulation results demonstrate that SBLNet performs better than the state-of-the-art methods in terms of estimation accuracy and successful probability. The SBLNet is also suitable for the practical scenario considering fast moving autonomous vehicles, while, the traditional block sparse recovery methods fail in this complex scenario.

New Concept for Studying the Classical and Quantum Three-Body Problem: Fundamental Irreversibility and Time’s Arrow of Dynamical Systems

The article formulates the classical three-body problem in conformal-Euclidean space (Riemannian manifold), and its equivalence to the Newton three-body problem is mathematically rigorously proved. It is shown that a curved space with a local coordinate system allows us to detect new hidden symmetries of the internal motion of a dynamical system, which allows us to reduce the three-body problem to the 6th order system. A new approach makes the system of geodesic equations with respect to the evolution parameter of a dynamical system (internal time) fundamentally irreversible. To describe the motion of three-body system in different random environments, the corresponding stochastic differential equations (SDEs) are obtained. Using these SDEs, Fokker-Planck-type equations are obtained that describe the joint probability distributions of geodesic flows in phase and configuration spaces. The paper also formulates the quantum three-body problem in conformal-Euclidean space. In particular, the corresponding wave equations have been obtained for studying the three-body bound states, as well as for investigating multichannel quantum scattering in the framework of the concept of internal time. This allows us to solve the extremely important quantum-classical correspondence problem for dynamical Poincaré systems.

Efficient object location determination and error analysis based on barycentric coordinates

In this paper, we propose an efficient computational method for converting local coordinates to world coordinates using specially structured coordinate data. The problem in question is the computation of world coordinates of an object throughout a motion, assuming that we only know the changing coordinates of some fixed surrounding reference points in the local coordinate system of the object. The proposed method is based on barycentric coordinates; by taking the aforementioned static positions as the vertices of a polyhedron, we can specify the coordinates of the object in each step with the help of barycentric coordinates. This approach can significantly help us to achieve more accurate results than by using other possible methods. In the paper, we describe the problem and barycentric coordinate-based solution in detail. We then compare the barycentric method with a technique based on transformation matrices, which we also tested for solving our problem. We also present various diagrams that demonstrate the efficiency of our proposed approach in terms of precision and performance.

Reliable interpretation of scapular kinematics depends on coordinate system definition

BackgroundInterpretation of shoulder motion across studies has been complicated due to the use of numerous scapular coordinate systems in the literature. Currently, there are no simple means by which to compare scapular kinematics between coordinate system definitions when data from only one coordinate system is known. Research questionHow do scapular kinematics vary based on the choice of coordinate system and can average rotation matrices be used to accurately convert kinematics between scapular local coordinate systems? MethodsAverage rotation matrices derived from anatomic landmarks of 51 cadaver scapulae (29 M/22 F; 59 ± 13 yrs; 26R/25 L; 171 ± 11 cm; 70 ± 19 kg; 23.7 ± 5.5 kg/m2) were generated between three common scapular coordinate systems. Absolute angle of rotation was used to determine if anatomical variability within the cadaver population influenced the matrices. To quantify the predictive capability to convert kinematics between the three coordinate systems, the average rotation matrices were applied to scapulothoracic motion data collected from 19 human subjects (10 M/9 F; 43 ± 17 yrs; 19R; 173 ± 9 cm; 71 ± 16 kg; 23.6 ± 4.5 kg/m2) using biplane fluoroscopy. Root mean squared error (RMSE) was used to compare kinematics from an original coordinate system to the kinematics expressed in each alternative coordinate system. ResultsThe choice of scapular coordinate system resulted in mean differences in scapulothoracic rotation of up to 23°, with overall different shapes and/or magnitudes of the curves. A single average rotation matrix between any two coordinate systems achieved accurate conversion of scapulothoracic kinematics to within 4° of RMSE of the known solution. The average rotation matrices were independent of sex, side, decomposition sequence, and motion. SignificanceScapulothoracic kinematic representations vary in shape and magnitude based solely on the choice of local coordinate system. The results of this study enhance interpretability and reproducibility in expressing scapulothoracic motion data between laboratories by providing a simple means to convert data between common coordinate systems. This is necessitated by the variety of available motion analysis techniques and their respective scapular landmark definitions.

Определение параметров местной системы координат с нестандартной долготой осевого меридиана. Анализ существующих способов

Processing the results of topographic and geodetic works is performed in local coordinate systems. The parameters of the local coordinate systems were established on the basis of SK-42 or SK-63 systems. At present, it is necessary to set new communication parameters with coordinate systems SK-95 and GSK-2011. In many MCSs, the central meridians do not coincide with the origin, and the coordinates of the starting points were obtained from the catalogs of the preliminary calculation geodetic network. To establish the new communication parameters, it is necessary to determine the longitude of the central meridian MCS in SK-95 and GSK-2011 systems. To find the errors in calculating the longitude of the central meridian, MCS the models were constructed with different positions of the central meridian relative to the origin. The longitude was calculated using well-known and new formulas and methods. Errors in calculating the longitude of the MSC are systematic. An increase in the calculation volume does not exclude the influence of systematic errors, reaching 4ʺ. For some lines, they make 8ʺ.

On Uniquely Registrable Networks

Consider a network with $N$ nodes in $d$ -dimensional Euclidean space, and $M$ subsets of these nodes $P_1,\ldots, P_M$ . Assume that the nodes in a given $P_i$ are observed in a local coordinate system. The registration problem is to compute the coordinates of the $N$ nodes in a global coordinate system, given the information about $P_1,\ldots, P_M$ and the corresponding local coordinates. The network is said to be uniquely registrable if the global coordinates can be computed uniquely (modulo Euclidean transforms). We formulate a necessary and sufficient condition for a network to be uniquely registrable in terms of rigidity of the body graph of the network. A particularly simple characterization of unique registrability is obtained for planar networks. Furthermore, we show that $k$ -vertex-connectivity of the body graph is equivalent to quasi $k$ -connectivity of the bipartite correspondence graph of the network. Along with results from rigidity theory, this helps us resolve a recent conjecture due to Sanyal et al. (R. Sanyal, M. Jaiswal, and K. N. Chaudhury, “On a registration-based approach to sensor network localization,” IEEE Trans. Signal Process. , vol. 65, no. 20, pp. 5357–5367, Oct. 2017.) that quasi three-connectivity of the correspondence graph is both necessary and sufficient for unique registrability in two dimensions. We present counterexamples demonstrating that while quasi $(d+1)$ -connectivity is necessary for unique registrability in any dimension, it fails to be sufficient in three and higher dimensions.

Point cloud semantic scene segmentation based on coordinate convolution

AbstractPoint cloud semantic segmentation, a crucial research area in the 3D computer vision, lies at the core of many vision and robotics applications. Due to the irregular and disordered of the point cloud, however, the application of convolution on point clouds is challenging. In this article, we propose the “coordinate convolution,” which can effectively extract local structural information of the point cloud, to solve the inapplicability of conventional convolution neural network (CNN) structures on the 3D point cloud. The “coordinate convolution” is a projection operation of three planes based on the local coordinate system of each point. Specifically, we project the point cloud on three planes in the local coordinate system with a joint 2D convolution operation to extract its features. Additionally, we leverage a self‐encoding network based on image semantic segmentation U‐Net structure as the overall architecture of the point cloud semantic segmentation algorithm. The results demonstrate that the proposed method exhibited excellent performances for point cloud data sets corresponding to various scenes.

Automated Geolocation in Urban Environments Using a Simple Camera-Equipped Unmanned Aerial Vehicle: A Rapid Mapping Surveying Alternative?

GNSS positioning accuracy can be degraded in areas where the surrounding object geometry and morphology interacts with the GNSS signals. Specifically, urban environments pose challenges to precise GNSS positioning because of signal interference or interruptions. Also, non-GNSS surveying methods, including total stations and laser scanners, involve time consuming practices in the field and costly equipment. The present study proposes the use of an Unmanned Aerial Vehicle (UAV) for autonomous rapid mapping that resolves the problem of localization for the drone itself by acquiring location information of characteristic points on the ground in a local coordinate system using simultaneous localization and mapping (SLAM) and vision algorithms. A common UAV equipped with a camera and at least a single known point, are enough to produce a local map of the scene and to estimate the relative coordinates of pre-defined ground points along with an additional arbitrary point cloud. The resulting point cloud is readily measurable for extracting and interpreting geometric information from the area of interest. Under two novel optimization procedures performing line and plane alignment of the UAV-camera-measured point geometries, a set of experiments determines that the localization of a visual point in distances reaching 15 m from the origin, delivered a level of accuracy under 50 cm. Thus, a simple UAV with an optical sensor and a visual marker, prove quite promising and cost-effective for rapid mapping and point localization in an unknown environment.

An analytical study of long wave propagation around two circular islands

The analytical solution of a linear long wave propagating around two circular islands is derived. Considering the mutual influence of scattered waves from each island, the multiple scattering method is used to define the local coordinate system on each island and describe the scattered waves. Then, the overall wave field at a spatial location is the superposition of the incident wave with the scattered waves from each island. Finally, Graf's addition theorem is adopted to translate the functions in different coordinate systems into the same coordinate system. The unknown parameters contained in the free surface function are obtained by coupling according to the match between the constant-depth and variable-depth boundary conditions of each island. On this basis, the influences of variations in the slopes of the two islands and the distance between them together with the incident wave period and direction on the amplitudes of the surrounding waves are analyzed.

Extended continuum model for dynamic analysis of beam-like truss structures with geometrical nonlinearity

An approach to extend the application of the continuum model to beam-like lattice truss structures with geometrical nonlinearity is presented in this paper. The geometrical nonlinearity within the truss structures is accounted for by dividing it into substructures and introducing a co-rotational coordinate system to decompose the substructure motion into rigid body motion and pure deformations. The linear continuum model of each substructure is derived using the continuum model based on the small deformation hypothesis in the local coordinate system, in which the deformation of the truss structure is still small. Then, the linear mass and stiffness matrices of the continuum elements are converted into the nonlinear equivalent mass and stiffness matrices for the global coordinate system. The equations of motion for the truss structure are established using Lagrange's equations. Three numerical simulation examples are considered and the results show that the proposed model requires fewer degrees of freedom and has better efficiency than the finite element model based on the truss elements while also obtaining the desired accuracy.