Geometric Point Research Articles

МОДЕЛИРОВАНИЕ РАБОЧИХ ПОВЕРХНОСТЕЙ ПРОМЫШЛЕННЫХ ИЗДЕЛИЙ НА ОСНОВЕ МАССИВА ТОЧЕК

The formation of a geometric model of a product according to a real physical sample requires the development of methods for modeling surfaces according to specified conditions. It is advisable to use such methods when modeling complex dynamic surfaces, which include surfaces whose functional purpose is to interact with the environment. When designing dynamic surfaces, it is necessary to ensure the laminar nature of the flow around them. When modeling surfaces based on a wireframe, the properties of surfaces are provided by the properties of its elements - flat and spatial curved lines. From a geometrical point of view, laminar flow can be achieved due to the regular change in curvature and torsion along the lines belonging to the surface. The article has developed a method for forming ruled frameworks of surfaces based on an array of points. From the original array of points, subsets are selected - point rows, on the basis of which linear elements of the surface frame are formed. The wireframe is based on a guideline family and a curved line generator family. Methods for the formation of linear elements of the frame with the provision of regular changes in geometric characteristics along the curve while monitoring the occurrence of singular points are proposed. The specified properties of the framing elements provide the required surface properties. The developed method was tested when modeling functional surfaces that limit the interscapular channel of a turbocharger impeller. Further development of the developed method is aimed at increasing its versatility and adaptability to the requirements of specific applied problems. This problem can be solved by increasing the conditions imposed on the bypass by increasing the number of shaping parameters. Key words: discretely represented curve, tangent, monotonic change of curvature, normal, radius of curvature, center of curvature.

Estimation of a statistical geometric model for the cervical vertebrae of children aged 10–18 years

Child neck injuries in motor vehicle crashes (MVCs) result in high morbidity and mortality rates. Estimating a statistical cervical vertebrae geometric model and quantifying the variations of the size and shape with age are very important for investigating the dynamic response and injury risk to a child's cervical spine, as well as for providing a geometric basis for developing child anthropomorphic test devices (ATDs) and finite element models (FEMs) of different ages. In this study, spatial geometric points were automatically extracted from the cervical vertebrae computed tomography (CT) scans of 30 children aged 10 to 18 years old (YO), and a statistical geometric model was estimated for the cervical vertebrae as a function of age and neck circumference/neck length according to the method of principal component analysis and regression (PCA&R). Based on this statistical model, geometric point sets representing cervical vertebrae geometries at different ages and percentiles were generated and formed to envelope surfaces. Meanwhile, the size changes of the cervical vertebrae with child growth from 10 to 18 YO were quantified. In general, the anteroposterior length (APL), transverse process width (TPW), vertebral body height (VBH), and vertebral body depth (VBD) of the cervical vertebrae increase with age; the VBH and VBD increase faster than the APL and TPW. Compared with other vertebrae, the APL of C7 is larger, and the rate of increase of C1 with age is evidently slower. The TPWs of C1 and C7 are greater than those of C2 to C6. C7 has higher average values for the VBH and VBD than C3 to C6.

GeoGraph

In many applications of graph processing, the input data is often generated from an underlying geometric point data set. However, existing high-performance graph processing frameworks assume that the input data is given as a graph. Therefore, to use these frameworks, the user must write or use external programs based on computational geometry algorithms to convert their point data set to a graph, which requires more programming effort and can also lead to performance degradation. In this paper, we present our ongoing work on the Geo- Graph framework for shared-memory multicore machines, which seamlessly supports routines for parallel geometric graph construction and parallel graph processing within the same environment. GeoGraph supports graph construction based on k-nearest neighbors, Delaunay triangulation, and b-skeleton graphs. It can then pass these generated graphs to over 25 graph algorithms. GeoGraph contains highperformance parallel primitives and algorithms implemented in C++, and includes a Python interface. We present four examples of using GeoGraph, and some experimental results showing good parallel speedups and improvements over the Higra library. We conclude with a vision of future directions for research in bridging graph and geometric data processing.

MELITOPOL SCHOOL OF APPLIED GEOMETRY. HISTORY AND WORK EXPERIENCE

The work examines the history of formation, development and the main scientific works of the Melitopol School of Applied Geometry. The materials give a general characteristic of the main scientific directions of the school: variable discrete geometric modeling (VDGM) and point calculus Balyub-Naidish (BN calculus). The materials cover the list and peculiarities of scientific and organizational measures carried out by scientists of the school. The scientific school of applied geometry was founded by Meer Moiseevich Yuditsky in the 60s of the last century. The active personal, scientific and organizational activities of M. M. Yuditsky, the participation of scientists of the department in conferences and seminars of various levels, the defense of dissertations that took place in subsequent years gave the basis for the formation of a regional scientific center for applied geometry on the basis of the department. In 1977, Vladimir Mikhailovich Naydysh became the head of the school, which was called the Melitopol Scientific School of Applied Geometry. One of the significant results of the work of the school and its head personally is the holding in Melitopol of the annual International Scientific and Practical Conference "Modern Problems of Geometric Modeling" (held since 1994). The main scientific direction of the school is the development of the theory and applied aspects of discrete applied geometry. Since 2007, Andrei Vladimirovich Naydysh, Doctor of Technical Sciences, took over the leadership of the scientific school. Today, the basic institution of higher education for the school is the Bogdan Khmelnitsky Melitopol State Pedagogical University. Materials The modern state of the school, the level of its scientific developments, the personal achievements of the school's specialists give reason to consider the Melitopol School of Applied Geometry as having all the features of a scientific school by type - a school as a research team.

Determination of load distribution in a given medium according to the values of the loads at certain points

Taking into account force, temperature and other loads, the stress and strain state calculations methods of spatial structures involve determining the distribution of the loads in the three-dimensional body of the structure [1, 2].
 In many cases the output data for this distribution can be the values of loadings in separate points of the structure. The problem of load distribution in the body of the structure can be solved by three-dimensional discrete interpolation in four-dimensional space based on the method of finite differences, which has been widely used in solving various engineering problems in different fields. A discrete conception of the load distribution at points in the body or in the environment is also required for solving problems by the finite elements method [3-7].
 From a geometrical point of view, the result of three-dimensional interpolation is a multivariate of the four-dimensional space [8], where the three dimensions are the coordinates of a three-dimensional body point, and the fourth is the loading at this point. Such interpolation provides for setting of the three coordinates of the point and determining the load at that point. The simplest three-dimensional grid in the three-dimensional space is the grid based on a single sided hypercube. The coordinates of the nodes of such a grid correspond to the numbering of nodes along the coordinate axes.
 Discrete interpolation of points by the finite difference method is directly related to the numerical solutions of differential equations with given boundary conditions and also requires the setting of boundary conditions.
 If we consider a three-dimensional grid included into a parallelepiped, the boundary conditions are divided into three types: 1) zero-dimensional (loads at points), where the three edges of the grid converge; 2) one-dimensional (loads at points of lines), where the four edges of the grid converge; 3) two-dimensional (loads at the points of faces), where the five edges of the grid converge. The zero-dimensional conditions are boundary conditions for one-dimensional interpolation of the one-dimensional conditions, which, in turn, are boundary conditions for two-dimensional conditions, and the two-dimensional conditions are boundary conditions for determining the load on the inner points of the grid.
 If a load is specified only at certain points of boundary conditions, then the interpolation problem is divided into three stages: one-dimensional load interpolation onto the line nodes, two-dimensional load interpolation onto the surface nodes and three-dimensional load interpolation onto internal grid nodes.
 The proposed method of discrete three-dimensional interpolation allows, according to the specified values of force, temperature or other loads at individual points of the three-dimensional body, to interpolate such loads on all nodes of a given regular three-dimensional grid with cubic cells.
 As a result of interpolation, a discrete point framework of the multivariate is obtained, which is a geometric model of the distribution of physical characteristics in a given medium according to the values of these characteristics at individual points.

A three-dimensional immersed boundary method based on an algebraic forcing-point-searching scheme for water impact problems

A new three-dimensional immersed boundary method combined with the level set method for the interface capturing is developed to simulate the interaction between the fixed∖moving structure and the two-phase fluid flow. The concept of the forcing point searching scheme developed for the two-dimensional situations in Yan et al. (2018) is extended in the present study to three dimensions, where the determination of intersections between the arbitrary body surface and the Cartesian background grid system is the major issue. This problem can be converted to the prediction of triangle–triangle intersection, which was traditionally solved from the geometrical point of view. Here, an algebraic algorithm is adopted for the triangle–triangle intersection, based on which the forcing points can be determined in the three-dimensional immersed boundary method. This algebraic algorithm is robust for any body geometry and easy for implementation. To demonstrate the accuracy and capability of the developed numerical model, three benchmark testing cases for water impact problems are conducted, including dam break over a fixed obstacle, water entry of a wedge and free decay of a bobber. Extensive comparisons with the experimental data and the numerical results obtained by other immersed boundary methods suggest that the developed immersed boundary method is accurate and effective for both fixed and moving bodies with complex geometries.

Higher nonabelian omni-Lie algebroids

In this paper, the structure of higher nonabelian omni-Lie algebroid is studied. The concept of higher nonabelian omni-Lie algebroids on direct sum bundle DE⊕∧nJE is introduced, and its related properties are given. It is concluded that the Pre-Dirac structures of higher nonabelian omni-Lie algebroid and n-Lie algebroid have a one-to-one correspondence. By analyzing the matched pair of Leibniz algebroids, it is concluded that higher nonabelian omni-Lie algebroid DE⊕∧nJE can be regarded as a matched pair of two Leibniz algebroids DE and ∧nJE. From the geometric point of view, higher nonabelian omni-Lie algebroid can be regarded as Weinstein linearization of higher analogue of Courant algebroid associated to Nambu-Poisson manifolds.

Peacock geodesics in Wasserstein space

Martingale optimal transport has attracted much attention due to its application in pricing and hedging in mathematical finance. The essential notion which makes martingale optimal transport different from optimal transport is peacock. A peacock is a sequence of measures which satisfies convex order property. In this paper we study peacock geodesics in Wasserstain space, and we hope this paper can provide some geometrical points of view to look at martingale optimal transport.

Cell Surface Area to Volume Relationship During Apoptosis and Apoptotic Body Formation.

Apoptosis is a programmed form of cell death culminating in packing cell content and corpse dismantling into membrane sealed vesicles called apoptotic bodies (ABs). Apoptotic bodies are engulfed and disposed by neighboring and immune system cells without eliciting a noxious inflammatory response, thus preventing sterile tissue damage. AB formation requires a total surface area larger than the apparent, initial cell's surface area. Apoptotic volume decrease (AVD) is a two-stage process leading to an isotonic, osmotic reduction in cell water content driven by net K+ and Cl- extrusion. In this article, the role of AVD is presented from a geometric point of view through the process of AB formation. AVD decisively contributes to (i) endowing the cell with the appropriate electrolytic environment for apoptotic execution; (ii) increasing the membrane surface area-to-volume ratio, along with the mobilization of membrane reservoirs (cell rounding, membrane folds and endosomal membranes), so that the cell corpse can be dismantled into ABs; and (iii) reducing plasmalemmal stretch, tension and stiffness, thus facilitating membrane bulging, blebbing and vesicle expansion ultimately leading to separation and release.

Planetary gear transmissions load sharing measurement from tooth root strains: Numerical evaluation of mesh phasing influence

The present work proposes a numerical approach to the problem of the calculation of the load sharing in planetary transmissions by measuring the strains in the root of the sun gear teeth, a rather common experimental procedure. The approach to model the virtual strain gauges is described in detail. This technique is modelled mimicking the experimental measuring procedure. The presented technique is employed in different simulation scenarios including in-phase and sequentially phased transmissions. Moreover, various tangential position errors are included. These configurations cover the most common scenarios in industrial applications. From these scenarios, the results show discrepancies between the real load sharing and the measured data. The nature of these discrepancies is studied in depth from the geometrical point of view.

Grooving of Metals by High-Intensity Focused Ultrasound-Assisted Water-Confined Laser Micromachining

Abstract Laser grooving (i.e., the production of surface grooves through laser machining) has several advantages and many current or potential industrial applications. However, conventional laser grooving in air may often suffer from quality defects such as debris depositions. A new machining process, with the name “ultrasound-assisted water-confined laser micromachining” (UWLM), was previously proposed by the corresponding author. In UWLM, in situ ultrasound is applied during laser machining of a water-immersed workpiece surface region to improve the machining quality and/or efficiency. If the ultrasound is applied using a high-intensity focused ultrasound (HIFU) transducer, the process can be called “HIFU-based UWLM.” Despite previous investigations on UWLM, to the authors' best knowledge, experimental studies on surface grooving using a HIFU-based UWLM process have been rarely reported in any paper. Such a study has been presented in this paper (for the first time in a paper to the authors' best knowledge). In this work, surface grooves are produced through the ablation of a moving workpiece immersed in water by laser pulses fired at a pulse repetition rate of 1 kHz or 3 kHz. Each laser pulse is followed by a focused ultrasound pulse (from a HIFU transducer) that reaches the workpiece surface approximately 30 µs later. The laser spot on the workpiece surface is approximately at the same location as the geometrical focal point of the HIFU transducer. Under the conditions investigated, it has been found that typically the grooves produced by the HIFU-based UWLM process appear much cleaner and have much smaller amounts of debris particles and recast material than those produced by laser ablation in air, and they typically have much larger depths than those by laser ablation in water without ultrasound. Some related fundamental physical mechanisms have been discussed. The study suggests that the HIFU-based UWLM process has a great potential to provide a new surface grooving technology with competitive performance.

ODEs together PDEs and Vector Fields in the SoftAge

At this moment when we can employ software, mathematics education has to be reviewed. In this article, we point out that ODEs should be taught from a geometric and qualitative point of view together with an introduction to PDEs and vector fields. This would increase the skills of the future mathematics user, not only to obtain explicit solutions from a straight command like DSolve, but also in the situations where this command does not help. The geometric interpretation and the concept of direction fields with images generated by software will give us a good understanding of possible system evolutions.

Large scale experimental facility for performance assessment of the vacuum vessel pressure suppression system of ITER

The nuclear fusion reactor ITER (International Thermonuclear Experimental Reactor) foresees a Pressure Suppression System (PSS) in order to manage a Loss of Coolant Accident (LOCA) in the Vacuum Vessel (VV). A LOCA scenario is postulated to occur in the cooling systems of plasma facing components. The Vacuum Vessel Pressure Suppression System (VVPSS) has a key safety function because a large internal pressure in the VV could lead to a breach of the primary confinement barrier.Steam condensation would occur in ITER at sub-atmospheric pressure, differently than the applications in nuclear fission reactors. Steam direct contact condensation (DCC) in sub-atmospheric conditions have never been implemented before, therefore an experimental assessment of the VVPSS is necessary to simulate this phenomenon in ITER's thermal-hydraulic conditions.Under the financial support of ITER Organization, an experimental program was performed at the Department of Civil and Industrial Engineering (DICI) of the University of Pisa in the past 3 years, using a small-scale experimental rig (1/22 scale factor).In order to assess the scale laws elaborated by means of the experimental results obtained in this small scale facility, a Large Scale facility was built at University of Pisa. This facility is almost a full scale mock-up of ITER's VVPSS from the geometric point of view (1/1.09 scale factor) and it is 1/10 scale factor from the steam mass flow rate point of view.This paper illustrates the results of the first test campaign. A 1/10 scale sparger system SPS-A (having a diameter equal to DN125 and 100 holes) was used with a maximum steam mass flow rate of 0.5 kg/s. This experimental configuration represents real operating conditions on the basis of the results of elaborated similitude analysis. The preliminary analysis of the experimental results confirms the agreement in terms of condensation regimes between the two reduced scale (1/22 and 1/10 scale) as foreseen by the elaborated scale laws.

Fuzzy intersection graph: a geometrical approach

The aim of fuzzy intersection graph is twofold: to work with objects with continuum grades of membership and to acknowledge their inter-relationships. Its working elements are fuzzy logic and reasoning with the objective of providing accessible representation of objects and relationships having a blurry backdrop. This article embarked a comprehensive study of fuzzy intersection graph using fuzzy geometry by defining fuzzy graph and fuzzy intersection region with the help of fuzzy points and fuzzy line segments. The main motive behind revamping fuzzy graphs using fuzzy geometry is to represent the linguistic variables and their inter-dependencies as an exact reflection of human thinking. We have interpreted a detailed study on parallel fuzzy lines and intersecting fuzzy lines and deduced a mathematical relation between the measure of parallelness and degree of intersection of fuzzy lines. Fuzzy intersection region, depending on the types of intersecting fuzzy sets, plays an important role. We have defined few of the most important and useful classes of fuzzy intersection graph from fuzzy geometric view point that will be helpful in expressing human thoughts and communication of information as has been demonstrated through an application on supplier–purchaser relationship in any business. The present study on fuzzy interval graph in detail, ensued in obtainment of results that nullified previously obtained results arising the question—are fuzzy interval graphs always strong intersection graphs?

Outer-star and star-outer matrices

To solve certain type of matrix equations and extend the notions of the Drazin-star and star-Drazin matrices, we define two new classes of rectangular matrices called the outer-star and star-outer matrices. We characterize these new matrices by algebraic and geometrical point of view and give properties of projectors determined by them. Various representations of outer-star and star-outer matrices as integral representations and limit representations are derived. We establish relations between outer-star and star-outer matrices with appropriate nonsingular matrices. Possible applications of outer-star and star-outer matrices in solving some systems of linear equations are presented.

An index for quantifying geometric point disorder in geospatial applications

Many techniques have been developed to quantify different conceptualizations of self-interaction and patterns within spatial data. We propose a new metric and related algorithm that describes the geometric spatial disorder of geographic point sets, the “Index of Disorder” (IoD). The IoD algorithm was applied to synthetic and natural datasets and was shown to be able to differentiate between areas of high spatial disorder (randomly placed points) and low spatial disorder (e.g., curvilinear grids, wallpaper groups, and other repeating patterns). Because the IoD is a quantitative metric, it can be used on its own as an aid for identifying areas of unusually high or low spatial disorder or as enrichment for machine learning classification algorithms.

An activity‐based framework for detecting human movement patterns in an urban environment

AbstractThe continuous development of positioning technologies and computing solutions for the integration of large trajectory data sets offers many novel research opportunities. Among various research domains, the extraction of users' movement patterns is an important issue that is yet to be addressed. While many previous studies have analyzed human and animal movements from a predominantly geometrical point of view, additional semantics are still required to provide a better understanding of the patterns that emerge. User activity data provide important information resources to analyze and predict movement patterns in urban environments. This study introduces a computational framework that combines the geometric and activity‐based dimensions of human trajectories. First, the geometrical dimension considers a series of parameters (i.e., turning points, curvature, and self‐intersection) that are extracted by a convex‐hull algorithm and characterizes a given trajectory. Second, user activity transitions are modeled and then denote some recurrent patterns. Finally, geometric and activity patterns are integrated into a unified trajectory modeling framework. This favors the analysis of human movement patterns by taking into account the geometric and activity dimensions. The entire approach and framework have experimented with the LifeMap Korean trajectory data set commonly considered as a reference benchmark. The experiments showed how the integration of geometrical and activity‐based dimensions could provide a better understanding of the patterns and trends that emerge from a large trajectory data set.

Adversarial Margin Maximization Networks.

The tremendous recent success of deep neural networks (DNNs) has sparked a surge of interest in understanding their predictive ability. Unlike the human visual system which is able to generalize robustly and learn with little supervision, DNNs normally require a massive amount of data to learn new concepts. In addition, research works also show that DNNs are vulnerable to adversarial examples-maliciously generated images which seem perceptually similar to the natural ones but are actually formed to fool learning models, which means the models have problem generalizing to unseen data with certain type of distortions. In this paper, we analyze the generalization ability of DNNs comprehensively and attempt to improve it from a geometric point of view. We propose adversarial margin maximization (AMM), a learning-based regularization which exploits an adversarial perturbation as a proxy. It encourages a large margin in the input space, just like the support vector machines. With a differentiable formulation of the perturbation, we train the regularized DNNs simply through back-propagation in an end-to-end manner. Experimental results on various datasets (including MNIST, CIFAR-10/100, SVHN and ImageNet) and different DNN architectures demonstrate the superiority of our method over previous state-of-the-arts. Code and models for reproducing our results will be made publicly available.

Visual Features Assisted Robot Localization in Symmetrical Environment Using Laser SLAM.

Localization for estimating the position and orientation of a robot in an asymmetrical environment has been solved by using various 2D laser rangefinder simultaneous localization and mapping (SLAM) approaches. Laser-based SLAM generates an occupancy grid map, then the most popular Monte Carlo Localization (MCL) method spreads particles on the map and calculates the position of the robot by a probabilistic algorithm. However, this can be difficult, especially in symmetrical environments, because landmarks or features may not be sufficient to determine the robot’s orientation. Sometimes the position is not unique if a robot does not stay at the geometric center. This paper presents a novel approach to solving the robot localization problem in a symmetrical environment using the visual features-assisted method. Laser range measurements are used to estimate the robot position, while visual features determine its orientation. Firstly, we convert laser range scans raw data into coordinate data and calculate the geometric center. Secondly, we calculate the new distance from the geometric center point to all end points and find the longest distances. Then, we compare those distances, fit lines, extract corner points, and calculate the distance between adjacent corner points to determine whether the environment is symmetrical. Finally, if the environment is symmetrical, visual features based on the ORB keypoint detector and descriptor will be added to the system to determine the orientation of the robot. The experimental results show that our approach can successfully determine the position of the robot in a symmetrical environment, while ordinary MCL and its extension localization method always fail.

Curved holographic optical elements from a geometric view point

We present a geometric framework to model the optical effects of deformations of planar holographic optical elements (HOE) into curved surfaces, such as sphere segments. In particular, we consider deformations which do not preserve the Gaussian curvature.