Exact and heuristic formulae to compute the geodetic height from the ellipse equation

The conversion of the cartesian coordinates of a point to its geodetic equivalent coordinates in reference to the geodetic ellipsoid is one of the main challenges in geodesy.The ellipse equation in the meridian plane significantly influences the value of the geodetic coordinates.This research analyzes this influence and how it can contribute to their solutions.The study investigates the mathematical relation between them and presents an exact formula relating to the geodetic height and the ellipse equation.In addition,a heuristic formula for the relation between the geodetic height and the ellipse equation is proposed,which is independent of the geodetic latitude and has a relative accuracy better than 99.9 %.The calculation is stable,and the cost is low.

Comparison of the Minimum Bounding Rectangle and Minimum Circumscribed Ellipse of Rain Cells from TRMM

Based on the TRMM dataset, this paper compares the applicability of the improved MCE(minimum circumscribed ellipse), MBR(minimum bounding rectangle), and DIA(direct indexing area) methods for rain cell fitting. These three methods can reflect the geometric characteristics of clouds and apply geometric parameters to estimate the real dimensions of rain cells. The MCE method shows a major advantage in identifying the circumference of rain cells. The circumference of rain cells identified by MCE in most samples is smaller than that identified by DIA and MBR, and more similar to the observed rain cells. The area of rain cells identified by MBR is relatively robust. For rain cells composed of many pixels(N> 20), the overall performance is better than that of MCE, but the contribution of MBR to the best identification results,which have the shortest circumference and the smallest area, is less than that of MCE. The DIA method is best suited to small rain cells with a circumference of less than 100 km and an area of less than 120 km^(2), but the overall performance is mediocre. The MCE method tends to achieve the highest success at any angle, whereas there are fewer “best identification”results from DIA or MBR and more of the worst ones in the along-track direction and cross-track direction. Through this comprehensive comparison, we conclude that MCE can obtain the best fitting results with the shortest circumference and the smallest area on behalf of the high filling effect for all sizes of rain cells.

Least Squares Evaluations for Form and Profile Errors of Ellipse Using Coordinate Data

To improve the measurement and evaluation of form error of an elliptic section, an evaluation method based on least squares fitting is investigated to analyze the form and profile errors of an ellipse using coordinate data. Two error indicators for defining ellipticity are discussed, namely the form error and the profile error, and the difference between both is considered as the main parameter for evaluating machining quality of surface and profile. Because the form error and the profile error rely on different evaluation benchmarks, the major axis and the foci rather than the centre of an ellipse are used as the evaluation benchmarks and can accurately evaluate a tolerance range with the separated form error and profile error of workpiece. Additionally, an evaluation program based on the LS model is developed to extract the form error and the profile error of the elliptic section, which is well suited for separating the two errors by a standard program. Finally, the evaluation method about the form and profile errors of the ellipse is applied to the measurement of skirt line of the piston, and results indicate the effectiveness of the evaluation. This approach provides the new evaluation indicators for the measurement of form and profile errors of ellipse, which is found to have better accuracy and can thus be used to solve the difficult of the measurement and evaluation of the piston in industrial production.

Similarity quantification of soil parametric data and sites using confidence ellipses

This paper presents a confidence ellipse-based method to evaluate the similarity of soil parametric data using the database from the site investigation reports.Then,the obtained similarity assessment results of parametric data are used to further estimate the site similarity via two proposed strategies,namely the mean and weighted mean approaches.The former referred to the average of parametric data similarity degrees,while the latter was the weighted average,and the weight was calculated using the coefficient of variation(COV)of each parameter.For illustration,the liquidity index(LI)dataset was firstly used to explore the performance of the presented method in the evaluation of parametric data similarity.Subsequently,the site similarity was assessed and the effects of numbers and weights of selected parameters for study were systematically studied.Lastly,the transformation models about the relationships between Cc and x as well as between Cc and e0 were constructed to illustrate the application of the similarity analysis in reduction of transformation uncertainty.Results show that the greatest site similarity degree is at about 0.76 in this study,and the maximum decrease of transformation uncertainty can reach up to 18%and 25.5%as union parametric data similarity degree increases.Moreover,the site similarity degree represents the whole similarity between two different sites,and the presented union parameter similarity degree maintains a good agreement with transformation uncertainty.

INTERPOLATION TECHNIQUE FOR SPARSE DATA BASED ON INFORMATION DIFFUSION PRINCIPLE-ELLIPSE MODEL

Addressing the difficulties of scattered and sparse observational data in ocean science,a new interpolation technique based on information diffusion is proposed in this paper.Based on a fuzzy mapping idea,sparse data samples are diffused and mapped into corresponding fuzzy sets in the form of probability in an interpolation ellipse model.To avoid the shortcoming of normal diffusion function on the asymmetric structure,a kind of asymmetric information diffusion function is developed and a corresponding algorithm-ellipse model for diffusion of asymmetric information is established.Through interpolation experiments and contrast analysis of the sea surface temperature data with ARGO data,the rationality and validity of the ellipse model are assessed.

ON THE BOUNDS OF THE PERIMETER OF AN ELLIPSE

In this paper,we present new bounds for the perimeter of an ellipse in terms of harmonic,geometric,arithmetic and quadratic means;these new bounds represent improvements upon some previously known results.

RESEARCH ON THE ON-LINE MEASURING SYSTEM FOR THE MIDDLE-CONVEX AND VARYING ELLIPSE PISTON SKIRT

The middle convex and varying ellipse piston is th e key component of an internal combustion engine In general,the piston is mac hined by non circular section CNC lathe,but the measuring of piston profile is manipulated by off line Because the off line measuring reference is differen t from the machining reference,the measurement result is diverse from the act ual dimension A new method to measure the middle convex and varying ellipse p iston profile, which is known as on line measuring, is presented By using thi s kind of method,the high measurement accuracy can be gained,as well as meeting the production requirement.

A new ellipse fitting method of the minimum differential-mode noise in the atom interference gravimeter

Ellipse fitting is a useful tool to obtain the differential signal of two atom interference gravimeters. The quality standard of ellipse fitting should be the deviation between the true phase and the fitting phase of the interference fringe. In this paper, we present a new algorithm to fit the ellipse. The algorithm is to minimize the differential noise of two interference gravimeters and obtain a more accurate value of the gravity gradient. We have theoretically derived the expression of the differential-mode noise and implemented the ellipse fitting in the program. This new algorithm is also compared with the classical methods.

Projection of the Semi-Axes of the Ellipse of Intersection

It is well known that the line of intersection of an ellipsoid and a plane is an ellipse (see for instance [1]). In this note the semi-axes of the ellipse of intersection will be projected from 3d space onto a 2d plane. It is shown that the projected semi-axes agree with results of a method used by Bektas [2] and also with results obtained by Schrantz [3].

The Research of Ellipse Parameter Fitting Algorithm of Ultrasonic Imaging Logging in the Casing Hole

In order to estimate intensity and direction of pressure acted on oil well in horizontal, this paper proposes an algorithm of ellipse fitting based on least square method for sections of oil well with ultrasonic imaging logging data. Five parameters about ellipse corresponding to the sections of oil well are extracted and their geometry deformations and direction are estimated. The tested results show that the fitting algorithm is robust and the estimating error of parameter is small, which have very important practical significance on processing the well logging.

An ellipse-guided routing algorithm in wireless sensor networks

In wireless sensor networks,sensor nodes are deployed to collect data,perform calculations,and forward information to either other nodes or sink nodes.Recently,geographic routing has become extremely popular because it only requires the locations of sensor nodes and is very efficient.However,the local minimum phenomenon,which hinders greedy forwarding,is a major problem in geographic routing.This phenomenon is attributed to an area called a hole that lacks active sensors,which either prevents the packet from being forwarded to a destination node or produces a long detour path.In order to solve the hole problem,mechanisms to detect holes and determine landmark nodes have been proposed.Based on the proposed mechanisms,landmark-based routing was developed in which the source node first sends a packet to the landmark node,and the landmark node then sends the packet to the destination.However,this approach often creates a constant node sequence,causing nodes that perform routing tasks to quickly run out of energy,thus producing larger holes.In this paper,a new approach is proposed in which two virtual ellipses are created with the source,landmark,and destination nodes.Then guide the forwarding along the virtual ellipses.Furthermore,a recursive algorithm is designed to ensure a shortcut even if there are multiple holes or a hole has multiple landmarks.Thus,the proposed approach improves both geographic routing and energy efficiency routing.Simulation experiments show that the proposed approach increases the battery life of sensor nodes,lowers the end-to-end delay,and generates a short path.

Enclosing Ellipses by Folding Disks

Ellipses can be constructed by folding disks. These folds are forming an envelope of tangents to the ellipse. In the paper of Gorkin and Shaffer, it was shown that the ellipse constructed by folding can be circumscribed by an arbitrary triangle of tangents, the vertices of which are lying on the circumference of the disk. They offered two non-elementary methods of proof, one using Poncelet’s Theorem, the other employing Blaschke products. In this paper, it is the intention to present an elementary proof by means of analytic geometry.

ASYMPTOTIC EXPRESSION NEAR THE ELLIPSE OF CONVERGENCE OF JACOBI SERIES IN COMPLEX PLANE

In this paper, we shall give an Abel type theorem of Jacobi series and then based on it discuss asymptotic expressions near the ellipse of convergence of Jacobi series in complex plane.

Design of Ellipse Antenna Array for Cellular Phone Localization Systems

This paper describes our contribution in the ANR (Agence Nationale de la Recherche) project called GELOCOM (GEo-LOCalisation de telephOnes Mobiles) managed by the THALES Communications company, dedicated to the emergency localization of cellular phones. This contribution takes place in the field of antennas, with the development of broad-band systems: a circular array of six elements with separated outputs for the receiving part. In this paper, we present the design and the characterization of broad-band double ellipse array antenna. This special structure is chosen in order to obtain a good omnidirectional radiation pattern, enhance the gain and maximize the V/H polarization ratio. In comparison with the already existing antenna systems in the wireless market for similar purposes, the proposed antenna has considerably shown better performance which makes it competitive among other antenna models. For the design and optimization of antennas, we use CST MWS software. The antennas have been designed and successfully measured.

Minimum-area Ellipse with Three Non-collinear Points and Its Application in Parametric Interpolation

The problem of determining a minimum-area ellipse through three non-collinear points is discussed in this paper. We give the proof and construction of the minimum-area ellipse through three non-collinear points from the geometric point of view, and present a new method of determining knots. This method replaces the chord length, which is closer to the arc length of the mini- mum-area ellipse with arc length, and avoids the occurrence of ＇oscillation＇ and ＇loops＇. We compare the new method with the uni- form method, chord length method and the centripetal method. The comparison is performed on the quality of cubic spline curves using these methods. In most cases, the result of our method is better than others.

An intuitive parameterization method with inherently high-order differentiability for compressor blade sections based on ellipse hierarchical deformation

Shape parameterization has a crucial influence on the optimal solution of aerodynamic optimization.This paper proposes a novel parameterization method for compressor blade sections based on the three-level deformation of the ellipse,which simultaneously satisfies the requirements of flexibility,smoothness,intuitiveness,and compactness.In proposed method,the first-level deformation directly controls nine key geometric parameters to construct the blade section profile,and then the second-and third-level deformations are performed respectively to coarsely and finely modify the profile while keeping the key geometric parameters unchanged.These three levels of deformation effectively decompose the design space without destroying the ellipse’s infinite differentiability,allowing designers to work only with intuitive shape-related parameters to design blade sections with inherently high-order continuity.To verify the effectiveness,six existing blade sections are first fitted and then one of them is selected for a three-level optimization.The results show that the geometry and aerodynamic performance of the fitted and the original blade sections are in good agreement,and the loss coefficient of the optimized blade section is reduced by a total of 36.41%,with 27.34%,8.45%,and 0.62%reductions for the first to the third level,respectively.Therefore,the proposed parameterization method facilitates the design of lower-loss and higher-load compressor blade sections.

Intelligent Breakage Assessment of Composite Insulators on Overhead Transmission Lines by Ellipse Detection Based on IRHT

With the development of unmanned aerial vehicle(UAV)technology,visible images are playing an important role in the maintenance of power systems.To achieve the shed breakage evaluation of composite insulators by UAV visible images,an intelligent fault assessment method is proposed.First,the composite insulators in visible light images are identified by Faster-RCNN.After image preprocessing,the image is enhanced and the noise is removed.Then,a canny operator is used to extract the edge of the sheds.An Improved Randomized Hough Transform(IRHT)is used to detect the ellipses in the edge image.The parameters of the detected ellipse,length of major axes and minor axes,center coordinates and deflection angle of major axes,are used to realize the segmentation of the composite insulator.Finally,the number of pixel points in the ellipse and the distance between the points and the ellipse boundary are used to judge whether there are breakage or cracks on the sheds.The area ratio of the breakage to the whole shed is calculated based on the number of pixel points inside the broken area.This method can be realized without a large amount of training dataset of the specific fault type and provides a technical basis for the online fault assessment of a composite insulator on overhead transmission lines.

Numerical modeling of seismic behavior of ellipse and peanut-shaped auxetic steel plate shear walls

This study proposes a new auxetic-shaped steel plate shear walls(simply referred to as ASSPSWs)consisting of boundary members and built-in perforated infill plates.The connection type between the boundary members is a hinge joint.The hole forms on the infill plates include orthogonal ellipse-shaped(ASSPSW-OE)and orthogonal peanutshaped(ASSPSW-OP).This paper studied the hysteretic performance of two steel plate shear walls’types based on the finite element analysis method.Within the study context,a parametric analysis was carried out to investigate the influence of various factors,such as hole size and hole distance,on the seismic performance of steel plate shear walls(SPSWs).The results indicated that reducing the the ratio of the ligament thickness to ellipse major axis(t/D)in orthogonal ellipse-shaped SPSWs can effectively increase the porosity while reducing the bearing and energy dissipation capacities.Under the condition with the t/D unchanged,increasing the ratio of the major to minor axis of the ellipse(d/D)raises the porosity and does not significantly reduce the bearing capacity and energy dissipation capacity of the SPSWs.For orthogonal peanut-shaped SPSWs,the holes’geometrical parameters significantly influence the hysteretic performance.Particularly,with the increase in the radial ratio of large to small circles in a peanut-shaped hole(R/r),the spacing between cells decreases.When drift exceeds 2%,the equivalent viscous damping ratio decreases sharply.Unlike the orthogonal ellipse-shaped SPSWs,changing the arrangement angle of peanut-shaped cells has no significant effect on orthogonal peanut-shaped SPSWs.However,the larger the angle,the greater the out-of-plane buckling of orthogonal ellipse-shaped SPSWs;thus,the energy dissipation capacity is reduced.The similarities lie in that the larger cell arrangement angle will make the steel plates have a complete stress field,and the bearing capacity will be slightly improved.When the cell arrangement angle(θ)is 45°,the SPSWs can develop high initial stiffness.

Spatiotemporal characteristics of cultivated land use eco-efficiency and its influencing factors in China from 2000 to 2020

Improving cultivated land use eco-efficiency(CLUE)can effectively promote agricultural sustainability,particularly in developing countries where CLUE is generally low.This study used provincial-level data from China to evaluate the spatiotemporal evolution of CLUE from 2000 to 2020 and identified the influencing factors of CLUE by using a panel Tobit model.In addition,given the undesirable outputs of agricultural production,we incorporated carbon emissions and nonpoint source pollution into the global benchmark-undesirable output-super efficiency-slacks-based measure(GB-US-SBM)model,which combines global benchmark technology,undesirable output,super efficiency,and slacks-based measure.The results indicated that there was an upward trend in CLUE in China from 2000 to 2020,with an increase rate of 2.62%.The temporal evolution of CLUE in China could be classified into three distinct stages:a period of fluctuating decrease(2000-2007),a phase of gradual increase(2008-2014),and a period of rapid growth(2015-2020).The major grain-producing areas(MPAs)had a lower CLUE than their counterparts,namely,non-major grain-production areas(non-MPAs).The spatial agglomeration effect followed a northeast-southwest strip distribution;and the movement path of barycentre revealed a"P"shape,with Luoyang City,Henan Province,as the centre.In terms of influencing factors of CLUE,investment in science and technology played the most vital role in improving CLUE,while irrigation index had the most negative effect.It should be noted that these two influencing factors had different impacts on MPAs and non-MPAs.Therefore,relevant departments should formulate policies to enhance the level of science and technology,improve irrigation condition,and promote sustainable utilization of cultivated land.

Experimental investigation of omnidirectional multiphysics bilayer invisibility cloak with anisotropic geometry

Thermal-electric bilayer invisibility cloak can prevent the heat flux and electric current from touching the object without distorting the external temperature and electric potential fields simultaneously.In this paper,we design an omnidirectional thermal-electric invisibility cloak with anisotropic geometry.Based on the theory of neutral inclusion,the anisotropic effective thermal and electric conductivities of confocal elliptical bilayer core-shell structure are derived,thus obtaining the anisotropic matrix material to eliminate the external disturbances omnidirectionally.The inner shell of the cloak is selected as an insulating material to shield the heat flux and electric current.Then,the omnidirectional thermal-electric cloaking effect is verified numerically and experimentally based on the theoretical anisotropic matrix and manufactured composite structure,respectively.Furthermore,we achieve the thermal-electric cloaking effect under a specific direction of heat flux and electric current using the isotropic natural materials to broaden the selection range of materials.The method proposed to eliminate anisotropy and achieve the omnidirectional effect could also be expanded to other different physical fields for the metadevices with different functions.