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.

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.

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.

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.

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.

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.

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.

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.

Numerical Simulation of Nonlinear Wave Force on a Quasi-ellipse Caisson

A three dimensional numerical model of nonlinear wave action on a quasi-ellipse caisson in a time domain was developed in this paper. Navier-Stokes equations were solved by the finite difference method, and the volume of fluid (VOF) method was employed to trace the free surface. The partial cell method was used to deal with the irregular boundary typical of this type of problem during first-time wave interaction with the structure, and a satisfactory result was obtained. The numerical model was verified and used to investigate the effects of the relative wave height H/d, relative caisson width kD, and relative length-width ratio B/D on the wave forces of the quasi-ellipse caisson. It was shown that the relative wave height H/d has a significant effect on the wave forces of the caisson. Compared with the non-dimensional inline wave force, the relative length-width ratio B/D was shown to have significant influence on the non-dimensional transverse wave force.

An Experimental Study of Irregular Wave Forces on Multiple Quasi-ellipse Caissons

伪椭圆沉箱结构上的不规则的波浪力量的试验性的调查被介绍。不规则的波浪从 1.19 s 与二重要波浪高度，和光谱高峰时期范围基于 Jonswap 光谱被产生到 1.81 s。相对多重沉箱的中心线的事件波浪方向从 0 敢琠敨搠獥慰物漠吗？

Shape Optimization of Pressure Vessel Head Based on the Super-ellipse Equation

This paper studies optimal shape design of pressure vessel head subject to internal uniform pressure.The optimization aims at minimizing its maximum stress while the volume of the vessel head remains no less than the standard ellipsoidal head.Super-ellipse curve is selected to describe the middle surface shape of the vessel head because it represents a large family of curves with only two or three parameters and makes the design and manufacture easy.The performance of different elements and element sizes of FEM modeling is carefully studied in view of computational cost,accuracy and noises of von Mises stress.The response surface of the maximum stress vs.shape design parameters is approximated by a Kriging surrogate model with EI criterion for sampling adding,based on the parameter optimization which is carried out to search the optimal shape.Finally,it is shown by numerical comparison that the super-ellipsoidal head is better than the standard ellipsoidal head and the other vessel heads in the literature.

Three-dimensional numerical simulation of wave interaction with perforated quasi-ellipse caisson

The finite difference method and the volume of fluid （VOF） method were used to develop a three-dimensional numerical model to study wave interaction with a perforated caisson. The partial cell method was adopted to solve this type of problem for the first time. The validity of the present model, with and without the presence of caisson structures, was examined by comparing the model results with experimental data. Then, the numerical model was used to investigate the effects of various wave and structure parameters on the wave force and wave runup of the perforated quasi-ellipse caisson. Compared with the solid quasi-ellipse caisson, the wave force on the perforated quasi-ellipse caisson is significantly reduced with increasing porosity of the perforated quasi-ellipse caisson. Furthermore, the perforated quasi-ellipse caisson can also reduce the wave runup, and it tends to decrease with the increase of the porosity of the perforated quasi-ellipse caisson and the relative wave height.

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.

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.

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.

Heat Transfer Coefficient of Film Cooling with Ellipse-Shaped Tab

The enhanced cooling performance caused by ellipse-shaped tabs located at the outlet of the film cooling holes is conducted.Three covering ratios of ellipse-shaped tabs on film holes and four blowing ratios are studied.The results show that:(1)The heat transfer coefficient ratio is higher than that without tab,indicating that the mixing of mainstream and coolant jet provides a better coverage film on the cooling wall,but increases the local turbulence production which enhances the heat transfer coefficient;(2)When the ellipse-shaped tabs are located at the film hole outlet,there is a larger pressure drop with the ellipse tab relative to the no-tab case.Thus,the discharge coefficient with ellipse tab is lower than that without tab.