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

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Chinese Journal of Aeronautics 2023年第8期36卷 74-90页

作者： Chuanrui SI Jinxin CHENG Zhengqing ZHU Zhitong CHEN Qinglong HAO School of Mechanical Engineering and Automation Beihang UniversityBeijing 100191China School of Mechanical Engineering University of Science and Technology BeijingBeijing 100083China Zaozhuang Beihang Machine Tool Innovation Research Institute Co. LtdZaozhuang 277500China Ningbo Institute of Technology Beihang UniversityNingbo 315832China

Shape parameterization has a crucial influence on the optimal solution of aerodynamic *** 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 *** 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 *** 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 *** verify the effectiveness,six existing blade sections are first fitted and then one of them is selected for a three-level *** 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,***,the proposed parameterization method facilitates the design of lower-loss and higher-load compressor blade sections.

关键词： Aerodynamics Blade sections Compressors Deformation ellipse Parameterization

ON THE BOUNDS OF THE PERIMETER OF AN ellipse

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Acta Mathematica Scientia 2022年第2期42卷 491-501页

作者：赵鉄洪王淼坤褚玉明 Department of Mathematics Hangzhou Normal UniversityHangzhou 311121China Department of Mathematics Huzhou UniversityHuzhou 313000China

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.

关键词： Gaussian hypergeometric function complete elliptic integral ellipse perimeter

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

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Chinese Journal of Mechanical Engineering 2016年第5期29卷 1020-1028页

作者： LIU Fei XU Guanghua LIANG Lin ZHANG Qing LIU Dan School of Mechanical Engineering Xi'an Jiaotong University State Key Laboratory for Manufacturing Systems Engineering Xi'an Jiaotong University Key Laboratory of Education Ministry for Modern Design and Rotor-Bearing System Xi'an Jiaotong University

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.

关键词： ellipse form Error profile error least squares method piston

The Closest and Farthest Points to an Affine ellipse or Ellipsoid

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Tsinghua Science and Technology 2012年第4期17卷 481-484页

作者： Shuangmin Chen,Shiqing Xin,Ying He,Guojin Wang School of Computer Engineering,Nanyang Technological University,Singapore 639798 State Key Lab of CAD&CG,Zhejiang University,Hangzhou 310054,China School of Computer Engineering Nanyang Technological University Singapore 639798 State Key Lab of CAD&CG Zhejiang University Hangzhou 310054 China

Affine ellipses/ellipsoids based bounding volumes are widely used in various graphics applications, such as ray tracing and collision detection. They provide a much tighter fit than the regular ellipses/ellipsoids. The most important operation involved is to compute the closest/farthest point, on a given ellipse/ellipsoid, with respect to a user specified point. In this paper, we first formulate such a problem for the ellipse case into solving a quartic equation and then for the ellipsoid case by solving a system of quartic equations. The method proposed in this paper is elegant and highly efficient.

关键词： ellipse ellipsoid closest point farthest point bounding volume collision detection

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

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Journal of Tropical Meteorology 2013年第1期19卷 59-66页

作者：张韧黄志松李佳讯刘巍 College of Meteorology and Oceanography PLA University of Science and Technology School of Information Science and Technology Southwest Jiaotong University

Addressing the difficulties of scattered and sparse observational data in ocean science,a new interpolation technique based on information diffusion is proposed in this *** 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 *** 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 *** interpolation experiments and contrast analysis of the sea surface temperature data with ARGO data,the rationality and validity of the ellipse model are assessed.

关键词： information diffusion interpolation algorithm sparse data ellipse model

Envelopes of Two Families of Chords of an ellipse

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Wuhan University Journal of Natural Sciences 2021年第5期26卷 365-368页

作者： ZHANG Yanfang SUN Peiru School of Science Huzhou UniversityHuzhou 313000ZhejiangChina

In this paper, we investigate the envelope of two special families of chords of an ellipse and prove that the envelopes are also ellipses. The obtained results are important for computerized design of the generation o... 详细信息

关键词： envelope chord family ellipse computerized design

Projection of the Semi-Axes of the ellipse of Intersection

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Applied Mathematics 2017年第9期8卷 1320-1335页

作者： P. P. Klein Computing Center University of Technology Clausthal Clausthal-Zellerfeld Germany

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].

关键词： Ellipsoid and Plane Intersection Projection of the Semi-Axes of the ellipse of Intersection

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

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Applied Mathematics 2014年第8期5卷 1317-1321页

作者： Jihui Tu Bin Yang Electronic Information Engineering School of HEBI College of Vocation and Technology Henan China Electronics & Information School of Yangtze University Jingzhou China

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.

关键词： BHTV ellipse Fitting Image Correction Tool Eccentricity

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谈谈德语中的ellipse

德语学习 2003年第4期 30-35页

作者：安士桐首都师范大学外语学院德语系