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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Flattening ： ウィキペディア英語版 Flattening Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution (spheroid) respectively. Other terms used are ellipticity, or oblateness. The usual notation for flattening is ''f'' and its definition in terms of the semi-axes of the resulting ellipse or ellipsoid is ::$\backslash mathrm\; =\; f\; =\backslash frac\; .$ The compression factor is ''b/a'' in each case. For the ellipse, this factor is also the aspect ratio of the ellipse. There are two other variants of flattening (see below) and when it is necessary to avoid confusion the above flattening is called the first flattening. The following definitions may be found in standard texts 〔Torge, W. (2001). ''Geodesy'' (3rd edition). de Gruyter. ISBN 3-11-017072-8〕 and online web texts〔Osborne, P. (2008). ''(The Mercator Projections )'' Chapter 5.〕〔Rapp, Richard H. (1991). ''Geometric Geodesy, Part I''. Dept. of Geodetic Science and Surveying, Ohio State Univ., Columbus, Ohio. ()〕 == Definitions of flattening == In the following, ''a'' is the larger dimension (e.g. semimajor axis), whereas ''b'' is the smaller (semiminor axis). All flattenings are zero for a circle (''a''=''b''). ::\,\! | style="width: 50%; padding-left: 0.5em "|Fundamental. The inverse 1/f is the normal choice for geodetic reference ellipsoids. |- | style="padding-left: 0.5em"|second flattening | style="padding-left: 0.5em"|$f\text{'}\backslash ,\backslash !$ | style="padding-left: 0.5em"|$\backslash frac\backslash ,\backslash !$   | style="padding-left: 0.5em"| Rarely used. |- | style="padding-left: 0.5em"| third flattening | style="padding-left: 0.5em"|$n\backslash quad(f\text{'}\text{'})\backslash ,\backslash !$   | style="padding-left: 0.5em"|$\backslash frac\backslash ,\backslash !$ | style="padding-left: 0.5em"| Used in geodetic calculations as a small expansion parameter.〔F. W. Bessel, 1825, ''Uber die Berechnung der geographischen Langen und Breiten aus geodatischen Vermessungen'', ''Astron.Nachr.'', 4(86), 241-254, , translated into English by C. F. F. Karney and R. E. Deakin as ''The calculation of longitude and latitude from geodesic measurements'', ''Astron. Nachr.'' 331(8), 852-861 (2010), E-print , 〕 |} 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Flattening」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.