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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 Transverse Mercator: Redfearn series ： ウィキペディア英語版 Transverse Mercator: Redfearn series The article Transverse Mercator projection restricts itself to general features of the projection. This article describes in detail one of the (two) implementations developed by Louis Krüger in 1912; that expressed as a power series in the longitude difference from the central meridian. These series were recalculated by Lee in 1946, by Redfearn in 1948, and by Thomas in 1952.〔Thomas, Paul D (1952). ''Conformal Projections in Geodesy and Cartography''. Washington: U.S. Coast and Geodetic Survey Special Publication 251.〕〔 They are often referred to as the Redfearn series, or the Thomas series. This implementation is of great importance since it is widely used in the U.S. State Plane Coordinate System,〔 in national (Britain,〔 Ireland〔See Irish grid reference system and Irish Transverse Mercator〕 and many others) and also international〔The EEA recommends the Transverse Mercator for conformal pan-European mapping at scales larger than 1:500,000〕 mapping systems, including the Universal Transverse Mercator coordinate system (UTM). They are also incorporated into the Geotrans coordinate converter made available by the United States National Geospatial-Intelligence Agency. When paired with a suitable geodetic datum, the series deliver high accuracy in zones less than a few degrees in east-west extent. ==Preliminaries I: datum and ellipsoid parameters== The series must be used with a geodetic datum which specifies the position, orientation and shape of a Reference ellipsoid. Although the projection formulae depend only on the shape parameters of the reference ellipsoid the full set of datum parameters is necessary to link the projection coordinates to true positions in three-dimensional space. The datums and reference ellipsoids associated with particular implementations of the Redfearn formulae are listed below. A comprehensive list of important ellipsoids is given in the article on the Figure of the Earth. In specifying ellipsoids it is normal to give the semi-major axis (equatorial axis), $a$, along with either the inverse flattening, $1/f$, or the semi-minor axis (polar axis), $b$, or sometimes both. The series presented below use the eccentricity, $e$, in preference to the flattening, $f$. In addition they use the parameters $n$, called the third flattening, and $e\text{'}$, the second eccentricity. There are only two independent shape parameters and there are many relations between them: in particular :$$ \begin f&=\frac, \qquad e^2=2f-f^2, \qquad e'^2=\frac\\ b&=a(1-f)=a(1-e^2)^,\qquad n=\frac. \end The projection formulae also involve $\backslash rho(\backslash phi)$, the radius of curvature of the meridian (at latitude $\backslash phi$), and $\backslash nu(\backslash phi)$, the radius of curvature in the prime vertical. (The prime vertical is the vertical plane orthogonal to the meridian plane at a point on the ellipsoid). The radii of curvature are defined as follows: :$$ \nu(\phi)=\frac. In addition the functions $\backslash beta(\backslash phi)$ and $\backslash eta(\backslash phi)$ are defined as: :$$ \beta(\phi)=\frac,\qquad \eta^2=\beta-1=. For compactness it is normal to introduce the following abbreviations: :$$ s=\sin\phi,\qquad c=\cos\phi,\qquad t=\tan\phi. 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「Transverse Mercator: Redfearn series」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.