Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Some formulae concerning the transverse mercator projection
Summary For special purposes relatively accurate projection formulae can be needed. For that reason this paper gives formulae concerning the transverseMercator projection for the plane coordinatesx andy as functions of φ and λ (latitude and longitude) complete up to and including terms containing $ λ^{τ} $ and for the scale factor as a function ofy and φ complete up to and including terms containingy6. In addition to that this paper gives a formula for the length of a geodesic as function of the plane coordinates of its end points, the transverseMercator projection still being valid. Having taken regard to the fact, thatr (the mean radius of curvature) varies the line along and that the projected geodesic is not rectilinear the result has been a formula allowing a relatively rapid computation and yet giving an error generally not exceeding 1 mm provided that the length of the geodesic ≤ about 1000 km and that the distance between its end points and the head meridian ≤ about 400 km.
Some formulae concerning the transverse mercator projection
Summary For special purposes relatively accurate projection formulae can be needed. For that reason this paper gives formulae concerning the transverseMercator projection for the plane coordinatesx andy as functions of φ and λ (latitude and longitude) complete up to and including terms containing $ λ^{τ} $ and for the scale factor as a function ofy and φ complete up to and including terms containingy6. In addition to that this paper gives a formula for the length of a geodesic as function of the plane coordinates of its end points, the transverseMercator projection still being valid. Having taken regard to the fact, thatr (the mean radius of curvature) varies the line along and that the projected geodesic is not rectilinear the result has been a formula allowing a relatively rapid computation and yet giving an error generally not exceeding 1 mm provided that the length of the geodesic ≤ about 1000 km and that the distance between its end points and the head meridian ≤ about 400 km.
Some formulae concerning the transverse mercator projection
Rune, G. A. (Autor:in)
1954
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
Geodäsie , Geometrie , Geodynamik , Mathematik , Mineralogie
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