Laborde projection in Madagascar cartography and its recovery in WGS84 datum
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ORIGINAL PAPER
Laborde projection in Madagascar cartography and its recovery in WGS84 datum Marco Roggero
Received: 7 April 2009 / Accepted: 16 October 2009 / Published online: 18 November 2009 # Società Italiana di Fotogrammetria e Topografia (SIFET) 2009
Abstract The International Ellipsoid 1924 was adopted in Madagascar in 1925 for the definition of the Tananarive 1925 datum, while Laborde projection have been used for Madagascar cartography in 1926. Direct and inverse Laborde formulas are reviewed to convert cartographic and geodetic coordinates. The Hotine approximation of the Laborde projection is also discussed. From the geodetic point of view, there is the need to recover the Madagascar cartographic heritage in the WGS84 datum; datum transformations in the Molodensky form are known by literature, with the three dimensional accuracy of some meters. A new set of Helmert parameters has been estimated taking in account geoid correction and giving metric accuracy. Keywords Laborde projection . Oblique azimuthal equidistant . Madagascar
History of Madagascar cartography Madagascar is the fourth largest island in the world for size; its length is nearly 1,600 km and its maximum width is 576 km. The island is obliquely oriented with respect to the cardinal points, roughly in the southwest–northeast direction, and this is crucial for the development of cartography of the island in the choice of map projection (Snyder 1993). The capital of the Republic of Madagascar is Antananarivo,
M. Roggero (*) DINSE, Politecnico di Torino, Viale Mattioli 39, 10125 Torino, Italia e-mail: [email protected]
in the center of the island. Among the first topographical observations, we were reminded by the campaigns between the years 1824 and 1825 by Owen, the British Royal Navy, and the subsequent campaigns of the French Navy in 1830 and 1850. Geodetic triangulation for the hydrographic surveying of the Diego Suarez Bay was initiated by colonial engineer M. Grégoire in 1887. A base line of 1,044.295 m was measured with great accuracy, and the repetition of the measure differs by only 1 mm. The first datum was established in 1887 in the pillars of Antsirana with coordinates 0 = −12° 16′ 25.5″ and λ0 = 46° 57′ 36.2″ east of Paris. The orientation was established between Antsirana and the signal of the landmark of Oronjia with azimuth α0 = 79° 12′ 19″. The Antsirana 1887 datum refers to the Clarke 1880 ellipsoid, with major semi axis a = 6,378,249.145 m and 1/f = 293.465. The datum used in Madagascar is presented in the Table 1. Note that the first three datum located in the northwest of Madagascar was associated with the Hatt azimuthal equidistant projection to map the respective hydrographic surveys. Recall that the equidistant azimuthal projection has been used mainly for the polar regions, centered on the North Pole and more rarely on the South Pole. The equatorial azimuthal equidistant projection is considered but with minor interest, unless it is necessary to represent without deformation distances and directions in the a
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