By Lev M. Bugayevskiy, John P. Snyder
Map projection matters the technological know-how of mathematical cartography, the recommendations in which the Earth's dimensions, form and lines are translated in map shape, be that two-dimensional paper or - or 3- dimensional digital representations. The relevant concentration of this ebook is at the thought of map projections. Mathematical cartography additionally takes in map scales and their version, the department of maps into units of sheets and nomenclature, and addresses the issues of creating measurements and carrying out investigations which utilize geodetic measurements and the advance of graphical tools for fixing difficulties of round trigonometry, marine- and aeronavigation, astronomy or even crystallography.
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Additional resources for Map Projections: A Reference Manual
3 Conformal transformation of the surface of the ellipsoid onto a sphere From conformality terms m = 11, e = 0, and (1. 33), respectively. Constants ex and C are parameters for which the prescribed conditions result in various types of transformations. Mol/weide method Suggested in 1807, this method is characterized by the fo llowing initial conditions. The linear scale is preserved along the equator, and the parallels a nd meridians of Map projections: a ref erence manual 34 the ellipsoid and the sphere are equal along the equator and the central meridian, respectively : if ¢ = 0 then ¢ ' = 0; if J..
2 s1n a (1. 54) for the local scale factor along a ny direction can be represented in the form = P cos 2 a + Q sin 2a + R sin 2 a meridian, azimu th a = 0. e. the formula for the local linear scale factor m along a meridian. 55) L Map projections: a reference manual 18 Correspondingly, along a parallel the direction a= 90°. e. the formula for the local linea r scale factor /1 along a parallel. __ sin 2 fl + _I_ sin 2(i µ2 11 2 m2 or ~ = P1 cos fl + Q µ 2 1 sin where P 1 = e - 1 M 2, Q 1 = - (e/h) - 1fM 2 , R 1 = (M 2f2 + e2 r 2 )(eh 2 ) - 1 From the formulas given above, it follows that the local linear scale factor in a particular direction depends on both point coordinates and azimuths of linear elements related to direction.
In the case where neither a ngular no r area distortion is desirable, it is advisable to use projections similar to equidistant ones; 3. map projections should be chosen so that no t only will they satisfy the condition of minimal distortion, but also the distortion characteristics should lead to maps with optima l conditions for the purpose, permitting the so lution of problems from the map. 6 Central line and central point A line and a point are called central if the distortion of length, angles, a nd areas there is at a minimum.