Local Linear Scale Factors in Map Projections of an Ellipsoid

Miljenko Lapaine
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Miljenko Lapaine: Faculty of Geodesy, University of Zagreb, Kačićeva 26, 10000 Zagreb, Croatia

Geographies, 2021, vol. 1, issue 3, 1-13

Abstract: The main problem in cartography is that it is not possible to map/project/transform a spherical or ellipsoidal surface into a plane without distortions. The distortions of areas, angles, and/or distances are immanent to all maps. It is known that scale changes from point to point, and at certain points, the scale usually depends on the direction. The local linear scale factor c is one of the most important indicators of distortion distribution in the theory of map projections. It is not possible to find out the values of the local linear scale factor c in directions of coordinate axes x and y immediately from the definition of c . To solve this problem, in this paper, we derive new formulae for the calculation of c for a rotational ellipsoid. In addition, we derive the formula for computing c in any direction defined by dx and dy . We also considered the position and magnitude of the extreme values of c and derived new formulae for a rotational ellipsoid.

Keywords: map projection; scale factor; distortion distribution (search for similar items in EconPapers)
JEL-codes: Q1 Q15 Q5 Q53 Q54 Q56 Q57 (search for similar items in EconPapers)
Date: 2021
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