CAMPREL: A New Adaptive Conformal Cartographic Projection

Abstract

The theoretical basis of CAMPREL is discussed. Previously derived partial, differential second- order equations describing the conformal mapping of a rotational ellepsoid onto a plane, and the contour conditions formulated on the basis of the Chebyshev-Grave theorem, have been used to determine the linear-scale function of a harmonic polynomial. A methodology is presented for finding the optimal CAMPREL projection which satisfies the minimax criterion expressed by the Chebyshev-Grave theorem, as well as the variables expressed in the optimization process. The optimal projection was selected from among thousands of projection variants by means of a multicriteria analysis The uniform and symmetric distribution of the extreme linear deformations thus represents a higher-order criterion which can be used to supplement other criteria. A comparison of the optimal CAMPREL projection with those of Gaus-Krüger and Lambert for small countries (e.g., the former Yugoslavia), and with Urmayev's for the European part of the former USSR, Frankich's for Canada, and Snyder's for USA, confirmed that the new CAMPREL projection yields fewer linear distortions when mapping a rotational ellipsoid onto a plane.