Best Map Projections

About the Book

This book presents the most condensed information about the theory of distortion theory developed by N.A. Tissot. It considers some of the issues of this theory to finding the best projections. Various criteria for ideal projections are analyzed.

Methodology

In finding an ideal projection using the Airy criterion for an arbitrary mapping region is solved by the variational method using the Euler–Ostrogradsky system of equations under natural boundary conditions. The same method is applied to a set of projections in which the sum of the extremal scale factors is equal to 2.

Results

It is shown that for these projections, the area distortions are quantities of the second order of smallness, while the linear distortions are quantities of the first order of smallness. The problem of finding the best projections using the Chebyshev criterion has been studied.

Projections Discussed

Airy, Postel, Gauss–Kruger, and Markov projections are considered in detail.