The development and analysis of quasi-linear map projections

Abstract

Map projections are an essential component of coordinate systems used in applications such as surveying, topographic mapping, and engineering, and care needs to be taken to select ones that minimize distortion for each case. This article explores the selection process for near-linear features on the surface of the Earth and derives limits for the extent of a project that can be projected within specified distortion tolerances. It is then demonstrated that a multifaceted set of projections of the Earth may be used to extend this concept to the mapping of features such as highways and railways that are quasi-linear but do not exactly follow a standard geometrical line (a great circle or a small circle) on the surface of the Earth. A continuous, conformal coordinate system may be derived in such situations, extending to indefinite length and applicable over a swath of several kilometers width, but it cannot be extended to cover situations with extensive variations in height. Instead, the Snake Projection is analyzed, and it is shown that this can be used to develop continuous (non-zonal) projected coordinate systems for major engineering projects extending for hundreds of kilometers and having extensive height ranges. Examples are shown of the application to railway projects.

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