TL;DR
This paper explores various map projections by deriving plotting equations and analyzing distortions in length, shape, and size, based on fundamental geometric concepts.
Contribution
It introduces a systematic derivation of plotting equations for known map projections using fundamental forms and Gaussian quantities.
Findings
Derived plotting equations for several map projections
Analyzed distortions in length, shape, and size
Provided a geometric framework for understanding map distortions
Abstract
In this paper, we introduce some known map projections from a model of the Earth to a flat sheet of paper or map and derive the plotting equations for these projections. The first fundamental form and the Gaussian fundamental quantities are defined and applied to obtain the plotting equations and distortions in length, shape and size for some of these map projections.
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