A mathematical investigation on the distance-preserving property of an equidistant cylindrical projection

TL;DR

This paper provides a geometric and mathematical analysis of the distance distortions inherent in equidistant cylindrical map projections, using Tissot's indicatrices and spherical trigonometry to quantify and understand the distortions.

Contribution

It introduces a detailed mathematical framework combining Tissot's indicatrices and spherical coordinates to analyze distance distortions in equidistant cylindrical projections.

Findings

Quantifies the degree of distance distortion in the projection

Provides a geometric interpretation of horizontal bending effects

Offers a mathematical approach to evaluate projection accuracy

Abstract

This research work aims to explore the distortions in distance in equidistant cylindrical projection. The horizontal bending that occurs in the projection process can be assessed by performing a geometric analysis using Tissot's indicatrices. In addition, the concept of the spherical coordinates, alongside with trigonometrical identities, can be used to illustrate the route from a point to another as a curve. With a combination of the knowledge extracted from the examination of the projection using those two theories, this research aims to fully unravel the degree of distortion in distance in equidistant cylindrical projections.