Computation of geodesics and rhumb lines on spheroid

Abstract

In Japan, domestic laws for surveying and hydrographic services define the shape of the Earth as an oblate spheroid (ellipsoid). Therefore, in order to determine precise positions and distances in accordance with those laws, the geometry on spheroid is required. The geometry is alsoessential to precise maritime delimitation such as computing equidistant lines between Japan and adjacent countries as the limit of exclusive economic zone of Japan. This report introduces some basic concepts of geometry on the spheroid, especially, geodesics and rhumb lines. It also describes a full detail of a method to compute geodesics proposed by T. Vincenty in 1975 .