Specifics of computational geometry tasks in the geodetic system of coordinates: Case study of median line contouring

Abstract

This article considers the problem of median line contouring, which lies at the heart of marine boundary delimitation methods. The specifics of computational geometry tasks in the geodetic system of coordinates are determined by the fact that there is no analytical description for geodetic lines on a spheroid and, therefore, no direct method of carrying out elementary geometrical operations. The approach suggested in this work is based on a preliminary evaluation of geodetic distances by converting coordinates (φ, λ) of original curves to Cartesian coordinates (X, Y, Z). In addition, we suggest a special data structure arranged as a circular probe. Our algorithm for computing the geodetic coordinates of points of a line equidistant from two given lines ensures high precision and efficiency.