Geodesic intersections

TL;DR

This paper provides a comprehensive analysis of geodesic intersections on ellipsoids, introducing algorithms for intersection detection, spacing bounds, and handling overlapping cases, enhancing computational geodesy methods.

Contribution

It offers a complete theoretical framework and practical algorithms for analyzing and computing intersections of geodesics on ellipsoids of revolution.

Findings

Developed algorithms for intersection detection and proximity analysis

Established bounds on intersection spacing

Addressed cases of overlapping geodesics

Abstract

A complete treatment of the intersections of two geodesics on the surface of an ellipsoid of revolution is given. With a suitable metric for the distances between intersections, bounds are placed on their spacing. This leads to fast and reliable algorithms for finding the closest intersection, determining whether and where two geodesic segments intersect, finding the next closest intersection to a given intersection, and listing all nearby intersections. The cases where the two geodesics overlap are also treated.