Finding Geodesics on Surfaces Using Taylor Expansion of Exponential Map

TL;DR

This paper introduces a numerical algorithm that employs Taylor expansion of the exponential map to accurately compute geodesics between two points on a 2D surface with a Riemannian metric.

Contribution

It presents a novel method leveraging Taylor expansion of the exponential map for geodesic computation on surfaces.

Findings

Effective in calculating geodesics on 2D surfaces

Provides a new numerical approach with potential for high accuracy

Applicable to surfaces with complex Riemannian metrics

Abstract

Our aim in this paper is to construct a numerical algorithm using Taylor expansion of exponential map to find geodesic joining two points on a 2-dimensional surface for which a Riemannian metric is defined