APPROXIMATION OF THE DISTANCE IN THE PLANE THROUGH THE NUMERICAL SOLUTION OF INITIAL VALUE PROBLEMS ASSOCIATED TO GEODESICS

Abstract

In this paper, we proposes an algorithm to approximate the Euclidean distance between points of plane, by doing a search of geodesic that depart from the point and arrive to a neighborhood of the point . This search is done through the numerical solution of initial value problems associated with the system of ordinary differential equations of the geodesics; for this is choose a set of directions in the plane.

Keywords

• euclidean distance
• intrinsec distance
• geodesic distance
• geodesics
• initial value problem
• approximation