Determining geodesics of a discrete surface

Geodesics are surface curves that possess special properties. In many cases a geodesic on a surface can be considered as the shortest path between its endpoints. A geodesic depends only on the intrinsic properties of a surface. The above properties prompted many uses of geodesics in many different fields. Until now almost all of the methods to calculate geodesics on a surface relied on the fact that somehow an analytical representation of the surface exists. Due to the increase in the use of digital computers and range finding systems, more and more objects are being described as a set of digitized points. In this paper we describe methods that would produce approximations to the geodesics of a surface based solely on the digitized points.<>