On Distance Function among Finite Set of Points

TL;DR

This paper explores defining a non-metric distance function among finite points on surfaces, aiming to improve applications in transportation and vehicle routing problems on 2D manifolds in 3D space.

Contribution

It introduces a new distance function suitable for finite point sets on surfaces, addressing limitations of traditional metrics in practical geometric problems.

Findings

Proposes a non-metric distance function for finite point sets

Applicable to transportation theory and vehicle routing problems

Enhances modeling of geometric relationships on surfaces

Abstract

In practical purposes for some geometrical problems in computer science we have as information the coordinates of some finite points in surface instead of the whole body of a surface. The problem arised here is: "How to define a distance function in a finite space?" as we will show the appropriate function for this purpose is not a metric function. Here we try to define this distance function in order to apply it in further proposes, specially in the field setting of transportation theory and vehicle routing problem. More precisely in this paper we consider VRP problem for two dimensional manifolds in R3.