  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.
