You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: spacing2numVertices.m
    path of file: ./repos/GIBBON/lib
    
    the code of the file until where you have to start completion: function nP=spacing2numVertices(F,V,pointSpacing)

A=sum(patchArea(F,V)); %Total area
At=(pointSpacing.^2*sqrt(3))/4; %Theoretical area of equilateral triangle
NF=(A/At);

E=patchEdges(F,1); %Edges
nE=size(E,1); %Number of edges
nF=size(F,1); %Number of faces
nV=size(V,1); %Number of vertices

%Compute Euler characteristic 
X=size(V,1)-size(E,1)+size(F,1); 


    
function nP=spacing2numVertices(F,V,pointSpacing)

A=sum(patchArea(F,V)); %Total area
At=(pointSpacing.^2*sqrt(3))/4; %Theoretical area of equilateral triangle
NF=(A/At);

E=patchEdges(F,1); %Edges
nE=size(E,1); %Number of edges
nF=size(F,1); %Number of faces
nV=size(V,1); %Number of vertices

%Compute Euler characteristic 
X=size(V,1)-size(E,1)+size(F,1); 

nRefScalar=(log(NF)-log(nF))/log(4);

if nRefScalar<0
    nRef=floor(nRefScalar);
    nRange=0:-1:nRef;
else
    nRef=ceil(nRefScalar);
    nRange=0:1:nRef;
end