Voronoi polygons distance between points

Hello

I have set of 2D points and after creation of voronoi polygons I want to calculeate distance between poit from one polygone and all neighborhood points (as in picture). Blue dots are my 2D points

Answer 1

[Matt J]

This returns the result as a distance matrix such as produced by pdist2, except that all entries not corresponding to neighboring points are set to NaN. Neighbors are defined as points whose Voronoi polygons share one or more (finite) vertices.

[V,C]=voronoin(points);

F=all(isfinite(V),2);

D=pdist2(points,points);

D(~common_vertex(C,F))=nan, %the result

                     function  map = common_vertex(C,F)
                        
                          n=numel(C);
                          map=false(n);
                          
                          for i=1:n
                              for j=1:i-1
                                  
                                 
                                  map(i,j)=any( F(intersect(C{i},C{j})) );
                                  
                              end
                          end
                          
                          map=logical(map+map.');
                          map(1:n+1:end)=1;
                          
                     end

[giometar]

Thank you very much

This is exactly what I was looking for

[giometar]

I have to accelerate code because I have large number of points and operations with iterative procedure. So here is code with using adjacent matrix (hope that is correct way):

% Generate some coordinates
x=rand(20,1);
y=rand(20,1);

% Perform Delaunay triangulation
dt=delaunayTriangulation(x(:),y(:));
tri=dt.ConnectivityList;

NP=size(x,1); % Number of points
points=[x y];
% Calculate adjacency matrix (this part of code is taken from mr. Akira
% Agata
%https://www.mathworks.com/matlabcentral/answers/369143-how-to-do-delaunay-triangulation-and-return-an-adjacency-matrix
AdjMat = false(NP);
for kk = 1:size(tri,1)
  AdjMat(tri(kk,1), tri(kk,2)) = true;
  AdjMat(tri(kk,2), tri(kk,3)) = true;
  AdjMat(tri(kk,3), tri(kk,1)) = true;
end
AdjMat = AdjMat | AdjMat';

% Calculate distance between all points
D=pdist2(points,points);
% Calculate distance between points conected with delaunay triangles 
Distance=AdjMat.*D; % All values between points which are not connected with delaunay tri are zeros

[Matt J]

hope that is correct way

Only you can know if it serves your needs, but I'm not sure it is equivalent to the neighborhood analysis you were originally pursuing. It assumes that points belonging to a common Delaunay triangle always occupy neighboring Voronoi poygons, and I'm not sure that's true.

[giometar]

that is the reason why I wrote "hope that is correct way"

I use both ways, to be sure that results are good :-)