How to tell if random points are in the same feature or not

I have a vornoi diagram populated with random points of 2 arrays. From each of the points I can calculate the distance between Array1 and Array 2. Since the voroin is treated like a grain structure . How can I tell if the distance between each of the 2 points are in the same Voronoi or not?

For example is x(1) and y(1) in the same voronoi or is x(555) and y(555) in the same Vornoi ?

Not entirely sure how I can achieve this or how to format the code. Any help would be appreciated.

X=rand([1 1000]); % points for Voronoi
Y=rand([1 1000]); % points for Voronoi

x = rand(1, 2000); % Random Points Array 1
y = rand(1, 2000); % Random Points Array 2


%% Distance between Random points Method 1

Distance = zeros(length(x) , length(y));
for i = 1:length(x)
   for j = 1:length(y)
      if i ~= j
        Distance(i,j) = sqrt((x(i)-x(j))^2 + (y(i)-y(j))^2);  
      end
   end
end

%% Distance between Random points Method 2

D = hypot(x-x.', y-y.'); % without using for loop


%% Plot Voronoi and scatter points onto plot

figure(1)
scatter(x, y ,'*')
hold on
voronoi(X,Y)

[Image Analyst]

You need to label your regions. We talked about this before in your last post. And I think I gave you some things to consider. Isn't your actual situation an image of metallic grains, not a voronoi diagram? If someone answers this question, it will not be applicable, adaptable, or appropriate to your actual situation. I know you're thinking you're making it simpler but I think you'd just get an answer that won't work in your actual real world situation. Can you post your actual image?

[David Harra]

Hey

I was using this Voronoi as an example before atually applying it to my real grain data, which I believe would be more complicated and I find coding really challenging, so aplogies. My actual grain structure you can see below where the grains are in sizes of microns.

Answer 1

[Dimitrios Patsatzis]

Hi David,

You could use the knnsearch built-in function to find the neigbhooring points

https://www.mathworks.com/help/stats/knnsearch.html

and then check if any of these in the same Voronoi cell with the reference one.

I haven't cross checked, but I hope it helps.

Dimitris