How can I find the set of vertices of hexagons which are adjacent to a random point?

I have a set of hexagons whose blue coordinates are known:

I have a random red point and I need to know the 4 (in some cases it would be 3) points which are immediately adjacent to it. These points are contained in the black box shown for illustration.

I tried to sort the blue points by measuring distances but I keep getting extra points (shown by black arrows) or missing the required points.

[Matt J]

Please give us the points so we can demonstrate solutions.

Answer 1

[Matt J]

hex=[         0   -1.0000
   -0.8660   -0.5000
   -0.8660    0.5000
         0    1.0000
    0.8660    0.5000
    0.8660   -0.5000
    1.7321   -1.0000
    0.8660   -0.5000
    0.8660    0.5000
    1.7321    1.0000
    2.5981    0.5000
    2.5981   -0.5000
    3.4641   -1.0000
    2.5981   -0.5000
    2.5981    0.5000
    3.4641    1.0000
    4.3301    0.5000
    4.3301   -0.5000]  %hexagon points

hex = 18x2

0 -1.0000 -0.8660 -0.5000 -0.8660 0.5000 0 1.0000 0.8660 0.5000 0.8660 -0.5000 1.7321 -1.0000 0.8660 -0.5000 0.8660 0.5000 1.7321 1.0000

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hex=unique(hex,'rows');

given=[1.2,-1];

pts=[given;hex];

DT=delaunayTriangulation(pts);

CL=DT.ConnectivityList;

idx=any(CL==1,2);
idx=setdiff(CL(idx,:),1);

nearest=pts(idx,:)

nearest = 3x2

0 -1.0000 0.8660 -0.5000 1.7321 -1.0000

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plot(hex(:,1),hex(:,2),'x', nearest(:,1),nearest(:,2),'o',given(:,1),given(:,2),'s'); 
legend Vertices Nearest Given
axis equal padded

[Aravind Varma Dantuluri]

I just saw your comment now. I noticed you generated the points on your own. Thanks for the effort and answer.

Answer 2

[Mario Malic]

Hi,

here's some code to give you an idea

X = rand(3,3);
Y = rand(3,3);

pts = [X(:), Y(:)];
distance = squareform(pdist(pts)); % symmetric matrix that contains distances between points

% distance between pt3 and all other pts
[~, idx] = sort(distance(:, 3));
closestPts = idx(2:5) % first one is distance between pt3 and pt3 so we ignore that

[Aravind Varma Dantuluri]

Thanks for the answer but this doesn't work.

1. Not all points are not random. Only 1 is. The rest are vertices of hexagon.
2. Sorting by distance won't work. Take the below example where the random point is blue mark:

We need to get the 4 points marked by the red line. But if we sort by distance, we omit the black mark and get the red mark.

[Mario Malic]

That random point is just an example, it can be arbitrary!