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

Question

Aravind Varma Dantuluri 2024-8-10，7:07

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评论： Aravind Varma Dantuluri 2024-8-13，2:19

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.

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Matt J 2024-8-13，0:32

Please give us the points so we can demonstrate solutions.

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Answer 1

Matt J 2024-8-13，0:53

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编辑：Matt J 2024-8-13，1:51

在 MATLAB Online 中打开

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

<mw-icon class=""></mw-icon>

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

plot(hex(:,1),hex(:,2),'x', nearest(:,1),nearest(:,2),'o',given(:,1),given(:,2),'s');

legend Vertices Nearest Given

axis equal padded

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Aravind Varma Dantuluri 2024-8-13，2:19

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

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Answer 2

Mario Malic 2024-8-10，11:04

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在 MATLAB Online 中打开

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

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Aravind Varma Dantuluri 2024-8-12，2:52

Thanks for the answer but this doesn't work.

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