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Meshgrid to be used for hexagons

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Nupur
Nupur on 16 Jun 2023
Edited: Bruno Luong on 28 Jun 2023
I want to use meshgrid for generating a hexagonal grid. Also I should get the cooridntes of each node in it.
  1 Comment
Angelo Yeo
Angelo Yeo on 16 Jun 2023
You can refer to the comment in the URL below.
https://www.mathworks.com/matlabcentral/answers/284805-create-hexagonal-grid-with-a-central-cell

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Accepted Answer

Subhajyoti Halder
Subhajyoti Halder on 28 Jun 2023
Hi Nupur,
It is my understanding, it is required to use meshgrid to generate a hexagonal grid and get the cooridntes of each node in it.
Here, I have implemented it using ‘meshgrid()’ in MATLAB R2023a.
In the below code,it is using the meshgrid function within a loop to generate the x and y coordinates for each row of the grid.
% Define the parameters of the hexagonal grid
% radius: radius of the hexagon
radius = 5;
% Number of rows in the grid
numRows = 10;
% Generate the x and y coordinates of the hexagonal grid
x = [];
y = [];
for row = 1:numRows
% xOffset, yOffset: variables to shift the coordinates of each row
% to form a hexagonal pattern.
xOffset = (mod(row, 2) * sqrt(3) / 2) * radius;
yOffset = row * (3 / 2) * radius;
% meshgrid() generates the x,y coordinates for each row of the grid.
[xRow, yRow] = meshgrid(0:radius*sqrt(3), 0:2*radius);
xRow = xRow(:)' + xOffset;
yRow = yRow(:)' + yOffset;
x = [x, xRow];
y = [y, yRow];
end
% Display the coordinates of each node in the hexagonal grid
for i = 1:numel(x)
fprintf('Node %d: (%.2f, %.2f)\n', i, x(i), y(i));
end
Node 1: (4.33, 7.50) Node 2: (4.33, 8.50) Node 3: (4.33, 9.50) Node 4: (4.33, 10.50) Node 5: (4.33, 11.50) Node 6: (4.33, 12.50) Node 7: (4.33, 13.50) Node 8: (4.33, 14.50) Node 9: (4.33, 15.50) Node 10: (4.33, 16.50) Node 11: (4.33, 17.50) Node 12: (5.33, 7.50) Node 13: (5.33, 8.50) Node 14: (5.33, 9.50) Node 15: (5.33, 10.50) Node 16: (5.33, 11.50) Node 17: (5.33, 12.50) Node 18: (5.33, 13.50) Node 19: (5.33, 14.50) Node 20: (5.33, 15.50) Node 21: (5.33, 16.50) Node 22: (5.33, 17.50) Node 23: (6.33, 7.50) Node 24: (6.33, 8.50) Node 25: (6.33, 9.50) Node 26: (6.33, 10.50) Node 27: (6.33, 11.50) Node 28: (6.33, 12.50) Node 29: (6.33, 13.50) Node 30: (6.33, 14.50) Node 31: (6.33, 15.50) Node 32: (6.33, 16.50) Node 33: (6.33, 17.50) Node 34: (7.33, 7.50) Node 35: (7.33, 8.50) Node 36: (7.33, 9.50) Node 37: (7.33, 10.50) Node 38: (7.33, 11.50) Node 39: (7.33, 12.50) Node 40: (7.33, 13.50) Node 41: (7.33, 14.50) Node 42: (7.33, 15.50) Node 43: (7.33, 16.50) Node 44: (7.33, 17.50) Node 45: (8.33, 7.50) Node 46: (8.33, 8.50) Node 47: (8.33, 9.50) Node 48: (8.33, 10.50) Node 49: (8.33, 11.50) Node 50: (8.33, 12.50) Node 51: (8.33, 13.50) Node 52: (8.33, 14.50) Node 53: (8.33, 15.50) Node 54: (8.33, 16.50) Node 55: (8.33, 17.50) Node 56: (9.33, 7.50) Node 57: (9.33, 8.50) Node 58: (9.33, 9.50) Node 59: (9.33, 10.50) Node 60: (9.33, 11.50) Node 61: (9.33, 12.50) Node 62: (9.33, 13.50) Node 63: (9.33, 14.50) Node 64: (9.33, 15.50) Node 65: (9.33, 16.50) Node 66: (9.33, 17.50) Node 67: (10.33, 7.50) Node 68: (10.33, 8.50) Node 69: (10.33, 9.50) Node 70: (10.33, 10.50) Node 71: (10.33, 11.50) Node 72: (10.33, 12.50) Node 73: (10.33, 13.50) Node 74: (10.33, 14.50) Node 75: (10.33, 15.50) Node 76: (10.33, 16.50) Node 77: (10.33, 17.50) Node 78: (11.33, 7.50) Node 79: (11.33, 8.50) Node 80: (11.33, 9.50) Node 81: (11.33, 10.50) Node 82: (11.33, 11.50) Node 83: (11.33, 12.50) Node 84: (11.33, 13.50) Node 85: (11.33, 14.50) Node 86: (11.33, 15.50) Node 87: (11.33, 16.50) Node 88: 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For more details on the ’meshgrid’, kindly go through the following documentation

More Answers (2)

Bruno Luong
Bruno Luong on 28 Jun 2023
Code from this thread. Not sure why you must use meshgrid
m = 7;
n = 8;
[A,B,C,X,Y] = HexGraphPart2(m,n);
G = graph(A+B+C);
close all
figure;
h = plot(G);
% Change node coordinates on regular hexagonal pattern
set(h,'XData',X(:),'YData',Y(:));
axis('equal');
function [H,NW,NE,X,Y]=HexGraphPart2(m,n)
x = (0:m-1)';
y = (0:n-1);
K = 1 + x + m*y;
p = m*n;
H = sparse(K(1:2:end-1,1:2:end),K(2:2:end,1:2:end),1,p,p) + ...
sparse(K(2:2:end-1,2:2:end),K(3:2:end,2:2:end),1,p,p);
NW = sparse(K(1:2:end,1:2:end-1),K(1:2:end,2:2:end),1,p,p) + ...
sparse(K(2:2:end,2:2:end-1),K(2:2:end,3:2:end),1,p,p);
NE = sparse(K(2:2:end,1:2:end-1),K(2:2:end,2:2:end),1,p,p) + ...
sparse(K(1:2:end,2:2:end-1),K(1:2:end,3:2:end),1,p,p);
H = H+H';
NW = NW+NW';
NE = NE+NE';
if nargout >= 5
X = (3*x - mod(x+y,2))/2;
Y = (sqrt(3)/2)*y + 0*x;
end
end
  1 Comment
Nupur
Nupur on 28 Jun 2023
Thanks, we can even think this approach if meshgrid usage wasnt mandatory

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Bruno Luong
Bruno Luong on 28 Jun 2023
Edited: Bruno Luong on 28 Jun 2023
If you need coordinates and no connectivity graph, the code can be simplified, you can use meshgrid if you wish to MATLAB autoexpansion is much prefered
m = 7;
n = 8;
x = (0:m-1)';
y = (0:n-1);
X = (3*x - mod(x+y,2))/2;
Y = (sqrt(3)/2)*y + 0*x;
close all
figure;
h = plot(X,Y,'ok');
axis('equal');
  2 Comments
Nupur
Nupur on 28 Jun 2023
We will require connectivity table,graph is just for interpretation
Bruno Luong
Bruno Luong on 28 Jun 2023
Edited: Bruno Luong on 28 Jun 2023
If you absolutely want to use meshgrid then
m = 7;
n = 8;
[x,y] = meshgrid(0:m-1, 0:n-1);
X = (3*x - mod(x+y,2)) / 2;
Y = (sqrt(3)/2)*y;
figure;
h = plot(X,Y,'ok');
axis('equal');

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