How to distribute points uniformly through the grid of multiple hexagons?

Hi all, I have the following code to draw hexagonal grid.

Rad3Over2 = sqrt(3) / 2;
[X Y] = meshgrid(-.2:0.2:1.6);
n = size(X,1);
X = Rad3Over2 * X;
Y = Y + repmat([0 0.5],[n,n/2]);
% Plot the hexagonal mesh, including cell borders
[XV YV] = voronoi(X(:),Y(:)); plot(XV,YV,'b-')
axis equal, axis([.2 1.2 .2 1]), zoom on

My question is:

How to distribute uniform number of points into each hexagonal (for example, 4 points into each hexagonal)?

Thanks in advance.

[Rik]

Is the placement allowed to be regular, or should it be a random position within each heaxagon?

[Image Analyst]

Original question (in case he changes it again):

How to distribute points uniformly through the grid of multiple hexagons?

Hi all, I have the following code to draw hexagonal grid.

Rad3Over2 = sqrt(3) / 2;
[X Y] = meshgrid(-.2:0.2:1.6);
n = size(X,1);
X = Rad3Over2 * X;
Y = Y + repmat([0 0.5],[n,n/2]);
% Plot the hexagonal mesh, including cell borders
[XV YV] = voronoi(X(:),Y(:)); plot(XV,YV,'b-')
axis equal, axis([.2 1.2 .2 1]), zoom on

My question is:

How to distribute uniform number of points into each hexagonal (for example, 4 points into each hexagonal)?

Thanks in advance.

[Rik]

@Eman, Why did you delete your comments?

Answer 1

[Jan]

You can do this for each hexagon:

1. Get the coordinates of the surrounding square (not rectangle) with the side length L.
2. Choose coordinates randomly using L * rand(1, 2) and reject points, which are outside the hexagon. If the point is inside, store the coordinates.
3. Proceed with step 2. until you have the wanted number of points.

Two examples for code:

• In a 3D shape: https://www.mathworks.com/matlabcentral/answers/353266-how-to-generate-100-random-points-inside-the-figure#answer_278594
• In 2D considering a minimal distance: https://www.mathworks.com/matlabcentral/answers/322431-randompoints-condition-distance.

For a constructive method without rejection see John D'Errico excellent instructions: https://www.mathworks.com/matlabcentral/answers/327990-generate-random-coordinates-inside-a-convex-polytope

[Eman S]

Thanks for your answer. But, the surrounding area should be rectangle(not square).

[Rik]

Why do you want the region to be rectangular? You're going to reject points anyway.

[Eman S]

I wouldn't reject points. As shown in attached picture,in the region (1.2*1) . There are hexagons until(1.1) and halves of hexagons also. The points should distributed through the (1.2*1 region).

[Jan]

@Eman: I do not understand your comment. What is a "1.2*1 region"? I've explained a way to create points in one hexagon. Pick each hexagon and use the suggested method to insert 4 random points. I have no idea how you want to treat the "half" hexagons.