I am trying to generate uniformly distributed points inside a hexagon of specific centre (other than the origin). Any help is most welcome, thank you.

I have seen codes like this with origin as centre only, but i need to apply it for hexagonal cells of different centres.

[jonas]

If you have a code for the origin, just move them by adding the coordinates of your centre?

[Mystery Mystery]

Here's the code. I don't understand how to add the centre, could you help please?

N = 400; %Number of users

R = 10; %Radius of Hexagon

%Define the vertexes of the hexagon. They for angles 0, 60, 120, 180, 240 and 300 withe origin.

%Vertexes

v_x = R * cos((0:6)*pi/3);

v_y = R * sin((0:6)*pi/3);

%The method used here is to generate many points in a square and choose N points that fall within the hexagon

%Generate 3N random points with square that is 2R by 2R

c_x = R-rand(1, 3*N)*2*R;

c_y = R-rand(1, 3*N)*2*R;

%There is a command in MATLAB inploygon.

%The command finds points within a polygon region.

%get the points within the polygon

IN = inpolygon(c_x, c_y, v_x, v_y);

%drop nodes outside the hexagon

c_x = c_x(IN);

c_y = c_y(IN);

%choose only N points

idx = randperm(length(c_x));

c_x = c_x(idx(1:N));

c_y = c_y(idx(1:N));

plot(c_x, c_y, 'r*');

hold on;

plot(v_x,v_y);

axis square;

hold off

Answer 1

[Star Strider]

Define the centre points, then add them as appropriate to ‘v_x’ and ‘v_y’ and ‘c_x’ and ‘c_y’:

xcntr = 7;                              % X-Coordinate Of Centre Of Hexagon & Points
ycntr = 5;                              % Y-Coordinate Of Centre Of Hexagon & Points
...
v_x = R * cos((0:6)*pi/3) + xcntr;
v_y = R * sin((0:6)*pi/3) + ycntr;
...
c_x = R-rand(1, 3*N)*2*R + xcntr;
c_y = R-rand(1, 3*N)*2*R + ycntr;

In context:

N = 400; %Number of users
R = 10; %Radius of Hexagon

xcntr = 7;                              % X-Coordinate Of Centre Of Hexagon & Points
ycntr = 5;                              % Y-Coordinate Of Centre Of Hexagon & Points
%Define the vertexes of the hexagon. They for angles 0, 60, 120, 180, 240 and 300 withe origin.

%Vertexes
v_x = R * cos((0:6)*pi/3) + xcntr;
v_y = R * sin((0:6)*pi/3) + ycntr;

%The method used here is to generate many points in a square and choose N points that fall within the hexagon

%Generate 3N random points with square that is 2R by 2R
c_x = R-rand(1, 3*N)*2*R + xcntr;
c_y = R-rand(1, 3*N)*2*R + ycntr;

%There is a command in MATLAB inploygon.
%The command finds points within a polygon region.

%get the points within the polygon
IN = inpolygon(c_x, c_y, v_x, v_y);

%drop nodes outside the hexagon
c_x = c_x(IN);
c_y = c_y(IN);

%choose only N points
idx = randperm(length(c_x));
c_x = c_x(idx(1:N));
c_y = c_y(idx(1:N));

plot(c_x, c_y, 'r*');
hold on;
plot(v_x,v_y);
hold off
axis equal
axis([-1  1    -1  1]*20)

[Mystery Mystery]

Thank you!

[Star Strider]

As always, my pleasure!

Answer 2

[jonas]

Simply move the center of the polygon and the random points a distance [xc;yc] from the origin. Here is your adjusted code:

N = 400; %Number of users
R = 10; %Radius of Hexagon

% Centers
xc=5;
yc=10;

%Define the vertexes of the hexagon. They for angles 0, 60, 120, 180, 240 and 300 withe origin.

%Vertexes
v_x = (R * cos((0:6)*pi/3))+xc;
v_y = (R * sin((0:6)*pi/3))+yc;

%The method used here is to generate many points in a square and choose N points that fall within the hexagon

%Generate 3N random points with square that is 2R by 2R
c_x = (R-rand(1, 3*N)*2*R)+xc;
c_y = (R-rand(1, 3*N)*2*R)+yc;

%There is a command in MATLAB inploygon.
%The command finds points within a polygon region.
%get the points within the polygon
IN = inpolygon(c_x, c_y, v_x, v_y);

%drop nodes outside the hexagon
c_x = c_x(IN);
c_y = c_y(IN);

%choose only N points
idx = randperm(length(c_x));
c_x = c_x(idx(1:N));
c_y = c_y(idx(1:N));
plot(c_x, c_y, 'r*');
hold on;
plot(v_x,v_y);
axis square;
hold off

[Mystery Mystery]

Thank you so much!

[jonas]

cheers!

Answer 3

[Bruno Luong]

Here is a method without rejection:

R = 3;
centerx = 3;
centery = 7;
n = 10000;

m = 3;
X = rand(m-1,n) .^ (1./(m-1:-1:1)'); % use bsxfun(@power,...) for old release
X = cumprod([ones(1,n);X]).*[ones(m,n)-[X;zeros(1,n)]];
z6 = exp(2i*pi/6);
Z = [0, 1, z6]*X;
Z = Z .* (z6.^floor(6*rand(1,n)));
x = centerx+R*real(Z);
y = centery+R*imag(Z);

plot(x,y,'.')
axis equal

[Mystery Mystery]

Thank you!

[Mystery Mystery]

Bruno Luong Could you please provide comments on the code for proper understanding? thanks in advance.

[Bruno Luong]

Code more with comments here

[Mystery Mystery]

Thank you so much!