generate uniformly distributed points inside a hexagon

am trying to generate uniformly distributed points inside a hexagon, but am stuck can any one help???

[the cyclist]

http://www.mathworks.com/matlabcentral/answers/6200-tutorial-how-to-ask-a-question-on-answers-and-get-a-fast-answer

[Jan]

Uniformly distributed or a random positions over a uniformly distributed randomness?

Answer 1

[SHUBHANGI VISHWAKARMA]

%In the code, I will create a hexagon centered at (0,0) with radius R. The snipplets can be used in mobile capacity predicts and general systems level simulation of cellular networks.

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

[EDITED, code formatted, Jan]

[Jenny]

How have you executed this code, because when I try to run it, it shows me an error at the idx?? It doesn't execute. Which are the outputs of this code?

[Jan]

@Jenny: This answer has been posted 3 years ago. This was the only contribution of the author. The code is not formatted correctly, so if you just copy&paste it, it is expected to crash. If you have done some further cleaning of the code, please post the version you use. If it produces an error message, post a copy of the complete message, such that the readers can reconsider, what you are doing and observing. Thanks.

[Eman S]

The code worked successfully after being formatted by @Jan.

After running the code, it gave the following output as shown in the following image;

[Mystery Mystery]

What changes should be done for a hexagon with a specific centre (other than the origin) please? Thanks in advance.

[Jan]

@Mystery Mystery: Use the original code and add the offset afterwards.

[Image Analyst]

Note: The code gives uniformly randomly distributed points, NOT uniformly distributed (like a grid or hexagonal honeycomb array) like the question asked for, where no randomness was mentioned. There IS a difference.

[Mystery Mystery]

Thank you peeps! but im getting ''index exceeds matrix dimensions'' for the line c_x= c_x(idx(1:N));

Answer 2

[Bruno Luong]

Here is a generating method without rejection

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

% Generate uniform points in the simplex
% convex combination of 3points in R^3: (1,0,0) (0,1,0) (0,0,1)
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)]];
% use X as a barycentric of the triangle (0,1,z6) in the complex plane
% so point Z is uniform in this triangle
z6 = exp(2i*pi/6);
Z = [0, 1, z6]*X;
% multiply by random 6th-roots of 1 to map into unit hexagonal
Z = Z .* (z6.^floor(6*rand(1,n)));
% shift and scale
x = centerx+R*real(Z);
y = centery+R*imag(Z);

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

[Mystery Mystery]

Thank you so much sir, could you please add a few comments in the code so that i get a clear view of the method? thanks again.

[Bruno Luong]

Done

[Amar Patra]

Hi Bruno, I want to store the coordinates of these points in a two column csv file. The first column will have the x-coordinate while the second will have the y-coordinate. I tried with putting these instructions right before plot(x,y,'.'):

a = [x y] dlmwrite('file.csv',a,'-append','delimiter',',','newline', 'pc')

but the generated csv file has all the points stored in the fashion (x1, x2, x3, ..., xn, y1, y2, y3, ..., yn).

Could you please help!

[Bruno Luong]

a = [x(:),y(:)]

before write it.

[Amar Patra]

Thank you so much Bruno!

[Omar Allahham]

hi bruno

if I want to make the points move randomly and continuously in this hexagonal what should i do?