Random Point from meshgrid

Hi everybody, I've a simple problem. I've to pick a certain number "N" of point from a meshgrid.

The constraints of the problem are the following:

• The number of point must be exactly N;
• The point must be part of the original set of point given by the meshgrid function;
• They must be random point from normal distribution (more dense at the center of the matrix and less dense near the boundaries of the matrix);
• The points need to be different each other;

Here is an example of the original grid that can be used as a starting point. The random point selected must belong to this grid and must satisfy the constraints stated above. Someone can help me? Thank you!

Nc = 20; Nr = 20; dx = 0.2; dy = 0.2;
x = -0.5*Nc*dx:dx:0.5*Nc*dx-dx; y = -0.5*Nr*dy:dy:0.5*Nr*dy-dy;
[X,Y] = meshgrid(x,y);
figure; plot(X,Y,'gs');

[Matt J]

The 3rd requirement can't be reconciled with the others. A finite set cannot be normally distributed. A normal distribution is a continuous distribution.

[Sargondjani]

I don't know if there is out-of-the-box solution but if i had to program it myself i would do it as follows. And I am sure this is not the most advanced solution, but it would be a start for a beginner.

First try to make it work for 1D:

• make a mapping of continuous values between 0 and 1 to discrete values of x (ie. gridpoints). Use a distribution that you want. You can now draw a random number, between 0 and 1, and it will give you a gridpoint.

For 2D:

• basically do the 1D thing twice, once for x, once for y.
• Add a check whether a grid point was already selected before
• Repeat draws until you reach N points.

You may also have a look at the function randperm, but im not sure you can tweak the distribution.

Answer 1

[Image Analyst]

I think this will do what you want:

Nc = 20; Nr = 20; dx = 0.2; dy = 0.2;
x = -0.5*Nc*dx:dx:0.5*Nc*dx-dx; y = -0.5*Nr*dy:dy:0.5*Nr*dy-dy;
[X,Y] = meshgrid(x,y);
plot(X,Y,'gs');
hold on;

% Define how many points to take.
N = 50;
% Get random X coordinates.
sdx = range(X(:))/5

sdx = 0.7600

mx = mean(X(:))

mx = -0.1000

% Get more than is needed in case we need to get rid of some outside grid.
xr = mx + sdx * randn(10*N, 1) 

xr = 500×1

-0.5417 0.0336 -0.8071 0.5022 -0.4305 -2.0277 -1.0875 0.7109 -0.3767 -0.9617

% Get random Y coordinates.
sdy = range(Y(:))/5

sdy = 0.7600

my = mean(Y(:))

my = -0.1000

% Get more than is needed in case we need to get rid of some outside grid.
yr = my + sdy * randn(10*N, 1)

yr = 500×1

0.5094 -0.0078 0.6382 -0.3101 1.0879 0.2568 -0.7538 -0.3464 -0.7417 0.5768

% Get rid of points outside the grid.
badIndexes = xr < min(x) | xr > max(x);
xr(badIndexes) = [];
xr = xr(1:N); % Extract only the number we actually want.
badIndexes = yr < min(y) | yr > max(y);
yr(badIndexes) = [];
yr = yr(1:N); % Extract only the number we actually want.
% Plot initial coordinates
plot(xr, yr, 'b.', 'MarkerSize', 9)
% Snap the original random points to the closest grid location.
for k = 1 : length(xr)
    distances = sqrt((xr(k) - X(:)).^2 + (yr(k) - Y(:)) .^ 2);
    [minDistance, indexOfClosest] = min(distances);
    % Replace (xr, yr) with grid points.
    xr(k) = X(indexOfClosest);
    yr(k) = Y(indexOfClosest);
end
% Plot snapped coordinates
plot(xr, yr, 'ms', 'MarkerSize', 9, 'LineWidth', 2)
title('Initial points in blue, final snapped points in magenta')

[Image Analyst]

@Antonio Ciociola, are you still there? Did this do what you want?