MATLAB: In a random distribution of points in square area how can we determine the density information of points in each region

Question

I want to distribute random points in a square region and then determine the density information of the points array form such that a density function can be defined for the most important points and least important points. for example in a 2D square area of 100×100 divide into four quardrants.

Lets say uniform random distribution of 100 points gives me 25 points in each quardrant (assumption). based on the distance from each other the points will be dense in certain area of quardrant but less dense in other I wish to define a density function which will highlight the importance of some points on others.

I know it might seem like a dispersed idea but could anyone give any relevant commants and codes that could help?

Thank you for taking time in reading.

Answer 1

So this is simply counting the number of points in each region. You can do this "by hand" region-by-region, something like this:

n_points = 5000;
r_point = rand(n_points,2);
reg_lims1 = [0 0.2 0.1 0.5];
dens_reg1 = find(reg_lims1(1)<=r_point(:,1)&r_point(:,1)<reg_lims1(2)&...
                 reg_lims1(3)<=r_point(:,2)&r_point(:,2)<reg_lims1(4));

which requires you to do the work. Or you could use histogram2.

HTH