Placing gaussian function at different points on mesh

Question

I am looking to create a random distribution of gaussian curve shapes on a large mesh. I basically want to take this function :

Z = 0.3*exp(-5*(x.^2+y.^2))-0.1;
Z(Z<0)=0;

and be able to choose its location (in x & y coords), and have multiple plots.

So at the moment, I have this:

But I would like to have this generated:

Is there a reasonably simple way to do this? I have tried to play around with the code but I am afraid I'm not a mathematics, nor a MATLAB expert.

Any help would be much appreciated.

Answer 1

Look at this!

the way this works:

1. Generate random point
2. Check if point is closer than sigma
3. If its not, then create a gaussian there!
4. repeat until Ngaussians reached

code:

clear
n_gaussians=15;
gaussians=0;
sigma=1; % std
mindist=sigma; % if distance is smaller than this gaussians "collide"

[x,y]= meshgrid(-5:0.1:5,-5:0.1:5);
used=[];
Z=zeros(size(x));
while gaussians<n_gaussians

    xm=(rand(1)-0.5)*10;
    ym=(rand(1)-0.5)*10;
    notvalid=0;
    for ii=1:size(used,2)
        % if we are too close to any point.
       if norm([xm-used(1,ii),ym-used(2,ii)])<mindist
           notvalid=1; % do not add this gauusian
       end
    end
    if notvalid
        continue
    end
    used(:,end+1)=[xm;ym];
    Zaux = 0.3/sigma*exp(-5*((x-xm).^2+(y-ym).^2)/sigma.^2)-0.1;
    Zaux(Zaux<0)=0;
    Z=Z+Zaux;
    gaussians=gaussians+1;
end

surf(x,y,Z);
axis equal