I have a set of points on a 2D surface and need to build a heatmap. However, I also need to smooth out the density/distribution by applying some sort of kernel (Gaussian kernel, for example).
I Know what Gaussian distribution is, and I have no idea, how mathematically apply the Gaussian kernel to the points on 2D so I can get a smooth distribution or density of points. I know there are functions in Wolfram to do that, but this is more like a research problem, so I need to understand how this is done.
Can someone, please, explain to me mathematically how this is done, and possibly with an example? Or take me to a website that I can read about it?
I'd much appreciate that.
Thanks
Since the points are discrete, you simply translate the kernel to each point and scale it by the height (value) at that point, and then sum the results.
$f(x,y)=\sum_{i=1}^{n}\sum_{j=1}^{n}{p_{i,j}f(x-x_{i},y-y_{j})}$
where $f(x,y)$ is your kernel and $p_{i,j}$ is the value of the point at $(x_{i},y_{j})$