How to apply Gaussian kernel to smooth density of points on 2D (algorithmically)

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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 the THEORY of it. Let's say, I am a theory person, and I am NOT in needs of programming. I just need to understand the underlying math of it, why it is still

Can someone, please, explain to me, possibly with an example? Or take me to a website that I can read about it?

I'd much appreciate that.

Thanks