A Function for multiple 2D Gaussians

[ThunderLight]

I'm trying to put together a function that sums multiple 2D Gaussian functions in one graph (i.e.; multiple Gaussian pyramids).

So far from my research, I formed the following function definition:

I'm not sure if my research led me to the correct way of forming the function. Is this how Gaussians can be represented to give me a graph of multiple Gaussians in one surface?

 

[BvU]

Yes. Kind of a landscape pocked with lots of hills.

 

[ThunderLight]

Yes. Kind of a landscape pocked with lots of hills.

Yes, that's what I'm looking for. But I'm worried about the notation, and placement of the i
Is it also correct for me to say ΣGaussians to represent how many hills, n? - Or there's a more formal notation for that?

 

[BvU]

Yes, I would say $n$ is the count of the hills. You confuse the issue somewhat by using the symbol $f$ twice.

 

[ThunderLight]

Yes, I would say $n$ is the count of the hills. You confuse the issue somewhat by using the symbol $f$ twice.

Would it be more proper/clearer to use only the first $f$ and go on directly to saying $=...$ instead of redefining what $f$ function is?Thank you for your answer and affirmation.

 

[BvU]

Either that, or you use a symbol g for a single gaussian:

I take it you want to pass $f$ to a surface plot program or something.

 

[mfb]

I would put the index i next to the function name: $g_i(x,y)$

"f(gaussians)" doesn't make sense. f is a function of x and y: f(x,y).

 

[ThunderLight]

Either that, or you use a symbol g for a single gaussian:
View attachment 114288

I take it you want to pass $f$ to a surface plot program or something.

Great, thank you for your tip.

 

[ThunderLight]

I would put the index i next to the function name: $g_i(x,y)$

"f(gaussians)" doesn't make sense. f is a function of x and y: f(x,y).

I just realized that, thank you for pointing this out. You're right.
Thank you very much