Plotting a 3d gaussian function using surf

Let me start off by saying that I am extremely new to MATLAB. I would to use these functions and turn them into a 3d plot using surf. I have already made a mesh grid of my x and y but I am confused on how to plug my gaussian function in as Z. I would like the surf plot to look like this http://i.stack.imgur.com/QiTPe.png

x=randn(1,10000);
y=x';
[X,Y]=meshgrid(x,y);
z=(1000/sqrt(2*pi)*exp(-X.^2/2))
surf(x,y,z);shading interp

Thanks in advance for the help.

[Xiang Chen]

This is garbage answer. Making the matrix smaller will be much better.

Answer 1

[Star Strider]

This works:

N = 3.0;
x=linspace(-N, N);
y=x;
[X,Y]=meshgrid(x,y);
z=(1000/sqrt(2*pi).*exp(-(X.^2/2)-(Y.^2/2)));
surf(X,Y,z);
shading interp
axis tight

Experiment to get the result you want.

[Desmond Johnson]

Thank you so much for the quick reply. I applied your concept into my code however it does not look like the picture I described instead it looks like this . Also I am curious as to why You subtracted X-Y from the z varian;e because wouldn't that completely cancel out the variables and leave only 1000/sqrt(2*pi) as the value for z. Thank you again for all of the help

[Star Strider]

My pleasure.

This is what I get with the same code (in R2014b):

I did the subtraction in the exp function because that’s the way the Gaussian is defined.

[Image Analyst]

Pretty picture. It's worth a vote, and officially "Accepting" his answer.

[Desmond Johnson]

Thank you for explaining your process to me and I already accepted your answer. I am still not able to plug in my data and get the same surf plot that you have. The only way I get the gaussian function to display correctly is if I sort the x and y values. Is it possible to make my gaussian function look like yours without using the sort function? Here is the code I am currently using and I am running MATLAB 2014a.

x=randn(1,10000);
y=x;
[X,Y]=meshgrid(x,y);
z=(1000/sqrt(2*pi).*exp(-(X.^2/2)-(Y.^2/2)));
surf(X,Y,z);

[Star Strider]

My pleasure.

You have to use a linear vector in x and y, as did I with linspace. I see no reason to use randn here, since it is by definition random and will create very strange matrices with meshgrid.

To experiment, do a simple surf plot of the meshgrid outputs using a randn vector and using linspace for x and y. Use different randn calls for x and y each in order to avoid the ‘banding’ you saw in the plot you posted.

If you want to use randn at all to look at the distribution of the points, consider using scatter3:

x = randn(1,10000);
y = randn(1,10000);
zf=@(X,Y) (1000/sqrt(2*pi).*exp(-(X.^2/2)-(Y.^2/2)));
z = zf(x,y);

figure(1)
scatter3(x, y, z, 'b.')
grid on

Rotate it in the GUI to get an interesting perspective on the density of the distribution.