Different results using mesh and surf

I'm trying to graph the function xye^(-(x.^2+y.^2)), and I used both surf and mesh to do so. Below is the code. The problem is the two graphs are different. The surf function seems to have gotten it correct, but the mesh function looks like it graphed the absolute value of the function. Why is there this difference?

clear
clc

r=100;
x1 = linspace(-10,10,r);
y2 = linspace(-10,10,r);

[x,y] = meshgrid(x1,y2);

z=x.*y.*exp(-(x.^2+y.^2));

figure
surf(x,y,z)
xlabel('x');
ylabel('y');
zlabel('z');
grid on
shading interp
colorbar

figure
mesh(x,y,z.^2)
xlabel('x');
ylabel('y');
zlabel('z');
grid on

Answer 1

[Adam Danz]

> The problem is the two graphs are different. The surf function seems to have gotten it correct, but the mesh function looks like it graphed the absolute value of the function

Hint

mesh(x,y,z.^2)
%         ^^^

Also see the difference in the z-axis values. The range of z values in the mesh version is not the absolute value of the z values in the surf version, it's squared (which forces negative values to be positive).

[Nathan Shapiro]

Oh, I can't believe I missed that. Thank you for your help!

[Adam Danz]

Sometimes a 2nd pair of eye is all that's needed.