3D mesh - Limit Z axis height, but just for the function, not the entire 3D domain

I'm trying to draw a parabola in 3D. However, I want to limit its extents.

I am able to limit the X and Y extents pretty easily, through the function.

ie: which limits the x to 0 to 2, and the y from -5 to 1.

X=linspace(0,2,20);
Y=linspace(-5,1,20);

However, the Z, I want to limit this aswell. So I used:

zlim([0 4])

It worked, but now my entire 3D domain is cropped! and I need to show other elements.

Any idea on how this can be achieved? I suspect my function is a bit primitive.

Sorry, I'm matlab illiterate but just starting out. I don't know enough to ask this question properly. THANK YOU for any Help!

total code:

%Curve, parabola in 3d, with limits
X=linspace(0,2,20);
Y=linspace(-5,1,20);
[X,Y]=meshgrid(X,Y);
Z=((Y.^2));
surf(X,Y,Z);
%Limit the Z axis
zlim([0 4])
%basic graphics
x1=[-3 3 3 -3];
y1=[0 0 0 0];
z1=[0 0 6 6];
patch(x1,y1,z1,	[0.71 0.72 .73]);
rotate3d on 

Answer 1

[Matt J]

One possibility.

X=linspace(0,2,20);
Y=linspace(-5,1,20);
[X,Y]=meshgrid(X,Y);
Z=((Y.^2));

Z(Z>=4)=nan;

surf(X,Y,Z);

%basic graphics
x1=[-3 3 3 -3];
y1=[0 0 0 0];
z1=[0 0 6 6];
patch(x1,y1,z1,	[0.71 0.72 .73]);

view(-75,25);

[philio63]

OH MY ! :)

Thank you for this, and for such a quick respose. I think this does it quite well!

[Matt J]

You're very welcome, but please Aceept-click the answer to certify that it worked.

[philio63]

Thanks Matt!