Define the region offunction in mesh MATLAB

Question

I want to 3D plot z=sqrt(1-x^2-y^2) for the region x^2+y^2<=1 in MATLAB.

clear all;
clc;
x=-1:0.05:1;
y=-1:0.05:1;
[X,Y]=meshgrid(x,y);
Z=sqrt(1-X.^2-Y.^2);
mesh(X,Y,Z);

I don't know how to define the region x^2+y^2<=1, because in mesh we can't define the region of function. How to define it?

Answer 1

Here's one solution (tested in Octave, but should work in MATLAB). I scale the X and Y values to lie in the unit disk.

clear all;
clc;
x=-1:0.05:1;
y=-1:0.05:1;
[X,Y]=meshgrid(x,y);
R = sqrt(1+(min(abs(X),abs(Y))./max(abs(X),abs(Y))).^2);
R(R==0) = 1;
X = X ./ R;
Y = Y ./ R;
Z = real(sqrt(1-X.^2-Y.^2));
mesh(X,Y,Z);