error in displaying a 3-D Plot in matlab

Question

I wanted to draw the following function in matlab:
f(x,y) = sqrt(1-x^2-4y^2) ,(if (x^2+4*y^2) <=1 )

        =  0                  ,otherwise.

I wrote the following code in matlab:

  x=0:0.1:10;  
  y=0:0.1:10;
  z=x.^2+4*y.^2;
  if (z <=1)
   surf(x,y,z);

  else
   surf(x,y,0);
  end

but the following error is displayed:
surface: rows (Z) must be the same as length (Y) and columns (Z) must be the same as length (X)
How shall I avoid this error...

Answer 1

I think you should really check what you are doing... line by line

x = 0:0.1:10; % define x-array 1x101
y = 0:0.1:10; % define y-array 1x101
z = x.^2+4*y.^2; % define z-array 1x101

However, surf needs a matrix as input for z therefore the syntax as you use it here is incorrect.

Instead, create a x-grid and y-grid:

[xx, yy] = meshgrid(x, y); % both being 101x101 matrices

zCheck = xx.^2+4*yy.^2; % 101x101
zz     = sqrt(1-xx.^2-4*y.^2)

Concerning the if statement, you better change the values before plotting:

zz(zCheck > 1) = 0; % replace the values larger than 1 by zero (use logical indexing)

figure(100);
surf(x, y, zz);