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Mesh plot of the function sqrt(y-x^2)

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I want to plot the function The function is defined for . With
f = @(x,y)sqrt(y-x.^2);
fmesh(f,[-3 3 0 9])
I get a mesh plot of the function in the rectangle [-3,3]X[0,9]. I want to plot the function using meshgrid. The following code results to complex values error message.
x = -3:1:3
y = 0:1:9
[X, Y] = meshgrid(x,y)
Z = sqrt(Y-X.^2)
mesh(X,Y,Z)
The problem is that Z is evaluated for not suitable pairs of (X,Y). What am I doing wrong?

Accepted Answer

Star Strider
Star Strider on 6 Apr 2021
Edited: Star Strider on 6 Apr 2021
Try this:
x = -3:1:3;
y = 0:1:9;
[X, Y] = meshgrid(x,y);
Y = Y.*(Y>=X.^2); % Select Y ≥ X^2
Z = sqrt(Y-X.^2);
Zre = Z.*(imag(Z)==0); % Select Only Real Values Of ‘Z’
figure
mesh(X,Y,Zre)
EDIT — (5 Apr 2021 at 15:56)
Added:
Y = Y.*(Y>=X.^2); % Select Y ≥ X^2
to accord with the edited Question.
  5 Comments
Star Strider
Star Strider on 6 Apr 2021
As always, my pleasure!
The easiest solution is to use fmesh. It is possible to examine the fmesh code using edit or type (however that is not very revealing, since it calls fsurf, that it is posible to examine in some detail) to see exactly how it works. The fsurf function then calls a number of other funcitons that I have not taken the time to examine closely. My information on the ‘f’ plotting functions derives from other discussions in MATLAB Central that I have read over the years.

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More Answers (2)

VBBV
VBBV on 6 Apr 2021
%f
x = -3:1:3
y = 0:1:9
[X, Y] = meshgrid(x,y)
Z = real(sqrt(Y-X.^2))
mesh(X,Y,Z)
Plot only the real part
  3 Comments
Dimitrios Anagnostou
Dimitrios Anagnostou on 6 Apr 2021
Thank you very much for your time and effort. Still it is not the required plot. Just compare it with
clear x,y
f = @(x,y)sqrt(y-x.^2);
fmesh(f,[-3 3 0 9])

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Bruno Luong
Bruno Luong on 6 Apr 2021
Here is the surface in meshgrid form
s = -1:0.01:1;
y = 0:0.1:9;
[S, Y] = meshgrid(s,y);
X = S.*sqrt(Y);
Z = sqrt(max(Y-X.^2,0));
figure
mesh(X,Y,Z)

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