Loop inside a loop isn't working

I am trying to create a hemisphere. But I seems like the loop inside the loop isn't working. Has somebody an idea what might be the problem?

% the values of the adjacent site
x =[-1:0.001:1];
%creating a template where I can fill in the values later on
y=zeros(2000, 2000);
% creating the highest arc (ARC A) of a hemisphere
j=0

j = 0

for i=x
    j=j+1;
y(j, 1000)=sqrt(1-(i^2));
end


%%
% filling in the other values, creating arcs based on the values of ARC A
for w=1:2000
    H=y(w,1000) ;
    L=round(H*1000);
    r=1000-L;
    L2=L/1000;
    for xmod=-L2:0.001:L2
        y(r,w)=sqrt(H^2-(xmod)^2); 
        r=r+1;
    end
end

Index in position 1 is invalid. Array indices must be positive integers or logical values.

% plotting the matrix
surfl(y)
shading interp

I have also attached a sketch of my idea so you can imagine it better.

Answer 1

[Dyuman Joshi]

There are 2001 elements in x, not 2000. (Imo) It's better to use numel() to get the number of elements, rather than manually using a value.

% the values of the adjacent site
%% Square brackets are super-fluous here
x = -1:0.001:1;

n = numel(x)

n = 2001

%creating a template where I can fill in the values later on
y=zeros(n);

%% Vectorized
y(:,1000) = sqrt(1-x.^2); % creating the highest arc (ARC A) of a hemisphere

% filling in the other values, creating arcs based on the values of ARC A
for w=1:n
    H=y(w,1000);
    L=round(H*1000);
    
    %% Correction, as H ranges from [0 1], L range from [0 1000]
    %% Thus, 1000-L would be 0 when L=1000, which can not be used as an index in MATLAB
    r = 1001-L;
    L2 = L/1000;
    xmod = -L2:0.001:L2;
    
    %% Vectorized
    y(r+(0:numel(xmod)-1), w) = abs(sqrt(H^2-xmod.^2));

end

% plotting the matrix
surfl(y)
shading interp

[M]

Thanks a lot, you really helped me! I realized that the main problem was that I haven't used abs, but I am also very grateful for your improvements because they make the code much easier. I am playing a bit around with Matlab and I am wondering whether it is possible to create a ball so you have 2 z-values for each xy-value. Is that possible?

[Dyuman Joshi]

You are welcome!

Yes, Vectorization improves the code by many factors!

"I am wondering whether it is possible to create a ball so you have 2 z-values for each xy-value."

Do you mean like this -

x = -1:0.001:1;

n = numel(x);

y=zeros(n);

y(:,1000) = sqrt(1-x.^2);

for w=1:n
    H=y(w,1000);
    L=round(H*1000);
    
    r = 1001-L;
    L2 = L/1000;
    xmod = -L2:0.001:L2;
    
    y(r+(0:numel(xmod)-1), w) = abs(sqrt(H^2-xmod.^2));

end

%% Plot half-sphere
surfl(y)
hold on
%% Plot the other half, using the negative of the values
surfl(-y)
shading interp

Answer 2

[Steven Lord]

If this isn't a homework assignment, I'd just use the sphere function.

[X, Y, Z] = sphere;
figure
surf(X, Y, Z)
title("Full sphere")
axis square

limits = axis(gca);
figure
% Chop off the bottom half of the sphere, leaving a copy of Z unchanged so
% you can compare the two arrays Z and Z2
Z2 = Z;
Z2(Z < 0) = NaN;
surf(X, Y, Z2)
title("Half sphere")
axis equal
axis(limits)