How to plot a function of multiple variables in Matlab?

Question

I'm trying to figure out a way to make a plot of a function in Matlab that accepts k parameters and returns a 3D point. Currently I've got this working for two variables m and n. How can I expand this process to any number of parameters?

K = zeros(360*360, number);
for m = 0:5:359
    for n = 1:5:360
            K(m*360 + n, 1) = cosd(m)+cosd(m+n);
            K(m*360 + n, 2) = sind(m)+sind(m+n);
            K(m*360 + n, 3) = cosd(m)+sind(m+n);
    end
end
K(all(K==0,2),:)=[];

plot3(K(:,1),K(:,2),K(:,3),'.');
end

The code you see above is for a similar problem but not exactly the same.

knedlsepp · Accepted Answer · 2015-01-06 10:06:35Z

Most of the time you can do this in a vectorized manner by using ndgrid.

[M, N] = ndgrid(0:5:359, 1:5:360);

X = cosd(M)+cosd(M+N);
Y = sind(M)+sind(M+N);
Z = cosd(M)+sind(M+N);

allZero = (X==0)&(Y==0)&(Z==0); % This ...
X(allZero) = [];                % does not ...
Y(allZero) = [];                % do ...
Z(allZero) = [];                % anything.

plot3(X,Y,Z,'b.');

A little explanation: The call [M, N] = ndgrid(0:5:359, 1:5:360); generates all combinations, where M is an element of 0:5:359 and N is an element of 1:5:360. This will be in the form of two matrices M and N. If you want you can reshape these matrices to vectors by using M = M(:); N = N(:);, but this isn't needed here. If you were to have yet another variable, you would use: [M, N, P] = ndgrid(0:5:359, 1:5:360, 10:5:1000).

By the way: The code part where you delete the entry [0,0,0] doesn't do anything here, because this value doesn't appear. I see you only needed it, because you were allocating a lot more memory than you actually needed. Here are two versions of your original code, that are not as good as the ndgrid version, but preferable to your original one:

m = 0:5:359;
n = 1:5:360;
K = zeros(length(m)*length(n), 3);
for i = 1:length(m)
    for j = 1:length(n)
            nextRow = (i-1)*length(n) + j;
            K(nextRow, 1) = cosd(m(i)) + cosd(m(i)+n(j));
            K(nextRow, 2) = sind(m(i)) + sind(m(i)+n(j));
            K(nextRow, 3) = cosd(m(i)) + sind(m(i)+n(j));
    end
end

Or simpler, but a bit slower:

K = [];
for m = 0:5:359
    for n = 1:5:360
            K(end+1,1:3) = 0;
            K(end, 1) = cosd(m)+cosd(m+n);
            K(end, 2) = sind(m)+sind(m+n);
            K(end, 3) = cosd(m)+sind(m+n);
    end
end

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