如何绘制球函数？

Question

I tried plotting a sphere to look like this .

This earlier question contains the code where i tried plotting.

That previous question was answered, but now I am having trouble plotting the sphere function as shown in the plot given by the link above.

Edit This is the sphere function i am using:

function ph = sphereFN(x)
    ph = sum(x.*x, 2);

end

Edit Outcome should look something like this:

NB: I have changed the function from sphere to sphereFN to avoid the conflict with the matlab sphere.

Answer 1

Your sphereFN may not be doing what you expect it to do. It looks like you are trying to implement a sum of different powers test based on this function:

However, your implementation as:

ph = sum(x.*x, 2);  

does not resemble that function. How about using this as a starting point:

x = linspace(-1,1,25);

for I=1:size(x,2)
    for J=1:size(x,2)
        s(I,J) = abs(x(I))^2 + abs(x(J))^3;
    end
end

[xx,yy] = meshgrid(linspace(-1,1,25));  

surfc(xx,yy,s)

As your are in essence describing a 2D problem, this crude implementation of the function will suffice. You can put the nested for -loops into a function called sum_of_different_powers_2D (for example) and call it, passing the vector x .

Edit

You may get a shape that looks more like your intended surface by replace the command inside the nested for -loops with:

s(I,J) = abs(x(I))^2 + abs(x(J))^2;  

This will resemble this function:

Edit 2

It is important to understand that n in the equation quoted above is the dimension of your problem. Which, as you showed, is 2 .

Edit 3

I recommend you use this function:

function ph = sphereFN(x)

for I=1:size(x,2)
    for J=1:size(x,2)
        ph(I,J) = abs(x(I))^2 + abs(x(J))^2;
    end
end

end

Answer 2

Matlab has a built in sphere function and the documentation shows how to plot it.

http://www.mathworks.com/help/matlab/ref/sphere.html