在 Matlab 中绘制 3D 曲面

Question

I have the following function:

I want to plot it in MATLAB at −15 ≤ x ≤ 15 and −15 ≤ y ≤ 15.

What i tried is this:

[x,y] = meshgrid(-15:1:15, -15:1:15);
z = ((x^4 + y^4 - 4 * x^2 * y^2)/(x^2 + y^2));
plot(x,y,z)

When I run it it says Warning: Matrix is singular to working precision. Data must be a single matrix Y or a list of pairs X,Y.

And my variable z only contains a 31x31 double filled with NaN.

Answer 1

The problem is generated by the division by the term x^2+y^2, which in some cases is actually zero, and your incorrect usage of the Matlab operators. Lastly, the plot function is not suited for plotting a 3D surface. I'd recommend using a symbolic computation for simplicity:

syms x y; 
z = ((x^4 + y^4 - 4 * x^2 * y^2)/(x^2 + y^2));
fsurf(z,[-15,15,-15,15])

You can also use your numeric version (faster), but take care to use the right operators - instead of matrix multiplication * , use element-wise multiplication .* for example. This is relevant for ^ and / as well.

[x,y] = meshgrid(-15:1:15, -15:1:15);
z = ((x.^4 + y.^4 - 4 .* x.^2 .* y.^2)./(x.^2 + y.^2));
surf(x,y,z)

Note that the origin is not defined in this case - due to the division by zero problem. You can use a different range to avoid this problem if you'd like.

[x,y] = meshgrid(-15:0.17:15, -15:0.17:15);
z = ((x.^4 + y.^4 - 4 .* x.^2 .* y.^2)./(x.^2 + y.^2));
surf(x,y,z,'EdgeAlpha',0) % The above range is dense - so we remove the edge coloring for clarity.