Aww, cute.
The reason you can't use surf or ezplot is that these are not designed for this kind of equation. To use surf you need to have a surface defined as z = f(x,y). You have g(x,y,z) = 0. If you could rearrange that into z = f(x,y), you could use surf, but the equation you have doesn't really allow that.
So... instead, go back to the definition of the surface as g(x,y,z) = 0. Think of this as a particular isosurface of the function g(x,y,z) (with isosurface value of 0).
To make a surface in MATLAB from that kind of setup, you need (surprise, surprise) isosurface. Look in the documentation at the examples for isosurface. They will guide you through the visualization.
The one thing you need that isn't in the isosurface doc is to create the data to plot. (The examples do [x,y,z,v] = flow; which creates the data from a canned routine for a specific example.) So:
- You need to create 3 3-D arrays for x, y, and z, in the given range -- hint: linspace and meshgrid.
- Then you need to evaluate the function g(x,y,z) at each of those x, y, z locations: V = (X.^2+9*Y.^2/4+Z.^2-1).^3 - X.^2.*Z.^3 (etc)
Now you have the data, you can plot, using the examples in the isosurface documentation.
You'll "love" the result. Haha. I'm so funny.
