It's 2D because you'll find that you probably want to rewrite it in terms of two independent variables and derive the third from those. For example, you could have something like this:
[u,v] = meshgrid(linspace(0,1,50));
w = 1-(u+v)
out = w<0;
u(out) = nan;
v(out) = nan;
w(out) = nan;
If you do surf(u,v,w) at this point, you'll see something like this:
Now you can use the same kron technique I described in that blog post to multiply these three arrays by your input points.
In the teapotdemo I was doing square patches instead of triangular patches, but you might find something you can mine from there.
I hope that's enough to get you rolling. Have fun, this is an interesting problem! There's a lot of interesting math hiding in these simple objects.
