I want to draw the surface x^2-y in PGFplots in 3D and intersect it with the plane z=1, emphasizing the intersection probably with some coloration or shading or something. I'd also like to emphasize the y-axis and the z-axis.
I've read a few similar posts on here and tried to edit them, but I can't seem to get them into the shape I want. Does anyone have a suggestion for something I can try?
EDIT:
I've been working up a minimum working example of the code, where the intersection is not at all emphasized. Also, I've read elsewhere now that there are problems drawing intersections with PGFplots and that sometimes PStricks is better. I'm fine with either solution, I just want something that works.
\documentclass[12pt]{standalone}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}
[
xlabel = $x_1$,
ylabel = $x_2$,
zlabel = $x_3$,
zlabel style={rotate = -90},
zmin = 0, zmax = 2
]
\addplot3[surf,mesh,shader=faceted,samples=20] (x,y,1);
\addplot3[surf,shader=interp,samples=50] {x*x - y};
\end{axis}
\end{tikzpicture}
\end{document}
The result looks like crap in my opinion, but I have no idea how to make it look nice.