# Intersection of two surfaces

I'm trying to create a signed distance function S(x), where I want to intersect S(x) = 0 with a plane. The problem is not to get the two functions into a plot, but to get the two functions to visual intersect with each other, i.e the nearest surface is in the foreground. Currently, I have something like:

\documentclass{standalone}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}[grid=major]
{-sqrt((x-0)^2/1 + (y-0)^2/1) + 5};
{0*x+0*y};
\end{axis}
\end{tikzpicture}
\end{document}


Which gives:

As you can see, the plane is only overlapping the function and not intersecting. How can it be done? Bonus question: Is it possible to create a contour on the 3d surf plot at the intersection?

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Unfortunately, this can't be done with pgfplots. From the manual: "pgfplots supports z buffering techniques up to a certain extent. (...) However, it can't combine different \addplot commands, those will be drawn in the order of appearance." – Jake Apr 23 '12 at 6:26
You can use Asymptote instead, it has better 3D support. – Leo Liu Apr 23 '12 at 6:45
Thanks for the quick response! Leo, I haven't tryout Asymptote before but I think I will stick with pgfplots for now. – aagaard Apr 23 '12 at 7:20

This can't be done automatically, unfortunately, since pgfplots can't do z buffering between different \addplot commands.

For this concrete application, you could construct the plot "by hand", however:

First, you draw the part of the cone below 0, then you draw the plane and the circle, then you draw the part of the cone above 0.

I've used a polar coordinate system for this, since it makes the input of polar functions easier:

\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}[grid=major,view={20}{40},z buffer=sort, data cs=polar]
\addplot3 [surf, domain=0:360, domain y=5:10,samples=30, samples y=10]
{-y+5};