Draw only regions of a hyperboloid in pgfplots

Question

I'm interested in the hyperboloid u^2 + v^2 - w^2 = 1, which can be parameterized as

u = cosh(x) cos(y),
v = cosh(x) sin(y),
w = sinh(x).

This parameterization can be used to draw the hyperboloid in pgfplots as follows:

\documentclass{article}

\usepackage{pgfplots}
\pgfplotsset{compat=1.6}

\begin{document}

\begin{tikzpicture}
 \begin{axis}
  \addplot3[surf,
            fill=white,
            samples=10,
            samples y=72,
            domain=-1:1,
            y domain=0:360,
            z buffer=sort]
            ( {cosh(x)*cos(y)}, {cosh(x)*sin(y)}, {sinh(x)} );
 \end{axis}
\end{tikzpicture}

\end{document}

That works beautifully, but now I would like to restrict the plot to, say, the region where v + w > 0. In terms of my (x,y) parameters this reads cosh(x) sin(y) + sinh(x) > 0. According to the PGFPlots manual I should be able to use the restrict expr to domain option to accomplish this, but when I try it I get a LaTeX error:

! Package PGF Math Error: Could not parse input '' as a floating point number, sorry. The unreadable part was near ''..

I'm assuming this option should be given at the \addplot3 level, not at the \begin{axis} level, but the error appears either way.

Actually what I would like to do is plot the hyperboloid twice; first, the full hyperboloid in a nice subdued gray, and then, on top of it, the region of interest in bright colors, so that it can actually be identified as part of the hyperboloid.

---

I'm providing an updated MWE since I guess the whole thing got a bit confusing with all the changing in variable names. Here's what I intended to do:

\documentclass{article}

\usepackage{pgfplots}

\begin{document}

\begin{tikzpicture}
 \begin{axis}[view={120}{5},
              samples=20,
              samples y=72,
              domain=-2:2,
              y domain=0:360,
              z buffer=sort,
              variable=\u,
              variable y=\v]
  \addplot3[surf,
            restrict expr to domain={y+z}{0:100}]
            ( {cosh(u)*cos(v)}, {cosh(u)*sin(v)}, {sinh(u)} );
 \end{axis}
\end{tikzpicture}

\end{document}

With the unstable version of pgfplots installed, this draws only half of the hyperboloid---the half determined by the condition y + z > 0---, as expected.

Answer 1

This is a bug in the current stable pgfplots 1.7 (sorry).

I have fixed it in the pgfplots unstable (available at http://pgfplots.sourceforge.net/).

Note that your example suffers from a usability issue in pgfplots: as soon as pgfplots has evaluated the parametric coordinates, it redefines x to be the resulting X coordinate and y to be the resulting Y coordinate. Thus, your example works if you switch to variable=u, variable y=w. Of course, you could also employ the usability issue and write restrict expr to domain={y + z}{0:99999}.