[Tex/LaTex] Artificial Line in PGFPlots 3D Parametric Plots

Question

I just tried to make a 3D parametric plot of the spiraling helix r(t) = {t, cos(2*pi*t), sin(2*pi*t)} using PGFPlots, but there seems to be an extra line connecting the points r(t_min) and r(t_max). What is causing this?

\documentclass{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.8} %Fix axis labels in 3D when axis lines=center

\begin{document}

\begin{tikzpicture}
    \begin{axis}[
            axis lines=center,
            width=800bp,
            xmin=-8,xmax=8,
            ymin=-8,ymax=8,
            zmin=-8,zmax=8,
            xlabel={$x$},
            ylabel={$y$},
            zlabel={$z$},
            view={60}{60},
            smooth
            ]
        \addplot3[
                blue,samples=60,
                domain=-4:4,
                ]
                ({x},{x*cos(deg(2*pi*x))},{x*sin(deg(2*pi*x))});    
    \end{axis}
\end{tikzpicture}

\end{document}

Here's the pgfplots output (with extra line):

Here's the same function plotted in Mathematica:

Answer 1

Hah, you have to read the fine print in the pgfplots manual (Chapter 4.6.2 or so):

Furthermore, \addplot3 has a way to decide whether a line visualization or a mesh visualization has to be done. The first one is a map from one dimension into R^3 and the latter one a map from two dimensions to R^3. Here, the keys mesh/rows and mesh/cols are used to define mesh sizes (matrix sizes). Usually, you don’t have to care about that because the coordinate input routines already allow either one- or two-dimensional structure.

Apparently, in your case, \addplot3 gets it wrong and tries to place a mesh on this curve. This leads to a couple of additional lines. A few pages after, the documentation specifies that you have to change the key y domain:

If y domain is empty, [y1,y2 ] = [x1,x2] will be assumed. If y domain=0:0 (or any other interval of length zero), it is assumed that the plot does not depend on y (thus, it is a line plot).

So the correct command is:

\addplot3[
            y domain=0:0,
            blue,samples=60,
            domain=-4:4,
            ]
            ({x},{x*cos(deg(2*pi*x))},{x*sin(deg(2*pi*x))});