# Artificial Line in PGFPlots 3D Parametric Plots?

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
]
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:

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))});

• Instead of y domain=0:0, you can also set samples y=0 to get the same result. – Jake Oct 14 '15 at 5:34
• I used \pgfplots{parametric nonclosed/.style={samples y=0}} to get this effect semantically. – Matthew Leingang Sep 16 '16 at 11:26