tikz-3dplot rotation around the x-axis

Question

I'm trying to create a simple spherical quadrant grid using the tikz-3dplot package. The longitudinal grid lines look fine but when I try to create the latitudinal lines I get really strange results that I don't understand. I was expecting to see a series of latitude arcs rotating around the x-axis (so they're not quite the same as latitude lines). Instead, it appears that my attempt to rotate around the x-axis is rotating around all three axes. I'm not sure what I'm doing wrong.

\documentclass{article}
\usepackage{tikz}
\usepackage{tikz-3dplot}

\begin{document}
\tdplotsetmaincoords{60}{155}
\usetikzlibrary{3d}

\begin{tikzpicture}[scale=5,tdplot_main_coords]
\tikzstyle{grid}=[thin,color=red,tdplot_rotated_coords]

\draw[thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};
\draw[thick,->] (0,0,0) -- (-1,0,0);
\draw[thick,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$y$};
\draw[thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z$};

\foreach \rot in {0, 30, 60, 90} {
    \tdplotsetrotatedcoords{\rot}{0}{0};
    \tdplotdrawarc[grid]{(0,0,0)}{1}{0}{180}{}{};
}

\foreach \rot in {-90, -60, -30, 0, 30, 60, 90} {
    \tdplotsetrotatedcoords{\rot}{90}{0};
    \tdplotdrawarc[grid]{(0,0,0)}{1}{90}{180}{}{};
}

\end{tikzpicture}
\end{document}

Edit:

After more investigation it appears that attempting to rotate around the x-axis actually rotates around the z-axis, as can be clearly seen in this image. Placing the \rot in the x- or z-position has the same effect.

Answer 1

Actually,this is not a bug. The rotations are not xyz rotations but rather zyz rotations. To make a 90 degree rotation around the x-axis you can make a 90 degree rotation around the z-axis, followed by a 90 degree rotation around the rotated y-axis, and finaly a 270 degree rotation around the rotated z-axis. These rotations are called Euler rotations. You can read more about Euler rotations on Wikipedia or tikz-3dplot documention.

Answer 2

This really seems to be a bug, rotations about the y and z axis work as expected, but around the x axis appears to be also to rotate about the z axis. So I think it would be best if you filed a bug report. If you can't wait for it to be fixed, you could use this much slower TikZ version, which uses only a little goniometry and approximating an arc by drawing 180 line segments:

Code

\documentclass[tikz,border=2mm]{standalone}
\usepackage{tikz-3dplot}

\begin{document}

\tdplotsetmaincoords{60}{155}
\usetikzlibrary{3d}
\begin{tikzpicture}[scale=5,tdplot_main_coords]
\tikzstyle{grid}=[thin,color=red,tdplot_rotated_coords]
    \foreach \a in {0,1,...,9}
    {   \draw (1,0,0)
        \foreach \b in  {1,...,180}
        { -- ({cos(\b)},{sin(\b)*cos(10*\a)},{sin(\b)*sin(10*\a)})
        }
        ;
    }
    \foreach \rot in {-90,-80,...,90} {
    \tdplotsetrotatedcoords{\rot}{90}{0};
    \tdplotdrawarc[grid]{(0,0,0)}{1}{90}{180}{}{};
    }
    \draw[thick,->] (-1,0,0) -- (1,0,0) node[anchor=north east]{$x$};
    \draw[thick,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$y$};
    \draw[thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z$};
\end{tikzpicture}

\end{document}

Output

Answer 3

A solution with PSTricks. Run it with xelatex:

\documentclass{article}
\usepackage{pst-3dplot}
\begin{document}

\begin{pspicture}(-5,0)(15,10)
\psset{unit=3cm,Alpha=45, Beta=15,linecolor=blue!60,linewidth=1.5pt}
\parametricplotThreeD[xPlotpoints=500, yPlotpoints=10](0,180)(0,90){
    /r 1.0 def
    r t cos mul u sin mul 
    r t sin mul u sin mul 
    r u cos  mul }
\parametricplotThreeD[xPlotpoints=500, yPlotpoints=8](0,90)(0,180){
    /r 1.0 def
    r u cos mul t sin mul 
    r u sin mul t sin mul 
    r t cos  mul }
\pstThreeDCoor[xMin=-2,xMax=2.0,yMin=-.5,yMax=2.0, zMin=-.5,zMax=1.5,linecolor=black,linewidth=0.6pt]
\end{pspicture}
\end{document}