Coordinate system with tikz-3dplot

Question

I am trying to use tikz-3dplot to draw a cube and I was particularly interested by the possibility to define a point using \tdplotsetcoord which allows to get x/y/z/xz... coordinates. But when I try to define a point in (4,4,4) of the main coordinate system of tikz-3dplot (so \tdplotsetcoord{P}{sqrt(3)*4}{45}{45} I think), I do not get what I am expecting as you can see below. The blue and black nodes should be the same in my figure. Any ideas ?

\documentclass[tikz]{standalone}
\usepackage{tikz-3dplot}
\begin{document}

\tdplotsetmaincoords{70}{110}
\begin{tikzpicture}[tdplot_main_coords]

% cube
\tdplotsetcoord{P}{sqrt(3)*4}{45}{45}
\draw[dashed] 
  (0,0,0) -- (Px)
  (0,0,0) -- (Py)
  (0,0,0) -- (Pz);
\draw[->] 
  (Px) -- ++ (1,0,0) node[anchor=north east]{$x$};
\draw[->]
   (Py) -- ++(0,1,0) node[anchor=north west]{$y$};
\draw[->] 
  (Pz) -- ++(0,0,1) node[anchor=south]{$z$};

\draw[thick]
  (Pxz) -- (P) -- (Pxy) -- (Px) -- (Pxz) -- (Pz) -- (Pyz) -- (P); 
\draw[thick]
  (Pyz) -- (Py) -- (Pxy);

\filldraw[dashed,blue] (0,0,0)-- (P) circle (2pt);

\filldraw[dashed] (0,0,0)-- (4,4,4) circle (2pt);

\end{tikzpicture}
\end{document}

Answer 1

Welcome to TeX-SE! One way to compute the spherical coordinates of (4,4,4) is to solve

(r*cos(theta)*cos(phi),r*cos(theta)*sin(phi),r*sin(theta))=(4,4,4)

which gives r=4*sqrt(3) and phi=45, as you got, and theta=asin(sqrt(2/3)), which differs from what you have. BTW, you can use also the spherical coordinates of the 3d library, which follow slightly different conventions. The following MWE shows that the outcome is consistent with the above considerations.

\documentclass[tikz]{standalone}
\usepackage{tikz-3dplot}
\usetikzlibrary{3d}
\begin{document}

\tdplotsetmaincoords{70}{110}
\begin{tikzpicture}[tdplot_main_coords]
\pgfmathsetmacro{\mytheta}{asin(sqrt(2/3))}
\typeout{\mytheta}
% cube
\tdplotsetcoord{P}{sqrt(3)*4}{\mytheta}{45}
\draw[dashed] 
  (0,0,0) -- (Px)
  (0,0,0) -- (Py)
  (0,0,0) -- (Pz);
\draw[->] 
  (Px) -- ++ (1,0,0) node[anchor=north east]{$x$};
\draw[->]
   (Py) -- ++(0,1,0) node[anchor=north west]{$y$};
\draw[->] 
  (Pz) -- ++(0,0,1) node[anchor=south]{$z$};

\draw[thick]
  (Pxz) -- (P) -- (Pxy) -- (Px) -- (Pxz) -- (Pz) -- (Pyz) -- (P); 
\draw[thick]
  (Pyz) -- (Py) -- (Pxy);

\filldraw[dashed,blue] (0,0,0)-- (P) circle (2pt);

\draw[green!70!black] (4,4,4) circle (3pt);

\draw[red] (xyz spherical cs:radius={4*sqrt(3)},
  longitude=45,latitude=90-\mytheta) circle (4pt);
\end{tikzpicture}
\end{document}