angle in a plane with tikz

Question

Here is a MWE:

\documentclass[10pt,a4paper]{article}

\usepackage{tikz}
\usetikzlibrary{angles}

\begin{document}

\begin{tikzpicture}
  \coordinate (ey) at (1,0,0);
  \coordinate (ez) at (0,1,0);
  \coordinate (ex) at (0,0,1);
  \begin{scope}[x={(ex)},y={(ey)},z={(ez)},scale=2]

  \def\xM{1.2}
  \def\yM{1.6}
  \def\zM{1.8}
  \def\ech{2}
  
  \coordinate (O) at (0,0,0);
  \coordinate (X) at (\ech,0,0);
  \coordinate (Y) at (0,\ech,0);
  \coordinate (Z) at (0,0,\ech);
  \coordinate (Px) at (\xM,0,0);
  \coordinate (Py) at (0,\yM,0);
  \coordinate (Pz) at (0,0,\zM);
  \coordinate (M) at (\xM,\yM,\zM);
  \coordinate (H) at (\xM,\yM,0); 
  \coordinate (ey) at (1,0,0);
  \coordinate (ez) at (0,1,0);
  \coordinate (ex) at (0,0,1);
  
  \draw[->,thick] (0,0,0) -- (1,0,0) node[above left] {$\vec{\imath}$};
  \draw[->,thick] (0,0,0) -- (0,1,0) node[below] {$\vec{\jmath}$};
  \draw[->,thick] (0,0,0) -- (0,0,1) node[left] {$\vec{k}$};
    \draw (O) -- (X);
    \draw (O) -- (Y);
    \draw (O) -- (Z);
    \draw[dashed] (H) -- (Px) node[left] {$x$};
    \draw[dashed] (H) -- (Py) node[above] {$y$};
    \draw[dashed] (H) -- (Py);
    \draw[->,blue] (O) -- (H);
    \draw[blue] (M) -- node[right,black] {$z$} (H);
    \draw[blue] (M) -- node[above,black] {$r$} (Pz);
    
    \path (H) node[below right] {$H$};
    \path (M) node[above right] {$M$};
    \draw pic [draw,->,angle radius=0.5cm] {angle = X--O--H};
    \draw (23:1) node {$\theta$};
    \end{scope}
\end{tikzpicture}

\end{document}

And here is the result:

I am not satisfied with the angle theta. It doesn't seem in the plane (Oxy). Probably because it is a circle instead of an ellipse (I hope I am clear). So is there a way to improve this?

Answer 1

You can use the 3d library and the option

canvas is xy plane at z=0

that draws precisely in the horizontal plane.

If you want another suggestion I'd use the quotes library too, this way you can specify the angle label as \draw option.

Something like this:

\documentclass[10pt,a4paper]{article}

\usepackage{tikz}
\usetikzlibrary{3d,     % for 'canvas is ... plane at ...' options
                angles,
                quotes} % angle labels

\begin{document}

\begin{tikzpicture}
  \coordinate (ey) at (1,0,0);
  \coordinate (ez) at (0,1,0);
  \coordinate (ex) at (0,0,1);
  \begin{scope}[x={(ex)},y={(ey)},z={(ez)},scale=2]

  \def\xM{1.2}
  \def\yM{1.6}
  \def\zM{1.8}
  \def\ech{2}

  \coordinate (O) at (0,0,0);
  \coordinate (X) at (\ech,0,0);
  \coordinate (Y) at (0,\ech,0);
  \coordinate (Z) at (0,0,\ech);
  \coordinate (Px) at (\xM,0,0);
  \coordinate (Py) at (0,\yM,0);
  \coordinate (Pz) at (0,0,\zM);
  \coordinate (M) at (\xM,\yM,\zM);
  \coordinate (H) at (\xM,\yM,0);
  \coordinate (ey) at (1,0,0);
  \coordinate (ez) at (0,1,0);
  \coordinate (ex) at (0,0,1);

  \draw[->,thick] (0,0,0) -- (1,0,0) node[above left] {$\vec{\imath}$};
  \draw[->,thick] (0,0,0) -- (0,1,0) node[above] {$\vec{\jmath}$};
  \draw[->,thick] (0,0,0) -- (0,0,1) node[left] {$\vec{k}$};
    \draw (O) -- (X);
    \draw (O) -- (Y);
    \draw (O) -- (Z);
    \draw[dashed] (H) -- (Px) node[left] {$x$};
    \draw[dashed] (H) -- (Py) node[above] {$y$};
    \draw[dashed] (H) -- (Py);
    \draw[->,blue] (O) -- (H);
    \draw[blue] (M) -- node[right,black] {$z$} (H);
    \draw[blue] (M) -- node[above,black] {$r$} (Pz);

    \path (H) node[below right] {$H$};
    \path (M) node[above right] {$M$};
    \draw pic [canvas is xy plane at z=0,% draws in the xy plane
               draw=red,->,angle radius=0.75cm,
               "$\theta$",               % angle label (requires quotes library)
               angle eccentricity=1.6    % angle position
              ] {angle = X--O--H};
    \pgfmathsetmacro\angletheta{atan(\yM/\xM)} % rotation angle for OHM plane (theta)
    \draw pic [rotate around z=\angletheta,canvas is xz plane at y=0,% draws in the OHM plane
               draw=red,<-,angle radius=0.75cm,
               "$\varphi$",              % angle label (requires quotes library)
                angle eccentricity=0.7   % angle position
               ] {angle = M--H--O};
    %\draw (23:1) node {$\theta$};
    \end{scope}
\end{tikzpicture}
\end{document}