Animating a 3d plane

Question

I'm learning how to produce animations in LaTeX. After some trials with different pictures, I would like to animate the following picture and start from the answer that Marmot provided me in this question Drawing a simple plane in 3D space. In particular, I would like to move the gray rectangle around (0,0,0) and lift it up, in order to illustrate what happens if it starts to intesect the positive orthant. The following MWE does something else, as it animates the dimensions of the rectangle. I think I should rather define the rectangle in terms of a plane and then I will change its slope. How can I do?

\documentclass{beamer}

\usepackage{amsmath}    % need for subequations
\usepackage{amsfonts}
\usepackage{tikz}

\usetikzlibrary{calc, shadings} 
\usetikzlibrary{calc,intersections} 
\usetikzlibrary{positioning,arrows.meta}
\usepackage{pgf,tikz,pgfplots}
\pgfplotsset{compat=1.15}
\usepackage{mathrsfs}
\usetikzlibrary{arrows}
\usepackage{animate}


\usepackage{tikz-3dplot}

\usetikzlibrary{3d} %add it to draw the plane
\makeatletter
\tikzoption{canvas is xy plane at z}[]{%
  \def\tikz@plane@origin{\pgfpointxyz{0}{0}{#1}}%
  \def\tikz@plane@x{\pgfpointxyz{1}{0}{#1}}%
  \def\tikz@plane@y{\pgfpointxyz{0}{1}{#1}}%
  \tikz@canvas@is@plane
}
\makeatother

\let\oldemptyset\emptyset 



\begin{document}
\begin{frame}

\tdplotsetmaincoords{105}{-30}

\begin{animateinline}[loop,poster=first,controls]{30}
\multiframe{36}{rt=0+10}
{

    \begin{tikzpicture}[tdplot_main_coords,font=\small]
     \tdplotsetrotatedcoords{00}{30}{0}
    \begin{scope}[tdplot_rotated_coords]

    \begin{scope}[canvas is xy plane at z=0]
    \fill[blue!40,fill opacity=0.3] (-{cos(\rt)*5},-{sin(\rt)*5}) rectangle ({cos(\rt)*5},{sin(\rt)*5}); 
    \draw[very thick] (-2,0) -- (2,0); %draws market line
    \path (-150:2) coordinate (H) (-1.5,0) coordinate(X);
    \pgflowlevelsynccm

    \draw[very thick,-stealth,gray] (0,0) -- (-30:1.5); %draws ``projection'' of $\Phi$
    \end{scope}

    \draw[stealth-] (H) -- ++ (-1,0,0.2) node[pos=1.3]{$H$}; %draws arrow
    \draw[stealth-] (X) -- ++ (0,1,0.2) node[pos=1.3]{$X$}; %draws arrow
    \draw[very thick,-stealth] (0,0,0) coordinate (O) -- (0,0,3) node[right]{$\varphi$}; %draws vector 
    \end{scope}

    \pgfmathsetmacro{\Radius}{1.5} %using a macro
    \draw[-stealth]  (O)-- (2.5*\Radius,0,0) node[pos=1.15] {spot $0$};
    \draw[-stealth] (O) -- (0,3.5*\Radius,0) node[pos=1.15] {spot $2$};
    \draw[-stealth] (O) -- (0,0,2.5*\Radius) node[pos=1.05] {spot $1$};
    \end{tikzpicture} 
}


\end{animateinline}

\end{frame}
\end{document}

Answer 1

This is something that rotates the plane (but I do not know if these are the planes and rotation axes you had in mind). It also adjusts the bounding box in such a way that it fits all animations steps fit tightly. To this end, a slight variation of this answer is used but you may also be interested in this answer, which I did not try out here. Please note that you need to compile twice. The animated gif is produced along the lines of this comment and, in particular, this answer, and the file has comments what you need to do in order to recreate the gif.

%\documentclass[export]{standalone} % <- use for multipage pdf
\documentclass{beamer}  % <- comment out for multipage pdf
\usepackage{animate}
\usepackage{tikz}


\usepackage{tikz-3dplot}

\usetikzlibrary{3d} %add it to draw the plane
\makeatletter
\tikzoption{canvas is xy plane at z}[]{%
  \def\tikz@plane@origin{\pgfpointxyz{0}{0}{#1}}%
  \def\tikz@plane@x{\pgfpointxyz{1}{0}{#1}}%
  \def\tikz@plane@y{\pgfpointxyz{0}{1}{#1}}%
  \tikz@canvas@is@plane
}

\def\ExportBB{\edef\figbb{(\xmin,\ymin) rectangle (\xmax,\ymax)}
\immediate\write\@mainaux{\xdef\string\figbb{\figbb}\relax}}
\makeatother

\let\oldemptyset\emptyset 



\begin{document}
\begin{frame} % <- comment out for multipage pdf

\tdplotsetmaincoords{105}{-30}
\pgfmathsetmacro{\xmin}{0}
\pgfmathsetmacro{\xmax}{0}
\pgfmathsetmacro{\ymin}{0}
\pgfmathsetmacro{\ymax}{0}
\begin{animateinline}[loop,poster=first,controls]{30}
\multiframe{36}{rt=0+10}
{

    \begin{tikzpicture}[tdplot_main_coords,font=\small]
    \ifdefined\figbb\relax
    \path \figbb;
    \fi

    % this is the stuff that gets rotated
    \tdplotsetrotatedcoords{00}{\rt}{0}
    \begin{scope}[tdplot_rotated_coords]

     \begin{scope}[canvas is xy plane at z=0]
     \fill[blue!40,fill opacity=0.3] (-5,-5) rectangle (5,5);
     % (-{cos(\rt)*5},-{sin(\rt)*5}) rectangle ({cos(\rt)*5},{sin(\rt)*5}); 
     \pgflowlevelsynccm

     \draw[very thick,-stealth,gray] (0,0) -- (-30:1.5); %draws ``projection'' of $\Phi$
     \end{scope}

     \draw[very thick,-stealth] (0,0,0) coordinate (O) -- (0,0,3) node[right]{$\varphi$}; %draws vector 
    \end{scope}

    \begin{scope}[canvas is xy plane at z=0]
     \draw[very thick] (-2,0) -- (2,0); %draws market line
     \path(-1.5,0) coordinate(X);
     \path (-150:2) coordinate (H);
    \end{scope}
    \draw[stealth-] (X) -- ++ (0,1,0.2) node[pos=1.3]{$X$}; %draws arrow
    \draw[stealth-] (H) -- ++ (-1,0,0.2) node[pos=1.3]{$H$}; %draws arrow

    \pgfmathsetmacro{\Radius}{1.5} %using a macro
    \draw[-stealth]  (O)-- (2.5*\Radius,0,0) node[pos=1.15] {spot $0$};
    \draw[-stealth] (O) -- (0,3.5*\Radius,0) node[pos=1.15] {spot $2$};
    \draw[-stealth] (O) -- (0,0,2.5*\Radius) node[pos=1.05] {spot $1$};
    \path let \p1=(current bounding box.south west),
    \p2=(current bounding box.north east)
    in \pgfextra{%
    \pgfmathsetmacro{\xmin}{min(\x1,\xmin)}
    \pgfmathsetmacro{\xmax}{max(\x2,\xmax)}
    \pgfmathsetmacro{\ymin}{min(\y1,\ymin)}
    \pgfmathsetmacro{\ymax}{max(\y2,\ymax)}
    \xdef\xmin{\xmin pt}
    \xdef\xmax{\xmax pt}    
    \xdef\ymin{\ymin pt}
    \xdef\ymax{\ymax pt}    
    };
    \end{tikzpicture} 
\ExportBB   
}


\end{animateinline}

\end{frame} % <- comment out for multipage pdf
\end{document}