TikZ (3d+perspective), fixed origin in a sequence of azimuth for animation

Question

I am trying to pick a good angle to show a plane through the origin and not touching any point in the positive quadrant. Then, I make it into an animation. Is it possible to fix the origin in the animation? Say, the OZ is fixed in every frame of the animation, the origin point is located at the same point on screen.

\documentclass[dvisvgm]{standalone}  %for svg
%\documentclass[export]{standalone}  %for pdf -> gif
\usepackage{tikz,xcolor}
\usepackage{graphicx}
\usepackage[draft]{animate}
\usetikzlibrary{3d,calc,perspective}
\begin{document}
\newcommand{\BM}[3]{
\def\U{#1}  %u
\def\D{#2}  %d
\def\R{#3}  %R_0
}
\BM{1.2}{0.9}{1.125}
\begin{animateinline}[final,controls={play},loop]{5}
\multiframe{71}{iAngle=5+5}{
%% \foreach \iAngle in {5,10,...,355}{
\begin{tikzpicture}[line cap=round,line join=round,
            3d view={\iAngle}{25},
                    scale=2]
%% \useasboundingbox (-2.5,-2.5) rectangle (3,3);
\pgfmathsetmacro{\gu}{(\R-\D)/(\U-\D)/\R}
\pgfmathsetmacro{\gd}{(\U-\R)/(\U-\D)/\R}
\pgfmathsetmacro{\gg}{1+\gu\gu}
\pgfmathsetmacro{\nu}{1/sqrt(\gg)}
\pgfmathsetmacro{\nd}{\nu/sqrt((\gg+\gd\gd))}
\coordinate (O)  at (0,0,0);
\coordinate (X)  at (1,0,0);
\coordinate (Y)  at (0,1,0);
\coordinate (Z)  at (0,0,1);
\coordinate (N)  at (\gu,\gd,1);
\coordinate (SPu)  at (1,0,-\gu);
\coordinate (SPd)  at (0,1,-\gd);
\coordinate (ux)  at (1,0,0);
\coordinate (uy)  at (0,1,0);
\coordinate (px)  at ($\nu(SPu)$);
\coordinate (py)  at ($\nd(\gd*\gd,-\gg,\gd)$);
\begin{scope}[red!70, plane origin={(O)},plane x={(px)},
    plane y={(py)},canvas is plane]
\filldraw [blue!7!white] (0,0) circle [radius=2];
\node at (1,1) {\iAngle};
%other draws in this plane
\end{scope}
% axes                                              with the desired length
\foreach\i/\j in {X/x,Y/y,Z/z}
{
  \draw[-latex] (O) -- ($(\i)!-1cm!(O)$);       %Distance Modifiers
  \node      at ($(\i)!-1.2cm!(O)$) {$\j$};
}
\filldraw[fill=green!20!white, draw=green!50!black, fill opacity=0.5, draw opacity=0.5] (O)
    -- ($1.5(ux)$) -- ($1.5(1,1,0)$) -- ($1.5(uy)$)  -- cycle;
\filldraw[fill=red!20!white, draw=red!50!black, fill opacity=0.5, draw opacity=0.5] (O)
    -- ($1.5(uy)$) -- ($1.5(0,1,1)$) -- ($1.5(0,0,1)$)  -- cycle;
%% \draw [blue] (current bounding box.south west) rectangle (current bounding box.north east);
\end{tikzpicture}
}
\end{animateinline}
\end{document}

Here is the output

For this gif file: \documentclass[export]{standalone} to generate pdf, and convert -density 300 -delay 8 -loop 0 -background white out.pdf out.gif

Nice. My speculation: the origin varies, because the dimensions can vary, i.e. the size and aspect ratio of the outermost rectangle (view). A bypass might be, without any proof, adding an invisible node with a large enough width and height, or 3 coordinates with the same function. Brainstorming other keywords, view or bounding box etc. might point you into the right direction. — MS-SPO, Dec 06 '23 at 15:21
Looks like a duplicate of https://tex.stackexchange.com/q/638191 — AlexG, Dec 06 '23 at 19:08

score 2 · Accepted Answer · answered Dec 07 '23 at 03:08

Much thanks to AlexG. I think I may work it out: using the viewport in https://tex.stackexchange.com/a/638202

\documentclass[export]{standalone}
%% %convert -density 300 -delay 8 -loop 0 -background white  out.pdf out.gif
\usepackage{tikz,xcolor}
\usepackage{graphicx}
\usepackage[draft]{animate}
\usetikzlibrary{3d,calc,perspective}
\begin{document}
\newcommand{\BM}[3]{
\def\U{#1}  %u
\def\D{#2}  %d
\def\R{#3}  %R_0
}
\BM{1.2}{0.9}{1.125}
\tikzset{viewport/.style 2 args={
    x={({cos(-#1)1cm},{sin(-#1)sin(#2)1cm})},
    y={({-sin(-#1)1cm},{cos(-#1)sin(#2)1cm})},
    z={(0,{cos(#2)*1cm})}   }}
%% \begin{animateinline}[final,controls={play},loop]{5}
\begin{animateinline}[final,autoplay,loop]{5}
\multiframe{71}{iAngle=5+5}{
%% \foreach \Angle in {345}{
%% \foreach \Angle in {5,10,...,355}{
\begin{tikzpicture}[line cap=round,line join=round,
                    scale=2]
\path [use as bounding box, draw=none] (0,0) circle [radius=2.57];
\node[red!70] at (2,2) {\iAngle};
\pgfmathsetmacro{\gu}{(\R-\D)/(\U-\D)/\R}
\pgfmathsetmacro{\gd}{(\U-\R)/(\U-\D)/\R}
\pgfmathsetmacro{\gg}{1+\gu\gu}
\pgfmathsetmacro{\nu}{1/sqrt(\gg)}
\pgfmathsetmacro{\nd}{\nu/sqrt((\gg+\gd\gd))}
\begin{scope}[viewport={\iAngle}{25}]
\coordinate (O)  at (0,0,0);
\coordinate (X)  at (1,0,0);
\coordinate (Y)  at (0,1,0);
\coordinate (Z)  at (0,0,1);
\coordinate (N)  at (\gu,\gd,1);
\coordinate (SPu)  at (1,0,-\gu);
\coordinate (SPd)  at (0,1,-\gd);
\coordinate (ux)  at (1,0,0);
\coordinate (uy)  at (0,1,0);
\coordinate (px)  at ($\nu(SPu)$);
\coordinate (py)  at ($\nd(\gd*\gd,-\gg,\gd)$);
\begin{scope}[red!70, plane origin={(O)},plane x={(px)},
    plane y={(py)},canvas is plane]
\filldraw [blue!7!white] (0,0) circle [radius=2];
\end{scope}
% axes                                              with the desired length
\foreach\i/\j in {X/x,Y/y,Z/z}
{
  \draw[-latex] (O) -- ($(\i)!-1cm!(O)$);       %Distance Modifiers
  \node      at ($(\i)!-1.2cm!(O)$) {$\j$};
}
\filldraw[fill=green!20!white, draw=green!50!black, fill opacity=0.5, draw opacity=0.5] (O)
    -- ($1.5(ux)$) -- ($1.5(1,1,0)$) -- ($1.5(uy)$)  -- cycle;
\filldraw[fill=red!20!white, draw=red!50!black, fill opacity=0.5, draw opacity=0.5] (O)
    -- ($1.5(uy)$) -- ($1.5(0,1,1)$) -- ($1.5(0,0,1)$)  -- cycle;
%% \draw [blue] (current bounding box.south west) rectangle (current bounding box.north east);
\end{scope}
\end{tikzpicture}
}
\end{animateinline}
\end{document}

Then, we have the following output

TikZ (3d+perspective), fixed origin in a sequence of azimuth for animation

1 Answers1