EudoxusPlanetary.tex

% Eudoxus planetary model (animated)
% Author: Tobit Flatscher (https://github.com/2b-t)
%
% Description
% This document creates an animated Eudoxus planetary model by using
% the integrated transformation features and a manual transformation.

% document settings
\documentclass{standalone}
\usepackage{tikz, tikz-3dplot}
\usepackage{xintexpr}
\usetikzlibrary{calc,patterns,fadings,decorations.pathreplacing}
\usepackage{animate}

% useful commands
\newcommand\pgfmathsinandcos[3]{
    \pgfmathsetmacro#1{sin(#3)}
    \pgfmathsetmacro#2{cos(#3)}
}
\newcommand\LongitudePlane[3][current plane]{
    \pgfmathsinandcos\sinEl\cosEl{#2} %elevation
    \pgfmathsinandcos\sint\cost{#3} %azimuth
    \tikzset{#1/.style={cm={\cost,\sint*\sinEl,0,\cosEl,(0,0)}}}
}
\newcommand\LatitudePlane[3][current plane]{
    \pgfmathsinandcos\sinEl\cosEl{#2} %elevation
    \pgfmathsinandcos\sint\cost{#3} %latitude
    \pgfmathsetmacro\yshift{\cosEl*\sint}
    \tikzset{#1/.style={cm={\cost,0,0,\cost*\sinEl,(0,\yshift)}}}
}
\newcommand\DrawLongitudeCircle[2][1]{
    \LongitudePlane{\angEl}{#2}
    \tikzset{current plane/.prefix style={scale=#1}} %angle of "visibility"
    \pgfmathsetmacro\angVis{atan(sin(#2)*cos(\angEl)/sin(\angEl))}
    \draw[current plane] (\angVis:1) arc (\angVis:\angVis+180:1);
}
\newcommand\DrawLatitudeCircle[2][1]{
    \LatitudePlane{\angEl}{#2}
    \tikzset{current plane/.prefix style={scale=#1}}
    \pgfmathsetmacro\sinVis{sin(#2)/cos(#2)*sin(\angEl)/cos(\angEl)} %angle of "visibility"
    \pgfmathsetmacro\angVis{asin(min(1,max(\sinVis,-1)))}
    \draw[current plane] (\angVis:1) arc (\angVis:-\angVis-180:1);
}

% document-wide Tikz options
\tikzset{
    >=latex, %option for nice arrows
    inner sep=0pt,
    outer sep=2pt,
    mark coordinate/.style={inner sep=0pt,outer sep=0pt,minimum size=3pt,
        fill=black,circle}
}

% colours (rgb)
\definecolor{earth}{rgb}{0.3, 0.3, 0.8}
\definecolor{inner}{rgb}{0.44, 0.31, 0.22}
\definecolor{outer}{rgb}{0.55, 0.44, 0.28}

% geometry parameters
\def\offset{80} %sphere radius offset
\def\Ra{2.5} %world sphere radius
\def\Rb{7} %inner sphere radius
\def\Rc{8} %outer sphere radius
\def\Rd{0.75} %sphere planet radius
\def\Re{6} %middle sphere radius
\def\angEl{35} %elevation angle

\begin{document}
    
    \tdplotsetmaincoords{50}{30}
    \begin{tikzpicture}
        \foreach \i in {0,...,359}
        {
            \tdplotsetrotatedcoords{-45}{\i}{110}
            \begin{scope}[tdplot_rotated_coords]
            
            \pgfmathsinandcos\sinC\cosC{\i-\offset}
            \pgfmathsinandcos\sinD\cosD{\i}    
            \coordinate (P\i) at ({0},{\sinC*\Rc},{\cosC*\Rc});
            \end{scope}
        }
    \end{tikzpicture}
    
\begin{animateinline}[loop, poster = first, controls]{24}
\multiframe{90}{iAngle=0+4}{
    
    \tdplotsetmaincoords{50}{30}
    \begin{tikzpicture}
    % bounding box
    \useasboundingbox[tdplot_screen_coords] (-10,-8) rectangle (10,8);
    
    \tdplotsetrotatedcoords{-45}{\iAngle}{110}
    \begin{scope}[tdplot_rotated_coords]
        \pgfmathsinandcos\sinC\cosC{\iAngle-\offset}
        \xintifboolexpr {\iAngle > 180}
        {\draw[outer,line width=0.5mm] (\Rc,0,0) [y={(0,\sinC,\cosC)}] arc(0:180:\Rc);}
        {\draw[outer,line width=0.5mm] (\Rc,0,0) [y={(0,\sinC,\cosC)}] arc(0:-180:\Rc);}    
    
    \end{scope}
    
    
    \tdplotsetrotatedcoords{-45}{\iAngle}{110}
    \begin{scope}[tdplot_rotated_coords]
        \xintifboolexpr {\iAngle > 180}
        {\draw[inner,line width=0.5mm] (\Rb,0,0) arc(0:180:\Rb);}
        {\draw[inner,line width=0.5mm] (\Rb,0,0) arc(0:-180:\Rb);}
    \end{scope}
    
    \draw[black,dashed] (0,-0.85*\Ra,0) -- (0,-\Re,0);
    \filldraw[ball color=earth] (0,0) circle (\Ra);
    \pgfmathsetmacro\a{\iAngle/3-5};
    \pgfmathsetmacro\b{\iAngle/3-35};
    \pgfmathsetmacro\c{\iAngle/3-175};
    \foreach \t in {-80,-60,...,80} { \DrawLatitudeCircle[\Ra]{\t} }
    \foreach \t in {\a,\b,...,\c} { \DrawLongitudeCircle[\Ra]{\t} }
    \draw[black,dashed] (0,0.85*\Ra,0) -- (0,\Re,0);
    \draw[line width=0.5mm] (0,0,0) [y={(0,1,0)}] circle (\Re);
    
    \tdplotsetrotatedcoords{-45}{\iAngle}{110}
    \begin{scope}[tdplot_rotated_coords]
        \xintifboolexpr {\iAngle > 180}
        {\draw[inner,line width=0.5mm] (\Rb,0,0) arc(0:-180:\Rb);}
        {\draw[inner,line width=0.5mm] (\Rb,0,0) arc(0:180:\Rb);}
    \end{scope}
    
    \foreach \i in {1,...,359}
    {
        \pgfmathsetmacro\j{\i-1};
        \draw[line width=0.25mm,gray] (P\j) -- (P\i);
    }
    
    \tdplotsetrotatedcoords{-45}{0}{0}
    \begin{scope}[tdplot_rotated_coords]
        \draw[inner,dashed] (0,\Rb,0) -- (0,\Re,0);
        \draw[inner,dashed] (0,-\Rb,0) -- (0,-\Re,0);
    \end{scope}
    
    \tdplotsetrotatedcoords{-45}{\iAngle}{110}
    \begin{scope}[tdplot_rotated_coords]
        
        \draw[outer,dashed] (\Rb,0,0) -- (\Rc,0,0);
        \draw[outer,dashed] (-\Rb,0,0) -- (-\Rc,0,0);
        
        \pgfmathsinandcos\sinC\cosC{\iAngle-\offset}
        \pgfmathsinandcos\sinD\cosD{\iAngle}
        
        \xintifboolexpr {\iAngle > 180}
        {\draw[outer,line width=0.5mm] (\Rc,0,0) [y={(0,\sinC,\cosC)}] arc(0:-180:\Rc);}
        {\draw[outer,line width=0.5mm] (\Rc,0,0) [y={(0,\sinC,\cosC)}] arc(0:180:\Rc);}
            
        \filldraw[ball color=white] (0, \sinC*\Rc, \cosC*\Rc) [y={(0,\sinD,\cosD)}] circle (\Rd);
        
    \end{scope}
    
    \end{tikzpicture}
}
\end{animateinline}
    
\end{document}