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example.tex
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example.tex
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\documentclass{article}
\usepackage{tikz,tikz-3dplot}
\begin{document}
\tdplotsetmaincoords{80}{30}
\section{Tait-Bryan-Angles}
\input{rotation_xyz.tex}
Left: intrinsic (relative) transformation) \\
Right: extrinsic (absolute) transformation)
\begin{center}
\begin{tikzpicture}[scale=1.5,tdplot_main_coords]
%------------------------------------------------------------------%
\coordinate (A0) at (0,0,0);
\coordinate (A1) at (0,0,3);
\coordinate (A2) at (0,0,6);
\coordinate (A3) at (0,0,9);
%------------------------------------------------------------------%
\coordinate (B0) at (4,4,0);
\coordinate (B1) at (4,4,3);
\coordinate (B2) at (4,4,6);
\coordinate (B3) at (4,4,9);
%==================================================================%
% intrinsic (relative) transformation (x-y'-z")
%==================================================================%
\begin{scope}[thick,->,>=latex]
\draw (A0) -- ++(1,0,0) node[anchor=north]{$x$};
\draw (A0) -- ++(0,1,0) node[anchor=south]{$y$};
\draw (A0) -- ++(0,0,1) node[anchor=south]{$z$};
\end{scope}
%------------------------------------------------------------------%
\tdsetxyzrel
\tdplotsetrotatedcoordsorigin{(A1)}
\tdplotsetrotatedcoords{90}{0}{0}
\begin{scope}[->,>=latex,thick,tdplot_rotated_coords,red]
\draw (A1) -- ++(1,0,0) node[anchor=north]{$x$};
\draw (A1) -- ++(0,1,0) node[anchor=south]{$y$};
\draw (A1) -- ++(0,0,1) node[anchor=south ]{$z$};
\end{scope}
%------------------------------------------------------------------%
\tdsetxyzrel
\tdplotsetrotatedcoordsorigin{(A2)}
\tdplotsetrotatedcoords{90}{90}{0}
\begin{scope}[->,>=latex,thick,tdplot_rotated_coords,violet]
\draw (A2) -- ++(1,0,0) node[anchor=north]{$x$};
\draw (A2) -- ++(0,1,0) node[anchor=south]{$y$};
\draw (A2) -- ++(0,0,1) node[anchor=south ]{$z$};
\end{scope}
%------------------------------------------------------------------%
\tdsetxyzrel
\tdplotsetrotatedcoordsorigin{(A3)}
\tdplotsetrotatedcoords{90}{90}{90}
\begin{scope}[->,>=latex,thick,tdplot_rotated_coords,blue]
\draw (A3) -- ++(1,0,0) node[anchor=north]{$x$};
\draw (A3) -- ++(0,1,0) node[anchor=south]{$y$};
\draw (A3) -- ++(0,0,1) node[anchor=south ]{$z$};
\end{scope}
%==================================================================%
% extrinsic (absolute) transformation (x-y-z)
%==================================================================%
\begin{scope}[thick,->,>=latex]
\draw (B0) -- ++(1,0,0) node[anchor=north]{$x$};
\draw (B0) -- ++(0,1,0) node[anchor=south]{$y$};
\draw (B0) -- ++(0,0,1) node[anchor=south]{$z$};
\end{scope}
%------------------------------------------------------------------%
\tdsetxyzabs
\tdplotsetrotatedcoordsorigin{(B1)}
\tdplotsetrotatedcoords{90}{0}{0}
\begin{scope}[->,>=latex,thick,tdplot_rotated_coords,red]
\draw (B1) -- ++(1,0,0) node[anchor=north]{$x$};
\draw (B1) -- ++(0,1,0) node[anchor=south]{$y$};
\draw (B1) -- ++(0,0,1) node[anchor=south ]{$z$};
\end{scope}
%------------------------------------------------------------------%
\tdsetxyzabs
\tdplotsetrotatedcoordsorigin{(B2)}
\tdplotsetrotatedcoords{90}{90}{0}
\begin{scope}[->,>=latex,thick,tdplot_rotated_coords,violet]
\draw (B2) -- ++(1,0,0) node[anchor=north]{$x$};
\draw (B2) -- ++(0,1,0) node[anchor=south]{$y$};
\draw (B2) -- ++(0,0,1) node[anchor=south ]{$z$};
\end{scope}
%------------------------------------------------------------------%
\tdsetxyzabs
\tdplotsetrotatedcoordsorigin{(B3)}
\tdplotsetrotatedcoords{90}{90}{90}
\begin{scope}[->,>=latex,thick,tdplot_rotated_coords,blue]
\draw (B3) -- ++(1,0,0) node[anchor=north]{$x$};
\draw (B3) -- ++(0,1,0) node[anchor=south]{$y$};
\draw (B3) -- ++(0,0,1) node[anchor=south ]{$z$};
\end{scope}
%------------------------------------------------------------------%
\end{tikzpicture}
\end{center}
\newpage
\section{Proper Euler angles}
\input{rotation_zyz.tex}
Left: intrinsic (relative) transformation) \\
Right: extrinsic (absolute) transformation)
\begin{center}
\begin{tikzpicture}[scale=1.5,tdplot_main_coords]
%------------------------------------------------------------------%
\coordinate (A0) at (0,0,0);
\coordinate (A1) at (0,0,3);
\coordinate (A2) at (0,0,6);
\coordinate (A3) at (0,0,9);
%------------------------------------------------------------------%
\coordinate (B0) at (4,4,0);
\coordinate (B1) at (4,4,3);
\coordinate (B2) at (4,4,6);
\coordinate (B3) at (4,4,9);
%==================================================================%
% intrinsic (relative) transformation (x-y'-z")
%==================================================================%
\begin{scope}[thick,->,>=latex]
\draw (A0) -- ++(1,0,0) node[anchor=north]{$x$};
\draw (A0) -- ++(0,1,0) node[anchor=south]{$y$};
\draw (A0) -- ++(0,0,1) node[anchor=south]{$z$};
\end{scope}
%------------------------------------------------------------------%
\tdsetzyzrel
\tdplotsetrotatedcoordsorigin{(A1)}
\tdplotsetrotatedcoords{90}{0}{0}
\begin{scope}[->,>=latex,thick,tdplot_rotated_coords,red]
\draw (A1) -- ++(1,0,0) node[anchor=north]{$x$};
\draw (A1) -- ++(0,1,0) node[anchor=south]{$y$};
\draw (A1) -- ++(0,0,1) node[anchor=south ]{$z$};
\end{scope}
%------------------------------------------------------------------%
\tdsetzyzrel
\tdplotsetrotatedcoordsorigin{(A2)}
\tdplotsetrotatedcoords{90}{90}{0}
\begin{scope}[->,>=latex,thick,tdplot_rotated_coords,violet]
\draw (A2) -- ++(1,0,0) node[anchor=north]{$x$};
\draw (A2) -- ++(0,1,0) node[anchor=south]{$y$};
\draw (A2) -- ++(0,0,1) node[anchor=south ]{$z$};
\end{scope}
%------------------------------------------------------------------%
\tdsetzyzrel
\tdplotsetrotatedcoordsorigin{(A3)}
\tdplotsetrotatedcoords{90}{90}{90}
\begin{scope}[->,>=latex,thick,tdplot_rotated_coords,blue]
\draw (A3) -- ++(1,0,0) node[anchor=north]{$x$};
\draw (A3) -- ++(0,1,0) node[anchor=south]{$y$};
\draw (A3) -- ++(0,0,1) node[anchor=south ]{$z$};
\end{scope}
%==================================================================%
% extrinsic (absolute) transformation (x-y-z)
%==================================================================%
\begin{scope}[thick,->,>=latex]
\draw (B0) -- ++(1,0,0) node[anchor=north]{$x$};
\draw (B0) -- ++(0,1,0) node[anchor=south]{$y$};
\draw (B0) -- ++(0,0,1) node[anchor=south]{$z$};
\end{scope}
%------------------------------------------------------------------%
\tdsetzyzabs
\tdplotsetrotatedcoordsorigin{(B1)}
\tdplotsetrotatedcoords{90}{0}{0}
\begin{scope}[->,>=latex,thick,tdplot_rotated_coords,red]
\draw (B1) -- ++(1,0,0) node[anchor=north]{$x$};
\draw (B1) -- ++(0,1,0) node[anchor=south]{$y$};
\draw (B1) -- ++(0,0,1) node[anchor=south ]{$z$};
\end{scope}
%------------------------------------------------------------------%
\tdsetzyzabs
\tdplotsetrotatedcoordsorigin{(B2)}
\tdplotsetrotatedcoords{90}{90}{0}
\begin{scope}[->,>=latex,thick,tdplot_rotated_coords,violet]
\draw (B2) -- ++(1,0,0) node[anchor=north]{$x$};
\draw (B2) -- ++(0,1,0) node[anchor=south]{$y$};
\draw (B2) -- ++(0,0,1) node[anchor=south ]{$z$};
\end{scope}
%------------------------------------------------------------------%
\tdsetzyzabs
\tdplotsetrotatedcoordsorigin{(B3)}
\tdplotsetrotatedcoords{90}{90}{90}
\begin{scope}[->,>=latex,thick,tdplot_rotated_coords,blue]
\draw (B3) -- ++(1,0,0) node[anchor=north]{$x$};
\draw (B3) -- ++(0,1,0) node[anchor=south]{$y$};
\draw (B3) -- ++(0,0,1) node[anchor=south ]{$z$};
\end{scope}
%------------------------------------------------------------------%
\end{tikzpicture}
\end{center}
\end{document}