BoxRotation
Author
Javi Pérez
Last Updated
2 years ago
License
Creative Commons CC BY 4.0
Abstract
Rotate a box around some axes: X axis, Y axix, Z axis, any axis
\documentclass[compress,9pt]{beamer}
\usepackage{pgfpages}
\usepackage{tikz} %TikZ is required for this to work. Make sure this exists before the next line
\usepackage{tikz-3dplot} %requires 3dplot.sty to be in same directory, or in your LaTeX installation
\begin{document}
\section{Rotate a box around some axes.}
\begin{frame}{Rotate box around $X$ axis.}
\begin{figure}[h]
\centering
\def\r{3.5}
\pgfmathsetmacro{\alphaNextBox}{90}
\pgfmathsetmacro{\betaNextBox}{-55}
\pgfmathsetmacro{\gammaNextBox}{-90}
%%% \pgfmathsetmacro{\inclination}{70}
\pgfmathsetmacro{\alphaEuler}{0}
\pgfmathsetmacro{\betaEuler}{0}
\pgfmathsetmacro{\gammaEuler}{47}
\tdplotsetmaincoords{70}{120}
\begin{tikzpicture}[tdplot_main_coords]
% Drawing XYZ coordinates system
\def \lenX {1.0*\r}
\def \lenY {1.3*\r}
\def \lenZ {1.0*\r}
\def \boxX{.7*\r}
\def \boxY{.9*\r}
\def \boxZ{.2*\r}
% Calculate box corner length
\pgfmathsetmacro{\boxCornerLen}{sqrt{((\boxX)^2 + (\boxY)^2 + (\boxZ)^2)}}
% Draw coordinate system
\draw[dashed] (0,0,0) -- (\boxX,0,0);
\draw[->,thick] (\boxX,0,0) -- (\lenX,0,0) node[left] {$X$};
\draw[dashed] (0,0,0) -- (0,\boxY,0);
\draw[->,thick] (0,\boxY,0) -- (0,\lenY,0) node[anchor=north west] {$Y$};
\draw[dashed] (0,0,0) -- (0,0,0.6*\lenZ);
\draw[->,thick] (0,0,0.6*\lenZ) -- (0,0,\lenZ) node[anchor=south] {$Z$};
% Draw gravity vector
\draw[-stealth,thin] (-0.8*\r,1.1*\r,0) -- (-0.8*\r,1.1*\r,-.3*\r) node[anchor=south west] {$\mathbf{g}$};
% Drawing horizontal box:
% Get corner polar coordinate
\tdplotgetpolarcoords{\boxX}{\boxY}{\boxZ}
\tdplotsetcoord{Box}{\boxCornerLen}{\tdplotrestheta}{\tdplotresphi}
% Draw a box
% \draw[] (O) -- (Boxx);
% \draw[] (O) -- (Boxy);
% \draw[] (O) -- (Boxz);
\draw[] (Boxx) -- (Boxxy);
\draw[] (Boxy) -- (Boxxy);
\draw[] (Boxx) -- (Boxxz);
\draw[] (Boxz) -- (Boxxz);
\draw[] (Boxy) -- (Boxyz);
\draw[] (Boxz) -- (Boxyz);
\draw[] (Boxxy) -- (Box);
\draw[] (Boxxz) -- (Box);
\draw[] (Boxyz) -- (Box);
\pause
% Create a new rotated system in the center
\tdplotsetrotatedcoords{\alphaEuler}{\betaEuler}{\gammaEuler}
% Draw new coordinates system
% Hidden line
\draw[dashed,tdplot_rotated_coords,red] (0,0,0) -- (1.4*\boxX,0,0);
% Visible line
\draw[thick,tdplot_rotated_coords,->,red] (1.4*\boxX,0,0) -- (1.3*\lenX,0,0) node[anchor=north east]{$E$};
% Hidden line
\draw[dashed,tdplot_rotated_coords,red] (0,0,0) -- (0,0.7*\boxY,0);
% Visible line
\draw[thick,tdplot_rotated_coords,->,red] (0,0.7*\boxY,0) -- (0,0.8*\lenY,0) node[anchor=south west]{$\mathbf{N}$};
% Hidden line
\draw[dashed,tdplot_rotated_coords,red] (0,0,0) -- (0,0,0.6*\lenZ);
% Visible line
\draw[thick,tdplot_rotated_coords,->,red] (0,0,0.6*\lenZ) -- (0,0,0.8*\lenZ) node[anchor=north east]{$Z$};
\pause
% Rotating box around X axis:
% Create a new rotated system in the center.
\tdplotsetrotatedcoords{\alphaNextBox}{\betaNextBox}{\gammaNextBox}
% Draw a box in the new coordinates system
\draw[tdplot_rotated_coords,gray] (\boxX,0,0) -- (\boxX,\boxY,0);
\draw[tdplot_rotated_coords,gray] (\boxX,\boxY,0) -- (0,\boxY,0);
\draw[tdplot_rotated_coords,gray] (0,\boxY,0) -- (0,\boxY,\boxZ);
\draw[tdplot_rotated_coords,dashed,gray] (0,\boxY,\boxZ) -- (0,0,\boxZ);
\draw[tdplot_rotated_coords,dashed,gray] (0,0,\boxZ) -- (\boxX,0,\boxZ);
\draw[tdplot_rotated_coords,gray] (\boxX,0,\boxZ) -- (\boxX,0,0);
\draw[tdplot_rotated_coords,gray] (\boxX,0,0) -- (\boxX,0,\boxZ);
\draw[tdplot_rotated_coords,gray] (\boxX,0,\boxZ) -- (\boxX,\boxY,\boxZ);
\draw[tdplot_rotated_coords,gray] (\boxX,\boxY,\boxZ) -- (0,\boxY,\boxZ);
\draw[tdplot_rotated_coords,gray] (\boxX,\boxY,\boxZ) -- (\boxX,\boxY,0);
\draw[tdplot_rotated_coords,dashed,gray] (0,0,\boxZ) -- (0,0,0);
\draw[tdplot_rotated_coords,gray] (0,0,0) -- (0,\boxY,0);
\tdplotsetrotatedcoordsorigin{(Shift)}
% Shift the rotated coordinates
\coordinate (Shift) at (\boxX,0,0);
% Draw rotation
\tdplotsetthetaplanecoords{90}
% \tdplotdrawarc[coordinate system, draw styles]{center}{r}{angle start}{angle end}{label options}{label}
\tdplotdrawarc[tdplot_rotated_coords,gray,thick,dotted,<->]{(Shift)}{\boxY}{90}{90+\betaNextBox}{anchor=west}{}
% Resets the origin of the rotated coordinate system back to the origin of the main coordinate system.
%\tdplotresetrotatedcoordsorigin
\coordinate (Shift) at (0,0,0);
\end{tikzpicture}
\end{figure}
\end{frame}
\begin{frame}[fragile]{Rotate box around $Y$ axis.}
\begin{figure}[h]
\centering
\def\r{3.5}
\pgfmathsetmacro{\alphaNextBox}{0}%{90}
\pgfmathsetmacro{\betaNextBox}{-50}%{-55}
\pgfmathsetmacro{\gammaNextBox}{0}%{-90}
%%% \pgfmathsetmacro{\inclination}{70}
\pgfmathsetmacro{\alphaEuler}{0}
\pgfmathsetmacro{\betaEuler}{0}
\pgfmathsetmacro{\gammaEuler}{47}
\tdplotsetmaincoords{70}{120}
\begin{tikzpicture}[tdplot_main_coords]
% Drawing XYZ coordinates system
\def \lenX {1.0*\r}
\def \lenY {1.3*\r}
\def \lenZ {1.0*\r}
\def \boxX{.7*\r}
\def \boxY{.9*\r}
\def \boxZ{.2*\r}
% Calculate box corner length
\pgfmathsetmacro{\boxCornerLen}{sqrt{((\boxX)^2 + (\boxY)^2 + (\boxZ)^2)}}
% Draw coordinate system
\draw[dashed] (0,0,0) -- (\boxX,0,0);
\draw[->,thick] (\boxX,0,0) -- (\lenX,0,0) node[left] {$X$};
\draw[dashed] (0,0,0) -- (0,\boxY,0);
\draw[->,thick] (0,\boxY,0) -- (0,\lenY,0) node[anchor=north west] {$Y$};
\draw[dashed] (0,0,0) -- (0,0,0.6*\lenZ);
\draw[->,thick] (0,0,0.6*\lenZ) -- (0,0,\lenZ) node[anchor=south] {$Z$};
% Draw gravity vector
\draw[-stealth,thin] (-0.8*\r,1.1*\r,0) -- (-0.8*\r,1.1*\r,-.3*\r) node[anchor=south west] {$\mathbf{g}$};
% Drawing horizontal box:
% Get corner polar coordinate
\tdplotgetpolarcoords{\boxX}{\boxY}{\boxZ}
\tdplotsetcoord{Box}{\boxCornerLen}{\tdplotrestheta}{\tdplotresphi}
% Draw a box
% \draw[] (O) -- (Boxx);
% \draw[] (O) -- (Boxy);
% \draw[] (O) -- (Boxz);
\draw[] (Boxx) -- (Boxxy);
\draw[] (Boxy) -- (Boxxy);
\draw[] (Boxx) -- (Boxxz);
\draw[] (Boxz) -- (Boxxz);
\draw[] (Boxy) -- (Boxyz);
\draw[] (Boxz) -- (Boxyz);
\draw[] (Boxxy) -- (Box);
\draw[] (Boxxz) -- (Box);
\draw[] (Boxyz) -- (Box);
\pause
% Create a new rotated system in the center
\tdplotsetrotatedcoords{\alphaEuler}{\betaEuler}{\gammaEuler}
% Draw new coordinates system
% Hidden line
\draw[dashed,tdplot_rotated_coords,red] (0,0,0) -- (1.4*\boxX,0,0);
% Visible line
\draw[thick,tdplot_rotated_coords,->,red] (1.4*\boxX,0,0) -- (1.3*\lenX,0,0) node[anchor=north east]{$E$};
% Hidden line
\draw[dashed,tdplot_rotated_coords,red] (0,0,0) -- (0,0.7*\boxY,0);
% Visible line
\draw[thick,tdplot_rotated_coords,->,red] (0,0.7*\boxY,0) -- (0,0.8*\lenY,0) node[anchor=south west]{$\mathbf{N}$};
% Hidden line
\draw[dashed,tdplot_rotated_coords,red] (0,0,0) -- (0,0,0.6*\lenZ);
% Visible line
\draw[thick,tdplot_rotated_coords,->,red] (0,0,0.6*\lenZ) -- (0,0,0.8*\lenZ) node[anchor=north east]{$Z$};
\pause
% Rotating box around one new axis:
% Create a new rotated system in the center.
\tdplotsetrotatedcoords{\alphaNextBox}{\betaNextBox}{\gammaNextBox}
% Draw a box in the new coordinates system
\draw[tdplot_rotated_coords,gray] (\boxX,0,0) -- (\boxX,\boxY,0);
\draw[tdplot_rotated_coords,gray] (\boxX,\boxY,0) -- (0,\boxY,0);
\draw[tdplot_rotated_coords,gray] (0,\boxY,0) -- (0,\boxY,\boxZ);
\draw[tdplot_rotated_coords,dashed,gray] (0,\boxY,\boxZ) -- (0,0,\boxZ);
\draw[tdplot_rotated_coords,dashed,gray] (0,0,\boxZ) -- (\boxX,0,\boxZ);
\draw[tdplot_rotated_coords,gray] (\boxX,0,\boxZ) -- (\boxX,0,0);
\draw[tdplot_rotated_coords,gray] (\boxX,0,0) -- (\boxX,0,\boxZ);
\draw[tdplot_rotated_coords,gray] (\boxX,0,\boxZ) -- (\boxX,\boxY,\boxZ);
\draw[tdplot_rotated_coords,gray] (\boxX,\boxY,\boxZ) -- (0,\boxY,\boxZ);
\draw[tdplot_rotated_coords,gray] (\boxX,\boxY,\boxZ) -- (\boxX,\boxY,0);
\draw[tdplot_rotated_coords,dashed,gray] (0,0,\boxZ) -- (0,0,0);
\draw[tdplot_rotated_coords,gray] (0,0,0) -- (0,\boxY,0);
\draw[tdplot_rotated_coords,gray] (0,0,0) -- (\boxX,0,0);
\tdplotsetthetaplanecoords{0}
\tdplotdrawarc[tdplot_rotated_coords,gray,thick,dotted,<->]{(0,0,0)}{\boxX}{90}{90+\betaNextBox}{anchor=west}{}
\end{tikzpicture}
%\caption{Giros en torno al eje $X$ para comprobar el comportamiento distorsionado de la brújula.}\label{fig:rollRotation}
\end{figure}
\end{frame}
\begin{frame}[fragile]{Rotate a box around $Z$ axis}
\begin{figure}[H]
\centering
\def\r{3.5}
\pgfmathsetmacro{\alphaEuler}{0}
\pgfmathsetmacro{\betaEuler}{0}
\pgfmathsetmacro{\gammaEuler}{47}
\pgfmathsetmacro{\nuSatellite}{55}
\pgfmathsetmacro{\gammaAngle}{290}
%\tdplotsetmaincoords{70}{155}
\tdplotsetmaincoords{70}{120}
\begin{tikzpicture}[tdplot_main_coords]
% Draw ENZ coordinates system
\def \lenX {1.0*\r}
\def \lenY {1.3*\r}
\def \lenZ {0.5*\r}
\def \boxX{.7*\r}
\def \boxY{.9*\r}
\def \boxZ{.2*\r}
% Calculate box corner length
\pgfmathsetmacro{\boxCornerLen}{sqrt{((\boxX)^2 + (\boxY)^2 + (\boxZ)^2)}}
% Draw coordinate system
\draw[dashed] (0,0,0) -- (\boxX,0,0);
\draw[->,thick] (\boxX,0,0) -- (\lenX,0,0) node[left] {$E$};
\draw[dashed] (0,0,0) -- (0,\boxY,0);
\draw[->,thick] (0,\boxY,0) -- (0,\lenY,0) node[anchor=north west] {$\mathbf{N}$};
\draw[dashed] (0,0,0) -- (0,0,0.6*\lenZ);
\draw[->,thick] (0,0,0.6*\lenZ) -- (0,0,\lenZ) node[anchor=south] {$Z$};
% Draw gravity vector
\draw[-stealth,thin] (-0.8*\r,1.1*\r,0) -- (-0.8*\r,1.1*\r,-.3*\r) node[anchor=south west] {$\mathbf{g}$};
% Drawing horizontal box:
% Get corner polar coordinate
\tdplotgetpolarcoords{\boxX}{\boxY}{\boxZ}
\tdplotsetcoord{Box}{\boxCornerLen}{\tdplotrestheta}{\tdplotresphi}
% Draw a box
% \draw[] (O) -- (Boxx);
% \draw[] (O) -- (Boxy);
% \draw[] (O) -- (Boxz);
\draw[] (Boxx) -- (Boxxy);
\draw[] (Boxy) -- (Boxxy);
\draw[] (Boxx) -- (Boxxz);
\draw[] (Boxz) -- (Boxxz);
\draw[] (Boxy) -- (Boxyz);
\draw[] (Boxz) -- (Boxyz);
\draw[] (Boxxy) -- (Box);
\draw[] (Boxxz) -- (Box);
\draw[] (Boxyz) -- (Box);
\pause
% Create a new rotated system in the center
\tdplotsetrotatedcoords{\alphaEuler}{\betaEuler}{\gammaEuler}
% Draw a box in the new coordinates system
\draw[tdplot_rotated_coords,gray] (\boxX,0,0) -- (\boxX,\boxY,0) -- (0,\boxY,0) -- (0,\boxY,\boxZ) -- (0,0,\boxZ) -- (\boxX,0,\boxZ) -- (\boxX,0,0);
\draw[tdplot_rotated_coords,gray] (\boxX,0,\boxZ) -- (\boxX,\boxY,\boxZ) -- (0,\boxY,\boxZ);
\draw[tdplot_rotated_coords,gray] (\boxX,\boxY,\boxZ) -- (\boxX,\boxY,0);
% Draw new coordinates system
% Hidden line
\draw[dashed,tdplot_rotated_coords,gray] (0,0,0) -- (\boxX,0,0);
% Visible line
\draw[thick,tdplot_rotated_coords,->,gray] (\boxX,0,0) -- (1.3*\lenX,0,0) node[anchor=north east]{$X$};
% Hidden line
\draw[dashed,tdplot_rotated_coords,gray] (0,0,0) -- (0,\boxY,0);
% Visible line
\draw[thick,tdplot_rotated_coords,->,gray] (0,\boxY,0) -- (0,1.3*\lenY,0) node[anchor=south west]{$Y$};
% Hidden line
\draw[dashed,tdplot_rotated_coords,gray] (0,0,0) -- (0,0,\boxZ);
% Visible line
\draw[thick,tdplot_rotated_coords,->,gray] (0,0,\boxZ) -- (0,0,0.8*\lenZ) node[anchor=north west]{$Z$};
% Draw rotation
% \tdplotdrawarc[coordinate system, draw styles]{center}{r}{angle start}{angle end}{label options}{label}
\tdplotdrawarc[thick,dotted,<->]{(0,0,0.5*\lenZ)}{0.5*\r}{-270}{0}{anchor=west}{}
\end{tikzpicture}
\end{figure}
\end{frame}
\begin{frame}[fragile]{Rotate a box aroud any axis}
\begin{figure}[h]
\centering
\def\r{3.5}
\pgfmathsetmacro{\alphaNorth}{40}
\pgfmathsetmacro{\betaNorth}{0}
\pgfmathsetmacro{\gammaNorth}{0}
\pgfmathsetmacro{\alphaNewAxis}{-35}
\pgfmathsetmacro{\betaNewAxis}{0}
\pgfmathsetmacro{\gammaNewAxis}{0}
\pgfmathsetmacro{\alphaNextBox}{\alphaNewAxis}
\pgfmathsetmacro{\betaNextBox}{-40}
\pgfmathsetmacro{\gammaNextBox}{0}
%%% \pgfmathsetmacro{\inclination}{70}
\tdplotsetmaincoords{70}{160}
\begin{tikzpicture}[tdplot_main_coords]
% Drawing XYZ coordinates system
\def \lenX {1.0*\r}
\def \lenY {1.3*\r}
\def \lenZ {1.0*\r}
\def \boxX{.7*\r}
\def \boxY{.9*\r}
\def \boxZ{.2*\r}
% Calculate box corner length
\pgfmathsetmacro{\boxCornerLen}{sqrt{((\boxX)^2 + (\boxY)^2 + (\boxZ)^2)}}
% Draw coordinate system
\draw[dashed] (0,0,0) -- (\boxX,0,0);
\draw[->,thick] (\boxX,0,0) -- (\lenX,0,0) node[left] {$X$};
\draw[dashed] (0,0,0) -- (0,\boxY,0);
\draw[->,thick] (0,\boxY,0) -- (0,\lenY,0) node[anchor=north west] {$Y$};
\draw[dashed] (0,0,0) -- (0,0,0.6*\lenZ);
\draw[->,thick] (0,0,0.6*\lenZ) -- (0,0,\lenZ) node[anchor=south] {$Z$};
% Draw gravity vector
\draw[-stealth,thin] (-0.8*\r,1.1*\r,0) -- (-0.8*\r,1.1*\r,-.3*\r) node[anchor=south west] {$\mathbf{g}$};
% Drawing horizontal box:
% Get corner polar coordinate
\tdplotgetpolarcoords{\boxX}{\boxY}{\boxZ}
\tdplotsetcoord{Box}{\boxCornerLen}{\tdplotrestheta}{\tdplotresphi}
% Draw a box
% \draw[] (O) -- (Boxx);
% \draw[] (O) -- (Boxy);
% \draw[] (O) -- (Boxz);
\draw[] (Boxx) -- (Boxxy);
\draw[] (Boxy) -- (Boxxy);
\draw[] (Boxx) -- (Boxxz);
\draw[] (Boxz) -- (Boxxz);
\draw[] (Boxy) -- (Boxyz);
\draw[] (Boxz) -- (Boxyz);
\draw[] (Boxxy) -- (Box);
\draw[] (Boxxz) -- (Box);
\draw[] (Boxyz) -- (Box);
\pause
% Create a new rotated system in the center for North direction
\tdplotsetrotatedcoords{\alphaNorth}{\betaNorth}{\gammaNorth}
% Draw new coordinates system
% Hidden line
\draw[dashed,tdplot_rotated_coords,red] (0,0,0) -- (1.4*\boxX,0,0);
% Visible line
\draw[thick,tdplot_rotated_coords,->,red] (1.4*\boxX,0,0) -- (1.3*\lenX,0,0) node[anchor=north east]{$E$};
% Hidden line
\draw[dashed,tdplot_rotated_coords,red] (0,0,0) -- (0,0.3*\boxY,0);
% Visible line
\draw[thick,tdplot_rotated_coords,->,red] (0,0.3*\boxY,0) -- (0,0.8*\lenY,0) node[anchor=south west]{$\mathbf{N}$};
% Hidden line
\draw[dashed,tdplot_rotated_coords,red] (0,0,0) -- (0,0,1.1*\boxZ);
% Visible line
\draw[thick,tdplot_rotated_coords,->,red] (0,0,1.1*\boxZ) -- (0,0,0.8*\lenZ) node[anchor=north east]{$Z$};
\pause
% Create a new rotated system in the center
\tdplotsetrotatedcoords{\alphaNewAxis}{\betaNewAxis}{\gammaNewAxis}
% Draw new coordinates system
%\draw[dashed,tdplot_rotated_coords,orange] (0,0,0) -- (1.3*\lenX,0,0) node[anchor=north east]{$x$};
\draw[dashed,tdplot_rotated_coords,blue] (0,0,0) -- (0,1.6*\lenY,0) node[anchor=north east]{Rotation axis};
%\draw[dashed,tdplot_rotated_coords,orange] (0,0,0) -- (0,0,1.3*\lenZ) node[anchor=north east]{$z$};
%
% Calculate Box coordinates in rotated system {\boxX}{\boxY}{\boxZ}
\tdplottransformmainrot{\boxX}{0}{0}
\pgfmathsetmacro{\BoxNewXoox}{\tdplotresx}
\pgfmathsetmacro{\BoxNewXooy}{\tdplotresy}
\pgfmathsetmacro{\BoxNewXooz}{\tdplotresz}
%\coordinate (BoxNewX00) at (\tdplotresx,\tdplotresy,\tdplotresz);
\tdplottransformmainrot{0}{\boxY}{0}
\pgfmathsetmacro{\BoxNewoYox}{\tdplotresx}
\pgfmathsetmacro{\BoxNewoYoy}{\tdplotresy}
\pgfmathsetmacro{\BoxNewoYoz}{\tdplotresz}
%\coordinate (BoxNew0Y0) at (\tdplotresx,\tdplotresy,\tdplotresz);
\tdplottransformmainrot{0}{0}{\boxZ}
\pgfmathsetmacro{\BoxNewooZx}{\tdplotresx}
\pgfmathsetmacro{\BoxNewooZy}{\tdplotresy}
\pgfmathsetmacro{\BoxNewooZz}{\tdplotresz}
%\coordinate (BoxNew00Z) at (\tdplotresx,\tdplotresy,\tdplotresz);
\tdplottransformmainrot{\boxX}{\boxY}{0}
\pgfmathsetmacro{\BoxNewXYox}{\tdplotresx}
\pgfmathsetmacro{\BoxNewXYoy}{\tdplotresy}
\pgfmathsetmacro{\BoxNewXYoz}{\tdplotresz}
%\coordinate (BoxNewXY0) at (\tdplotresx,\tdplotresy,\tdplotresz);
\tdplottransformmainrot{\boxX}{0}{\boxZ}
\pgfmathsetmacro{\BoxNewXoZx}{\tdplotresx}
\pgfmathsetmacro{\BoxNewXoZy}{\tdplotresy}
\pgfmathsetmacro{\BoxNewXoZz}{\tdplotresz}
%\coordinate (BoxNewX0Z) at (\tdplotresx,\tdplotresy,\tdplotresz);
\tdplottransformmainrot{0}{\boxY}{\boxZ}
\pgfmathsetmacro{\BoxNewoYZx}{\tdplotresx}
\pgfmathsetmacro{\BoxNewoYZy}{\tdplotresy}
\pgfmathsetmacro{\BoxNewoYZz}{\tdplotresz}
%\coordinate (BoxNew0YZ) at (\tdplotresx,\tdplotresy,\tdplotresz);
\tdplottransformmainrot{\boxX}{\boxY}{\boxZ}
\pgfmathsetmacro{\BoxNewXYZx}{\tdplotresx}
\pgfmathsetmacro{\BoxNewXYZy}{\tdplotresy}
\pgfmathsetmacro{\BoxNewXYZz}{\tdplotresz}
%\coordinate (BoxNewXYZ) at (\tdplotresx,\tdplotresy,\tdplotresz);
\coordinate (0) at (0,0,0);
%\draw[tdplot_rotated_coords, orange] (0) -- (\BoxNewXoox,\BoxNewXooy,\BoxNewXooz) -- (\BoxNewXYox,\BoxNewXYoy,\BoxNewXYoz) -- (\BoxNewoYox,\BoxNewoYoy,\BoxNewoYoz) -- (0);
%
%\draw[tdplot_rotated_coords, orange] (\BoxNewooZx,\BoxNewooZy,\BoxNewooZz) -- (\BoxNewXoZx,\BoxNewXoZy,\BoxNewXoZz) -- (\BoxNewXYZx,\BoxNewXYZy,\BoxNewXYZz) -- (\BoxNewoYZx,\BoxNewoYZy,\BoxNewoYZz) -- (\BoxNewooZx,\BoxNewooZy,\BoxNewooZz);
%
%\draw[tdplot_rotated_coords, orange] (\BoxNewooZx,\BoxNewooZy,\BoxNewooZz) -- (0);
%\draw[tdplot_rotated_coords, orange] (\BoxNewXoZx,\BoxNewXoZy,\BoxNewXoZz) -- (\BoxNewXoox,\BoxNewXooy,\BoxNewXooz);
%\draw[tdplot_rotated_coords, orange] (\BoxNewXYZx,\BoxNewXYZy,\BoxNewXYZz) -- (\BoxNewXYox,\BoxNewXYoy,\BoxNewXYoz);
%\draw[tdplot_rotated_coords, orange] (\BoxNewoYZx,\BoxNewoYZy,\BoxNewoYZz) -- (\BoxNewoYox,\BoxNewoYoy,\BoxNewoYoz);
%\draw[tdplot_rotated_coords,green] (0) -- (BoxNewX00) -- (BoxNewXY0) -- (BoxNew0Y0) -- (0);
%\draw[tdplot_rotated_coords, green] (BoxNew00Z) -- (BoxNewX0Z) -- (BoxNewXYZ) -- (BoxNew0YZ) -- (BoxNew00Z);
%%%\foreach \stepNumber in {1,2,3}
\foreach \slideNumber in {4,5,6}
%%%\foreach \betaNextBox in {-15,-30,-45}
{
\pause
%%%\pgfmathsetmacro{\betaNextBox}{(-15)*\stepNumber}
\pgfmathsetmacro{\betaNextBox}{(-15)*(\slideNumber-3)}
%%%\pgfmathsetmacro{\slideNumber}{3+\stepNumber}
\only<\slideNumber>{
% Rotating box around one new axis:
% Create a new rotated system in the center.
\tdplotsetrotatedcoords{\alphaNextBox}{\betaNextBox}{\gammaNextBox}
%\draw[dashed,tdplot_rotated_coords,gray] (0,0,0) -- (1.3*\lenX,0,0) node[anchor=north east]{$x$};
%\draw[dashed,tdplot_rotated_coords,gray] (0,0,0) -- (0,1.3*\lenY,0) node[anchor=south east]{$y$};
%\draw[dashed,tdplot_rotated_coords,gray] (0,0,0) -- (0,0,1.3*\lenZ) node[anchor=north east]{$z$};
% Draw a box in the new coordinates system
\draw[dashed,tdplot_rotated_coords, gray] (0) -- (\BoxNewXoox,\BoxNewXooy,\BoxNewXooz);
\draw[tdplot_rotated_coords, gray] (\BoxNewXoox,\BoxNewXooy,\BoxNewXooz) -- (\BoxNewXYox,\BoxNewXYoy,\BoxNewXYoz) -- (\BoxNewoYox,\BoxNewoYoy,\BoxNewoYoz);
\draw[dashed,tdplot_rotated_coords, gray] (\BoxNewXYox,\BoxNewXYoy,\BoxNewXYoz) -- (\BoxNewoYox,\BoxNewoYoy,\BoxNewoYoz) -- (0);
\draw[tdplot_rotated_coords, gray] (\BoxNewooZx,\BoxNewooZy,\BoxNewooZz) -- (\BoxNewXoZx,\BoxNewXoZy,\BoxNewXoZz) -- (\BoxNewXYZx,\BoxNewXYZy,\BoxNewXYZz) -- (\BoxNewoYZx,\BoxNewoYZy,\BoxNewoYZz) -- (\BoxNewooZx,\BoxNewooZy,\BoxNewooZz);
\draw[tdplot_rotated_coords, gray] (\BoxNewooZx,\BoxNewooZy,\BoxNewooZz) -- (0);
\draw[tdplot_rotated_coords, gray] (\BoxNewXoZx,\BoxNewXoZy,\BoxNewXoZz) -- (\BoxNewXoox,\BoxNewXooy,\BoxNewXooz);
\draw[tdplot_rotated_coords, gray] (\BoxNewXYZx,\BoxNewXYZy,\BoxNewXYZz) -- (\BoxNewXYox,\BoxNewXYoy,\BoxNewXYoz);
\draw[tdplot_rotated_coords, gray] (\BoxNewoYZx,\BoxNewoYZy,\BoxNewoYZz) -- (\BoxNewoYox,\BoxNewoYoy,\BoxNewoYoz);
\tdplotsetthetaplanecoords{0}
\tdplotdrawarc[tdplot_rotated_coords,gray,thick,dotted,<->]{(0,0,0)}{\boxX}{90}{90+\betaNextBox}{anchor=west}{}
}
} % end \foreach
\end{tikzpicture}
\end{figure}
\end{frame}
\end{document}