\newcommand{\tdplotmainfig}{%
%Angle Definitions
%-----------------
%
%set the plot display orientation
%synatax: \tdplotsetdisplay{\theta_d}{\phi_d}
\tdplotsetmaincoords{60}{110}
%
%define polar coordinates for some vector
%TODO: look into using 3d spherical coordinate system
\pgfmathsetmacro{\rvec}{.8}
\pgfmathsetmacro{\thetavec}{30}
\pgfmathsetmacro{\phivec}{60}
%
%start tikz picture, and use the tdplot_main_coords style to implement the display coordinate transformation provided by 3dplot
\begin{tikzpicture}[scale=3,tdplot_main_coords]

       %set up some coordinates
       %-----------------------
       \coordinate (O) at (0,0,0);

       %determine a coordinate (P) using (r,\theta,\phi) coordinates.  This command also determines (Pxy), (Pxz), and (Pyz): the xy-, xz-, and yz-projections of the point (P).
       %synatax: \tdplotsetcoord{Coordinate name without parentheses}{r}{\theta}{\phi}
       \tdplotsetcoord{P}{\rvec}{\thetavec}{\phivec}

       %draw figure contents
       %--------------------

       %draw the main coordinate system axes
       \draw[thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};
       \draw[thick,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$y$};
       \draw[thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z$};

       %draw a vector from origin to point (P)
       \draw[-stealth,color=red] (O) -- (P);

       %draw projection on xy plane, and a connecting line
       \draw[dashed, color=red] (O) -- (Pxy);
       \draw[dashed, color=red] (P) -- (Pxy);

       %draw the angle \phi, and label it
       %syntax: \tdplotdrawarc[coordinate frame, draw options]{center point}{r}{angle}{label options}{label}
       \tdplotdrawarc{(O)}{0.2}{0}{\phivec}{anchor=north}{$\phi$}


       %set the rotated coordinate system so the x'-y' plane lies within the "theta plane" of the main coordinate system
       %syntax: \tdplotsetthetaplanecoords{\phi}
       \tdplotsetthetaplanecoords{\phivec}

       %draw theta arc and label, using rotated coordinate system
       \tdplotdrawarc[tdplot_rotated_coords]{(0,0,0)}{0.5}{0}{\thetavec}{anchor=south west}{$\theta$}

       %draw some dashed arcs, demonstrating direct arc drawing
       \draw[dashed,tdplot_rotated_coords] (\rvec,0,0) arc (0:90:\rvec);
       \draw[dashed] (\rvec,0,0) arc (0:90:\rvec);

       %set the rotated coordinate definition within display using a translation coordinate and Euler angles in the "z(\alpha)y(\beta)z(\gamma)" euler rotation convention
       %syntax: \tdplotsetrotatedcoords{\alpha}{\beta}{\gamma}
       \tdplotsetrotatedcoords{\phivec}{\thetavec}{0}

       %translate the rotated coordinate system
       %syntax: \tdplotsetrotatedcoordsorigin{point}
       \tdplotsetrotatedcoordsorigin{(P)}

       %use the tdplot_rotated_coords style to work in the rotated, translated coordinate frame
       \draw[thick,tdplot_rotated_coords,->] (0,0,0) -- (.5,0,0) node[anchor=north west]{$x'$};
       \draw[thick,tdplot_rotated_coords,->] (0,0,0) -- (0,.5,0) node[anchor=west]{$y'$};
       \draw[thick,tdplot_rotated_coords,->] (0,0,0) -- (0,0,.5) node[anchor=south]{$z'$};

       %WARNING:  coordinates defined by the \coordinate command (eg. (O), (P), etc.) cannot be used in rotated coordinate frames.  Use only literal coordinates.

       %draw some vector, and its projection, in the rotated coordinate frame
       \draw[-stealth,color=blue,tdplot_rotated_coords] (0,0,0) -- (.2,.2,.2);
       \draw[dashed,color=blue,tdplot_rotated_coords] (0,0,0) -- (.2,.2,0);
       \draw[dashed,color=blue,tdplot_rotated_coords] (.2,.2,0) -- (.2,.2,.2);

       %show its phi arc and label
       \tdplotdrawarc[tdplot_rotated_coords,color=blue]{(0,0,0)}{0.2}{0}{45}{anchor=north west,color=black}{$\phi'$}

       %change the rotated coordinate frame so that it lies in its theta plane.  Note that this overwrites the original rotated coordinate frame
       %syntax: \tdplotsetrotatedthetaplanecoords{\phi'}
       \tdplotsetrotatedthetaplanecoords{45}

       %draw theta arc and label
       \tdplotdrawarc[tdplot_rotated_coords,color=blue]{(0,0,0)}{0.2}{0}{55}{anchor=south west,color=black}{$\theta'$}

\end{tikzpicture}
}

\newcommand{\threedcoord}[2]{%
\tdplotsetmaincoords{#1}{#2}
\begin{tikzpicture}[tdplot_main_coords]
       \draw[thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};
       \draw[thick,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$y$};
       \draw[thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z$};
\end{tikzpicture}
}

\newcommand{\threedrotcoordsystem}{%
\tdplotsetmaincoords{50}{140}
\begin{tikzpicture}[scale=5,tdplot_main_coords]
       \draw[thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};
       \draw[thick,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$y$};
       \draw[thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z$};

       \tdplotsetrotatedcoords{34}{26}{12}

       \draw[thick,color=blue,tdplot_rotated_coords,->] (0,0,0) -- (.5,0,0) node[anchor=north east]{$x'$};
       \draw[thick,color=blue,tdplot_rotated_coords,->] (0,0,0) -- (0,.5,0) node[anchor=north west]{$y'$};
       \draw[thick,color=blue,tdplot_rotated_coords,->] (0,0,0) -- (0,0,.5) node[anchor=south]{$z'$};

\end{tikzpicture}
}

\newcommand{\threedconventions}{%
\tdplotsetmaincoords{50}{110}
\begin{tikzpicture}[scale=2,tdplot_main_coords]
       \draw[thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};
       \draw[thick,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$y$};
       \draw[thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z$};

       \draw[color=blue] (0,0,0) -- (.5,.5,0);

       \draw[color=blue,->] (.5,0,0) arc (0:45:.5);
\end{tikzpicture}
}


\newcommand{\threedalphabetagamma}{%
\beginpgfgraphicnamed{Figures/alphabetagamma}
\tdplotsetmaincoords{50}{140}
%
\begin{tikzpicture}[scale=2,tdplot_main_coords]
       \draw[thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};
       \draw[thick,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$y$};
       \draw[thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z$};

       \tdplotsetrotatedcoords{0}{0}{30}

       \draw[thick,color=red,tdplot_rotated_coords,->] (0,0,0) -- (.7,0,0) node[anchor=north]{$x'$};
       \draw[thick,color=green!50!black,tdplot_rotated_coords,->] (0,0,0) -- (0,.7,0) node[anchor=west]{$y'$};
       \draw[thick,color=blue,tdplot_rotated_coords,->] (0,0,0) -- (0,0,.7) node[anchor=west]{$z'$};

       \tdplotdrawarc[color=orange!50!black]{(0,0,0)}{.4}{0}{30}{anchor=north east}{$\gamma$}
\end{tikzpicture}
%
\begin{tikzpicture}[scale=2,tdplot_main_coords]
       \draw[thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};
       \draw[thick,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$y$};
       \draw[thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z$};

       \tdplotsetrotatedcoords{0}{0}{30}

       \draw[dashed,color=red,tdplot_rotated_coords] (0,0,0) -- (.5,0,0);
       \draw[dashed,color=green!50!black,tdplot_rotated_coords] (0,0,0) -- (0,.5,0);
       \draw[dashed,color=blue,tdplot_rotated_coords] (0,0,0) -- (0,0,.5);

       \tdplotsetrotatedcoords{0}{40}{30}

       \draw[thick,color=red,tdplot_rotated_coords,->] (0,0,0) -- (.7,0,0) node[anchor=north]{$x'$};
       \draw[thick,color=green!50!black,tdplot_rotated_coords,->] (0,0,0) -- (0,.7,0) node[anchor=west]{$y'$};
       \draw[thick,color=blue,tdplot_rotated_coords,->] (0,0,0) -- (0,0,.7) node[anchor=south]{$z'$};

       \tdplotsetthetaplanecoords{0}
       \tdplotdrawarc[tdplot_rotated_coords,color=orange!50!black]{(0,0,0)}{.4}{0}{40}{anchor=south}{$\beta$}

\end{tikzpicture}
%
\begin{tikzpicture}[scale=2,tdplot_main_coords]
       \draw[thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};
       \draw[thick,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$y$};
       \draw[thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z$};

       \tdplotsetrotatedcoords{0}{40}{30}

       \draw[dashed,color=red,tdplot_rotated_coords] (0,0,0) -- (.5,0,0);
       \draw[dashed,color=green!50!black,tdplot_rotated_coords] (0,0,0) -- (0,.5,0);
       \draw[dashed,color=blue,tdplot_rotated_coords] (0,0,0) -- (0,0,.5);

       \tdplotsetrotatedcoords{60}{0}{0}
       \draw[dotted,color=blue,tdplot_rotated_coords] (0,0,0) -- (.4,0,0);
       \tdplotsetrotatedcoords{60}{40}{30}

       \draw[thick,color=red,tdplot_rotated_coords,->] (0,0,0) -- (.7,0,0) node[anchor=north]{$x'$};
       \draw[thick,color=green!50!black,tdplot_rotated_coords,->] (0,0,0) -- (0,.7,0) node[anchor=west]{$y'$};
       \draw[thick,color=blue,tdplot_rotated_coords,->] (0,0,0) -- (0,0,.7) node[anchor=south]{$z'$};


       \tdplotdrawarc[color=orange!50!black]{(0,0,0)}{.2}{0}{60}{anchor=north east}{$\alpha$}
\end{tikzpicture}
\endpgfgraphicnamed
}

\newcommand{\threedthetaarc}{%
%
\tdplotsetmaincoords{70}{110}
%
\begin{tikzpicture}[scale=5,tdplot_main_coords]
       \draw[thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};
       \draw[thick,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$y$};
       \draw[thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z$};

       \tdplotsetcoord{P}{.8}{50}{70}

       %draw a vector from origin to point (P)
       \draw[-stealth,color=red] (O) -- (P);

       %draw projection on xy plane, and a connecting line
       \draw[dashed, color=red] (O) -- (Pxy);
       \draw[dashed, color=red] (P) -- (Pxy);


       \tdplotsetthetaplanecoords{70}

       \draw[tdplot_rotated_coords,color=blue,thick,->] (0,0,0) -- (.2,0,0) node[anchor=east]{$x'$};
       \draw[tdplot_rotated_coords,color=blue,thick,->] (0,0,0) -- (0,.2,0) node[anchor=north]{$y'$};
       \draw[tdplot_rotated_coords,color=blue,thick,->] (0,0,0) -- (0,0,.2) node[anchor=west]{$z'$};


       \tdplotdrawarc[tdplot_rotated_coords,color=orange!50!black]{(0,0,0)}{.4}{0}{50}{anchor=north east}{$\theta$}
\end{tikzpicture}
}

\newcommand{\threedparamplot}{%
%
\beginpgfgraphicnamed{Figures/threedparamplot}
\tdplotsetmaincoords{70}{110}
%
\begin{tikzpicture}[scale=2,tdplot_main_coords]
       \draw[thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};
       \draw[thick,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$y$};
       \draw[thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z$};

       \pgfplothandlerlineto
       \pgfplotfunction{\thetaen}{0,6,...,360}{%
               \pgfpointxyz{cos(\thetaen)}%
                       {sin(\thetaen)}%
                       {\thetaen/400}
       }
       \pgfusepath{stroke}

\end{tikzpicture}
\endpgfgraphicnamed
}

\newcommand{\threedsurfaceplot}{%
\beginpgfgraphicnamed{Figures/threedsurfaceplot}
%
\tdplotsetmaincoords{70}{135}
%
\begin{tikzpicture}[scale=3,line join=bevel,tdplot_main_coords, fill opacity=.6]

\tdplotsphericalsurfaceplot[parametricfill]{72}{36}%
%{0.3}{black}{red}%
%{0.5*sin(\tdplottheta)*sin(\tdplottheta)}{black}{red}%
%{0.5*sin(\tdplottheta)*sin(\tdplottheta)*sin(\tdplotphi)*sin(\tdplotphi)}{black}{red}%
%{0.5*cos(\tdplottheta)*cos(\tdplottheta)}{black}{red}%
%{0.25*cos(\tdplottheta)}{black}{red}%
{(sin(\tdplottheta)*cos(\tdplottheta))}{black}{\tdplotphi}%
%{ .15*(3*cos(\tdplottheta)*cos(\tdplottheta) - 1 )^2}{black}{\tdplotphi}
       {\draw[color=black,thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};}%
       {\draw[color=black,thick,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$y$};}%
       {\draw[color=black,thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z$};}%

\end{tikzpicture}
\endpgfgraphicnamed

}

\newcommand{\colortest}{%
\begin{tikzpicture}
       \foreach \thetawheel in {0,1,...,360}
       {
               %\tdplotcalcrgb{\thetawheel}
               \pgfmathdivide{\thetawheel}{360}
               \definecolor{tdplotcolor}{hsb}{\pgfmathresult, 1, 1}
               \color{tdplotcolor}
               \filldraw(\thetawheel:3) circle (1pt);
       }
\end{tikzpicture}
}

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