blochsphere (17aug15)

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+% \iffalse meta-comment
+%
+% Copyright (C) 2015 by Matthew Wardrop <mister.wardrop@gmail.com>
+% ---------------------------------------------------------------------------
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+%
+% This work has the LPPL maintenance status `maintained'.
+%
+% The Current Maintainer of this work is Matthew Wardrop
+%
+% This work consists of the files blochsphere.dtx and blochsphere.ins
+% and the derived filebase blochsphere.sty.
+%
+% \fi
+%
+% \iffalse
+%<*driver>
+\ProvidesFile{blochsphere.dtx}
+%</driver>
+%<package>\NeedsTeXFormat{LaTeX2e}[1999/12/01]
+%<package>\ProvidesPackage{blochsphere}
+%<*package>
+    [2015/08/17 v1.0 blochsphere drawing package]
+%</package>
+%
+%<*driver>
+\documentclass{ltxdoc}
+\EnableCrossrefs
+\CodelineIndex
+\RecordChanges
+\usepackage{blochsphere}
+\usepackage{minted}
+\usepackage{hyperref}
+
+\setlength{\parskip}{0.7em}
+
+\newenvironment{key}[2]{
+	\noindent{\llap{Option: \bf\tt #2\hskip 9pt}}
+}{}
+\newcommand{\DescribeKey}[3][]{
+	\noindent{\llap{\bf\tt #2\hskip 9pt}[default = #1] #3}
+}
+
+\usepackage{listings}
+\lstset{breaklines=true}
+
+\begin{document}
+  \DocInput{blochsphere.dtx}
+  \PrintChanges
+  \PrintIndex
+\end{document}
+%</driver>
+% \fi
+%
+% \CheckSum{841}
+%
+% \CharacterTable
+%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
+%   Digits        \0\1\2\3\4\5\6\7\8\9
+%   Exclamation   \!     Double quote  \"     Hash (number) \#
+%   Dollar        \$     Percent       \%     Ampersand     \&
+%   Acute accent  \'     Left paren    \(     Right paren   \)
+%   Asterisk      \*     Plus          \+     Comma         \,
+%   Minus         \-     Point         \.     Solidus       \/
+%   Colon         \:     Semicolon     \;     Less than     \<
+%   Equals        \=     Greater than  \>     Question mark \?
+%   Commercial at \@     Left bracket  \[     Backslash     \\
+%   Right bracket \]     Circumflex    \^     Underscore    \_
+%   Grave accent  \`     Left brace    \{     Vertical bar  \|
+%   Right brace   \}     Tilde         \~}
+%
+%
+% \changes{v1.0}{2015/08/17}{Initial version}
+%
+% \DoNotIndex{\newcommand,\newenvironment}
+%
+% \providecommand*{\url}{\texttt}
+% \GetFileInfo{blochsphere.dtx}
+% \title{The \textsf{blochsphere} package}
+% \author{Matthew Wardrop \\ \url{mister.wardrop@gmail.com}}
+% \date{\fileversion~from \filedate}
+%
+% \maketitle
+%
+% \tableofcontents
+%
+% \section{Introduction}
+%
+% The |blochsphere| package is used to draw pseudo-3D Blochsphere diagrams, such as that
+% shown in figure \ref{fig:blochsphere}. It supports various annotations, such as
+% great and small circles, axes, rotation markings and state vectors. It can be used
+% in a standalone fashion, or nested within a |tikzpicture| environment by setting
+% the environment option |nested| to |true|.
+%
+% \section{Usage}
+%
+% Using |blochsphere| is as simple as creating a `blochsphere' environment.
+% \begin{minted}{LaTeX}
+% \begin{blochsphere}[<options>]
+% ...
+% \end{blochsphere}
+% \end{minted}
+% By default, this will create a blank Bloch sphere ready for annotation. The options can be
+% any of those described in the next section.
+%
+% \noindent\DescribeMacro{\drawBall} \oarg{options}\\
+% This macro draws the basic Bloch sphere, according to the options defined in the next section.
+%
+% \noindent\DescribeMacro{\drawBallGrid} \oarg{options} \marg{latdegsep} \marg{longdegsep}\\
+% This macro draws latitude and longitude circles at an interval defined by |latdegsep| and |longdegsep| respectively.
+%
+% \noindent\DescribeMacro{\setDrawingPlane} \oarg{options} \marg{tiltangle} \marg{rotationangle}\\
+% This macro defines a transformation matrix within TikZ to create the effect of 2D projections of 3D planes,
+% named according to the |plane| option. This is used internally in all of the drawing commands.
+%
+% \noindent\DescribeMacro{\setLatitudinalDrawingPlane} \oarg{options} \marg{latitude}\\
+% This is a special case of |\setDrawingPlane| that constructs the transform required to draw a 2D image in
+% a latitudinal plane.
+%
+% \noindent\DescribeMacro{\setLongitudinalDrawingPlane} \oarg{options} \marg{longitude}\\
+% This is a special case of |\setDrawingPlane| that constructs the transform required to draw a 2D image in
+% a longitudinal plane.
+%
+% \noindent\DescribeMacro{\drawCircle} \oarg{options} \marg{tiltangle} \marg{rotationangle}\\
+% Draws a circle on the surface of a Bloch sphere around the axis which is tilted by |tiltangle|
+% from the z-axis and with a rotation of |rotationangle| about the z-axis.
+%
+% \noindent\DescribeMacro{\drawGreatCircle} \oarg{options} \marg{tiltangle} \marg{rotationangle}\\
+% An alias of |\drawCircle|.
+%
+% \noindent\DescribeMacro{\drawSmallCircle} \oarg{options} \marg{tiltangle} \marg{rotationangle} \marg{offsetLatitude}\\
+% Draws a circle on the surface of a Bloch sphere around the axis which is tilted by |tiltangle|
+% from the z-axis and with a rotation of |rotationangle| about the z-axis, with an offset along the axis
+% such that it reaches an effective latitude of |offsetLatitude|.
+%
+% \noindent\DescribeMacro{\drawLatitudeCircle} \oarg{options} \marg{latitude}\\
+% Draws a circle on the Bloch sphere corresponding to the given latitude.
+%
+% \noindent\DescribeMacro{\drawLongitudeCircle} \oarg{options} \marg{longitude}\\
+% Draws a great circle on the Bloch sphere corresponding to the given longitude.
+%
+% \noindent\DescribeMacro{\drawRotationLeft} \oarg{options} \marg{tiltangle} \marg{rotationangle} \marg{axisoffset} \marg{clearangle}\\
+% Draw a left-handed rotation about the Bloch sphere, titled and rotated as for a circle
+% with the same parameters, with a gap in the line where the arrow should go of
+% |clearangle| degrees.
+%
+% \noindent\DescribeMacro{\drawRotationRight} \oarg{options} \marg{tiltangle} \marg{rotationangle} \marg{axisoffset} \marg{clearangle}\\
+% As above, but a right-handed rotation annotation.
+%
+% \noindent\DescribeMacro{\drawAxis} \oarg{options} \marg{tiltangle} \marg{rotationangle}\\
+% Draw a line along the axis tilted |tiltangle| degrees from the z-axis, rotated about
+% the z-axis by |rotationangle| degrees.
+%
+% \noindent\DescribeMacro{\labelPolar} \oarg{options} \marg{tikzlabel} \marg{tiltangle} \marg{rotationangle}\\
+% Assign a tikz label to the point identified by an angle |tiltangle| from the z-axis
+% and a rotation |rotationangle| about the z-axis.
+%
+% \noindent\DescribeMacro{\labelLatLon} \oarg{options} \marg{tikzlabel} \marg{latitude} \marg{longitude}\\
+% Assign a tikz label to the point identified the specified latitude and longitude.
+%
+% \noindent\DescribeMacro{\drawStatePolar} \oarg{options} \marg{tikzlabel} \marg{tiltangle} \marg{rotationangle}\\
+% Draw a vector from the origin to the point identified by an angle |tiltangle|
+% from the z-axis and a rotation |rotationangle| about the z-axis, which will
+% be labelled |tikzlabel|.
+%
+% \noindent\DescribeMacro{\drawStateLatLon} \oarg{options} \marg{tikzlabel} \marg{latitude} \marg{longitude}\\
+% Draw a vector from the origin to the point identified by the provided
+% latitude and longitude, which will be labelled |tikzlabel|.
+%
+%
+% \section{Package, Environment and Macro options}
+% For convenience, all options at all levels share the same namespace. Therefore, all
+% options passed to the package will be the defaults for all environment, which will
+% in turn be the defaults for all subsequent macro calls.
+%
+%
+% \DescribeKey[1.5cm]{radius}
+% {This option controls the radius of the qubit, and can be specified in any valid \LaTeX units.}
+%
+%
+% \DescribeKey[15]{tilt}{This option controls the tilt (into the page) of the top of the bloch sphere (in degrees).}
+%
+%
+% \DescribeKey[-20]{rotation}{This option controls the (right-handed) rotation of the Blochsphere around the (potentially tilted) z-axis, also specified in degrees.}
+%
+%
+% \DescribeKey[white]{color}{This specifies the colour of the drawn ball.}
+%
+%
+% \DescribeKey[0.7]{opacity}{This option controls the opacity of the ball, allowing lines drawn behind the ball to be visible.}
+%
+%
+% \DescribeKey[]{style}{This option controls the current drawing style, and supports any valid tikz styling.}
+%
+%
+% \DescribeKey[1]{scale}{This option allows one to temporarily change the scale of drawn circles/etc, allowing annotations to ``hover'' over the Bloch sphere.}
+%
+%
+% \DescribeKey[current plane]{plane}{The name which should label the current plane being defined, or the plane to be used.}
+%
+%
+% \DescribeKey[(0,0,0)]{shift}{The three dimensional offset by which the currently being drawn objects should be shifted.}
+%
+%
+% \DescribeKey[3d]{ball}{Specifies how the ball should be drawn. Options are: {\tt 3d}, {\tt circle}, {\tt none}}
+%
+%
+% \DescribeKey[black]{statecolor}{The color with which the state vectors should be drawn.}
+%
+%
+% \DescribeKey[0.4pt]{statewidth}{The width with which state vectors should be drawn.}
+%
+%
+% \DescribeKey[]{axisarrow}{The arrow to use at the end of a drawn axis.}
+%
+%
+% \DescribeKey[false]{labelmark}{Whether a black dot should be drawn at the point being labelled.}
+%
+%
+% \DescribeKey[false]{nested}{Whether the {\tt blochsphere} environment is being nested in a |tikzpicture| environment. If it is nested, then this should be set to true.}
+%
+%
+% \section{Example}
+% In this section we provide example code to generate the following diagram:
+%
+% \begin{figure}[h!]
+% \begin{center}
+% \includegraphics{example.pdf}
+% \end{center}
+% \caption{Example Bloch Sphere \label{fig:blochsphere}}
+% \end{figure}
+%
+% \newminted{latex}{gobble=2,linenos}
+% \begin{latexcode}
+% \begin{blochsphere}[radius=1.5 cm,tilt=15,rotation=-20]
+%     \drawBallGrid[style={opacity=0.3}]{30}{30}
+%
+%     \drawGreatCircle[style={dashed}]{-60}{0}{0}
+%     \drawGreatCircle[style={dashed}]{60}{0}{0}
+%
+%     \drawRotationLeft[scale=1.3,style={red}]{-60}{0}{0}{15}
+%     \drawRotationRight[scale=1.3,style={red}]{60}{0}{0}{15}
+%
+%     \node at (-0.8,1.9) {\textcolor{red}{\tiny $J_{12}(t)$}};
+%     \node at (1.1,1.8) {\textcolor{red}{\tiny $J_{23}(t)$}};
+%
+%     \labelLatLon{up}{90}{0};
+%     \labelLatLon{down}{-90}{90};
+%     \node[above] at (up) {{\tiny $\left|1\right>$ }};
+%     \node[below] at (down) {{\tiny $\left|0\right>$}};
+%
+%     \labelLatLon[labelmark=false]{d}{15}{90};
+%     \node at (d) {\color{gray}\fontsize{0.15cm}{1em}\selectfont $60^\circ$};
+%
+%     \labelLatLon[labelmark=falsa]{d2}{5}{78};
+%     \node at (d2) {\color{gray}\fontsize{0.15cm}{1em}\selectfont $60^\circ$};
+% \end{blochsphere}
+% \end{latexcode}
+%
+% \StopEventually{}
+%
+% \section{Implementation}
+%
+% \iffalse
+%<*package>
+% \fi
+% \subsection{Preamble}
+%    \begin{macrocode}
+\NeedsTeXFormat{LaTeX2e}[1994/06/01]
+\ProvidesPackage{blochsphere}[2015/08/17]
+%    \end{macrocode}
+% \iffalse
+%% \usepackage{trace}
+%%\tracingall
+% \fi
+%
+%    \begin{macrocode}
+\usepackage{tikz,etoolbox,environ,ifthen,kvsetkeys,kvoptions}
+\usetikzlibrary{decorations.pathreplacing, decorations.markings, calc, fadings}
+%    \end{macrocode}
+%
+% \subsection{Package/Environment/Macro options}
+%
+% \begin{key}{blochsphere}{radius}
+%    \begin{macrocode}
+\define@key{blochsphere}{radius}{%
+	\def\blochsphere@radius{#1}%
+}
+\providecommand{\blochsphere@radius}{1cm}
+%    \end{macrocode}
+% \end{key}
+%
+%
+% \begin{key}{blochsphere}{tilt}
+%    \begin{macrocode}
+\define@key{blochsphere}{tilt}{%
+	\def\blochsphere@tilt{#1}%
+}
+\providecommand{\blochsphere@tilt}{15}
+%    \end{macrocode}
+% \end{key}
+%
+%
+% \begin{key}{blochsphere}{rotation}
+%    \begin{macrocode}
+\define@key{blochsphere}{rotation}{%
+	\def\blochsphere@rotation{#1}%
+}
+\providecommand{\blochsphere@rotation}{-20}
+%    \end{macrocode}
+% \end{key}
+%
+%
+% \begin{key}{blochsphere}{color}
+%    \begin{macrocode}
+\define@key{blochsphere}{color}{%
+	\def\blochsphere@color{#1}%
+}
+\providecommand{\blochsphere@color}{white}
+%    \end{macrocode}
+% \end{key}
+%
+%
+% \begin{key}{blochsphere}{opacity}
+%    \begin{macrocode}
+\define@key{blochsphere}{opacity}{%
+	\def\blochsphere@opacity{#1}%
+}
+\providecommand{\blochsphere@opacity}{0.7}
+%    \end{macrocode}
+% \end{key}
+%
+%
+% \begin{key}{blochsphere}{style}
+%    \begin{macrocode}
+\define@key{blochsphere}{style}{%
+	\def\blochsphere@style{#1}%
+}
+\providecommand{\blochsphere@style}{}
+%    \end{macrocode}
+% \end{key}
+%
+%
+% \begin{key}{blochsphere}{scale}
+%    \begin{macrocode}
+\define@key{blochsphere}{scale}{%
+	\def\blochsphere@scale{#1}%
+}
+\providecommand{\blochsphere@scale}{1}
+%    \end{macrocode}
+% \end{key}
+%
+%
+% \begin{key}{blochsphere}{plane}
+%    \begin{macrocode}
+\define@key{blochsphere}{plane}{%
+	\def\blochsphere@plane{#1}%
+}
+\providecommand{\blochsphere@plane}{current plane}
+%    \end{macrocode}
+% \end{key}
+%
+%
+% \begin{key}{blochsphere}{shift}
+%    \begin{macrocode}
+\define@key{blochsphere}{shift}{%
+	\def\blochsphere@shift{{#1}}%
+}
+\providecommand{\blochsphere@shift}{{0,0,0}}
+%    \end{macrocode}
+% \end{key}
+%
+%
+% \begin{key}{blochsphere}{ball}
+%    \begin{macrocode}
+\define@key{blochsphere}{ball}{%
+	\def\blochsphere@ball{#1}%
+}
+\providecommand{\blochsphere@ball}{3d}
+%    \end{macrocode}
+% \end{key}
+%
+%
+% \begin{key}{blochsphere}{statecolor}
+%    \begin{macrocode}
+\define@key{blochsphere}{statecolor}{%
+	\def\blochsphere@statecolor{#1}%
+}
+\providecommand{\blochsphere@statecolor}{black}
+%    \end{macrocode}
+% \end{key}
+%
+%
+% \begin{key}{blochsphere}{statewidth}
+%    \begin{macrocode}
+\define@key{blochsphere}{statewidth}{%
+	\def\blochsphere@statewidth{#1}%
+}
+\providecommand{\blochsphere@statewidth}{0.4pt}
+%    \end{macrocode}
+% \end{key}
+%
+%
+% \begin{key}{blochsphere}{axisarrow}
+%    \begin{macrocode}
+\define@key{blochsphere}{axisarrow}{%
+	\def\blochsphere@axisarrow{#1}%
+}
+\providecommand{\blochsphere@axisarrow}{}
+%    \end{macrocode}
+% \end{key}
+%
+%
+% \begin{key}{blochsphere}{labelmark}
+%    \begin{macrocode}
+\define@key{blochsphere}{labelmark}{%
+    \setboolean{blochsphere@labelmark}{#1}%
+}
+\newboolean{blochsphere@labelmark}
+\setboolean{blochsphere@labelmark}{false}
+%    \end{macrocode}
+% \end{key}
+%
+%
+% \begin{key}{blochsphere}{nested}
+%    \begin{macrocode}
+\define@key{blochsphere}{nested}{%
+	\setboolean{blochsphere@nested}{#1}%
+}
+\newboolean{blochsphere@nested}
+\setboolean{blochsphere@nested}{false}
+%    \end{macrocode}
+% \end{key}
+%	\begin{macrocode}
+\ProcessKeyvalOptions{blochsphere}\relax
+%    \end{macrocode}
+%
+% \subsection{{\bfseries\tt blochsphere} Environment}
+%	 This is the central environment definition. Note that all macros defined
+%	 below will only be defined within this environment.
+%
+% \begin{environment}{blochsphere}
+%    \begin{macrocode}
+\newenvironment{blochsphere}[1][]{
+	\begingroup
+	\makeatletter
+	\ignorespaces\setkeys{blochsphere}{#1}\unskip%
+	\pgfdeclarelayer{back}%
+	\pgfdeclarelayer{front}%
+	\pgfsetlayers{back,main,front}%
+	\pgfkeys{%
+		/tikz/on layer/.code={%
+			\pgfonlayer{##1}\begingroup%
+			\aftergroup\endpgfonlayer%
+			\aftergroup\endgroup%
+		},%
+		/tikz/node on layer/.code={%
+			\gdef\node@@on@layer{%
+			\setbox\tikz@tempbox=\hbox\bgroup\pgfonlayer{##1}\unhbox\tikz@tempbox\endpgfonlayer\egroup}%
+			\aftergroup\node@on@layer%
+		},%
+		/tikz/end node on layer/.code={%
+			\endpgfonlayer\endgroup\endgroup%
+		}%
+	}%
+	\def\node@on@layer{\aftergroup\node@@on@layer}%
+%    \end{macrocode}
+%    \begin{macro}{\drawBall}
+%        \begin{macrocode}
+	\newcommand\drawBall[1][]{
+	\begingroup
+		\setkeys{blochsphere}{##1}
+		\expandafter\ifstrequal\expandafter{\blochsphere@ball}{3d}{
+			\fill[on layer=main,ball color=\blochsphere@color,opacity=\blochsphere@opacity] (0,0) circle (\blochsphere@radius); % 3D lighting effect
+		}{}
+		\expandafter\ifstrequal\expandafter{\blochsphere@ball}{circle}{
+			\draw[on layer=main,color=\blochsphere@color] (0,0) circle (\blochsphere@radius); % 3D lighting effect
+		}{}
+	\endgroup
+	}%
+%    \end{macrocode}
+%    \end{macro}
+%    \begin{macro}{\drawBallGrid}
+%        \begin{macrocode}
+	\newcommand\drawBallGrid[3][]{
+	\begingroup
+		\setkeys{blochsphere}{##1}
+		\foreach \phi in {0,##2,...,89} {
+			\drawLatitudeCircle{\phi}
+			\drawLatitudeCircle{-\phi}
+		}
+		\foreach \theta in {0,##3,...,179} {
+			\drawLongitudeCircle{\theta}
+		}
+	\endgroup
+	}%
+%    \end{macrocode}
+%    \end{macro}
+%    \begin{macro}{\setDrawingPlane}
+%        \begin{macrocode}
+	\newcommand\setDrawingPlane[3][]{%
+		\setkeys{blochsphere}{##1}
+		\pgfmathsetmacro\aphi{##2}
+		\pgfmathsetmacro\atheta{##3}
+		\pgfmathsetmacro\dot{cos(\aphi)}
+		\ifdim\dot pt<0.7 pt\relax%
+			\pgfmathsetmacro\norm{cos(asin(\dot))}
+			\pgfmathsetmacro\xx{-sin(\aphi)*sin(\blochsphere@rotation - \atheta)}
+			\pgfmathsetmacro\xy{sin(\aphi)*sin(\blochsphere@tilt)*cos(\blochsphere@rotation - \atheta)}
+			\pgfmathsetmacro\yx{-sin(2*\aphi - \blochsphere@rotation + \atheta)/4 - sin(2*\aphi + \blochsphere@rotation - \atheta)/4}
+			\pgfmathsetmacro\yy{(sin(\aphi)*cos(\blochsphere@tilt) - sin(\blochsphere@tilt)*sin(\blochsphere@rotation - \atheta)*cos(\aphi))*sin(\aphi)}
+		\else
+			\pgfmathsetmacro\norm{sqrt(abs(sin(\blochsphere@rotation - \atheta)*cos(\aphi))^2 + abs(sin(\blochsphere@tilt)*cos(\aphi)*cos(\blochsphere@rotation - \atheta))^2 + abs(cos(\aphi)*cos(\blochsphere@tilt)*cos(\blochsphere@rotation - \atheta))^2)}
+			\pgfmathsetmacro\xx{-sin(\blochsphere@rotation - \atheta)*cos(\aphi)}
+			\pgfmathsetmacro\xy{sin(\blochsphere@tilt)*cos(\aphi)*cos(\blochsphere@rotation - \atheta)}
+			\pgfmathsetmacro\yx{-cos(\aphi)^2*cos(\blochsphere@rotation - \atheta)}
+			\pgfmathsetmacro\yy{(sin(\aphi)*cos(\blochsphere@tilt) - sin(\blochsphere@tilt)*sin(\blochsphere@rotation - \atheta)*cos(\aphi))*cos(\aphi)}
+		\fi
+		\computeOffset{shift}
+	 	\begingroup\newcommand\tmp[1]{\endgroup\noexpand\relax%
+			\tikzset{\blochsphere@plane/.style={cm={\xx/\norm, \xy/\norm, \yx/\norm, \yy/\norm, \unexpanded\expandafter{####1} }}}%
+		} \tmp{\shift}
+	}%
+%    \end{macrocode}
+%	\end{macro}
+%	\begin{macro}{\setLatitudinalDrawingPlane}
+%    \begin{macrocode}
+	\newcommand\setLatitudinalDrawingPlane[2][]{%
+		\pgfmathsetmacro\yshift{sin(##2)*\the\blochsphere@radius}
+		\setDrawingPlane[##1,shift={{0,0,\yshift}}]{0}{0}
+	}%
+%    \end{macrocode}
+%	\end{macro}
+%	\begin{macro}{\setLatitudinalDrawingPlane}
+%    \begin{macrocode}
+	\newcommand\setLongitudinalDrawingPlane[2][]{%
+		\setDrawingPlane[##1]{90}{##2}
+	}%
+%    \end{macrocode}
+%	\end{macro}
+%	\begin{macro}{\drawCircle}
+%    \begin{macrocode}
+	\newcommand\drawCircle[3][]{
+	\begingroup
+		\setkeys{blochsphere}{##1}
+		\setDrawingPlane{##2}{##3}
+		\computeVisibility{##2}{##3}{agamma}{abeta}
+		\begingroup\edef\tmp{\endgroup%
+			\noexpand\draw[current plane,on layer=back,\unexpanded\expandafter{\blochsphere@style}] \unexpanded\expandafter{(\agamma-\abeta-0.2:\blochsphere@radius+\the\pgflinewidth*0.5) arc (\agamma-\abeta-0.2:\agamma+\abeta+0.2:\blochsphere@radius+\the\pgflinewidth*0.5)};
+			\noexpand\draw[current plane,on layer=front,\unexpanded\expandafter{\blochsphere@style}] \unexpanded\expandafter{(\agamma+\abeta:\blochsphere@radius+\the\pgflinewidth*0.5) arc (\agamma+\abeta:\agamma-\abeta+360:\blochsphere@radius+\the\pgflinewidth*0.5)};
+		} \tmp
+	\endgroup
+	}%
+%    \end{macrocode}
+%	\end{macro}
+%	\begin{macro}{\drawGreatCircle}
+%    \begin{macrocode}
+	\newcommand\drawGreatCircle[3][]{
+		\drawCircle[##1]{##2}{##3}
+	}
+%    \end{macrocode}
+%	\end{macro}
+%   \begin{macro}{\drawSmallCircle}
+%    \begin{macrocode}
+	\newcommand\drawSmallCircle[4][]{
+	\begingroup
+		\pgfmathsetmacro\xshift{sin(##2)*cos(##3)*\blochsphere@radius*sin(##4)}
+		\pgfmathsetmacro\yshift{sin(##2)*sin(##3)*\blochsphere@radius*sin(##4)}
+		\pgfmathsetmacro\zshift{cos(##2)*\blochsphere@radius*sin(##4)}
+		\pgfmathsetmacro\radius{\blochsphere@radius*cos(##4)}
+		\drawCircle[##1,shift={{\xshift,\yshift,\zshift}},radius=\radius]{##2}{##3}
+	\endgroup
+	}%
+%    \end{macrocode}
+%   \end{macro}
+%	\begin{macro}{\drawLatitudeCircle}
+%    \begin{macrocode}
+	\newcommand\drawLatitudeCircle[2][]{
+	\begingroup
+		\pgfmathsetmacro\yshift{sin(##2)*\blochsphere@radius}
+		\pgfmathsetmacro\radius{\blochsphere@radius*cos(##2)}
+		\drawCircle[##1,shift={{0,0,\yshift}},radius=\radius]{0}{0}
+	\endgroup
+	}%
+%    \end{macrocode}
+%	\end{macro}
+%	\begin{macro}{\drawLongitudeCircle}
+%    \begin{macrocode}
+	\newcommand\drawLongitudeCircle[2][]{
+	\begingroup
+		\drawCircle[##1]{90}{##2+90}
+	\endgroup
+	}%
+%    \end{macrocode}
+%	\end{macro}
+%	\begin{macro}{\drawRotationLeft}
+%    \begin{macrocode}
+	\newcommand\drawRotationLeft[5][]{
+	\begingroup
+		\setkeys{blochsphere}{##1}
+		\pgfmathsetmacro\xshift{sin(##2)*cos(##3)*##4}
+		\pgfmathsetmacro\yshift{sin(##2)*sin(##3)*##4}
+		\pgfmathsetmacro\zshift{cos(##2)*##4}
+		\setDrawingPlane[shift={\xshift,\yshift,\zshift}]{##2}{##3}
+		\computeVisibility{##2}{##3}{agamma}{abeta}
+		\begingroup\edef\tmp{\endgroup%
+			\noexpand\draw[current plane,on layer=back,\unexpanded\expandafter{\blochsphere@style}] \unexpanded\expandafter{(\agamma-\abeta-0.2:\blochsphere@radius*\blochsphere@scale+\the\pgflinewidth*0.5) arc (\agamma-\abeta-0.2:\agamma+\abeta+0.2:\blochsphere@radius*\blochsphere@scale+\the\pgflinewidth*0.5)};
+			\noexpand\draw[<-,current plane,on layer=front,\unexpanded\expandafter{\blochsphere@style}] \unexpanded\expandafter{(\agamma+\abeta+##5:\blochsphere@radius*\blochsphere@scale+\the\pgflinewidth*0.5) arc (\agamma+\abeta+##5:\agamma-\abeta+360:\blochsphere@radius*\blochsphere@scale+\the\pgflinewidth*0.5)};
+		} \tmp
+	\endgroup
+	}%
+%    \end{macrocode}
+%	\end{macro}
+%	\begin{macro}{\drawRotationRight}
+%    \begin{macrocode}
+	\newcommand\drawRotationRight[5][]{
+	\begingroup
+		\setkeys{blochsphere}{##1}
+		\pgfmathsetmacro\xshift{sin(##2)*cos(##3)*##4}
+		\pgfmathsetmacro\yshift{sin(##2)*sin(##3)*##4}
+		\pgfmathsetmacro\zshift{cos(##2)*##4}
+		\setDrawingPlane[shift={\xshift,\yshift,\zshift}]{##2}{##3}
+		\computeVisibility{##2}{##3}{agamma}{abeta}
+		\begingroup\edef\tmp{\endgroup%
+			\noexpand\draw[current plane,on layer=back,\unexpanded\expandafter{\blochsphere@style}] \unexpanded\expandafter{(\agamma-\abeta-0.2:\blochsphere@radius*\blochsphere@scale+\the\pgflinewidth*0.5) arc (\agamma-\abeta-0.2:\agamma+\abeta+0.2:\blochsphere@radius*\blochsphere@scale+\the\pgflinewidth*0.5)};
+			\noexpand\draw[->,current plane,on layer=front,\unexpanded\expandafter{\blochsphere@style}] \unexpanded\expandafter{(\agamma+\abeta:\blochsphere@radius*\blochsphere@scale+\the\pgflinewidth*0.5) arc (\agamma+\abeta:\agamma-\abeta+360-##5:\blochsphere@radius*\blochsphere@scale+\the\pgflinewidth*0.5)};
+		} \tmp
+	\endgroup
+	}%
+%    \end{macrocode}
+%	\end{macro}
+%	\begin{macro}{\drawAxis}
+%    \begin{macrocode}
+	\newcommand\drawAxis[3][] {
+	\begingroup
+		\setkeys{blochsphere}{##1}
+		\pgfmathsetmacro\behind{ifthenelse(-sin(##2)*sin(\blochsphere@rotation - ##3)*cos(\blochsphere@tilt) + sin(\blochsphere@tilt)*cos(##2)<0, 1, 0)}
+		\pgfmathsetmacro\newphi{180-##2}
+		\pgfmathsetmacro\newtheta{##3+180}
+		\ifnum\behind=0\relax
+			\labelPolar[scale=1,mark=0]{blochspheretmpp}{##2}{##3}
+			\labelPolar[mark=0]{blochspheretmps}{##2}{##3}
+			\labelPolar[mark=0]{blochspheretmpe}{\newphi}{\newtheta}
+		\else
+			\labelPolar[scale=1,mark=0]{blochspheretmpp}{\newphi}{\newtheta}
+			\labelPolar[mark=0]{blochspheretmpe}{##2}{##3}
+			\labelPolar[mark=0]{blochspheretmps}{\newphi}{\newtheta}
+		\fi
+		\begingroup\edef\tmp{\endgroup%
+			\ifnum\behind=0\relax
+				\noexpand\draw[on layer=front,\unexpanded\expandafter{\blochsphere@style},\blochsphere@axisarrow] (blochspheretmpp) -- (blochspheretmps);
+				\noexpand\draw[on layer=back,\unexpanded\expandafter{\blochsphere@style}] (blochspheretmpe) -- (blochspheretmpp);
+			\else
+				\noexpand\draw[on layer=front,\unexpanded\expandafter{\blochsphere@style},\blochsphere@axisarrow] (blochspheretmpp) -- (blochspheretmpe);
+				\noexpand\draw[on layer=back,\unexpanded\expandafter{\blochsphere@style}] (blochspheretmps) -- (blochspheretmpp);
+			\fi
+		} \tmp
+	\endgroup
+	}%
+%    \end{macrocode}
+%	\end{macro}
+%	\begin{macro}{\labelPolar}
+%    \begin{macrocode}
+	\newcommand\labelPolar[4][]{%
+	\begingroup
+		\setkeys{blochsphere}{##1}
+		\setLongitudinalDrawingPlane{##4+90}
+		\pgfmathsetmacro\behind{ifthenelse(-sin(##3)*sin(\blochsphere@rotation - ##4)*cos(\blochsphere@tilt) + sin(\blochsphere@tilt)*cos(##3)<0, 1, 0)}
+		\ifthenelse{\boolean{blochsphere@labelmark}}
+        {
+            \ifnum\behind=1\relax
+                \path[current plane,on layer=back] (90-##3:\blochsphere@radius*\blochsphere@scale) coordinate[mark coordinate] (##2); %
+            \else
+                \path[current plane,on layer=front] (90-##3:\blochsphere@radius*\blochsphere@scale) coordinate[mark coordinate] (##2); %
+            \fi
+        }
+        {
+            \ifnum\behind=1\relax
+                \path[current plane,on layer=back] (90-##3:\blochsphere@radius*\blochsphere@scale) coordinate (##2); %
+            \else
+                \path[current plane,on layer=front] (90-##3:\blochsphere@radius*\blochsphere@scale) coordinate (##2); %
+            \fi
+        }
+	\endgroup
+	}%
+%    \end{macrocode}
+%	\end{macro}
+%	\begin{macro}{\labelLatLon}
+%    \begin{macrocode}
+	\newcommand\labelLatLon[4][]{%
+	\begingroup
+		\pgfmathsetmacro\newphi{90-##3}
+		\labelPolar[##1]{##2}{\newphi}{##4}
+	\endgroup
+	}%
+%    \end{macrocode}
+%	\end{macro}
+%	\begin{macro}{\drawStateLatLon}
+%    \begin{macrocode}
+	\newcommand\drawStateLatLon[4][]{
+	\begingroup
+		\pgfmathsetmacro\newphi{90-##3}
+		\drawStatePolar[##1]{##2}{\newphi}{##4}
+	\endgroup
+	}%
+%    \end{macrocode}
+%	\end{macro}
+%	\begin{macro}{\drawStatePolar}
+%    \begin{macrocode}
+	\newcommand\drawStatePolar[4][]{
+	\begingroup
+		\setkeys{blochsphere}{##1}
+		\labelPolar{##2}{##3}{##4}
+		\pgfmathsetmacro\behind{ifthenelse(-sin(##3)*sin(\blochsphere@rotation - ##4)*cos(\blochsphere@tilt) + sin(\blochsphere@tilt)*cos(##3)<0, 1, 0)}
+		\ifnum\behind=1\relax
+			\tikzset{test/.style={
+			postaction={
+			decorate,
+			decoration={
+			markings,
+			mark=at position \pgfdecoratedpathlength-0.5pt with {\arrow[\blochsphere@statecolor,line width=\blochsphere@statewidth,opacity=0.2] {>}; },
+			mark=between positions 0 and \pgfdecoratedpathlength-5pt step 0.5pt with {
+			\pgfmathsetmacro\myval{multiply(divide(
+			\pgfkeysvalueof{/pgf/decoration/mark info/distance from start}, \pgfdecoratedpathlength),100)};
+			\pgfsetfillcolor{\blochsphere@statecolor};
+			\pgfsetfillopacity{0.4-\myval/100*0.2}
+			\pgfpathcircle{\pgfpointorigin}{\blochsphere@statewidth};
+			\pgfusepath{fill};}
+			}}}}
+		\else
+			\tikzset{test/.style={
+			postaction={
+			decorate,
+			decoration={
+			markings,
+			mark=at position \pgfdecoratedpathlength-0.5pt with {\arrow[\blochsphere@statecolor,line width=\blochsphere@statewidth] {>}; },
+			mark=between positions 0 and \pgfdecoratedpathlength-5pt step 0.5pt with {
+			\pgfmathsetmacro\myval{multiply(divide(
+			\pgfkeysvalueof{/pgf/decoration/mark info/distance from start}, \pgfdecoratedpathlength),100)};
+			\pgfsetfillcolor{\blochsphere@statecolor};
+			\pgfsetfillopacity{0.4+\myval/100*0.6}
+			\pgfpathcircle{\pgfpointorigin}{\blochsphere@statewidth};
+			\pgfusepath{fill};}
+			}}}}
+		\fi
+		\path [test,on layer=main] (0,0) -- (##2);
+	\endgroup
+	}%
+%    \end{macrocode}
+%	\end{macro}
+%	\begin{macro}{\computeOffset}
+%    \begin{macrocode}
+	\newcommand\computeOffset[2][]{%
+		\setkeys{blochsphere}{##1}%
+		\pgfmathsetmacro{\x}{\blochsphere@shift[0]*cos(\blochsphere@rotation) + \blochsphere@shift[1]*sin(\blochsphere@rotation)}%
+		\pgfmathsetmacro\y{\blochsphere@shift[0]*sin(\blochsphere@rotation)*sin(\blochsphere@tilt) - \blochsphere@shift[1]*sin(\blochsphere@tilt)*cos(\blochsphere@rotation) + \blochsphere@shift[2]*cos(\blochsphere@tilt)}
+		\expandafter\def\csname ##2\endcsname{(\x pt,\y pt)}%
+	}%
+%    \end{macrocode}
+%	\end{macro}
+%	\begin{macro}{\computeVisibility}
+%    \begin{macrocode}
+	\newcommand\computeVisibility[5][]{
+		\setkeys{blochsphere}{##1}
+		\pgfmathsetmacro\aphi{##2}
+		\pgfmathsetmacro\atheta{##3}
+		\pgfmathsetmacro\d{sqrt(\blochsphere@shift[0]^2+\blochsphere@shift[1]^2+\blochsphere@shift[2]^2)}%% distance from origin of shift
+		\pgfmathsetmacro\tatheta{\atheta+\blochsphere@rotation}
+		\pgfmathsetmacro\dot{cos(\aphi)}
+		\ifdim\dot pt<0.7 pt\relax%
+			\pgfmathsetmacro\domaintest{ifthenelse(and(\blochsphere@rotation - \atheta==0,or(\aphi==0,sin(\blochsphere@tilt==0))),0,1)}
+			\ifdim\domaintest pt=0 pt\relax
+				\pgfmathsetmacro\agamma{0}
+			\else
+				\pgfmathsetmacro\agamma{-90+atan(cos(\blochsphere@tilt)*cos(\blochsphere@rotation - \atheta)/(sin(\aphi)*sin(\blochsphere@tilt) + sin(\blochsphere@rotation - \atheta)*cos(\aphi)*cos(\blochsphere@tilt)))}
+			\fi
+		\else
+			\pgfmathsetmacro\domaintest{ifthenelse(and(Mod(\blochsphere@rotation-\atheta,180)==90,Mod(\blochsphere@tilt,180)==90),0,1)}
+			\pgfmathsetmacro\domaintesttwo{ifthenelse(Mod(\blochsphere@rotation-\atheta,180)==90,0,1)}
+			\pgfmathsetmacro\domaintestthree{ifthenelse(Mod(\blochsphere@tilt,180)==90,0,1)}
+			\ifdim\domaintest pt=0 pt\relax
+				\pgfmathsetmacro\agamma{360-90*\blochsphere@tilt/abs(\blochsphere@tilt)}
+			\else
+				\ifdim\domaintesttwo pt=0 pt\relax
+					\pgfmathsetmacro\agamma{360-90*(sin(\aphi)*tan(\blochsphere@tilt)+cos(\aphi)*sin(\blochsphere@rotation-\atheta))/abs(sin(\aphi)*tan(\blochsphere@tilt)+cos(\aphi)*sin(\blochsphere@rotation-\atheta))}
+				\else
+					\ifdim\domaintestthree pt=0 pt\relax
+						\pgfmathsetmacro\agamma{360-90*\blochsphere@tilt/abs(\blochsphere@tilt)*cos(\blochsphere@rotation-\atheta)/abs(cos(\blochsphere@rotation-\atheta))}
+					\else
+						\pgfmathsetmacro\agamma{360-atan( (sin(\aphi)*tan(\blochsphere@tilt)+cos(\aphi)*sin(\blochsphere@rotation-\atheta))/cos(\blochsphere@rotation-\atheta) )}
+					\fi
+				\fi
+			\fi
+		\fi
+		\pgfmathsetmacro\aalpha{acos(-sin(\aphi)*sin(\blochsphere@rotation)*cos(\atheta)*cos(\blochsphere@tilt) + sin(\aphi)*sin(\atheta)*cos(\blochsphere@rotation)*cos(\blochsphere@tilt) + sin(\blochsphere@tilt)*cos(\aphi))}
+		\pgfmathsetmacro\aalphatest{atan(\d/\blochsphere@radius)}
+		\ifdim\aalpha pt<\aalphatest pt\relax
+			\pgfmathsetmacro\abeta{0}
+		\else
+			\pgfmathsetmacro\abeta{acos(\d*cot(\aalpha)/\blochsphere@radius)}
+		\fi
+		\pgfmathsetmacro\abeta{ifthenelse(\blochsphere@shift[2]<0,\abeta+2*(90-\abeta),\abeta)}
+		\expandafter\pgfmathsetmacro\csname ##4\endcsname{\agamma}
+		\expandafter\pgfmathsetmacro\csname ##5\endcsname{\abeta}
+	}%
+%    \end{macrocode}
+%	\end{macro}
+%	\begin{macrocode}
+	\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}%
+	}%
+	\pgfdeclareradialshading[tikz@ball]{ball}{\pgfqpoint{-10bp}{10bp}}{%
+		color(0bp)=(tikz@ball!30!white);
+		color(9bp)=(tikz@ball!75!white);
+		color(18bp)=(tikz@ball!90!black);
+		color(25bp)=(tikz@ball!70!black);
+		color(50bp)=(black)
+	}%
+	\ifthenelse{\boolean{blochsphere@nested}}{}{%
+		\begin{tikzpicture}
+		\drawBall
+	}%
+}
+%    \end{macrocode}
+% \end{environment}
+%    \begin{macrocode}
+{
+	\ifthenelse{\boolean{blochsphere@nested}}{}{
+		\end{tikzpicture}%
+	}%
+	\endgroup%
+}
+\endinput
+%    \end{macrocode}
+
+%
+% \iffalse
+%</package>
+% \fi
+%
+% \Finale
+\endinput