% \iffalse meta-comment
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% 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
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% \iffalse
%<*driver>
\ProvidesFile{blochsphere.dtx}
%</driver>
%<package>\NeedsTeXFormat{LaTeX2e}[1999/12/01]
%<package>\ProvidesPackage{blochsphere}
%<*package>
[2015/09/15 v1.1 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
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% \CheckSum{841}
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% {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
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% Commercial at \@ Left bracket \[ Backslash \\
% Right bracket \] Circumflex \^ Underscore \_
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% Right brace \} Tilde \~}
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%
% \changes{v1.1}{2015/09/15}{Fix \\drawAxis using removed keyval "mark"}
% \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]{blochspheretmpp}{##2}{##3}
\labelPolar{blochspheretmps}{##2}{##3}
\labelPolar{blochspheretmpe}{\newphi}{\newtheta}
\else
\labelPolar[scale=1]{blochspheretmpp}{\newphi}{\newtheta}
\labelPolar{blochspheretmpe}{##2}{##3}
\labelPolar{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