~tex-sx/tex-sx/development

% \iffalse meta-comment
%<*internal>
\iffalse
%</internal>
%<*readme>
----------------------------------------------------------------
tikz3d --- More general 3d capabilities for TikZ
E-mail: stacey@math.ntnu.no
Released under the LaTeX Project Public License v1.3c or later
See http://www.latex-project.org/lppl.txt
----------------------------------------------------------------

This package extends the 3 dimensional capabilities of TikZ.
%</readme>
%<*internal>
\fi
\def\nameofplainTeX{plain}
\ifx\fmtname\nameofplainTeX\else
  \expandafter\begingroup
\fi
%</internal>
%<*install>
\input docstrip.tex
\keepsilent
\askforoverwritefalse
\preamble
----------------------------------------------------------------
tikz3d --- More general 3d capabilities for TikZ
E-mail: stacey@math.ntnu.no
Released under the LaTeX Project Public License v1.3c or later
See http://www.latex-project.org/lppl.txt
----------------------------------------------------------------

\endpreamble
\postamble

Copyright (C) 2011 by Andrew Stacey <stacey@math.ntnu.no>

This work may be distributed and/or modified under the
conditions of the LaTeX Project Public License (LPPL), either
version 1.3c of this license or (at your option) any later
version.  The latest version of this license is in the file:

http://www.latex-project.org/lppl.txt

This work is "maintained" (as per LPPL maintenance status) by
Andrew Stacey.

This work consists of the file  tikz3d.dtx
and the derived files           tikz3d.ins,
                                tikz3d.pdf, and
                                tikz3d.sty.

\endpostamble
\usedir{tex/latex/tikz3d}
\generate{
  \file{\jobname.sty}{\from{\jobname.dtx}{package}}
}
%</install>
%<install>\endbatchfile
%<*internal>
\usedir{source/latex/tikz3d}
\generate{
  \file{\jobname.ins}{\from{\jobname.dtx}{install}}
}
\nopreamble\nopostamble
\usedir{doc/latex/demopkg}
\generate{
  \file{README.txt}{\from{\jobname.dtx}{readme}}
}
\ifx\fmtname\nameofplainTeX
  \expandafter\endbatchfile
\else
  \expandafter\endgroup
\fi
%</internal>
%<*package>
\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{tikz3d}[2011/06/03 v1.0 TikZ with extended 3D]
%</package>
%<*driver>
\documentclass{ltxdoc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
%\usepackage{morefloats}
\usepackage{tikz}
\usepackage{\jobname}
\usepackage[numbered]{hypdoc}
\definecolor{lstbgcolor}{rgb}{0.9,0.9,0.9} 
 
\usepackage{listings}
\lstloadlanguages{[LaTeX]TeX}
\lstset{breakatwhitespace=true,breaklines=true,language=TeX}
 
\usepackage{fancyvrb}

\newenvironment{example}
  {\VerbatimEnvironment
   \begin{VerbatimOut}[gobble=2]{example.out}}
  {\end{VerbatimOut}
   \begin{center}
%   \setlength{\parindent}{0pt}
   \fbox{\begin{minipage}{.9\linewidth}
     \lstset{breakatwhitespace=true,breaklines=true,language=TeX,basicstyle=\small}
     \lstinputlisting[]{example.out}
   \end{minipage}}

   \fbox{\begin{minipage}{.9\linewidth}
     \input{example.out}
   \end{minipage}}
\end{center}
}
\EnableCrossrefs
\CodelineIndex
\RecordChanges
\begin{document}
  \DocInput{\jobname.dtx}
\end{document}
%</driver>
% \fi
%
%
% \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{1.0}{2011/05/03}{Converted to DTX file}
%
% \DoNotIndex{\newcommand,\newenvironment}
%
% \providecommand*{\url}{\texttt}
% \GetFileInfo{tikz3d.dtx}
% \title{The \textsf{tikz3d} package}
% \author{Andrew Stacey \\ \url{stacey@math.ntnu.no}}
% \date{\fileversion~from \filedate}
%
%
% \maketitle
%
% 
% \section{Introduction}
%
% There are many programs which convert data representing a 3 dimensional object to a 2 dimensional picture.
% A crude, but straightforward, measure of the ``true 3 dimensionality'' of such a program is to find the point at which the 3 dimensional data is transformed down to 2 dimensions.
% This produces a scale ranging from programs such as \Verb+blender+ to \Verb+TikZ/PGF+.
% I place TikZ at the bottom end of this scale because it converts the 3 dimensional data to 2 dimensions at the time of input.
% It is therefore not possible to do anything ``fancy'' with the 3 dimensional data.
% This package is designed to push TikZ a little further up that scale.
%
% The right way to do this would be to redesign TikZ (and much of PGF) to internally use 3 dimensional coordinates at all times, saving the conversion to 2 dimensions to the last minute when a path is ``baked''.
% However, that would be a massive undertaking.
% So we do this the wrong way, but hopefully right enough to be useful.
% Thus rather than trying to push TikZ as far as possible up the ``3 dimensional'' scale, we simply try to correct some of the more obvious failings of TikZ when it comes to dealing with 3 dimensions.
% This is subjective (and possibly argumentative).
% My list is the following:
%
% \begin{enumerate}
% \item The possibilities for converting from 3 dimensions to 2 are severely limited: only linear projections are allowed.
% Thus a cube in TikZ can look a little ``pushed out'' in the corners.
%
% \begin{example}
% \begin{center}
% \begin{tikzpicture}[scale=2,line join=round,ultra thick]
% \draw[fill=red] (1,1,1) -- (1,1,-1) -- (1,-1,-1) -- (1,-1,1) -- cycle;
% \draw[fill=green] (-1,1,1) -- (1,1,1) -- (1,-1,1) -- (-1,-1,1) -- cycle;
% \draw[fill=blue] (1,1,-1) -- (-1,1,-1) -- (-1,1,1) -- (1,1,1) -- cycle;
% \draw (1,-1,.33333) -- (1,1,.33333) -- (-1,1,.33333);
% \draw (1,-1,-.33333) -- (1,1,-.33333) -- (-1,1,-.33333);
% \draw (1,.33333,-1) -- (1,.33333,1) -- (-1,.33333,1);
% \draw (1,-.33333,-1) -- (1,-.33333,1) -- (-1,-.33333,1);
% \draw (.33333,1,-1) -- (.33333,1,1) -- (.33333,-1,1);
% \draw (-.33333,1,-1) -- (-.33333,1,1) -- (-.33333,-1,1);
% \end{tikzpicture}
% \end{center}
% \end{example}
%
% \item The basic path shapes (rectangles, circles, arcs) do not, or not easily, take into account the third dimension even if it is specified.
%
% \begin{example}
% \begin{center}
% \begin{tikzpicture}
% \draw (0,0,0) rectangle (2,2,2);
% \draw (2,0,0) arc[radius=1,start angle=180,delta angle=-180];
% \end{tikzpicture}
% \end{center}
% \end{example}
%
% \end{enumerate}
%
% This package extends TikZ's 3 dimension syntax as follows:
%
% \begin{enumerate}
% \item It is possible to specify more general transformations from 3 dimensions to 2 dimensions.
%
% \begin{example}
% \begin{center}
% \begin{tikzpicture}[scale=2,line join=round,ultra thick,3d/perspective eye={5,5,10}]
% \draw[fill=red] (3d cs:1,1,1) -- (3d cs:1,1,-1) -- (3d cs:1,-1,-1) -- (3d cs:1,-1,1) -- cycle;
% \draw[fill=green] (3d cs:-1,1,1) -- (3d cs:1,1,1) -- (3d cs:1,-1,1) -- (3d cs:-1,-1,1) -- cycle;
% \draw[fill=blue] (3d cs:1,1,-1) -- (3d cs:-1,1,-1) -- (3d cs:-1,1,1) -- (3d cs:1,1,1) -- cycle;
% \draw (3d cs:1,-1,.33333) -- (3d cs:1,1,.33333) -- (3d cs:-1,1,.33333);
% \draw (3d cs:1,-1,-.33333) -- (3d cs:1,1,-.33333) -- (3d cs:-1,1,-.33333);
% \draw (3d cs:1,.33333,-1) -- (3d cs:1,.33333,1) -- (3d cs:-1,.33333,1);
% \draw (3d cs:1,-.33333,-1) -- (3d cs:1,-.33333,1) -- (3d cs:-1,-.33333,1);
% \draw (3d cs:.33333,1,-1) -- (3d cs:.33333,1,1) -- (3d cs:.33333,-1,1);
% \draw (3d cs:-.33333,1,-1) -- (3d cs:-.33333,1,1) -- (3d cs:-.33333,-1,1);
% \end{tikzpicture}
% \end{center}
% \end{example}
%
% \item The basic shapes are adapted to 3 dimensions.
%
% \begin{example}
% \begin{center}
% \begin{tikzpicture}
% \draw (3d cs:3,0,-3) circle[3d circle,radius=1,3d/circle/x axis={0,0,1}];
% \draw (3d cs:3,0,-3) -- (+3d cs:0,0,1);
% \draw (3d cs:3,0,-3) -- (+3d cs:0,1,0);
% \draw (3d cs:0,0,0) to[3d rectangle] (3d cs:1,1,1);
% \draw (3d cs:2,0,0) arc[3d arc,radius=1,start angle=0,delta angle=180,3d/circle/x axis={0,0,1},3d/circle/y axis={1,0,0}];
% \end{tikzpicture}
% \end{center}
% \end{example}
%
% \end{enumerate}
%
% \section{Usage}
%
% This package defines a new coordinate system \Verb+3d+.
% To specify a coordinate using this system, write it as, for example, \Verb+(3d cs:1,1,1)+.
% As with the standard TikZ \Verb+xyz+ coordinate system, this gets converted to a 2 dimensional coordinate.
% However, unlike the standard system, it is possible to change the transformation used to convert from 3 dimensions to 2 dimensions.
%
% Where it gets a little complicated is with relative coordinates and saved coordinates (via nodes).
% With a linear transformation (as in the standard TikZ transformation), there is no difference between specifying relative coordinates in 3 dimensions as in 2 dimensions.
% But to allow the possibility of non-linear transformations, the method for handling relative coordinates needs to be a little more complicated.
% The system has to remember the original 3 dimensional coordinates and not the 2 dimensional result of the transformation.
% To handle this, instead of using the standard TikZ system for relative coordinates, you have to use the syntaxes \Verb+(+3d cs:1,1,1)+ and \Verb+(++3d cs:1,1,1)+.
%
% When saving a coordinate via a node, the 3 dimensional coordinate is also saved.
% To access the saved coordinate, use the syntax \Verb+(3d n cs:node.anchor)+.
% The node shape itself is not transformed, but the 3 dimensional coordinate of its centre can be used as a 3 dimensional coordinate later.
%
% \section{Limitations}
%
% This package works on the coordinate level.
% Therefore it is not guaranteed that actual paths will be transformed correctly.
% The transformation of a straight line will still be a straight line, and similarly that of a bezier curve.
% There are two difficulties with fixing this limitation.
% The first is that knowing what a straight line should become depends on the transformation being used.
% The second is that the underlying engine only knows about straight lines and bezier curves, and so any replacement will have to be phrased in terms of one of them.
%
% There are plenty of other limitations, but they all follow from the basic one above.
% Even though this package preserves the illusion of 3-dimensionality a little longer than previously, once the path is laid out then it is a 2 dimensional object.
% For example, any decorations will not take into account the third dimension.
% Similarly, line thickness will not vary (though if simulated by a \Verb+fill+ this would work).
%
% \section{Transformations}
%
% At the moment, the only transformation that is available is that of projection from a point on to the \(x-y\)-plane.
% The point from which the scene is projected is set by the key \Verb+3d/perspective eye+.
%
% \section{Paths}
%
% Certain paths have been modified to take in to account the available information on the third dimension.
% Specifically, there are 3-dimensional variants of the rectangle, the circle, and the arc.
%
% \StopEventually{}
%
% \section{Implementation}
%
% \iffalse
%<*package>
% \fi
%
%    \begin{macrocode}

\long\def\ge@addto@macro#1#2{%
  \begingroup
  \toks@\expandafter\expandafter\expandafter{\expandafter#1#2}%
  \xdef#1{\the\toks@}%
  \endgroup}

\newif\ifthd@save@point
\thd@save@pointtrue

\newif\ifthd@save@this@point
\thd@save@this@pointtrue

\newdimen\thd@x
\newdimen\thd@y
\newdimen\thd@z
\newdimen\thd@thisx
\newdimen\thd@thisy
\newdimen\thd@thisz
\newdimen\thd@xa
\newdimen\thd@ya
\newdimen\thd@za
\newdimen\thd@xb
\newdimen\thd@yb
\newdimen\thd@zb
\newdimen\thd@xc
\newdimen\thd@yc
\newdimen\thd@zc
\newdimen\thd@lastxsaved
\newdimen\thd@lastysaved
\newdimen\thd@lastzsaved
\newdimen\thd@curvebx
\newdimen\thd@curveby
\newdimen\thd@curvebz

\tikzset{
  every node/.style={3d/coordinate/save node},
  3d rectangle/.style={%
    3d/rectangle
  },
  3d arc/.style={%
    3d/arc
  },
  3d circle/.style={%
    3d/circle
  },
  3d/.is family,
  3d,
  3d projection/.is choice,
  3d projection/project from point/.code={%
    \let\thd@to@twd=\thd@persp@proj
  },
  perspective eye/x/.initial={10cm},
  perspective eye/y/.initial={5cm},
  perspective eye/z/.initial={20cm},
  perspective eye/.code={
    \thd@split@xyz#1\relax
    \edef\thd@temp{\the\thd@x}%
    \pgfkeyslet{/tikz/3d/perspective eye/x}{\thd@temp}%
    \edef\thd@temp{\the\thd@y}%
    \pgfkeyslet{/tikz/3d/perspective eye/y}{\thd@temp}%
    \edef\thd@temp{\the\thd@z}%
    \pgfkeyslet{/tikz/3d/perspective eye/z}{\thd@temp}%
  },
  rectangle/direction/.initial={1,0,0},
  rectangle/.style={
    to path={%
      \pgfextra{\thd@rectangle\tikztotarget}%
      \thd@path@cmd
    },
    3d/rectangle/.cd
  },
  circle/x axis/.initial={1,0,0},
  circle/y axis/.initial={0,1,0},
  circle/.code={%
    \let\pgfsyssoftpath@curveto=\thd@circle@pathcurveto
    \let\pgfsyssoftpath@moveto=\thd@circle@pathmoveto
  },
  arc/.code={%
    \let\pgfsyssoftpath@curveto=\thd@arc@pathcurveto
    \let\tikz@@@arcfinal=\thd@@@arcfinal
  },
  coordinate/.is family,
  coordinate,
  x length/.initial={1cm},
  y length/.initial={1cm},
  z length/.initial={1cm},
  x/.code={%
    \tikz@checkunit{#1}%
    \iftikz@isdimension
     \pgfmathsetlength{\thd@x}{#1}%
    \else
     \pgfmathsetlength{\thd@x}{#1 * \pgfkeysvalueof{/tikz/3d/coordinate/x length}}%
    \fi
  },
  y/.code={%
    \tikz@checkunit{#1}%
    \iftikz@isdimension
     \pgfmathsetlength{\thd@y}{#1}%
    \else
     \pgfmathsetlength{\thd@y}{#1 * \pgfkeysvalueof{/tikz/3d/coordinate/y length}}%
    \fi
  },
  z/.code={%
    \tikz@checkunit{#1}%
    \iftikz@isdimension
     \pgfmathsetlength{\thd@z}{#1}%
    \else
     \pgfmathsetlength{\thd@z}{#1 * \pgfkeysvalueof{/tikz/3d/coordinate/z length}}%
    \fi
  },
  save node/.code={%
    \tikz@addoption{%
      \expandafter\global\expandafter\let\csname thd@node@\tikz@fig@name\endcsname\thd@this@node
    }
  },
  new/.code={%
    \def\thd@next@coord{x}%
  },
  .unknown/.code={%
    \tikz@checkunit{\pgfkeyscurrentname}%
    \iftikz@isdimension
      \expandafter\pgfmathsetlength\csname thd@\thd@next@coord\endcsname{\pgfkeyscurrentname}%
    \else
      \expandafter\pgfmathsetlength\csname thd@\thd@next@coord\endcsname{\pgfkeyscurrentname * \pgfkeysvalueof{/tikz/3d/coordinate/\thd@next@coord\space length}}%
    \fi
    \edef\thd@next@coord{\csname thd@next@coord@\thd@next@coord\endcsname}%
  },
}

\def\thd@next@coord@x{y}
\def\thd@next@coord@y{z}
\def\thd@next@coord@z{x}

\def\thd@split@xyz#1,#2,#3\relax{%
  \tikz@checkunit{#1}%
  \iftikz@isdimension
   \pgfmathsetlength{\thd@x}{#1}%
  \else
   \pgfmathsetlength{\thd@x}{#1 *     \pgfkeysvalueof{/tikz/3d/coordinate/x length}}%
  \fi
  \tikz@checkunit{#2}%
  \iftikz@isdimension
   \pgfmathsetlength{\thd@y}{#2}%
  \else
   \pgfmathsetlength{\thd@y}{#2 *     \pgfkeysvalueof{/tikz/3d/coordinate/y length}}%
  \fi
  \tikz@checkunit{#3}%
  \iftikz@isdimension
   \pgfmathsetlength{\thd@z}{#3}%
  \else
   \pgfmathsetlength{\thd@z}{#3 *     \pgfkeysvalueof{/tikz/3d/coordinate/z length}}%
  \fi
}

\newcommand{\thdset}[1]{%
  \tikzset{3d/.cd,#1}%
}

\def\thd@save@point{%
  \ifthd@save@point
  \global\thd@lastxsaved=\thd@x%
  \global\thd@lastysaved=\thd@y%
  \global\thd@lastzsaved=\thd@z%
  \fi
}

\def\thd@save@this@point{%
  \ifthd@save@this@point
  \global\thd@thisx=\thd@x%
  \global\thd@thisy=\thd@y%
  \global\thd@thisz=\thd@z%
  \fi
}

\def\thd@this@point{%
  \thd@x=\thd@thisx%
  \thd@y=\thd@thisy%
  \thd@z=\thd@thisz%
}

\def\thd@lastsaved@point{%
  \thd@x=\thd@lastxsaved%
  \thd@y=\thd@lastysaved%
  \thd@z=\thd@lastzsaved%
}

\def\thd@save@curveB{%
  \global\thd@curvebx=\thd@thisx%
  \global\thd@curveby=\thd@thisy%
  \global\thd@curvebz=\thd@thisz%
}

\def\thd@curveB{%
  \thd@x=\thd@curvebx%
  \thd@y=\thd@curveby%
  \thd@z=\thd@curvebz%
}

\def\thd@make@global{%
  \global\thd@x=\thd@x%
  \global\thd@y=\thd@y%
  \global\thd@z=\thd@z%
}

\def\thd@point@origin{%
  \thd@x=0pt%
  \thd@y=0pt%
  \thd@z=0pt%
}

\def\thd@add#1#2{%
  #1%
  \thd@xa=\thd@x
  \thd@ya=\thd@y
  \thd@za=\thd@z
  #2%
  \advance\thd@x by \thd@xa
  \advance\thd@y by \thd@ya
  \advance\thd@z by \thd@za
}

\def\thd@diff#1#2{%
  #2%
  \thd@xa=\thd@x
  \thd@ya=\thd@y
  \thd@za=\thd@z
  #1%
  \advance\thd@x by -\thd@xa
  \advance\thd@y by -\thd@ya
  \advance\thd@z by -\thd@za
}

\def\thd@scale#1#2{%
  #1%
  \thd@x=#2\thd@x
  \thd@y=#2\thd@y
  \thd@z=#2\thd@z
}

% Orthogonal projection of #2 on to #1
\def\thd@proj#1#2{%
  #1%
  \thd@xa=\thd@x
  \thd@ya=\thd@y
  \thd@za=\thd@z
  #2%
  \thd@xb=\thd@x
  \thd@yb=\thd@y
  \thd@zb=\thd@z
  \pgfmathsetlength{\pgfutil@tempdima}{(\thd@xa * \thd@xb + \thd@ya * \thd@yb + \thd@za * \thd@zb) / (\thd@xa^2 + \thd@ya^2 + \thd@za^2)}%
  \pgfmathsetlength{\thd@x}{\thd@xa * \pgfutil@tempdima}%
  \pgfmathsetlength{\thd@y}{\thd@ya * \pgfutil@tempdima}%
  \pgfmathsetlength{\thd@z}{\thd@za * \pgfutil@tempdima}%
}

\def\thd@pt#1#2#3{%
  \pgfmathsetlength{\thd@x}{#1}%
  \pgfmathsetlength{\thd@y}{#2}%
  \pgfmathsetlength{\thd@z}{#3}%
}

\def\thd@qpt#1#2#3{%
  \thd@x=#1\relax%
  \thd@y=#2\relax%
  \thd@z=#3\relax%
}

\def\thd@process#1{%
  \begingroup
  #1%
  \global\thd@x=\thd@x
  \global\thd@y=\thd@y
  \global\thd@z=\thd@z
  \endgroup
}

\def\thd@persp@proj{%
  \pgfmathsetmacro{\thd@t}{\pgfkeysvalueof{/tikz/3d/perspective eye/z}/(\pgfkeysvalueof{/tikz/3d/perspective eye/z} - \thd@z)}%
  \pgfmathsetlength{\pgf@x}{(1 - \thd@t) * \pgfkeysvalueof{/tikz/3d/perspective eye/x} + \thd@t * \thd@x}%
  \pgfmathsetlength{\pgf@y}{(1 - \thd@t) * \pgfkeysvalueof{/tikz/3d/perspective eye/y} + \thd@t * \thd@y}%
}  

\let\thd@to@twd=\thd@persp@proj

\tikzdeclarecoordinatesystem{3d}{%
  \thd@point@origin
  \thdset{coordinate,new,#1}%
  \thd@make@global
  \thd@to@twd
  \thd@save@point
  \thd@save@node
  \thd@save@this@point
  \global\let\tikz@curveB=\thd@orig@tikz@curveB
}

\tikzdeclarecoordinatesystem{+3d}{%
  \thd@point@origin
  \thdset{coordinate,new,#1}%
  \thd@save@this@point
  \thd@add{\thd@qpt{\thd@x}{\thd@y}{\thd@z}}{\thd@lastsaved@point}%
  \thd@make@global
  \thd@to@twd
  \thd@save@node
  \global\let\tikz@curveB=\thd@tikz@curveB
}

\tikzdeclarecoordinatesystem{++3d}{%
  \thd@point@origin
  \thdset{coordinate,new,#1}%
  \thd@save@this@point
  \thd@add{\thd@qpt{\thd@x}{\thd@y}{\thd@z}}{\thd@lastsaved@point}%
  \thd@make@global
  \thd@to@twd
  \thd@save@point
  \thd@save@node
  \global\let\tikz@curveB=\thd@tikz@curveB
}

\def\thd@nodename#1.#2\relax{#1}

\tikzdeclarecoordinatesystem{3d n}{%
  \thd@point@origin
  \pgfutil@in@.{#1}% Ok, flag this
  \ifpgfutil@in@
    \tikz@calc@anchor#1\tikz@stop%
    \pgf@xa=\pgf@x
    \pgf@ya=\pgf@y
    \expandafter\tikz@calc@anchor\thd@nodename#1\relax.center\tikz@stop%
    \advance\pgf@xa by -\pgf@x
    \advance\pgf@ya by -\pgf@y
    \csname thd@node@\thd@nodename#1\relax\endcsname
    \thd@to@twd
    \advance\pgf@x by \pgf@xa
    \advance\pgf@y by \pgf@ya
  \else%
    \csname thd@node@#1\endcsname
    \tikz@calc@anchor#1.center\tikz@stop%
    \expandafter\ifx\csname pgf@sh@ns@#1\endcsname\tikz@coordinate@text%
    \else
      \tikz@shapebordertrue%
      \def\tikz@shapeborder@name{#1}%
    \fi%
    \thd@to@twd
  \fi%
  \thd@make@global
  \thd@save@point
  \thd@save@this@point
  \thd@save@node
}

\def\thd@save@node{%
  \xdef\thd@this@node{\noexpand\thd@qpt{\the\thd@x}{\the\thd@y}{\the\thd@z}}%
}

\let\thd@orig@tikz@curveC=\tikz@curveC

\def\thd@tikz@curveC#1{%
  \thd@add{\thd@curveB}{\thd@lastsaved@point}%
  \thd@to@twd
  \xdef\tikz@curve@second{\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
  \global\let\tikz@curveC=\thd@orig@tikz@curveC
  \tikz@curveC{#1}%
}

\let\thd@orig@tikz@curveB=\tikz@curveB

\def\thd@tikz@curveB#1{%
  \global\let\tikz@curveC=\thd@tikz@curveC
  \global\let\tikz@curveB=\thd@orig@tikz@curveB
  \thd@save@curveB
  \tikz@curveB{#1}%
}

\def\thd@rectangle#1{%
  \let\thd@path@cmd=\pgfutil@empty
  \thd@xc=\thd@x
  \thd@yc=\thd@y
  \thd@zc=\thd@z
  \thd@save@pointfalse
  \expandafter\tikz@scan@one@point\expandafter\pgfutil@gobble\expandafter(#1)\relax%
  \edef\thd@marshal{%
    \noexpand\thd@diff{\noexpand\thd@qpt{\the\thd@x}{\the\thd@y}{\the\thd@z}}{\noexpand\thd@qpt{\the\thd@xc}{\the\thd@yc}{\the\thd@zc}}}%
  \thd@process{\thd@marshal}%
  \thd@xa=\thd@x
  \thd@ya=\thd@y
  \thd@za=\thd@z
  \edef\thd@rect@dir{(3d cs:\pgfkeysvalueof{/tikz/3d/rectangle/direction})}
  \expandafter\tikz@scan@one@point\expandafter\pgfutil@firstofone\thd@rect@dir\relax
  \edef\thd@marshal{%
    \noexpand\thd@proj{\noexpand\thd@qpt{\the\thd@x}{\the\thd@y}{\the\thd@z}}{\noexpand\thd@qpt{\the\thd@xa}{\the\thd@ya}{\the\thd@za}}}%
  \thd@process{\thd@marshal}%
  \thd@xb=\thd@x
  \thd@yb=\thd@y
  \thd@zb=\thd@z
  \edef\thd@temp{ (+3d cs:0pt,0pt,0pt) -- (+3d cs:\the\thd@x,\the\thd@y,\the\thd@z) -- (+3d cs:\the\thd@xa,\the\thd@ya,\the\thd@za)}%
  \ge@addto@macro\thd@path@cmd\thd@temp
  \edef\thd@marshal{%
    \noexpand\thd@diff{\noexpand\thd@qpt{\the\thd@xa}{\the\thd@ya}{\the\thd@za}}{\noexpand\thd@qpt{\the\thd@xb}{\the\thd@yb}{\the\thd@zb}}}%
  \thd@process{\thd@marshal}%
  \edef\thd@temp{ -- (+3d cs:\the\thd@x,\the\thd@y,\the\thd@z) -- cycle (\tikztotarget)}%
  \ge@addto@macro\thd@path@cmd\thd@temp
  \thd@save@pointtrue
}

% Drop in for \Verb+\pgfsyssoftpath@curveto+ in \Verb+\pgf@arc+
% Interpret the coordinates in an x-y-z system
\let\thd@orig@pgfsyssoftpath@curveto=\pgfsyssoftpath@curveto
\let\thd@orig@pgfsyssoftpath@moveto=\pgfsyssoftpath@moveto
\def\thd@arc@pathcurveto#1#2#3#4#5#6{%
  \begingroup
  \thd@this@point
  \thd@xc=\thd@x
  \thd@yc=\thd@y
  \thd@zc=\thd@z
  \edef\thd@rect@dir{(3d cs:\pgfkeysvalueof{/tikz/3d/circle/x axis})}
  \expandafter\tikz@scan@one@point\expandafter\pgfutil@firstofone\thd@rect@dir\relax
  \thd@xa=\thd@x
  \thd@ya=\thd@y
  \thd@za=\thd@z
  \edef\thd@rect@dir{(3d cs:\pgfkeysvalueof{/tikz/3d/circle/y axis})}
  \expandafter\tikz@scan@one@point\expandafter\pgfutil@firstofone\thd@rect@dir\relax
  \thd@xb=\thd@x
  \thd@yb=\thd@y
  \thd@zb=\thd@z
  \pgfmathsetlength{\thd@x}{\thd@xc + (#1 - \pgf@path@lastx)/1cm * \thd@xa + (#2 - \pgf@path@lasty)/1cm * \thd@xb}
  \pgfmathsetlength{\thd@y}{\thd@yc + (#1 - \pgf@path@lastx)/1cm * \thd@ya + (#2 - \pgf@path@lasty)/1cm * \thd@yb}
  \pgfmathsetlength{\thd@z}{\thd@zc + (#1 - \pgf@path@lastx)/1cm * \thd@za + (#2 - \pgf@path@lasty)/1cm * \thd@zb}
  \thd@to@twd
% I don't understand why, but the transformation here is scaled
% up by 1cm
  \pgfmathsetlength{\pgf@x}{\pgf@x/1cm}%
  \pgfmathsetlength{\pgf@y}{\pgf@y/1cm}%
  \pgfpointtransformed{\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
  \pgf@xa=\pgf@x
  \pgf@ya=\pgf@y
  \pgfmathsetlength{\thd@x}{\thd@xc + (#3 - \pgf@path@lastx)/1cm * \thd@xa + (#4 - \pgf@path@lasty)/1cm * \thd@xb}
  \pgfmathsetlength{\thd@y}{\thd@yc + (#3 - \pgf@path@lastx)/1cm * \thd@ya + (#4 - \pgf@path@lasty)/1cm * \thd@yb}
  \pgfmathsetlength{\thd@z}{\thd@zc + (#3 - \pgf@path@lastx)/1cm * \thd@za + (#4 - \pgf@path@lasty)/1cm * \thd@zb}
  \thd@to@twd
% I don't understand why, but the transformation here is scaled
% up by 1cm
  \pgfmathsetlength{\pgf@x}{\pgf@x/1cm}%
  \pgfmathsetlength{\pgf@y}{\pgf@y/1cm}%
  \pgfpointtransformed{\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
  \pgf@xc=\pgf@x
  \pgf@yc=\pgf@y
  \pgfmathsetlength{\thd@x}{\thd@xc + (#5 - \pgf@path@lastx)/1cm * \thd@xa + (#6 - \pgf@path@lasty)/1cm * \thd@xb}
  \pgfmathsetlength{\thd@y}{\thd@yc + (#5 - \pgf@path@lastx)/1cm * \thd@ya + (#6 - \pgf@path@lasty)/1cm * \thd@yb}
  \pgfmathsetlength{\thd@z}{\thd@zc + (#5 - \pgf@path@lastx)/1cm * \thd@za + (#6 - \pgf@path@lasty)/1cm * \thd@zb}
  \thd@save@point
  \thd@save@this@point
  \thd@to@twd
% I don't understand why, but the transformation here is scaled
% up by 1cm
  \pgfmathsetlength{\pgf@x}{\pgf@x/1cm}%
  \pgfmathsetlength{\pgf@y}{\pgf@y/1cm}%
  \pgfpointtransformed{\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
  \pgf@xb=\pgf@x
  \pgf@yb=\pgf@y
  \thd@orig@pgfsyssoftpath@curveto{\the\pgf@xa}{\the\pgf@ya}{\the\pgf@xc}{\the\pgf@yc}{\the\pgf@xb}{\the\pgf@yb}%
  \endgroup
}

\def\thd@circle@pathmoveto#1#2{%
  \begingroup
  \thd@save@pointfalse
  \thd@save@this@pointfalse
  \edef\thd@temp{%
    \noexpand\pgf@xa=#1\relax
    \noexpand\pgf@ya=#2\relax
  }%
  \thd@temp
  \thd@this@point% Corresponds to the centre of the circle in 3D-space
  \thd@xc=\thd@x
  \thd@yc=\thd@y
  \thd@zc=\thd@z
  \thd@to@twd
  \pgf@xb=\pgf@x
  \pgf@yb=\pgf@y
  \edef\thd@rect@dir{(3d cs:\pgfkeysvalueof{/tikz/3d/circle/x axis})}
  \expandafter\tikz@scan@one@point\expandafter\pgfutil@firstofone\thd@rect@dir\relax
  \thd@xa=\thd@x
  \thd@ya=\thd@y
  \thd@za=\thd@z
  \edef\thd@rect@dir{(3d cs:\pgfkeysvalueof{/tikz/3d/circle/y axis})}
  \expandafter\tikz@scan@one@point\expandafter\pgfutil@firstofone\thd@rect@dir\relax
  \thd@xb=\thd@x
  \thd@yb=\thd@y
  \thd@zb=\thd@z
  \pgfmathsetlength{\thd@x}{\thd@xc + (\pgf@xa - \pgf@xc)/1cm * \thd@xa + (\pgf@ya - \pgf@yc)/1cm * \thd@xb}
  \pgfmathsetlength{\thd@y}{\thd@yc + (\pgf@xa - \pgf@xc)/1cm * \thd@ya + (\pgf@ya - \pgf@yc)/1cm * \thd@yb}
  \pgfmathsetlength{\thd@z}{\thd@zc + (\pgf@xa - \pgf@xc)/1cm * \thd@za + (\pgf@ya - \pgf@yc)/1cm * \thd@zb}
  \thd@to@twd
% I don't understand why, but the transformation here is not scaled
% up by 1cm
  \pgfpointtransformed{\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
  \advance\pgf@x by -\pgf@xb
  \advance\pgf@y by -\pgf@yb
  \thd@orig@pgfsyssoftpath@moveto{\the\pgf@x}{\the\pgf@y}%
  \endgroup
}

\def\thd@circle@pathcurveto#1#2#3#4#5#6{%
  \begingroup
  \thd@save@pointfalse
  \thd@save@this@pointfalse
  \edef\thd@temp{%
    \noexpand\pgf@xa=#1\relax
    \noexpand\pgf@ya=#2\relax
    \noexpand\pgf@xc=#3\relax
    \noexpand\pgf@yc=#4\relax
    \noexpand\pgf@xb=#5\relax
    \noexpand\pgf@yb=#6\relax
    \noexpand\pgfutil@tempdima=\the\pgf@xc\relax
    \noexpand\pgfutil@tempdimb=\the\pgf@yc\relax
  }%
  \thd@temp
  \thd@this@point% Centre of the circle in 3D-space
  \thd@xc=\thd@x\relax
  \thd@yc=\thd@y\relax
  \thd@zc=\thd@z\relax
  \edef\thd@rect@dir{(3d cs:\pgfkeysvalueof{/tikz/3d/circle/x axis})}
  \expandafter\tikz@scan@one@point\expandafter\pgfutil@firstofone\thd@rect@dir\relax
  \thd@xa=\thd@x
  \thd@ya=\thd@y
  \thd@za=\thd@z
  \edef\thd@rect@dir{(3d cs:\pgfkeysvalueof{/tikz/3d/circle/y axis})}
  \expandafter\tikz@scan@one@point\expandafter\pgfutil@firstofone\thd@rect@dir\relax
  \thd@xb=\thd@x
  \thd@yb=\thd@y
  \thd@zb=\thd@z
  \pgfmathsetlength{\thd@x}{\thd@xc + (\pgf@xa - \pgfutil@tempdima)/1cm * \thd@xa + (\pgf@ya - \pgfutil@tempdimb)/1cm * \thd@xb}
  \pgfmathsetlength{\thd@y}{\thd@yc + (\pgf@xa - \pgfutil@tempdima)/1cm * \thd@ya + (\pgf@ya - \pgfutil@tempdimb)/1cm * \thd@yb}
  \pgfmathsetlength{\thd@z}{\thd@zc + (\pgf@xa - \pgfutil@tempdima)/1cm * \thd@za + (\pgf@ya - \pgfutil@tempdimb)/1cm * \thd@zb}
  \thd@to@twd
% I don't understand why, but the transformation here is not scaled
% up by 1cm
  \pgfpointtransformed{\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
  \pgf@xa=\pgf@x
  \pgf@ya=\pgf@y
  \thd@this@point% Centre of the circle in 3D-space
  \thd@to@twd
  \advance\pgf@xa by -\pgf@x
  \advance\pgf@ya by -\pgf@y
  \pgfmathsetlength{\thd@x}{\thd@xc + (\pgf@xc - \pgfutil@tempdima)/1cm * \thd@xa + (\pgf@yc - \pgfutil@tempdimb)/1cm * \thd@xb}
  \pgfmathsetlength{\thd@y}{\thd@yc + (\pgf@xc - \pgfutil@tempdima)/1cm * \thd@ya + (\pgf@yc - \pgfutil@tempdimb)/1cm * \thd@yb}
  \pgfmathsetlength{\thd@z}{\thd@zc + (\pgf@xc - \pgfutil@tempdima)/1cm * \thd@za + (\pgf@yc - \pgfutil@tempdimb)/1cm * \thd@zb}
  \thd@to@twd
% I don't understand why, but the transformation here is not scaled
% up by 1cm
  \pgfpointtransformed{\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
  \pgf@xc=\pgf@x
  \pgf@yc=\pgf@y
  \thd@this@point% Centre of the circle in 3D-space
  \thd@to@twd
  \advance\pgf@xc by -\pgf@x
  \advance\pgf@yc by -\pgf@y
  \pgfmathsetlength{\thd@x}{\thd@xc + (\pgf@xb - \pgfutil@tempdima)/1cm * \thd@xa + (\pgf@yb - \pgfutil@tempdimb)/1cm * \thd@xb}
  \pgfmathsetlength{\thd@y}{\thd@yc + (\pgf@xb - \pgfutil@tempdima)/1cm * \thd@ya + (\pgf@yb - \pgfutil@tempdimb)/1cm * \thd@yb}
  \pgfmathsetlength{\thd@z}{\thd@zc + (\pgf@xb - \pgfutil@tempdima)/1cm * \thd@za + (\pgf@yb - \pgfutil@tempdimb)/1cm * \thd@zb}
  \thd@to@twd
% I don't understand why, but the transformation here is not scaled
% up by 1cm
  \pgfpointtransformed{\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
  \pgf@xb=\pgf@x
  \pgf@yb=\pgf@y
  \thd@this@point% Centre of the circle in 3D-space
  \thd@to@twd
  \advance\pgf@xb by -\pgf@x
  \advance\pgf@yb by -\pgf@y
  \edef\thd@temp{%
    \noexpand\thd@orig@pgfsyssoftpath@curveto{\the\pgf@xa}{\the\pgf@ya}{\the\pgf@xc}{\the\pgf@yc}{\the\pgf@xb}{\the\pgf@yb}}%
  \thd@temp
  \endgroup
}

\def\thd@@@arcfinal#1#2#3{%
  #1%
  \xdef\tikz@arc@save@first{\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}%
  \thd@lastsaved@point%
  \thd@to@twd%
  \xdef\tikz@arc@save@second{\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
}

%    \end{macrocode}
% \iffalse
%</package>
% \fi
%
% \Finale

\endinput