% curves.sty version 1.41 for LaTeX 2.09, SLiTeX, and LaTeX2e.
% I.L. Maclaine-cross, The University of New South Wales.
% Internet: ian@ilm.mech.unsw.edu.au
\typeout{Document Style Option `curves' <22 August 1995>}
% Draws curves in LaTeX picture environment using parabolas between points
%   with continuous slope at points. Equivalent to technical pens with
%   compasses and French curves.
% A Command Summary is at the end of this file.
%
% curvesls.sty is a faster equivalent requiring less memory which uses
% straight line drawing \specials like emTeX's.

% Make `;' appear like a letter so control sequences can use it and they 
% will not be accidently used by other macro packages.
\catcode`\;=11 

\newcount\;sc % number of symbols on Bezier segment
\newcount\;scp
\newcount\;t
\newcount\;cc % coordinate count
\newcount\;cnd % actual point count to next dot
\newcount\;mcnd % maximum point count to next dot
\newcount\;np
\newcount\;overhang
\newcount\;pns
\newcount\;psc % maximum dot spacing on line in sp.
\newcount\;pbs
\newcount\;rc
\newcount\;rtc
\newcount\;tc
\let\;tca=\@tempcnta
\let\;tcb=\@tempcntb

\newdimen\csdiameter
\newdimen\curvelength
\newdimen\overhang \overhang\z@
\newdimen\;dx
\newdimen\;ddx
\newdimen\;dy
\newdimen\;ddy
\newdimen\;pl \;pl\z@
\newdimen\;ucd
\newdimen\;y
\let\;td=\@tempdima
\let\;ytd=\@tempdimb

\newsavebox{\;csbox}
\newsavebox{\;pt}

\newif\ifcurvewarn \curvewarntrue % Warn about curve problems
\newif\if;ccn  % coordinate number correct
\newif\if;pt   % plot points if true
\newif\if;csym % curve symbol defined
\newif\if;scnt % symbol or pattern count <>0

\newhelp\;strline{curve straight from}
\newhelp\m;ssingcoord{curve needs more points, add them.}
\newhelp\;negdash{curvedashes needs the same sign for all arguments.}
\newhelp\;oddcoord{curve requires two co-ordinates for each point,
  count them.}

\newcommand\arc{\@ifnextchar[\;arc{\;arc[0]}}
\newcommand\;arc{}
\def\;arc[#1](#2,#3)#4{\;setpoint{#1}\scaleput(#2,#3){\;ddx-#3\unitlength
  \;ddy#2\unitlength \;firstpoint \;td#4\p@ \;drwarc}}


% Redefines version in LaTeX 2e of 1 June 1994.
\def\bezier#1)#2(#3)#4({\@bezier#1)(#3)(}
\def\@bezier#1(#2,#3)(#4,#5)(#6,#7){\;dx#4\unitlength \;ddx-\;dx
  \advance\;dx-#2\unitlength \advance\;ddx#6\unitlength \;dy#5\unitlength
  \;ddy-\;dy \advance\;dy-#3\unitlength \advance\;ddy#7\unitlength
  \;setpoint{#1}\scaleput(#2,#3){\;firstpoint \;bezier}}

\newcommand\bigcircle{\@ifnextchar[\;bgcrcl{\;bgcrcl[0]}}
\newcommand\;bgcrcl{}
\def\;bgcrcl[#1]#2{\;setpoint{#1}\;dx\unitlength \global\divide\unitlength\tw@
  \scaleput(#2,0){\;ddx\z@ \;ddy#2\unitlength \global\unitlength\;dx \;td360\p@
    \;drwarc}}

\newcommand\closecurve{\@ifnextchar[\;closecurve{\;closecurve[0]}}
\newcommand\;closecurve{}
\def\;closecurve[#1](#2){\;coordn\closecurve\thr@@{#2}{#1}%
  \if;ccn\scaleput(\;xb,\;yb){\edef\;ci{\;xa,\;ya,#2,\;xb,\;yb,\;xc,\;yc}%
    \advance\;cc\thr@@ \;tagcurve\;ci}\fi}

\newcommand\curve{\@ifnextchar[\;curve{\;curve[0]}}
\newcommand\;curve{}
\def\;curve[#1](#2){\;coordn\curve\tw@{#2}{#1}%
  \if;ccn \scaleput(\;xa,\;ya){\;firstpoint
    \ifnum\;cc=\tw@ \;slbezd \;slbez
    \else \;scbezd\;dx\;ddx\;xa\;xb\;xc \;scbezd\;dy\;ddy\;ya\;yb\;yc
      \;bezier \;tagcurve{#2}\ifnum\;cc>6\;endcurve\fi \fi}\fi}
\newcommand\;scbezd[5]{\;slcd#2#3#5\divide#24\;slcd#1#3#4\advance#1-#2}
\newcommand\;xa{} \newcommand\;xb{} \newcommand\;xc{}
\newcommand\;ya{} \newcommand\;yb{} \newcommand\;yc{}
\newcommand\;ci{}

\newcommand\curvesymbol[1]{\def\;curvesymbol{#1}\ch;ckcs
  \global\setbox\;csbox\hbox{#1}\csdiameter\wd\;csbox}
\newcommand\;curvesymbol{} \def\;curvesymbol{}

\newcommand\curvedashes{\@ifnextchar[\;crvdshs{\;crvdshs[\unitlength]}}
\newcommand\;crvdshs{}
\def\;crvdshs[#1]#2{\;ucd#1\def\;icurvedashes{#2}\;ccnfalse \;pl\z@
  \@for \;ci:=#2\do{\ifdim\;ci\;ucd<\z@ \;ccntrue \@latexerr{\string
      \curvedashes\space sign bad at \;ci}{\the\;negdash ^^J\@eha}%
    \else \advance\;pl\;ci\;ucd \fi}\if;ccn\;pl\z@\fi}
\newcommand\;icurvedashes{}

\newcommand\diskpitchstretch{\@ne}

\newcommand\tagcurve{\@ifnextchar[\;tgcrv{\;tgcrv[0]}}
\newcommand\;tgcrv{}
\def\;tgcrv[#1](#2){\;coordn\tagcurve\thr@@{#2}{#1}\if;ccn
  \scaleput(\;xb,\;yb){\;firstpoint \;tagcurve{#2}}\fi}

\newcommand\scaleput{}
\long\def\scaleput(#1,#2)#3{\@killglue \;td#2\unitlength
  \raise\yscale\;td \hbox to \z@{\kern\xscaley\;td \;td#1\unitlength
  \kern\xscale\;td \raise\yscalex\;td \hbox{#3}\hss}\ignorespaces}
\newcommand\xscale{\@ne}
\newcommand\xscaley{0}
\newcommand\yscale{\@ne}
\newcommand\yscalex{0}

% Plot first point if any.
\newcommand\;firstpoint{\ifdim\;pl=\z@\;point\fi}

% Calculates segment count, sine, cosine and differences then plots segments.
\newcommand\;drwarc{\;cc\;td \;np\;td \;td23\p@ \divide\;cc\;td
  \;abs\;cc \advance\;cc\@ne \;pns\p@ \divide\;pns\tw@
  \divide\;np\;cc \;rc\;np \divide\;rc\;pns \;abs\;rc
  \advance\;rc\@ne \divide\;np\;rc \multiply\;np\;pns \divide\;np14668 %
  \multiply\;np\;rc \divide\;np\@cclvi \;scp\p@ \multiply\;scp\@cclvi
  \;t\;pns \;csi\;csi\;csi\;csi \;rxy\;ddx\;ddy \divide\;rc\p@
  \advance\;rc\@ne \;rtc\;rc \advance\;rc\;rc \;ndd\;ddx \;ndd\;ddy
  \;csi \;rxy\;ddx\;ddy \divide\;rc\;pns \advance\;rc\@ne
  \@whilenum\;cc>\z@ \do{\advance\;cc\m@ne \;dx\;ddx \;dy\;ddy
    \divide\;ddx\;rc \divide\;ddy\;rc \;td\;ddx \;ddx\;t\;td
    \advance\;ddx-\;np\;ddy \;ddy\;t\;ddy \advance\;ddy\;np\;td
    \divide\;ddx\;pns \divide\;ddy\;pns \;ddx\;rc\;ddx \;ddy\;rc\;ddy
    {\;bezier \global\;ytd\;y \global\;tca\;overhang}\;y\;ytd \;overhang\;tca}}
\newcommand\;ndd[1]{\divide#1\;rc \multiply#1\;np \divide#1\;t #1\;rtc#1}
% Cosine and sine half angle iteration.
\newcommand\;csi{\;tcb\;np \multiply\;np\;t \divide\;np\;pns \;t\;tcb
  \multiply\;t\;t \divide\;t-\;scp \advance\;t\;pns \divide\;scp4 }

% Count the number of co-ordinate specified and warns if incorrect.
\newcommand\;coordn[4]{\;setpoint{#4}\ifx#1\closecurve\;cc\tw@\else\;cc\z@\fi
  \@for\;ci:=#3\do{\advance\;cc\@ne
    \ifcase\;cc \or \;d;f\;xa \or \;d;f\;ya \or \;d;f\;xb
      \or \;d;f\;yb \or \;d;f\;xc \or \;d;f\;yc \fi
    \ifx#1\closecurve\ifodd\;cc \;d;f\;xa \else \;d;f\;ya \fi\fi}%
  \;ccnfalse \ifx#1\closecurve \advance\;cc-\tw@ \fi
  \ifodd\;cc \@latexerr{\string #1\space points odd}{\the\;oddcoord ^^J\@eha}%
  \else \divide\;cc\tw@
    \ifnum#2>\;cc \@latexerr{\string #1 needs \the#2 points}%
      {\the\m;ssingcoord ^^J\@eha}%
    \else \;ccntrue \fi\fi}

% Sets symbol, character or disk depending on how line is to be plotted.
% Corrects overhang to be positive or zero but no greater than \;pl.
\newcommand\;setpoint[1]{\curvelength\z@ \def\;po;nt{\raise\;y\copy\;pt}\ch;ckcs
  \ifnum#1=\z@\;scntfalse\else\;scnttrue\fi  \;sc#1\relax \;abs\;sc \;psc\;sc
  \ifdim\;pl>\z@ \;overhang\overhang
    \ifnum\;overhang=\z@\else \;np\;overhang \divide\;np\;pl \multiply\;np\;pl
      \ifnum\;overhang<\z@ \advance\;overhang\;pl
      \else \ifnum\;overhang=\;np\advance\;overhang\;pl\fi
      \fi \advance\;overhang-\;np
    \fi \if;csym \if;scnt\;setdisk\else\;setsymbol\;td\p@\fi \else \;setdisk \fi
    \s;tpitch
  \else\ifnum#1>\z@ \s;tcirc{\hss\vrule\@height\@wholewidth\@width\@wholewidth}%
  \else\ifnum#1<\z@ \if;csym\;setsymbol\else\set;pt{}\fi
  \else \;setdisk \s;tpitch \fi\fi\fi
  \edef\;point{\;po;nt}\;y\dp\;pt \advance\;y-\ht\;pt \divide\;y\tw@}
\newcommand\;setsymbol{\s;tcirc{\hss\unhcopy\;csbox}\edef\;po;nt{\;po;nt
  \s;tcirc{\hss\noexpand\noexpand\noexpand\;curvesymbol}%
  \global\setbox\;csbox\copy\;pt}}
\newcommand\s;tpitch{\;td\diskpitchstretch\;td \;psc\;td}
\newcommand\;po;nt{} \newcommand\;point{}

% Sets LaTeX disk character and calculates maximum spacing or selects period.
\newcommand\;setdisk{\ifdim\@halfwidth>.85\p@
    \s;tcirc{\@circ{\@wholewidth}{112}}\;td\@wholewidth
    \divide\;td 8\advance\;td.6\p@ \ifdim\;td>\thr@@\p@\;td\thr@@\p@\fi
  \else \;setperiod \fi}%

% OFSS, SLiTeX or NFSS version for period selected at load time.
% NFSS fix requested by Peter Vanroose and
% Michel Goossens who also supplied a workable patch.
\@ifundefined{selectfont}{\@ifundefined{fourteenrm}{%
\newcommand\;setperiod{\ifdim\@halfwidth>.6\p@ \let\;ci\svtnrm \;td.7\p@
  \else\ifdim\@wholewidth>.85\p@ \let\;ci\twlrm \;td.48\p@
  \else \ifdim\@wholewidth>.6\p@ \let\;ci\egtrm \else \let\;ci\fivrm \fi
    \;td.34\p@ \fi\fi \s;tcirc{\;ci\hss.}}%
    }{%
\newcommand\;setperiod{\;td.7\p@ \s;tcirc{\fourteenrm\hss.}}%
   }}{%
\newcommand\;setperiod{%
  \ifdim\@halfwidth>.6\p@ \;tcb17\;td.7\p@
  \else\ifdim\@wholewidth>.85\p@ \;tcb12\;td.48\p@
  \else \ifdim\@wholewidth>.6\p@ \;tcb8\else \;tcb5\fi \;td.34\p@ \fi\fi
  \s;tcirc{\rm \fontseries m\fontshape n\fontsize{\the\;tcb}\p@
    \selectfont \hss.}}%
     }

% Check if curvesymbol exists and set switch.
\newcommand\ch;ckcs{\ifx\;curvesymbol\@empty\;csymfalse\else\;csymtrue\fi}

% Makes zero width box \;pt of point
\newcommand\s;tcirc[1]{\set;pt to\z@{#1\hss}}

% Set global box \;pt
\newcommand\set;pt{\global\setbox\;pt\hbox}

% Plots last segment of curve from coordinates already read.
\newcommand\;endcurve{\;ecbezd\;dx\;ddx\;xa\;xb\;xc
  \;ecbezd\;dy\;ddy\;ya\;yb\;yc \;bezier}
\newcommand\;ecbezd[5]{\;slcd#1#3#5\divide#14 #2-#1\advance#2#5\unitlength
  \advance#2-#4\unitlength}

% Reads coordinates of four points before going to difference calculation.
\newcommand\;tagcurve[1]{\ifnum\;cc=\thr@@ \;endcurve \else \;cc\z@
  \@for\;ci:=#1\do{\advance\;cc\@ne \ifnum\;cc>6 %
    \ifodd\;cc \;slcd\;dx\;xa\;xc \let\;xa\;xb \let\;xb\;xc \;d;f\;xc
    \else \t;gcrv \fi \fi}\fi}

% Calculates differences over whole segment from four points.
\newcommand\t;gcrv{\;slcd\;dy\;ya\;yc \let\;ya\;yb \let\;yb\;yc \;d;f\;yc
  \;rxy\;dx\;dy \divide\;dx\;rtc \divide\;dy\;rtc
  \;ddx-\;ya\;dx \advance\;ddx\;xa\;dy \;ddy\;ddx
  \advance\;ddx\;yb\;dx \advance\;ddx-\;xb\;dy
  \advance\;ddy\;yc\;dx \advance\;ddy-\;xc\;dy
  \;slbezd \;td\;ddy \divide\;td\@m
  \ifdim\;td=\z@ \ifcurvewarn
    \@warning{\the\;strline \;xa,\;ya\space to \;xb,\;yb}\fi \;slbez
  \else \;td\unitlength \;rtc\;td \advance\;rtc\;rtc
    \divide\;rtc\p@ \advance\;rtc\@ne \divide\;td\;rtc
    \;t\;ddx \;scp\;t \;abs\;t
    \advance\;t\;t \divide\;t\p@ \advance\;t\@ne \divide\;scp\;t
    \multiply\;td\;scp \divide\;td\;ddy \multiply\;td\;rtc \multiply\;td\;t
    \;ddx\;xc\;td \advance\;ddx-\;xa\;td \advance\;dx-\;ddx
    \;ddy\;yc\;td \advance\;ddy-\;ya\;td \advance\;dy-\;ddy \;bezier \fi}

% Avoid repeating {\;ci}
\newcommand\;d;f[1]{\edef#1{\;ci}}

\newcommand\;slbezd{\;slcd\;dx\;xa\;xb \;slcd\;dy\;ya\;yb}

% Calculates difference between two coordinates.
\newcommand\;slcd[3]{#1#3\unitlength \advance#1-#2\unitlength}

% Calculates differences for bezier straight line.
\newcommand\;slbez{\divide\;dx\tw@ \;ddx\;dx \divide\;dy\tw@ \;ddy\;dy \;bezier}

% Scales segment differences, then calculates segment pattern and disk count,
% and initial disk differences; selects line or dashes.
\newcommand\;bezier{\;scale\;dx\;dy \;scp\;rc \;np\;rc \;scale\;ddx\;ddy
  \ifnum\;rc>\;np\;np\;rc\fi \advance\;np\;np
  \advance\;scp\;rc \;bezc\;dx\;ddx \;bezc\;dy\;ddy  \;rxy\;ddx\;ddy
  \divide\;rc\p@ \advance\;rc\thr@@
  \;tc\;rc \;sroot\;sroot\;sroot \;tca\;rc \;rxy\;dx\;dy
  \advance\;rc\;scp \divide\;rc\thr@@ \global\advance\curvelength\;rc sp%
  \divide\;np\;psc \ifnum\;np<\@ne\;np\@ne\fi \;t\;np 
  \if;scnt\ifdim\;pl=\z@ \;t\;sc
    \else\;np
      \if;csym \;rc \divide\;np\;sc \advance\;np-\csdiameter
        \;td\;pl \divide\;td\tw@ \advance\;np\;td \divide\;np\;pl
        \ifnum\;np<\@ne\;np\@ne\fi \multiply\;np\;sc
      \else \;sc \fi \advance\;t\;np \divide\;t\;np \multiply\;t\;np
  \fi \fi 
  \ifnum\;t>\;tca \;mcnd\;t \divide\;mcnd\;tca \else \;mcnd\@ne \;tca\;t \fi
  \;tc\;t \advance\;tc\;tc \;rtc\;tc
  \;tcb\;tca \advance\;tcb\@ne \multiply\;tcb\;mcnd \advance\;rtc-\;tcb
  \multiply\;rtc\;tca \;tcb\;t \multiply\;tcb\;tcb \divide\;tcb\;mcnd 
  \;bezd\;dx\;ddx \;bezd\;dy\;ddy \edef\;tplot{\;po;nts}\;cnd\;mcnd 
  \ifdim\;pl>\z@ \;dashes \else \;points \fi}
\newcommand\;scale[2]{\;td\xscale#1\advance\;td\xscaley#2%
  #2\yscale#2\advance#2\yscalex#1#1\;td \;rxy#1#2}
\newcommand\;bezc[2]{\advance#1#1\advance#2#2\;td#2\advance#2-#1\advance#1\;td}
\newcommand\;bezd[2]{\divide#2\;tcb \;td#2\multiply\;td\;rtc \advance#1-\;td
  \divide#1\;tc}

% Calculates length of vector \;rc from coordinates #1,#2
\newcommand\;rxy[2]{\;tc#1\;abs\;tc \;tcb#2\;abs\;tcb 
  \;rc\;tc \advance\;rc\;tcb 
  \ifnum\;rc>\z@ \;rtc\;rc \advance\;rtc\;rtc \divide\;rtc\p@ 
    \ifnum\;rtc>\z@ \advance\;rtc\@ne \divide\;tc\;rtc
      \divide\;tcb\;rtc \divide\;rc\;rtc
    \else \;rtc\@ne \fi \multiply\;tc\;tc \multiply\;tcb\;tcb
    \advance\;tc\;tcb \;sroot \multiply\;rc\;rtc \fi}
  
% Replaces argument by magnitude
\newcommand\;abs[1]{\ifnum#1<\z@ #1-#1\fi}

% Iteration of square root calculation by Newton's method.
\newcommand\;sroot{\;rroot\;rroot\;rroot}
\newcommand\;rroot{\;tcb\;tc \divide\;tcb\;rc \advance\;rc\;tcb \divide\;rc\tw@}

% Variable uses in \;dashes, \;scdashes, \;nscdashes, \;pdashes and \;dash.
% counts
% \;scp = distance between points.
% \;rc = length of Bezier segment.
% \;rtc = total points in Bezier segment.
% \;np = number of whole patterns in Bezier segment or scratch.
% \;overhang = of dash pattern past symbol or end of segment.
% \;pbs = total points between symbols
% \;pns = points to next symbol or dot.
% \;tc = number of points to blank for curve symbol.
% \;tcb = number of points along pattern.
% dimens
% \;pl = length of dash pattern.
% \;ucd = dash pattern unit length.

% Initializes dash plot for segment and selects symbol count alternative.
\newcommand\;dashes{\let\;ticd\;icurvedashes \let\;tucd\;ucd \divide\;rc\;t
  \;rtc\;t \;tc\;rc \advance\;tc\csdiameter \divide\;tc\;rc 
  \divide\;tc\tw@ \;t\;tc \multiply\;tc\tw@ \;ptfalse 
  \;pbs\;rc \divide\;pbs\tw@ \advance\;overhang\;pbs \divide\;overhang-\;rc
  \if;scnt \;scdashes \else \;nscdashes \fi \multiply\;overhang\;rc}

% Plots dash pattern when a nonzero symbol count is specified.
\newcommand\;scdashes{\;pbs\;rtc \divide\;pbs\;sc \;ccss \;scp
  \if;csym \;pl \multiply\;scp\;np \divide\;scp\;sc \advance\;pbs-\;tc
  \else \;pbs \multiply\;scp\;rc \fi \;np\;overhang \;overhang\z@
  \divide\;scp\;pbs \;tcb\z@ \;pns\;t \;dash \;overhang\;np
  \if;csym\else \advance\;overhang-\;tcb \advance\;rtc-\;tcb
    \advance\;pbs-\;tc \fi
  \;pns\;pbs \advance\;pns-\;np \if;csym\else\advance\;pns\;tcb\fi
  \@whilenum\;rtc>\z@\do{\;pdashes \;ptfalse \;t\;tc \;pns\;t \;dash
    \;pns\;pbs \;overhang\if;csym\;np\else-\;overhang\fi
    \advance\;pns-\;overhang}\;overhang-\if;csym\;np\else\;overhang 
      \;ptfalse \;t\;tc \;tcb\;overhang
      \divide\;t\tw@ \;rtc\;t \;pns\;t \;dash \fi}

% Plots symbols at natural pattern length but shrinks pattern to fit between.
\newcommand\;nscdashes{\advance\;pbs\;pl \divide\;pbs\;rc
  \if;csym \;bpdashes \fi \;ccss \;pns\;t
  \;dash \advance\;pbs-\;tc \;scp\;pl \divide\;scp\;pbs \;pns\;pbs
  \@whilenum\;rtc>\z@\do{\;pdashes \;ptfalse \;t\;tc \;pns\;t \;dash
    \;pns\;pbs}\if;csym \else \divide\;tc\tw@ \advance\;overhang\;tc \fi}

% If large symbol spaces, blank curve.
\newcommand\;ccss{\ifnum\;pbs>\;tc\else \;bpdashes \fi}

% A blank or symbol plotting dash pattern
\newcommand\;bpdashes{\let\;tucd\;pl \let\;ticd\;ricd \;tc\z@ \;t\z@}
\newcommand\;ricd{1,0}

% Reads dash pattern plotting dashes and spaces up to next symbol space.
\newcommand\;pdashes{\ifnum\;pns>\z@ \;td\z@ \;tcb\z@ \;ptfalse
    \@for\;ci:=\;ticd \do{\advance\;td\;ci\;tucd \;t\;scp \divide\;t\tw@
      \advance\;t\;td \divide\;t\;scp  \advance\;t-\;tcb \;dash
      \if;pt\;ptfalse\else\;pttrue\fi}%
  \let\n;xt\;pdashes \else \let\n;xt\relax \fi \n;xt}

% Checks if dash or space occurs before or after curve, calculates fractions.
\newcommand\;dash{\ifnum\;t=\z@ \if;csym\ifnum\;rtc>\z@\if;pt\;point\fi\fi\fi
  \else \advance\;tcb\;t \advance\;pns-\;t
    \ifnum\;overhang<\z@ \advance\;overhang\;t
      \ifnum\;overhang<\z@ \;t\z@ \else \;t\;overhang \;overhang\;tcb \fi
    \else \;overhang\;tcb \fi
    \ifnum\;pns<\z@ \advance\;overhang\;pns \advance\;tcb\;pns
      \advance\;t\;pns \;pns\z@ \fi \advance\;rtc-\;t
    \ifnum\;rtc<\z@ \advance\;overhang\;rtc \advance\;t\;rtc\fi
    \ifnum\;t>\z@ \if;pt\;point\;points\else\let\n;xt\;space\;space\fi \fi\fi}
                                         
% Makes \;tplot then plots a single dash.
\newcommand\;points{\let\n;xt\;sdash \;sdash}
\newcommand\;sdash{\let\n;;t\;tplot \ifnum\;t<\;cnd \let\n;xt\relax
    \advance\;cnd-\;t \;tca\;t \;tplot
  \else \advance\;t-\;cnd \;tca\;cnd \;tplot 
    \advance\;dx\;ddx \advance\;dy\;ddy \;cnd\;mcnd 
  \fi \n;xt}

% A fast single macro for drawing straight lines.
\newcommand\;tplot{}
\newcommand\;po;nts{\noexpand\ifnum\;tca>\z@ 
  \advance\;y\;dy \kern\;dx \;po;nt \advance\;tca\m@ne
  \noexpand\else \let\noexpand\n;;t\relax \noexpand\fi \noexpand\n;;t}

% Plots a single space at high speed.
\newcommand\;space{\ifnum\;t<\;cnd \let\n;xt\relax
    \advance\;cnd-\;t \advance\;y\;t\;dy \kern\;t\;dx
  \else \advance\;t-\;cnd \advance\;y\;cnd\;dy \kern\;cnd\;dx 
    \advance\;dx\;ddx \advance\;dy\;ddy \;cnd\;mcnd 
  \fi \n;xt}

% Make `;' a punctuation mark again.
 \catcode`\;=12 

\endinput

MODIFICATION HISTORY
--------------------
1.0  26 June 1991
1.1  8 Jan 1992  large \diskpitchstretch and maximum integer=2^30 - 1.
1.11 6 April 1993 Correct \@setdisk defined for SLiTeX.
1.12 20 April 1993 Scaling improved in \t@gcrv to allow large \curves.
1.13 23 April 1993 Calculation of differences corrected in \@bezier.
1.14 29 April 1993 Alignment of spaces improved in \@nscdashes, \overhang
     normalized.
1.15 1 May 1993 Rounding  errors in \nscdashes and \pdashes improved.
1.16 8 May 1993 Increased speed and dots corrected.
1.2  23 May 1993 Variable curve symbol introduced.
1.21 8 June 1993 \unitlength corrected in \bigcircle.
1.22 15 June 1993 \csb@x saves curve symbol, pattern selection rounded.
1.23 18 June 1993 test for bad point order tightened. 1st network release.
      2421 words of TeX main memory.
1.30 9 July 1993 2nd network release.
     Bugs Fixed:
       Blank curve if \csdiameter too large;
       Thicknesses of thin curves set correct for 300dpi fonts;
       Made compatible with NFSS of Mittelbach and Sch\"opf;
       Transfer of \@y and \@overhang from inner loop of \@drwarc;
       Missing \pt@false in \@ncsdashes and \@pdashes;
       Check for zero \@np in \@bezier.
     Improvements (?):
       New internal macros to save tokens;
       Uses LaTeX error messages and warnings;
       Checks \curvedashes signs;
       Potential conflicts with other macros reduced with new \@y, \@tc;
       Warns more readily and replaces possible inflexions with straight line;
       Some internal variable names rationalized.
     2410 words of TeX main memory with NFSS, 2400 with OFSS.
1.31 10 July 1993 \shape changed to \fontshape etc. for NFSS.
1.32 14 June 1994 3rd network release tested with LaTeX 2e of February 1994.
1.33 28 June 1994 4th network release tested with LaTeX 2e of 1 June 1994.
      Redefines \bezier  from June LaTeX 2e.
      \@bezier renamed to \@Vbezier to avoid conflict with June LaTeX 2e.
1.40 20 August 1995 .
     Bug Fixed: All curves use straight segments to reduce rounding error.
     Improvements:
       \curvewarnfalse stops warning of straight line use between points;
       ; catcoded to character to protect internal names;
       New internal macros save tokens and increase speed;
     1799 nett extra words of TeX main memory (LaTeX 2e 1995/6/1 pl1).
1.41 22 August 1995 5th network release tested with LaTeX 2e of 1 June 1995
     \edef\;tplot moved to speed dash plotting.
 
CURVES SUMMARY
--------------
The commands following are for the picture environment in the LaTeX manual.

Arguments of Commands:
<blank length> decimal number of <unit len> blank. Not negative.
<character or symbol> is anything which a \put or \multiput may plot.
<coordinates> are decimal numbers giving alternate x and y coordinates of
  the curve as multiples of \unitlength, comma separated.
<[,dash...]> optional continuation of alternating dash and blank numbers
  of unit lengths, comma separated.  Not negative. Decimals allowed.
<diameter> is a decimal number giving the diameter in \unitlengths.
<symbol count> is the number of symbols or patterns to be plotted, default 0.
<unit len> unit length dimension e.g., 2.5mm, 10pt, used in measuring
  blanks and dashes. Not negative. Default value is \unitlength.

Lengths used by Commands:
\csdiameter is the size of the space left for a symbol and can be
  increased or set with \settowidth{\csdiameter}{<character or symbol>}.
\curvelength is the total length of the curve calculated before drawing
  by using Simpson's rule once between each pair of coordinate points.
\overhang length of as drawn dash pattern overlapping start of dashes.

Control Commands:
\curvewarntrue warns every time a straight line is used between points 
  to avoid possible worse errors (default). 
\curvewarnfalse use the straight line without warning.
 
Parameter Setting Commands:
\curvesymbol{<character or symbol>} sets symbol and \csdiameter.
\curvedashes[<unit len>]{<blank length><[,dash...]>} Drawing commands before a
  \curvedashes or after one with an empty or zero length pattern will draw:
  if <symbol count> is zero or missing, a continuous curve;
  else if <symbol count> is positive, <symbol count>-1 squares of line
    thickness size between and additional squares at coordinates or bezier
    end points;
  else if no <character or symbol> exists, nothing;
  else, -<symbol count>-1 characters or symbols between coordinates and
    additional ones at coordinates or bezier end points.
After a \curvedashes command defining a pattern whose length exceeds
  zero, commands draw:
  if <symbol count> is zero or missing then at a spacing equal to the
    specified pattern length,
    if no <character or symbol> exists, a dash pattern reduced in length
      by \csdiameter to fit between symbol spaces of \csdiameter,
    else if \overhang is not 0pt, a <character or symbol> at all positions,
    else a <character or symbol> with the first position blank;
  else, \csdiameter wide symbol spaces, one at and |<symbol count>|-1 between
    coordinate points with dash pattern lengths,
    if no <character or symbol> exists, exact but broken by the spaces,
    else, adjusted to give a whole number of patterns between spaces.
\diskpitchstretch is initially 1 but \renewcommand can change it to a higher
  value like 5 to save memory in drafts of complex documents or a lower local
  value like 0.5 to smooth curve digitization.
\linethickness{<len>} sets line or dash thicknesses to <len> from 0.5pt up to
  15pt (0.17mm to 5mm). \thicklines and \thinlines also set the thickness.
\xscale, \xscaley, \yscale and \yscalex are scale factors initially set to
  1, 0, 1 and 0 respectively which \renewcommand or \def can reset.

Curve Drawing Commands:
Curves drawn consist of parabolic arcs between coordinate points with
tangents at each point parallel to the straight line through adjacent points.
\arc[<symbol count>](X1,Y1){<angle>} draws a circular arc centred on current
  position, starting from (X1,Y1) and proceeding counterclockwise for
  <angle> degrees.
\bezier{<symbol count>}(X1,Y1)(X2,Y2)(X3,Y3) draws a curve through the points
  (X1,Y1) and (X3,Y3) tangent to the straight lines joining them to (X2,Y2).
  Faster and more powerful replacement for bezier.sty version.
\bigcircle[<symbol count>]{<diameter>} draws a circle of diameter equal to
  <diameter> times \unitlength.
\closecurve[<symbol count>](<coordinates>) draws a closed curve with continuous
  tangents at all points. At least 6 coordinates required.
\curve[<symbol count>](<coordinates>) draws a curve through the specified
  <coordinates>. For 4 coordinates this is a straight line.
\scaleput(X1,Y1){<picture object>} places a picture object in a position
  scaled by \xscale, \xscaley, \yscale and \yscalex for axonometric projection
  or rotations.
\tagcurve[<symbol count>](<coordinates>) draws a curve without its first and
  last segments but if only 6 coordinates draws the last segment only.