\typeout{%
Enhancements to Picture Environment. Version 1.2 - Released June 1, 1986}
%----------------------------------------------------------------------
% Copyright (C) podar@sbcs (Sunil Podar) July 14,1986.
% You may use this file in whatever way you wish. You are requested to 
% leave this notice intact, and report any bugs, enhancements, comments,
% suggestions, etc. to:
% USmail: Sunil Podar,Dept. of Computer Science,SUNY at Stony Brook,NY 11794.
%  CSNET: podar@sbcs.csnet
%   ARPA: podar%suny-sb.csnet@csnet-relay.arpa
%   UUCP: {allegra, hocsd, philabs, ogcvax}!sbcs!podar
%----------------------------------------------------------------------
% This file contains implementation of:
% \multiputlist	\matrixput	\grid		\picsquare
% \dottedline	\dashline	\drawline	\jput
% \putfile
% Environments: dottedjoin, dashjoin and drawjoin
%
% For documentation, see the accompanying manual.
%----------------------------------------------------------------------
% usage: \multiputlist(x,y)(delta-x,delta-y)[tbrl]{item1,item2,item3,.....}
% \lop and \lopoff taken from TeXbook.
%----------------------------------------------------------------------
\def\lop#1\to#2{\expandafter\lopoff#1\lopoff#1#2}
\long\def\lopoff,#1,#2\lopoff#3#4{\def#4{#1}\def#3{,#2}}
\def\@@mlistempty{,}
\newif\iflistnonempty
\def\multiputlist(#1,#2)(#3,#4){\@ifnextchar
[{\@imultiputlist(#1,#2)(#3,#4)}{\@imultiputlist(#1,#2)(#3,#4)[]}}

\long\def\@imultiputlist(#1,#2)(#3,#4)[#5]#6{{%
\@xdim=#1\unitlength \@ydim=#2\unitlength
\listnonemptytrue \def\@@mlist{,#6,} % need this for end condition
\loop
\lop\@@mlist\to\@@firstoflist
\@killglue\raise\@ydim\hbox to\z@{\hskip
\@xdim\@imakepicbox(0,0)[#5]{\@@firstoflist}\hss}
\advance\@xdim #3\unitlength\advance\@ydim #4\unitlength
\ifx\@@mlist\@@mlistempty \listnonemptyfalse\fi
\iflistnonempty
\repeat\relax
\ignorespaces}}
%----------------------------------------------------------------------
% two-dimensional version of \multiput
% \matrixput(0,0)(20,0){5}(0,20){3}{\circle{2}}
%----------------------------------------------------------------------
\newcount\@@multicnt
\def\matrixput(#1,#2)(#3,#4)#5(#6,#7)#8#9{%
\ifnum#5>#8\@matrixput(#1,#2)(#3,#4){#5}(#6,#7){#8}{#9}%
\else\@matrixput(#1,#2)(#6,#7){#8}(#3,#4){#5}{#9}\fi}

%% here #5 >= #8
\long\def\@matrixput(#1,#2)(#3,#4)#5(#6,#7)#8#9{{\@killglue%
\@multicnt=#5\relax\@@multicnt=#8\relax%
\@xdim=0pt%
\@ydim=0pt%
\setbox\@tempboxa\hbox{\@whilenum \@multicnt > 0\do {%
%%\typeout{\the\@multicnt, \the\@@multicnt}%
\raise\@ydim\hbox to \z@{\hskip\@xdim #9\hss}%
\advance\@multicnt \m@ne%
\advance\@xdim #3\unitlength\advance\@ydim #4\unitlength}}%
\@xdim=#1\unitlength%
\@ydim=#2\unitlength%
\@whilenum \@@multicnt > 0\do {%
\raise\@ydim\hbox to \z@{\hskip\@xdim \copy\@tempboxa\hss}%
\advance\@@multicnt \m@ne%
\advance\@xdim #6\unitlength\advance\@ydim #7\unitlength}%
\ignorespaces}}
%----------------------------------------------------------------------
%\grid(wd,ht)(delta-wd,delta-ht)[initial-X-integer,initial-Y-integer]
% example: 1. \put(0,0){\grid(95,100)(9.5,10)}
%          2. \put(0,0){\grid(100,100)(10,5)[-10,0]}
%          or \put(0,0){\tiny \grid(100,100)(5,5)[0,0]}%numbers in \tiny font
%----------------------------------------------------------------------
\newcount\d@lta
\newdimen\@delta
\newdimen\@@delta
\newcount\@gridcnt
\def\grid(#1,#2)(#3,#4){\@ifnextchar [{\@igrid(#1,#2)(#3,#4)}%
{\@igrid(#1,#2)(#3,#4)[@,@]}}

\long\def\@igrid(#1,#2)(#3,#4)[#5,#6]{%
\makebox(#1,#2){%
\@delta=#1pt\@@delta=#3pt\divide\@delta \@@delta\d@lta=\@delta%
\advance\d@lta \@ne\relax\message{grid=\the\d@lta\space x}%
%% copied the definition of \line(0,1){#2} for some efficiency!.
\multiput(0,0)(#3,0){\d@lta}{\hbox to\z@{\hskip -\@halfwidth \vrule
	 \@width \@wholewidth \@height #2\unitlength \@depth \z@\hss}}%
\ifx#5@\relax\else%
\global\@gridcnt=#5%
\multiput(0,0)(#3,0){\d@lta}{%
\makebox(0,-2)[t]{\number\@gridcnt\global\advance\@gridcnt by #3}}%
\global\@gridcnt=#5%
\multiput(0,#2)(#3,0){\d@lta}{\makebox(0,0)[b]{\number\@gridcnt\vspace{2mm}%
\global\advance\@gridcnt by #3}}%
\fi%
\@delta=#2pt\@@delta=#4pt\divide\@delta \@@delta\d@lta=\@delta%
\advance\d@lta \@ne\relax\message{\the\d@lta . }%
%% copied the definition of \line(1,0){#1} for some efficiency!.
\multiput(0,0)(0,#4){\d@lta}{\vrule \@height \@halfwidth \@depth \@halfwidth
	 \@width #1\unitlength}%
\ifx#6@\relax\else
\global\@gridcnt=#6%
\multiput(0,0)(0,#4){\d@lta}{%
\makebox(0,0)[r]{\number\@gridcnt\ \global\advance\@gridcnt by #4}}%
\global\@gridcnt=#6%
\multiput(#1,0)(0,#4){\d@lta}{%
\makebox(0,0)[l]{\ \number\@gridcnt\global\advance\@gridcnt by #4}}%
\fi}}
%----------------------------------------------------------------------
% \picsquare is a centered square of dimensions governed by \thinlines,
% \thicklines or \linethickness declarations.
\def\picsquare{\hskip -0.5\@wholewidth%
\vrule height \@halfwidth depth \@halfwidth width \@wholewidth}
%
% just a square dot with reference point at bottom-left
\def\picsquare@bl{\vrule height \@wholewidth depth \z@  width \@wholewidth}
%----------------------------------------------------------------------
% \begin{dottedjoin}{interdot-gap in units}
% .....			
% \end{dottedjoin}
% \begin{dashjoin}{dash-length in units}{interdotgap in each dash}
% .....			
% \end{dashjoin}
% \begin{drawjoin}
% .....
% \end{drawjoin}
% \jput(x,y){character}
% \dottedline[opt. dotcharacter]{dotgap in units}(x1,y1)(x2,y2)...(xN,yN)
% \dashline[#]{dash-length}[opt. dotgap](x1,y1)(x2,y2)...(xN,yN)
% \drawline[#](x1,y1)(x2,y2)...(xN,yN)
%----------------------------------------------------------------------
% definitions for *join environment. had to do all this mess because of
% optional arguments.
%----------------------------------------------------------------------
\newif\if@jointhem \global\@jointhemfalse
\newif\if@firstpoint \global\@firstpointtrue
\newcount\@joinkind
%\newenvironment{dottedjoin}[1]%[opt char]{dotgap}
%{\global\@jointhemtrue \gdef\dotgap@join{#1}\global\@joinkind=0\relax}%
%{\global\@jointhemfalse \global\@firstpointtrue}
%----------------------------------------------------------------------
\def\dottedjoin{\global\@jointhemtrue \global\@joinkind=0\relax
  \bgroup\@ifnextchar[{\@idottedjoin}{\@idottedjoin[\picsquare@bl]}}
\def\@idottedjoin[#1]#2{\gdef\dotchar@join{#1}\gdef\dotgap@join{#2}}
\def\enddottedjoin{\global\@jointhemfalse \global\@firstpointtrue\egroup}
%----------------------------------------------------------------------
\def\dashjoin{\global\@jointhemtrue \global\@joinkind=1\relax
  \bgroup\@ifnextchar[{\@idashjoin}{\@idashjoin[\dashlinestretch]}}
\def\@idashjoin[#1]#2{\edef\dashlinestretch{#1}\gdef\dashlen@join{#2}%
\@ifnextchar[{\@iidashjoin}{\gdef\dotgap@join{}}}
\def\@iidashjoin[#1]{\gdef\dotgap@join{#1}}
\let\enddashjoin\enddottedjoin
%----------------------------------------------------------------------
\def\drawjoin{\global\@jointhemtrue \global\@joinkind=2\relax
  \bgroup\@ifnextchar[{\@idrawjoin}{}}
\def\@idrawjoin[#1]{\def\drawlinestretch{#1}}
\let\enddrawjoin\enddottedjoin
%----------------------------------------------------------------------
%% this is equiv to \put(x,y){#1} when not in {dot*join} environment.
\long\def\jput(#1,#2)#3{{\@killglue\raise#2\unitlength\hbox to \z@{\hskip
#1\unitlength #3\hss}\ignorespaces}
\if@jointhem
 \if@firstpoint \gdef\x@one{#1} \gdef\y@one{#2} \global\@firstpointfalse
 \else\ifcase\@joinkind
	\@dottedline[\dotchar@join]{\dotgap@join\unitlength}%
(\x@one\unitlength,\y@one\unitlength)(#1\unitlength,#2\unitlength)
	\or\@dashline[\dashlinestretch]{\dashlen@join}[\dotgap@join]%
(\x@one,\y@one)(#1,#2)
	\else\@drawline[\drawlinestretch](\x@one,\y@one)(#1,#2)\fi
    \gdef\x@one{#1} \gdef\y@one{#2}
 \fi
\fi}
%----------------------------------------------------------------------
\newdimen\@dotgap
\newdimen\@ddotgap
\newcount\@x@diff
\newcount\@y@diff
\newdimen\x@diff
\newdimen\y@diff
\newbox\@dotbox
\newcount\num@segments
\newcount\num@segmentsi
\newif\ifsqrt@done
%% from sqrtandstuff func basically need \num@segments.
%% given a deltax, deltay and dotgap, it calculates \num@segments = number of
%% segments along the hypotenuse. used by \dottedline & \dashline.
%% It finishes quickly if any of deltax or deltay are zero or close to zero.
\def\sqrtandstuff#1#2#3{
\ifdim #1 <0pt \@x@diff= -#1 \else\@x@diff=#1\fi
\ifdim #2 <0pt \@y@diff= -#2 \else\@y@diff=#2\fi
%% @diff's will be positive and diff's will retain their sign.
\@dotgap=#3 \divide\@dotgap \tw@
\advance\@x@diff \@dotgap \advance\@y@diff \@dotgap% for round-off errors
\@dotgap=#3
\divide\@x@diff \@dotgap \divide\@y@diff \@dotgap
\sqrt@donefalse
\ifnum\@x@diff < 2
   \ifnum\@y@diff < 2 \num@segments=\@x@diff \advance\num@segments \@y@diff
		      \sqrt@donetrue
        \else\num@segments=\@y@diff \sqrt@donetrue\fi
   \else\ifnum\@y@diff < 2 \num@segments=\@x@diff \sqrt@donetrue\fi
\fi
\ifsqrt@done \ifnum\num@segments=\z@ \num@segments=\@ne\fi\relax
 \else \ifnum\@y@diff >\@x@diff
		 \@tempcnta=\@x@diff \@x@diff=\@y@diff \@y@diff=\@tempcnta
       \fi    		%exchange @x@diff & @y@diff, so now @x@diff > @y@diff
  \num@segments=\@y@diff
  \multiply\num@segments \num@segments
  \multiply\num@segments by 457
  \divide\num@segments \@x@diff
  \advance\num@segments by 750 % for round-off, going to divide by 1000.
  \divide\num@segments \@m
  \advance\num@segments \@x@diff
		%num@segments = @x@diff + (0.457*sqr(@y@diff)/@x@diff)
\fi}
%----------------------------------------------------------------------
% \dottedline[opt. char]{interdot gap in units}(x1,y1)(x2,y2)....(xN,yN)
%----------------------------------------------------------------------
%% Used the following construction earlier but that results in box memory
%% full much too soon although it works perfectly.
%% \setbox\@dotbox\vbox to\z@{\vss \hbox to\z@{\hss #1\hss}\vss}\relax}
%% The cenetering of characters is achieved by substracting half the ht, wd
%% of character from the (x,y) coordinates where they are to be put. We
%% chose to use a macro for the ``dot'' instead of \copy\box to save memory
%% at the expense of extra cpu, since memory becomes an issue very soon.
%% \picsquare is already centered, whereas other characters, except \circle,
%% will not be cenetered, hence to handle them all in a similar fashion,
%% used \picsquare@bl.
%
% kind of tail recursion.
\def\dottedline{\@ifnextchar [{\@idottedline}{\@idottedline[\picsquare@bl]}}
\def\@idottedline[#1]#2(#3,#4){\@ifnextchar (%
{\@iidottedline[#1]{#2}(#3,#4)}{\relax}}
\def\@iidottedline[#1]#2(#3,#4)(#5,#6){\@dottedline[#1]{#2\unitlength}%
(#3\unitlength,#4\unitlength)(#5\unitlength,#6\unitlength)%
\@idottedline[#1]{#2}(#5,#6)}
%
%% user not supposed to use this directly. arguments in absolute dimensions.
%% need to pass absolute dimens here because dashline calls dottedline and
%% can supply only absolute dimensions.
\long\def\@dottedline[#1]#2(#3,#4)(#5,#6){{%
\x@diff=#5\relax\advance\x@diff by -#3\relax
\y@diff=#6\relax\advance\y@diff by -#4\relax
\sqrtandstuff{\x@diff}{\y@diff}{#2}
\divide\x@diff \num@segments
\divide\y@diff \num@segments
\advance\num@segments \@ne     % to put the last point at destination.
%%\typeout{num@segments= \the\num@segments}
\setbox\@dotbox\hbox{#1}% just to get the dimensions of the character.
\@xdim=#3 \@ydim=#4
\ifdim\ht\@dotbox >\z@% otherwise its a circle.
  \advance\@xdim -0.5\wd\@dotbox
  \advance\@ydim -0.5\ht\@dotbox
  \advance\@ydim .5\dp\@dotbox\fi
%%circle's have a ht=0, this is one way I could think of to catch circles.
%%following loop is equiv to
%%\multiput(\@xdim,\@ydim)(\x@diff,\y@diff){\num@segments}{#1}
%%with arguments in absolute dimensions.
\@killglue
\loop \ifnum\num@segments > 0
\unskip\raise\@ydim\hbox to\z@{\hskip\@xdim #1\hss}%
\advance\num@segments \m@ne\advance\@xdim\x@diff\advance\@ydim\y@diff%
\repeat
\ignorespaces}}
%----------------------------------------------------------------------
% \dashline[#]{dash-length}[optional dotgap](x1,y1)(x2,y2)...(xN,yN)
% The minimum # of dashes put is 2, one at either end point; dash-length is
% reduced accordingly if necessary. Also have to some dirty work to account
% for stretch & shrink.
% \renewcommand{\dashlinestretch}{-50}  %ONLY INTEGERS PERMITTED.
%----------------------------------------------------------------------
\def\dashlinestretch{0} %well, could have used a counter.
\def\dashline{\@ifnextchar [{\@idashline}{\@idashline[\dashlinestretch]}}
\def\@idashline[#1]#2{\@ifnextchar [{\@iidashline[#1]{#2}}%
{\@iidashline[#1]{#2}[\@empty]}} %\@empty needed-- later checked with \ifx 
\def\@iidashline[#1]#2[#3](#4,#5){\@ifnextchar (%
{\@iiidashline[#1]{#2}[#3](#4,#5)}{\relax}}
%
\def\@iiidashline[#1]#2[#3](#4,#5)(#6,#7){%
\@dashline[#1]{#2}[#3](#4,#5)(#6,#7)%
\@iidashline[#1]{#2}[#3](#6,#7)}
%
\long\def\@dashline[#1]#2[#3](#4,#5)(#6,#7){{%
\x@diff=#6\unitlength \advance\x@diff by -#4\unitlength
\y@diff=#7\unitlength \advance\y@diff by -#5\unitlength
%% correction to get actual width since the dash-length as taken in arguement
%% is the center-to-center of the end-points.
\@tempdima=#2\unitlength \advance\@tempdima -\@wholewidth
\sqrtandstuff{\x@diff}{\y@diff}{\@tempdima}
\ifnum\num@segments <3 \num@segments=3\fi% min number of dashes I can plot
% is 2, 1 at either end, thus min num@segments is 3 (including 'empty dash').
\@tempdima=\x@diff \@tempdimb=\y@diff
\divide\@tempdimb by\num@segments
\divide\@tempdima by\num@segments
%% ugly if-then-else. If optional dotgap specified, then use it otherwise
%% make a solid looking dash.
{\ifx#3\@empty \relax
    \ifdim\@tempdima < 0pt \x@diff=-\@tempdima\else\x@diff=\@tempdima\fi
    \ifdim\@tempdimb < 0pt \y@diff=-\@tempdimb\else\y@diff=\@tempdimb\fi
    \ifdim\x@diff < 0.3pt %it's a vertical dashline
           \ifdim\@tempdimb > 0pt
	        \global\setbox\@dotbox\hbox{\hskip -\@halfwidth \vrule
		 \@width \@wholewidth \@height \@tempdimb}
	   \else\global\setbox\@dotbox\hbox{\hskip -\@halfwidth \vrule
		 \@width \@wholewidth \@height\z@ \@depth -\@tempdimb}\fi
       \else\ifdim\y@diff < 0.3pt %it's a horizontal dashline
               \ifdim\@tempdima >0pt
		  \global\setbox\@dotbox\hbox{\vrule \@height \@halfwidth
		 		\@depth \@halfwidth \@width \@tempdima}
		\else\global\setbox\@dotbox\hbox{\hskip \@tempdima
			 \vrule \@height \@halfwidth \@depth \@halfwidth
				 \@width -\@tempdima \hskip \@tempdima}\fi
	    \else\global\setbox\@dotbox\hbox{%
\@dottedline[\picsquare]{0.98\@wholewidth}(0pt,0pt)(\@tempdima,\@tempdimb)}
\fi\fi
\else\global\setbox\@dotbox\hbox{%
\@dottedline[\picsquare]{#3\unitlength}(0pt,0pt)(\@tempdima,\@tempdimb)}
\fi}
\advance\x@diff by -\@tempdima % both have same sign
\advance\y@diff by -\@tempdimb
%
%%here we correct the number of dashes to be put by reducing them
%%appropriately. (num@segments*\@wholewidth) is in some way the slack we
%%have,and division by dash-length gives the reduction. reduction =
%%(2*num@segments*\@wholewidth)/dash-length
%% (num@segments includes empty ones)
\@tempdima=\num@segments\@wholewidth \@tempdima=2\@tempdima 
\@tempcnta=\@tempdima \@tempdima=#2\unitlength \@tempdimb=0.5\@tempdima
\@tempcntb=\@tempdimb \advance\@tempcnta by \@tempcntb % round-off error
\divide\@tempcnta by\@tempdima \advance\num@segments by -\@tempcnta
%
\ifnum #1=0 \relax\else\ifnum #1 < -100
  \typeout{***dashline: reduction > -100 percent implies blankness!***}
\else\num@segmentsi=#1 \advance\num@segmentsi by 100
     \multiply\num@segments by\num@segmentsi \divide\num@segments by 100
\fi\fi
%
\divide\num@segments by 2 % earlier num@segments included 'empty dashes' too.
\ifnum\num@segments >0 % if =0 then don't divide => \x@diff & \y@diff
 \divide\x@diff by\num@segments%   remain same.
 \divide\y@diff by\num@segments
 \advance\num@segments by\@ne %for the last segment for which I subtracted
	 		     %\@tempdima & \@tempdimb from \x@diff & \y@diff
 \else\num@segments=2 % one at each end.
\fi
%%\typeout{num@segments finally = \the\num@segments}
%% equiv to \multiput(#4,#5)(\x@diff,\y@diff){\num@segments}{\copy\@dotbox}
%% with arguements in absolute dimensions.
\@xdim=#4\unitlength \@ydim=#5\unitlength
\@killglue
\loop \ifnum\num@segments > 0
\unskip\raise\@ydim\hbox to\z@{\hskip\@xdim \copy\@dotbox\hss}%
\advance\num@segments \m@ne\advance\@xdim\x@diff\advance\@ydim\y@diff%
\repeat
\ignorespaces}}
%----------------------------------------------------------------------
%%1.00   .833333  .80  .75  .66666   .60  .50  .40  .33333    .25 .20  .16666
%% .916666 .816666 .775 .708333 .633333 .55 .45 .366666 .291666 .225 .183333
%% 0.0
%%0.083333
%% the first line has absolute slopes corresponding to various permissible
%% integer combinations representing slopes. The second line is the midpoint
%% of all those slopes (attempted to show them in the middle of two entries).
%%
%% \lineslope(x@diff dimen, y@diff dimen)
%% Given base (x@diff) and height (y@diff) in dimensions, determines the
%% closest available slope and returns the two required integers in \@xarg
%% and \@yarg. The given base and height can be ANYTHING, -ve or +ve, or
%% even 0pt. \lineslope knows about (0,1) and (1,0) slopes too and returns
%% correct values if the conditions regarding x@diff & y@diff are obeyed
%% (see NOTE). Used by \drawline. This is the simplest and only way I could
%% figure out to accomplish it!.
%% NOTE: both the dimensions (x@diff & y@diff) must be in SAME units and the
%% larger of the two dimensions must be atleast 1pt (i.e. 65536sp). To avoid
%% dividing by 0, I make the larger dimension = 1pt if it is < 1pt.
%% will need a similar one for vectors, or maybe this can be used. For
%% vectors the range is -4, 4 unlike lines where it is -6, 6.
\newif\if@flippedargs
\def\lineslope(#1,#2){%
\ifdim #1 <0pt \@xdim= -#1 \else\@xdim=#1\fi
\ifdim #2 <0pt \@ydim= -#2 \else\@ydim=#2\fi
%%\typeout{xdim,ydim= \the\@xdim, \the\@ydim}
\ifdim\@xdim >\@ydim \@tempdima=\@xdim \@xdim=\@ydim \@ydim=\@tempdima
\@flippedargstrue\else\@flippedargsfalse\fi% x < y
\ifdim\@ydim >1pt \@tempcnta=\@ydim
            \divide\@tempcnta by 65536% now \@tempcnta=integral part of #1.
            \divide\@xdim \@tempcnta\fi
\ifdim\@xdim <.083333pt \@xarg=1 \@yarg=0
 \else\ifdim\@xdim <.183333pt	\@xarg=6 \@yarg=1
 \else\ifdim\@xdim <.225pt 	\@xarg=5 \@yarg=1
 \else\ifdim\@xdim <.291666pt 	\@xarg=4 \@yarg=1
 \else\ifdim\@xdim <.366666pt 	\@xarg=3 \@yarg=1
 \else\ifdim\@xdim <.45pt 	\@xarg=5 \@yarg=2
 \else\ifdim\@xdim <.55pt 	\@xarg=2 \@yarg=1
 \else\ifdim\@xdim <.633333pt 	\@xarg=5 \@yarg=3
 \else\ifdim\@xdim <.708333pt 	\@xarg=3 \@yarg=2
 \else\ifdim\@xdim <.775pt 	\@xarg=4 \@yarg=3
 \else\ifdim\@xdim <.816666pt 	\@xarg=5 \@yarg=4
 \else\ifdim\@xdim <.916666pt 	\@xarg=6 \@yarg=5
       \else			\@xarg=1 \@yarg=1%
\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi
\if@flippedargs\relax\else\@tempcnta=\@xarg \@xarg=\@yarg
			  \@yarg=\@tempcnta\fi
\ifdim #1 <0pt \@xarg= -\@xarg\fi
\ifdim #2 <0pt \@yarg= -\@yarg\fi
%%\typeout{closest slope integers = \the\@xarg, \the\@yarg}
}
%----------------------------------------------------------------------
% usage: \drawline[#](x1,y1)(x2,y2)....(xN,yN)
%       		 % # is an optional integer between -100 & infinity.
% \renewcommand{\drawlinestretch}{-50}  %ONLY INTEGERS PERMITTED.
%----------------------------------------------------------------------
\newif\if@toosmall
\newif\if@drawit
\newif\if@horvline
\def\drawlinestretch{0} %well, could have used a counter.
% kind of tail recursion.
\def\drawline{\@ifnextchar [{\@idrawline}{\@idrawline[\drawlinestretch]}}
\def\@idrawline[#1](#2,#3){\@ifnextchar ({\@iidrawline[#1](#2,#3)}{\relax}}
\def\@iidrawline[#1](#2,#3)(#4,#5){\@drawline[#1](#2,#3)(#4,#5)
\@idrawline[#1](#4,#5)}
%
\def\@drawline[#1](#2,#3)(#4,#5){{%
\x@diff=#4\unitlength \advance\x@diff by -#2\unitlength
\y@diff=#5\unitlength \advance\y@diff by -#3\unitlength
%% override any linethickness declarations, and since horiz & vertical lines
%% come out thinner than the slanted ones, assign slightly larger values.
%% default values are: thinlines=0.4pt, thicklines=0.8pt
\ifx\@linefnt\tenln \linethickness{0.5pt} \else \linethickness{0.9pt}\fi
\lineslope(\x@diff,\y@diff)% returns the two integers in \@xarg & \@yarg.
%------
\@toosmalltrue
{\ifdim\x@diff <\z@ \x@diff=-\x@diff\fi
 \ifdim\y@diff <\z@ \y@diff=-\y@diff\fi
 \ifdim\x@diff >10pt \global\@toosmallfalse\fi
 \ifdim\y@diff >10pt \global\@toosmallfalse\fi}
%------
%% For efficiency, if the line is horiz or vertical then we draw it in one
%% shot, only if the stretch is not -ve and the line is not too small.
\@drawitfalse\@horvlinefalse
\ifnum#1 <0 \relax\else\@horvlinetrue\fi
\if@toosmall\@horvlinetrue\fi% to get 'or' condition. We necessarily draw a 
% solid line if the line is too small ignoring any -ve stretch.
\if@horvline
 \ifdim\x@diff =0pt \put(#2,#3){\ifdim\y@diff >0pt \@linelen=\y@diff \@upline
 				\else\@linelen=-\y@diff \@downline\fi}%
 \else\ifdim\y@diff =0pt
          \ifdim\x@diff >0pt \put(#2,#3){\vrule \@height \@halfwidth \@depth
				\@halfwidth \@width \x@diff}
		\else \put(#4,#5){\vrule \@height \@halfwidth \@depth
				\@halfwidth \@width -\x@diff}\fi
       \else\@drawittrue\fi\fi % construct the line explicitly
\else\@drawittrue\fi
%-------------------------------
\if@drawit
\ifnum\@xarg< 0 \@negargtrue\else\@negargfalse\fi
\ifnum\@xarg =0 \setbox\@linechar%
\hbox{\hskip -\@halfwidth \vrule \@width \@wholewidth \@height 10.2pt
 \@depth \z@}
\else \ifnum\@yarg =0 \setbox\@linechar%
\hbox{\vrule \@height \@halfwidth \@depth \@halfwidth \@width 10.2pt}
\else \if@negarg \@xarg -\@xarg \@yyarg -\@yarg
        \else \@yyarg \@yarg\fi
\ifnum\@yyarg >0 \@tempcnta\@yyarg \else \@tempcnta -\@yyarg\fi
\setbox\@linechar\hbox{\@linefnt\@getlinechar(\@xarg,\@yyarg)}%
\fi\fi
%------
\if@toosmall% => it isn't a horiz or vert line and is toosmall.
  \@dottedline[\picsquare]{.98\@wholewidth}%
(#2\unitlength,#3\unitlength)(#4\unitlength,#5\unitlength)%
\else
%% following is neat. The last segment takes \wd\@linechar & \ht\@linechar
%% so plot the line as though it were from (#2,#3) to
%% (#4-\wd\@linechar,#5-\ht\@linechar) (i.e. for positive slope; of course,
%% signs are reversed for other slopes). For horizontal & vertical dashes we
%% don't have to subtract the ht & wd resp. since they are already centered.
\ifnum\@xarg=0\relax\else\ifdim\x@diff >\z@ \advance\x@diff -\wd\@linechar
  \else\advance\x@diff \wd\@linechar\fi\fi
\ifnum\@yarg=0\relax\else\ifdim\y@diff >\z@\advance\y@diff -\ht\@linechar
  \else\advance\y@diff \ht\@linechar\fi\fi
\ifdim\x@diff <\z@ \@x@diff=-\x@diff \else\@x@diff=\x@diff\fi
\ifdim\y@diff <\z@ \@y@diff=-\y@diff \else\@y@diff=\y@diff\fi
%%\typeout{x@diff,y@diff=\the\x@diff , \the\y@diff}
\num@segments=0 \num@segmentsi=0
\ifdim\wd\@linechar >1pt
 \num@segmentsi=\@x@diff \divide\num@segmentsi \wd\@linechar\fi
\ifdim\ht\@linechar >1pt
 \num@segments=\@y@diff \divide\num@segments \ht\@linechar\fi
\ifnum\num@segmentsi >\num@segments \num@segments=\num@segmentsi\fi
\advance\num@segments \@ne %to account for round-off error
%
\ifnum #1=0 \relax \else\ifnum #1 < -99
  \typeout{***drawline: reduction <= -100 percent implies blankness!***}
\else\num@segmentsi=#1 \advance\num@segmentsi by 100
     \multiply\num@segments \num@segmentsi
     \divide\num@segments by 100
\fi\fi
%%\typeout{num@segments after = \the\num@segments}
%
\divide\x@diff \num@segments
\divide\y@diff \num@segments
\advance\num@segments \@ne %for the last segment for which I subtracted
			  %\wd & \ht of \@linechar from \@x@diff & \@y@diff.
%%\typeout{numseg,x@diff,y@diff= \the\num@segments, \the\x@diff, \the\y@diff}
%
\@xdim=#2\unitlength \@ydim=#3\unitlength
\if@negarg \advance\@xdim -\wd\@linechar\fi
\ifnum\@yarg <0 \advance\@ydim -\ht\@linechar\fi
%%following loop equiv to \multiput@abs(\@xdim,\@ydim)%
%%(\x@diff,\y@diff){\num@segments}{\copy\@linechar}
%%with arguements in absolute dimensions.
\@killglue
\loop \ifnum\num@segments > 0
\unskip\raise\@ydim\hbox to\z@{\hskip\@xdim \copy\@linechar\hss}%
\advance\num@segments \m@ne\advance\@xdim\x@diff\advance\@ydim\y@diff%
\repeat
\ignorespaces
\fi%the if of @toosmall
\fi}}% for \if@drawit
%----------------------------------------------------------------------
%usage: \putfile{datafile}{OBJECT}
% The OBJECT is plotted at EACH of the coordinates read from the datafile.
% The idea of these macros is to generate (x,y) pairs using some program
% and then directly use those coordinates. Since TeX doesn't have real
% floating point calculations, it is much more efficient and accurate to do
% things this way. One can also use the unix facility 'spline' now to
% generate smooth curves with equidistant ``dots''.
% NOTE: the external file of coordinates must have x y pairs with a space
% between them. Also it is suggested that some extension such as '.put'
% be used for such datafiles to distinguish them in which case it must
% be explicitely specified in the 1st argument so that TeX doesn't look
% for a .tex extension.
% The % char remains valid as a comment char and such lines are ignored;
% however, there should be atleast one space after the second entry if a
% comment is on the same line as data since % eats up the newline.
%-----------------------------------------------------------------------
\long\def\splittwoargs#1 #2 {(#1,#2)}
%
\newif\if@stillmore
\newread\@datafile
\long\def\putfile#1#2{\openin\@datafile = #1
\@stillmoretrue
\loop
\ifeof\@datafile\relax\else\read\@datafile to\@dataline\fi
%if file nonexistent, do nothing.
\ifeof\@datafile\@stillmorefalse
\else\ifx\@dataline\@empty \relax
     \else
\expandafter\expandafter\expandafter\put\expandafter\splittwoargs%
\@dataline{#2}
     \fi
\fi
\if@stillmore
\repeat
\closein\@datafile
}
%----------------------------------------------------------------------