\def\fileversion{v1.1}
\def\filedate{4 Dec 91}
\immediate\write16{Document style option `epsfig', \fileversion\space
<\filedate> (edited by SPQR)}
%%%--------------------------------------------------------------------
%%% psfig merged with EPSF =epsfig Release 1 
%%%
%%% code rearranged by Sebastian Rahtz from work by
%%% Trevor Darrell; Tom Rokicki; Daniel Smith; H. Payne, Robert Russell
%%%
%%% This is a version of Darrell's `psfig' macros which are designed  only
%%% to be used with Rokicki's dvips program and the `epsf' macros (these
%%% are automaticaly included by the style file). I did this because the
%%% \special commands used by `epsf' appear to be more robust and 
%%% portable than the raw \specials used by `psfig', but I preferred the
%%% psfig interface, and wanted to use some of its features which epsf
%%% did not offer (specifically, clipping to the BoundingBox). This system
%%% preserves the psfig interface, but mainly uses epsf macros to carry out
%%% the job. The user interface is identical to \psfig, but you just use  
%%% \epsfig instead. Clipping and rotation uses the original psfig macros, 
%%% as do specific settings of the Bounding Box in the call to the macro. 
%%% I could not work out how to do rotation or clipping with the epsf macros.
%%%
%%% The same applies to `rheight' and `rwidth'
%%%
%%% One behaviour which may confuse people is that setting width= and 
%%% height will *not* force a change in the aspect ratio. If you need
%%% this behaviour, use the \psfig macro instead of \epsfig. Rokicki's macros
%%% do not provide a way of doing the aspect ration stuff.
%%%  
%%% If you *really* want old psfig behaviour regardless, use \psfig. It is
%%% still there. Some of the features have gone, however. \figurepath
%%% seemed redundant, since it could be controlled by the TEXINPUTS
%%% variable anyway. 
%%%  
%%% As an added feature, if a file cannot be found, a file called `file'.bb
%%% is searched for. This should simply contain a %%BoundingBox line. It is
%%% assumed that if this exists, then `file'.Z exists, and is a Unix
%%% compressed file. The macros then read the BB from `file'.bb, but insert
%%% "zcat `file'.Z" in the  output for dvips to interpret (don't worry, it
%%% knows about this). Saves a lot  of space! Actually, its more
%%% complicated than that; the string passed to dvips for file `foo.ps' is
%%% actually "zcat `texfind foo.ps.Z`", where `texfind' is assumed to be  a
%%% shell script which searches the TEXINPUTS path for `foo.ps.Z'. Such a
%%% script comes with dvips. Just alias it to `cat' if you have problems.
%%% If you are *not* on a Unix system and use this, deliberately or by 
%%% mischance, you will have problems!
%%% 
%%% This file can be included in a dumped format, or used as a LaTeX
%%% style file, or used in plain TeX. It does not load itself twice (I hope!)
%%%
%%% Sebastian Rahtz December 1991 spqr@uk.ac.soton.ecs
%--------------------------------------------------------------------
%--------------------------------------------------------------------
%%% previous notes. this copy of psfig.tex inherited from version 1.7
%--------------------------------------------------------------------
%%% All psfig/tex software, documentation, and related files
%%% in this distribution of psfig/tex are 
%%% Copyright 1987, 1988, 1991 Trevor J. Darrell
%
%%% Permission is granted for use and non-profit distribution of psfig/tex 
%%% providing that this notice be clearly maintained. The right to
%%% distribute any portion of psfig/tex for profit or as part of any commercial
%%% product is specifically reserved for the author(s) of that portion.
%%%
%%% Thanks to Greg Hager (GDH) and Ned Batchelder for their contributions
%%% to this project.
%%%--------------------------------------------------------------------------
%%% GDH 7/26/87 -- changed so that it first looks in the local directory,
%%% then in a specified global directory for the ps file.
%%% SPQR 12/91 removed that last change. it follows TEXINPUTS anyway
%%% RPR 6/25/91 -- changed so that it defaults to user-supplied name if
%%% boundingbox info is specified, assuming graphic will be created by
%%% print time.
%%% SPQR 12/91 removed that last change. use LaTeX error message instead
%%% SPQR 12/91 -- `no file found' produces LaTeX error message.
%%%                If you recover from that the file name is set in draft
%%%                mode in place of the file.
%%%
%%% Modified by J. Daniel Smith on 9 October 1990 to accept the
%%% %%BoundingBox: comment with or without a space after the colon.  Stole
%%% file reading code from Tom Rokicki's EPSF.TEX file (see below).
%%% --- SPQR 12.91 removed most of this to use epsf directly
%%%
%%% More modifications by J. Daniel Smith on 29 March 1991 to allow the
%%% the included PostScript figure to be rotated.  The amount of
%%% rotation is specified by the "angle=" parameter of the \epsfig command.
%%%
%%% Modified by Robert Russell on June 25, 1991 to allow users to specify
%%% .ps filenames which don't yet exist, provided they explicitly provide
%%% boundingbox information via the \epsfig command. Note: This will only work
%%% if the "file=" parameter follows all four "bb???=" parameters in the
%%% command. This is due to the order in which psfig interprets these params.
%%% ---- SPQR 12.91 removed all this
%%%
%%% 3 Jul 1991	JDS	check if file already read in once
%%%
%%% Modified by H. Payne on 9 October 1991 to allow rotation through
%%% arbitrary angles, not just angles in the first quadrant.
%--------------------------------------------------------------------------
%%%
%%% from a suggestion by eijkhout@csrd.uiuc.edu to allow
%%% loading as a style file:
\edef\epsfigRestoreAt{\catcode`@=\number\catcode`@\relax}
\catcode`\@=11\relax
% copies of bits of LaTeX we need....
\ifx\@ifundefined\undefined
\long\def\@ifundefined#1#2#3{\expandafter\ifx\csname
  #1\endcsname\relax#2\else#3\fi}
\fi
%
\@ifundefined{typeout}
{\gdef\typeout#1{\immediate\write\sixt@@n{#1}}}
{\relax}
%
%%% check to see if macros already loaded in (maybe some other file says
%%% "\input epsfig") ...
\@ifundefined{epsfig}{}{\typeout{EPSFIG --- already loaded}\endinput}
%
% we try to put a box round space of missing figures. plain TeX
% doesn't have an easy command, so just ignore it
\@ifundefined{fbox}{\def\fbox#1{#1}}{}
%%%
%%% we need Rokicki's EPSF macros anyway, unless they are already loaded
%
\@ifundefined{epsfbox}{\input epsf}{}
%
%% SPQR 12.91 handling of errors using standard LaTeX error 
%% mechanism. In case we are plain TeX we first define the
%% error routines...
\ifx\undefined\@latexerr
	\newlinechar`\^^J
	\def\@spaces{\space\space\space\space}
	\def\@latexerr#1#2{%
	\edef\@tempc{#2}\expandafter\errhelp\expandafter{\@tempc}%
	\typeout{Error. \space see a manual for explanation.^^J
	 \space\@spaces\@spaces\@spaces Type \space H <return> \space for
	 immediate help.}\errmessage{#1}}
\fi
%------------------------
%% a couple of LaTeX error messages
\def\@whattodo{You tried to include a PostScript figure which 
cannot be found^^JIf you press return to carry on anyway,^^J
The failed name will be printed in place of the figure.^^J
or type X to quit}
\def\@whattodobb{You tried to include a PostScript figure which 
has no^^Jbounding box, and you supplied none.^^J
If you press return to carry on anyway,^^J
The failed name will be printed in place of the figure.^^J
or type X to quit}
%------------------------
%
%------------------------------------------------------------------------
%------------------------------------------------------------------------
%%% @psdo control structure -- similar to Latex @for.
%%% I redefined these with different names so that psfig can
%%% be used with TeX as well as LaTeX, and so that it will not 
%%% be vunerable to future changes in LaTeX's internal
%%% control structure,
%
\def\@nnil{\@nil}
\def\@empty{}
\def\@psdonoop#1\@@#2#3{}
\def\@psdo#1:=#2\do#3{\edef\@psdotmp{#2}\ifx\@psdotmp\@empty \else
    \expandafter\@psdoloop#2,\@nil,\@nil\@@#1{#3}\fi}
\def\@psdoloop#1,#2,#3\@@#4#5{\def#4{#1}\ifx #4\@nnil \else
       #5\def#4{#2}\ifx #4\@nnil \else#5\@ipsdoloop #3\@@#4{#5}\fi\fi}
\def\@ipsdoloop#1,#2\@@#3#4{\def#3{#1}\ifx #3\@nnil 
       \let\@nextwhile=\@psdonoop \else
      #4\relax\let\@nextwhile=\@ipsdoloop\fi\@nextwhile#2\@@#3{#4}}
\def\@tpsdo#1:=#2\do#3{\xdef\@psdotmp{#2}\ifx\@psdotmp\@empty \else
    \@tpsdoloop#2\@nil\@nil\@@#1{#3}\fi}
\def\@tpsdoloop#1#2\@@#3#4{\def#3{#1}\ifx #3\@nnil 
       \let\@nextwhile=\@psdonoop \else
      #4\relax\let\@nextwhile=\@tpsdoloop\fi\@nextwhile#2\@@#3{#4}}
%%% 
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% file reading stuff from epsf.tex
%%%   EPSF.TEX macro file:
%%%   Written by Tomas Rokicki of Radical Eye Software, 29 Mar 1989.
%%%   Revised by Don Knuth, 3 Jan 1990.
%%%   Revised by Tomas Rokicki to accept bounding boxes with no
%%%      space after the colon, 18 Jul 1990.
%%%   Portions modified/removed for use in PSFIG package by
%%%      J. Daniel Smith, 9 October 1990.
%%%   Just the bit which knows about (atend) as a BoundingBox
%
%%%    hacked back a bit by SPQR 12/91
%
\long\def\epsfaux#1#2:#3\\{\ifx#1\epsfpercent
   \def\testit{#2}\ifx\testit\epsfbblit
	\@atendfalse
        \epsf@atend #3 . \\%
	\if@atend	
	   \if@verbose
		\typeout{epsfig: found `(atend)'; continuing search}
	   \fi
        \else
		\epsfgrab #3 . . . \\%
        	\global\no@bbfalse
        \fi
   \fi\fi}%
%
%%% Determine if the stuff following the %%BoundingBox is `(atend)'
%%% J. Daniel Smith.  Copied from \epsf@grab above.
%
\def\epsf@atendlit{(atend)} 
%
\def\epsf@atend #1 #2 #3\\{%
   \def\epsf@tmp{#1}\ifx\epsf@tmp\empty
      \epsf@atend #2 #3 .\\\else
   \ifx\epsf@tmp\epsf@atendlit\@atendtrue\fi\fi}


%%% End of file reading stuff from epsf.tex
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% trigonometry stuff from "trig.tex"
\chardef\letter = 11
\chardef\other = 12

\newif\ifdebug %%% turn me on to see TeX hard at work ...
\newif\ifc@mpute %%% don't need to compute some values
\newif\if@atend
\c@mputetrue % but assume that we do

\let\then = \relax
\def\r@dian{pt }
\let\r@dians = \r@dian
\let\dimensionless@nit = \r@dian
\let\dimensionless@nits = \dimensionless@nit
\def\internal@nit{sp }
\let\internal@nits = \internal@nit
\newif\ifstillc@nverging
\def \Mess@ge #1{\ifdebug \then \message {#1} \fi}

{ %%% Things that need abnormal catcodes %%%
	\catcode `\@ = \letter
	\gdef \nodimen {\expandafter \n@dimen \the \dimen}
	\gdef \term #1 #2 #3%
	       {\edef \t@ {\the #1}%%% freeze parameter 1 (count, by value)
		\edef \t@@ {\expandafter \n@dimen \the #2\r@dian}%
				   %%% freeze parameter 2 (dimen, by value)
		\t@rm {\t@} {\t@@} {#3}%
	       }
	\gdef \t@rm #1 #2 #3%
	       {{%
		\count 0 = 0
		\dimen 0 = 1 \dimensionless@nit
		\dimen 2 = #2\relax
		\Mess@ge {Calculating term #1 of \nodimen 2}%
		\loop
		\ifnum	\count 0 < #1
		\then	\advance \count 0 by 1
			\Mess@ge {Iteration \the \count 0 \space}%
			\Multiply \dimen 0 by {\dimen 2}%
			\Mess@ge {After multiplication, term = \nodimen 0}%
			\Divide \dimen 0 by {\count 0}%
			\Mess@ge {After division, term = \nodimen 0}%
		\repeat
		\Mess@ge {Final value for term #1 of 
				\nodimen 2 \space is \nodimen 0}%
		\xdef \Term {#3 = \nodimen 0 \r@dians}%
		\aftergroup \Term
	       }}
	\catcode `\p = \other
	\catcode `\t = \other
	\gdef \n@dimen #1pt{#1} %%% throw away the ``pt''
}

\def \Divide #1by #2{\divide #1 by #2} %%% just a synonym

\def \Multiply #1by #2%%% allows division of a dimen by a dimen
       {{%%% should really freeze parameter 2 (dimen, passed by value)
	\count 0 = #1\relax
	\count 2 = #2\relax
	\count 4 = 65536
	\Mess@ge {Before scaling, count 0 = \the \count 0 \space and
			count 2 = \the \count 2}%
	\ifnum	\count 0 > 32767 %%% do our best to avoid overflow
	\then	\divide \count 0 by 4
		\divide \count 4 by 4
	\else	\ifnum	\count 0 < -32767
		\then	\divide \count 0 by 4
			\divide \count 4 by 4
		\else
		\fi
	\fi
	\ifnum	\count 2 > 32767 %%% while retaining reasonable accuracy
	\then	\divide \count 2 by 4
		\divide \count 4 by 4
	\else	\ifnum	\count 2 < -32767
		\then	\divide \count 2 by 4
			\divide \count 4 by 4
		\else
		\fi
	\fi
	\multiply \count 0 by \count 2
	\divide \count 0 by \count 4
	\xdef \product {#1 = \the \count 0 \internal@nits}%
	\aftergroup \product
       }}

\def\r@duce{\ifdim\dimen0 > 90\r@dian \then   % sin(x) = sin(180-x)
		\multiply\dimen0 by -1
		\advance\dimen0 by 180\r@dian
		\r@duce
	    \else \ifdim\dimen0 < -90\r@dian \then  % sin(x) = sin(360+x)
		\advance\dimen0 by 360\r@dian
		\r@duce
		\fi
	    \fi}

\def\Sine#1%
       {{%
	\dimen 0 = #1 \r@dian
	\r@duce
	\ifdim\dimen0 = -90\r@dian \then
	   \dimen4 = -1\r@dian
	   \c@mputefalse
	\fi
	\ifdim\dimen0 = 90\r@dian \then
	   \dimen4 = 1\r@dian
	   \c@mputefalse
	\fi
	\ifdim\dimen0 = 0\r@dian \then
	   \dimen4 = 0\r@dian
	   \c@mputefalse
	\fi
%
	\ifc@mpute \then
        	% convert degrees to radians
		\divide\dimen0 by 180
		\dimen0=3.141592654\dimen0
%
		\dimen 2 = 3.1415926535897963\r@dian %%% a well-known constant
		\divide\dimen 2 by 2 %%% we only deal with -pi/2 : pi/2
		\Mess@ge {Sin: calculating Sin of \nodimen 0}%
		\count 0 = 1 %%% see power-series expansion for sine
		\dimen 2 = 1 \r@dian %%% ditto
		\dimen 4 = 0 \r@dian %%% ditto
		\loop
			\ifnum	\dimen 2 = 0 %%% then we've done
			\then	\stillc@nvergingfalse 
			\else	\stillc@nvergingtrue
			\fi
			\ifstillc@nverging %%% then calculate next term
			\then	\term {\count 0} {\dimen 0} {\dimen 2}%
				\advance \count 0 by 2
				\count 2 = \count 0
				\divide \count 2 by 2
				\ifodd	\count 2 %%% signs alternate
				\then	\advance \dimen 4 by \dimen 2
				\else	\advance \dimen 4 by -\dimen 2
				\fi
		\repeat
	\fi		
			\xdef \sine {\nodimen 4}%
			%\typeout {Sin: sine of #1 \space is \sine \space}%
       }}

%%% Now the Cosine can be calculated easily by calling \Sine:
%%%  cos(x) = sin(90-x)
\def\Cosine#1{\ifx\sine\UnDefined\edef\Savesine{\relax}\else
		             \edef\Savesine{\sine}\fi
	{\dimen0=#1\r@dian\multiply\dimen0 by -1
	 \advance\dimen0 by 90\r@dian
	 \Sine{\nodimen 0}
	 \xdef\cosine{\sine}
	 %\typeout {Cosine: cos of \space \nodimen 0 \space is \cosine \space}%
	 \xdef\sine{\Savesine}}}	      
%%% end of trig stuff
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\psdraft{\def\@psdraft{0}}
\def\psfull{\def\@psdraft{100}}
\psfull
%
\newif\if@draftbox
\def\psnodraftbox{\@draftboxfalse}
\@draftboxtrue
%
\newif\if@noisy
\def\pssilent{\@noisyfalse}
\def\psnoisy{\@noisytrue}
\@noisyfalse

%%% These are for the option list.
%%% A specification of the form a = b maps to calling \@p@@sa{b}
\newif\if@bbllx
\newif\if@bblly
\newif\if@bburx
\newif\if@bbury
\newif\if@height
\newif\if@width
\newif\if@rheight
\newif\if@rwidth
\newif\if@angle
\newif\if@clip
\newif\if@verbose
\newif\if@prologfile
\def\@p@@sprolog#1{\@prologfiletrue\def\@prologfileval{#1}}
\def\@p@@sclip#1{\@cliptrue}
%
%%% if this is true, the original Darrell macros and specials are used
\newif\ifuse@psfig
%
\def\@p@@sfile#1{%
\def\@p@sfile{NO FILE: #1}%
\def\@p@sfilefinal{NO FILE: #1}%
	\openin1=#1
	\ifeof1\closein1
		\openin1=#1.bb
			\ifeof1\closein1
				\if@bbllx\if@bblly\if@bburx\if@bbury% added 6/91 Rob Russell
			      		\def\@p@sfile{#1}%
			      		\def\@p@sfilefinal{#1}%
					\fi\fi\fi
				\else
					\@latexerr{ERROR! PostScript file #1 not found}\@whattodo
					\@p@@sbbllx{100bp}
					\@p@@sbblly{100bp}
					\@p@@sbburx{200bp}
					\@p@@sbbury{200bp}
					\def\@p@scost{200}
				\fi
			\else
				\closein1%
				\edef\@p@sfile{#1.bb}%
				\edef\@p@sfilefinal{"`zcat `texfind #1.Z`"}%
			\fi
	\else\closein1
		    \edef\@p@sfile{#1}%
		    \edef\@p@sfilefinal{#1}%
	\fi%
}
 % alternative syntax: figure=
\let\@p@@sfigure\@p@@sfile
%
\def\@p@@sbbllx#1{
		%\typeout{bbllx is #1}
		\use@psfigtrue
		\@bbllxtrue
		\dimen100=#1
		\edef\@p@sbbllx{\number\dimen100}
}
\def\@p@@sbblly#1{
		%\typeout{bblly is #1}
		\use@psfigtrue
		\@bbllytrue
		\dimen100=#1
		\edef\@p@sbblly{\number\dimen100}
}
\def\@p@@sbburx#1{
		%\typeout{bburx is #1}
		\use@psfigtrue
		\@bburxtrue
		\dimen100=#1
		\edef\@p@sbburx{\number\dimen100}
}
\def\@p@@sbbury#1{
		%\typeout{bbury is #1}
		\use@psfigtrue
		\@bburytrue
		\dimen100=#1
		\edef\@p@sbbury{\number\dimen100}
}
\def\@p@@sheight#1{
		\@heighttrue
		\epsfysize=#1
		\dimen100=#1
   		\edef\@p@sheight{\number\dimen100}
		%\typeout{Height is \@p@sheight}
}
\def\@p@@swidth#1{
		%\typeout{Width is #1}
		\@widthtrue
		\epsfxsize=#1
		\dimen100=#1
		\edef\@p@swidth{\number\dimen100}
}
\def\@p@@srheight#1{
		%\typeout{Reserved height is #1}
		\@rheighttrue\use@psfigtrue
		\dimen100=#1
		\edef\@p@srheight{\number\dimen100}
}
\def\@p@@srwidth#1{
		%\typeout{Reserved width is #1}
		\@rwidthtrue\use@psfigtrue
		\dimen100=#1
		\edef\@p@srwidth{\number\dimen100}
}
\def\@p@@sangle#1{
		%\typeout{Rotation is #1}
		\use@psfigtrue
		\@angletrue
%		\dimen100=#1
		\edef\@p@sangle{#1} %\number\dimen100}
}
\def\@p@@ssilent#1{ 
		\@verbosefalse
}
\def\@cs@name#1{\csname #1\endcsname}
\def\@setparms#1=#2,{\@cs@name{@p@@s#1}{#2}}
%
%%% initialize the defaults (size the size of the figure)
%
\def\ps@init@parms{
		\@bbllxfalse \@bbllyfalse
		\@bburxfalse \@bburyfalse
		\@heightfalse \@widthfalse
		\@rheightfalse \@rwidthfalse
		\def\@p@sbbllx{}\def\@p@sbblly{}
		\def\@p@sbburx{}\def\@p@sbbury{}
		\def\@p@sheight{}\def\@p@swidth{}
		\def\@p@srheight{}\def\@p@srwidth{}
		\def\@p@sangle{0}
		\def\@p@sfile{}
		\def\@p@scost{10}
		\use@psfigfalse
		\@prologfilefalse
		\def\@sc{}
		\if@noisy
			\@verbosetrue
		\else
			\@verbosefalse
		\fi
		\@clipfalse
}
%
%%% Go through the options setting things up.
%
\def\parse@ps@parms#1{
	 	\@psdo\@psfiga:=#1\do
		   {\expandafter\@setparms\@psfiga,}
\if@prologfile 
\special{header=\@prologfileval}
\fi
}
%
%%% Compute bb height and width
%
\newif\ifno@bb
\def\bb@missing{
	\epsfgetbb{\@p@sfile}
        \ifepsfbbfound\no@bbfalse\else\no@bbtrue\bb@cull\epsfllx\epsflly\epsfurx\epsfury\fi
}	
\def\bb@cull#1#2#3#4{
	\dimen100=#1 bp\edef\@p@sbbllx{\number\dimen100}
	\dimen100=#2 bp\edef\@p@sbblly{\number\dimen100}
	\dimen100=#3 bp\edef\@p@sbburx{\number\dimen100}
	\dimen100=#4 bp\edef\@p@sbbury{\number\dimen100}
	\no@bbfalse
}

\newdimen\p@intvaluex
\newdimen\p@intvaluey
\newdimen\@ffsetvalue
\newdimen\x@ffsetvalue
\newdimen\y@ffsetvalue

%%% Calculate \@ffsetvalue = (#2 - #1) \sin\theta
%%%  The sine of the angle is already stored in \sine.
%%%  If (#2-#1)>0, then the result is zero in the 2nd and 4th quadrants, and
%%%  if (#2-#1)<0, then the result is zero in the 1st and 3rd quadrants.
%%%  Only the x coordinate needs an offset in the 1st and 3rd quadrants,
%%%  and only the y coordinate needs an offset otherwise.

\def\compute@offset#1#2{{\dimen0=#1 sp\dimen1=#2 sp
			\advance\dimen1 by -\dimen0
			\dimen1=\sine\dimen1
			\dimen0=\cosine\dimen1
			\ifdim\dimen0<0sp \dimen1=0sp \fi
			\global\@ffsetvalue=\dimen1}}

%%% rotate point (#1,#2) about (0,0).
%%% The sine and cosine of the angle are already stored in \sine and
%%% \cosine.  The result is placed in (\p@intvaluex, \p@intvaluey).
\def\rotate@#1#2{{\dimen0=#1 sp\dimen1=#2 sp
%%%            	calculate x' = x \cos\theta - y \sin\theta
		  \global\p@intvaluex=\cosine\dimen0
		  \dimen3=\sine\dimen1
		  \global\advance\p@intvaluex by -\dimen3
%%% 		calculate y' = x \sin\theta + y \cos\theta
		  \global\p@intvaluey=\sine\dimen0
		  \dimen3=\cosine\dimen1
		  \global\advance\p@intvaluey by \dimen3
		  }}
%%% rotate point (#1,#2) about the point (#3,#4), finding the x value.
%%% The sine and cosine of the angle are already stored in \sine and
%%% \cosine.  The result is placed in \p@intvaluex
%\def\rotate@x#1#2#3#4{{\dimen0=#1 sp
%			\dimen1=#2 sp
%			\dimen2=#3 sp
%			\dimen4=#4 sp
%			\advance\dimen0 by -\dimen3
%			\dimen0=\cosine\dimen0
%			\advance\dimen4 by -\dimen2
%			\dimen4=\sine\dimen4
%		   	\global\p@intvaluex=\dimen0
%		   	\global\advance\p@intvaluex by \dimen4
%			\global\advance\p@intvaluex by \dimen3
%
%}}
\def\compute@bb{
		\no@bbfalse
		\if@bbllx \else \no@bbtrue \fi
		\if@bblly \else \no@bbtrue \fi
		\if@bburx \else \no@bbtrue \fi
		\if@bbury \else \no@bbtrue \fi
		\ifno@bb \bb@missing \fi
		\ifno@bb
			\@latexerr{ERROR! cannot locate BB!}\@whattodobb
			\@p@@sbbllx{100bp}
			\@p@@sbblly{100bp}
			\@p@@sbburx{200bp}
			\@p@@sbbury{200bp}
			\def\@p@scost{200}
		\fi
		%\typeout{BB: \@p@sbbllx, \@p@sbblly, \@p@sbburx, \@p@sbbury} 
		\if@angle 
			\Sine{\@p@sangle}\Cosine{\@p@sangle}
			\compute@offset{\@p@sbblly}{\@p@sbbury}
			\x@ffsetvalue=\@ffsetvalue
			% Note that arguments are reversed to
			%  give a negative interval:
			\compute@offset{\@p@sbburx}{\@p@sbbllx}
			\y@ffsetvalue=\@ffsetvalue

			\rotate@{\@p@sbbllx}{\@p@sbblly}
			\advance\p@intvaluex by -\x@ffsetvalue
			\advance\p@intvaluey by -\y@ffsetvalue
			\edef\@p@sbbllx{\number\p@intvaluex}
			\edef\@p@sbblly{\number\p@intvaluey}

			\rotate@{\@p@sbburx}{\@p@sbbury}
			\advance\p@intvaluex by \x@ffsetvalue
			\advance\p@intvaluey by \y@ffsetvalue
			\edef\@p@sbburx{\number\p@intvaluex}
			\edef\@p@sbbury{\number\p@intvaluey}
%		swap LL and UR if necessary
%\typeout{rotated BB: \@p@sbbllx, \@p@sbblly, \@p@sbburx, \@p@sbbury}
			{
			 \count0=\@p@sbbllx \count1=\@p@sbblly
		 	 \count2=\@p@sbburx \count3=\@p@sbbury
			 \dimen0=\@p@sbbllx sp\dimen1=\@p@sbblly sp
		 	 \dimen2=\@p@sbburx sp\dimen3=\@p@sbbury sp
			 \dimen203=\dimen2 \advance\dimen203 by -\dimen0
			 \dimen204=\dimen3 \advance\dimen204 by -\dimen1
			 \ifdim\dimen203<0sp 
			      \count203=\count2 \count2=\count0 
			      \count0=\count203 
			      \global\edef\@p@sbbllx{\number\count0}
			      \global\edef\@p@sbburx{\number\count2}
			 \fi
			 \ifdim\dimen204<0sp 
			       \count204=\count3
			       \count3=\count1
			       \count1=\count204
			       \global\edef\@p@sbblly{\number\count1}
			       \global\edef\@p@sbbury{\number\count3}
			 \fi
			}
%\typeout{after swap BB: \@p@sbbllx, \@p@sbblly, \@p@sbburx, \@p@sbbury}
		\fi
		\count203=\@p@sbburx
		\count204=\@p@sbbury
		\advance\count203 by -\@p@sbbllx
		\advance\count204 by -\@p@sbblly
		\edef\@bbw{\number\count203}
		\edef\@bbh{\number\count204}
		%\typeout{ bbh = \@bbh, bbw = \@bbw }
}
%
%%% \in@hundreds performs #1 * (#2 / #3) correct to the hundreds,
%	then leaves the result in @result
%
\def\in@hundreds#1#2#3{\count240=#2 \count241=#3
		     \count100=\count240	% 100 is first digit #2/#3
		     \divide\count100 by \count241
		     \count101=\count100
		     \multiply\count101 by \count241
		     \advance\count240 by -\count101
		     \multiply\count240 by 10
		     \count101=\count240	%101 is second digit of #2/#3
		     \divide\count101 by \count241
		     \count102=\count101
		     \multiply\count102 by \count241
		     \advance\count240 by -\count102
		     \multiply\count240 by 10
		     \count102=\count240	% 102 is the third digit
		     \divide\count102 by \count241
		     \count200=#1\count205=0
		     \count201=\count200
			\multiply\count201 by \count100
		 	\advance\count205 by \count201
		     \count201=\count200
			\divide\count201 by 10
			\multiply\count201 by \count101
			\advance\count205 by \count201
			%
		     \count201=\count200
			\divide\count201 by 100
			\multiply\count201 by \count102
			\advance\count205 by \count201
			%
		     \edef\@result{\number\count205}
}
\def\compute@wfromh{
		% computing : width = height * (bbw / bbh)
		\in@hundreds{\@p@sheight}{\@bbw}{\@bbh}
		%\typeout{ \@p@sheight * \@bbw / \@bbh, = \@result }
		\edef\@p@swidth{\@result}
		%\typeout{w from h: width is \@p@swidth}
}
\def\compute@hfromw{
		% computing : height = width * (bbh / bbw)
		\in@hundreds{\@p@swidth}{\@bbh}{\@bbw}
		%\typeout{ \@p@swidth * \@bbh / \@bbw = \@result }
		\edef\@p@sheight{\@result}
		%\typeout{h from w : height is \@p@sheight}
}
\def\compute@handw{
		\if@height 
			\if@width
			\else
				\compute@wfromh
			\fi
		\else 
			\if@width
				\compute@hfromw
			\else
				\edef\@p@sheight{\@bbh}
				\edef\@p@swidth{\@bbw}
			\fi
		\fi
}
\def\compute@resv{
		\if@rheight \else \edef\@p@srheight{\@p@sheight} \fi
		\if@rwidth \else \edef\@p@srwidth{\@p@swidth} \fi
		%\typeout{rheight = \@p@srheight, rwidth = \@p@srwidth}
}
%		
%%% Compute any missing values
\def\compute@sizes{
	\compute@bb
	\compute@handw
	\compute@resv
}
%
%%% \epsfig
%%% usage : \epsfig{file=, height=, width=, bbllx=, bblly=, bburx=, bbury=,
%			rheight=, rwidth=, angle=, clip=}
%
%%% "clip=" is a switch and takes no value, but the `=' must be present.
%------------------------------------------------------------------
%%% by the way, possible parameters to the PSfile= command in dvips are:
%%%                    llx
%%%                    lly
%%%                    urx
%%%                    ury
%%%                    rwi
%	hoffset	The horizontal offset (default 0)
%	voffset	The vertical offset (default 0)
%	hsize	The horizontal clipping size (default 612)
%	vsize	The vertical clipping size (default 792)
%	hscale	The horizontal scaling factor (default 100)
%	vscale	The vertical scaling factor (default 100)
%	angle	The rotation (default 0)
%------------------------------------------------------------------
\def\psfig#1{\vbox {
	% do a zero width hard space so that a single
	% \epsfig in a centering enviornment will behave nicely
	%{\setbox0=\hbox{\ }\ \hskip-\wd0}
	%
	\ps@init@parms
	\parse@ps@parms{#1}
	%
	\ifnum\@p@scost<\@psdraft
		\typeout{[\@p@sfilefinal]}
		\if@verbose
			\typeout{epsfig: using PSFIG macros}
		\fi
		\psfig@method
	\else
		\epsfig@draft
	\fi
}}

\def\epsfig#1{\vbox {
	% do a zero width hard space so that a single
	% \epsfig in a centering enviornment will behave nicely
	%{\setbox0=\hbox{\ }\ \hskip-\wd0}
	%
	\ps@init@parms
	\parse@ps@parms{#1}
	%
	\ifnum\@p@scost<\@psdraft
		\typeout{[\@p@sfilefinal]}
		\if@clip\use@psfigtrue\fi
		\if@angle\use@psfigtrue\fi
		\ifuse@psfig
			\if@verbose
				\typeout{epsfig: using PSFIG macros}
			\fi
			\psfig@method
		\else
			\if@verbose
				\typeout{epsfig: using EPSF macros}
			\fi
			\epsf@method
		\fi
	\else
		\epsfig@draft
	\fi
}}


\def\epsf@method{%
	\epsfgetbb{\@p@sfile}%
	\epsfsetgraph{\@p@sfilefinal}
}
\def\psfig@method{%
	\compute@sizes
	\special{ps::[begin]  \@p@swidth \space \@p@sheight \space%
	\@p@sbbllx \space \@p@sbblly \space%
	\@p@sbburx \space \@p@sbbury \space%
	startTexFig \space }%
	\if@angle
		\special {ps:: \@p@sangle \space rotate \space} 
	\fi
	\if@clip
		\if@verbose
			\typeout{(clipped to BB) }
		\fi
		\special{ps:: doclip \space }%
	\fi
	\special{ps: plotfile \@p@sfilefinal \space }%
	\special{ps::[end] endTexFig \space }%
	% Create the vbox to reserve the space for the figure%
	\vbox to \@p@srheight true sp{\hbox to \@p@srwidth true sp{\hss}\vss}
}
%
% draft figure, just reserve the space and print the
% path name.
\def\epsfig@draft{
\compute@sizes
\if@draftbox
	% Verbose draft: print file name in box
	% NOTE: fbox is a LaTeX command!
	\hbox{\fbox{\vbox to \@p@srheight true sp{
	\vss\hbox to \@p@srwidth true sp{ \hss \@p@sfilefinal \hss }\vss
	}}}
\else
	% Non-verbose draft
	\vbox to \@p@srheight true sp{%
	\vss\hbox to \@p@srwidth true sp{\hss}\vss}
\fi	
}
\epsfigRestoreAt