% TeXdraw macros
% $Id: texdraw.tex 2.7 2019/04/18 TeXdraw-v2r3 $
% Copyright (C) 1991-2019 Peter Kabal
% This work is licensed under the Creative Commons Attribution (CC-BY)
% License, any version. To view the licenses, visit
% creativecommons.org/licenses/by or send a letter to
% Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.
% Peter Kabal
% Department of Electrical & Computer Engineering
% McGill University
% peter dot kabal at mcgill dot ca
%
http://www-mmsp.ece.mcgill.ca/MMSP/Documents/Software/
\def\setRevDate $#1 #2 #3${#2}
\def\TeXdrawId{\setRevDate $Date: 2019/04/18 14:10:45 $ TeXdraw V2R3}
% ===============================================================
% The TeXdraw macros allow PostScript line drawings and such to be
% generated from within TeX and LaTeX.
% (1) TeXdraw allows TeX text (either horizontal or rotated) to be
% superimposed on the figure.
% (2) TeXdraw implements a \bsegment-\esegment environment which allows
% parameter changes and coordinate changes to be kept local. In
% effect these segments are self-contained relocatable procedures.
% (3) TeX's macro facility can be used to modularize drawing units and
% produce more complex entities from simple elements.
% (4) The drawing can be positioned on the page like any other TeX box.
% TeXdraw coordinate units have positive X to the right and positive Y up.
% The drawing units can be selected (initially inches). In addition, two
% scaling parameters - unit scale and segment scale - are available. Their
% effects are multiplicative.
% Segments allow for relocatable drawing units. Inside each segment the
% coordinates are relative to the initial point, which becomes (0 0).
% Scaling is local to segments. Each segment inherits the unit scale
% scaling from outside the segment, but any changes apply to that segment
% and inferior segments. The segment scale factor is reset to unity on
% entry to each segment.
% The coordinates given as command arguments are used to determine
% the size of the drawing. The width of the plot line, sizes of
% arrowheads, arcs or text do not affect the size of the drawing.
% TeXdraw writes PostScript commands to an intermediate file. After the
% drawing is finished, the PostScript file is included in the document as a
% PostSript include file.
% This file is divided into 4 parts,
% - TeXdraw user interface
% - Utility definitions
% - Low level definitions
% - PostScript file macros
\chardef\catamp=\the\catcode`\@
\catcode`\@=11
% ===============================================================
% ===== TeXdraw user interface ==================================
\long % \centertexdraw needs to be very \long
\def\centertexdraw #1{\hbox to \hsize{\hss
\btexdraw #1\etexdraw
\hss}}
% ====== Begin TeXdraw
% Inside the texdraw box:
% The \vbox should be of zero size; none of the TeXdraw drawing commands
% generate text, the TeXdraw text commands generate zero size boxes.
\def\btexdraw {\x@pix=0 \y@pix=0
\x@segoffpix=\x@pix \y@segoffpix=\y@pix
\let\p@sfile=\p@sundef
% Set the default values (define outside of the group so that \etexdraw can
% see the scaling parameters)
\t@exdrawdef
\setbox\t@xdbox=\vbox\bgroup\offinterlineskip
\global\d@bs=0 % pending segments
\global\p@osinitfalse
\s@avemove \x@pix \y@pix % capture the initial position
\m@pendingfalse
\global\p@osinitfalse % capture the next move
\p@athfalse
\the\everytexdraw}
% ====== End TeXdraw
% Write out a trailer, close the file, bring in the PostScript code as
% a \special include file. The \special is offset on the page to be at
% (llx,ury) in PostScript coordinates.
% The drawing is placed in a \vbox of appropriate size (zero depth). The
% temporary PostScript file is superimposed with offsets such that the
% lower lefthand corner of the drawing is aligned with the lower lefthand of
% the box.
\def\etexdraw {\p@sclose % close the PostScript file
\egroup % ends the \vbox \bgroup
\vbox {\offinterlineskip
\pixtobp \xminpix \l@lxbp \pixtobp \yminpix \l@lybp
\pixtobp \xmaxpix \u@rxbp \pixtobp \ymaxpix \u@rybp
\ifx\p@sfile\p@sundef
\hbox{\t@xdempty
[{\l@lxbp},{\l@lybp}][{\u@rxbp},{\u@rybp}]}%
\else
\hbox{\t@xdinclude
[{\l@lxbp},{\l@lybp}][{\u@rxbp},{\u@rybp}]{\p@sfile}}%
\fi
\t@xdtext}%
}
% Superimpose TeX text. The position is temporarily offset to a position
% corresponding to (0 0) to place the TeX text.
\def\t@xdtext {
\ifdim \wd\t@xdbox>0pt
\t@xderror {TeXdraw box non-zero size, possible extraneous text}%
\fi
\pixtodim \xminpix \t@xpos \pixtodim \yminpix \t@ypos
\kern \t@ypos
\hbox {\kern -\t@xpos
\box\t@xdbox % TeX text
\kern \t@xpos}%
\kern -\t@ypos\relax
}
% ===== Drawing scaling
% The units in any segment may be scaled arbitrarily. A unit scale is
% local to a segment but affects enclosed segments unless specifically
% overridden in that segment. In addition there is a segment scale. The
% overall scale is the product of the two scaling factors.
%
% Scaling is handled entirely on the TeX side, the PostScript side gets
% absolute pixel coordinates.
% Drawing units, e.g. "in" or "cm"
\def\drawdim #1 {\def\d@dim{#1\relax}}
% \u@nitsc - unit scale
% \s@egsc - segment scale
% \d@sc - drawing scale, product of the unit scale and segment scale
% Note that successive application of relative scale factors can lead
% to poor accuracy of the final scale factor. Each scale factor is
% represented to about 5 decimal digits after the decimal point.
\def\setunitscale #1 {\edef\u@nitsc{#1}%
\realmult \u@nitsc \s@egsc \d@sc}
\def\relunitscale #1 {\realmult {#1}\u@nitsc \u@nitsc
\realmult \u@nitsc \s@egsc \d@sc}
\def\setsegscale #1 {\edef\s@egsc {#1}%
\realmult \u@nitsc \s@egsc \d@sc}
\def\relsegscale #1 {\realmult {#1}\s@egsc \s@egsc
\realmult \u@nitsc \s@egsc \d@sc}
% ===== Drawing segments
% The position is restored after a segment.
% Segments use TeX grouping on the TeX side and gsave/grestore on the
% PostScript side to keep changes local. On the TeX side segments have
% (0 0) as the initial point, while the PostScript side sees no scale
% changes or translations.
\def\bsegment {\ifp@ath
\f@lushbs
\f@lushmove
\fi
\begingroup
\x@segoffpix=\x@pix
\y@segoffpix=\y@pix
\setsegscale 1
\global\advance \d@bs by 1\relax}
\def\esegment {\endgroup
\ifnum \d@bs=0
\writetx {es}%
\else
\global\advance \d@bs by -1
\fi}
% Save a position
% Save each coordinate as the macro "*name". The macro is defined to
% be the pixel coordinate value.
\def\savecurrpos (#1 #2){\getsympos (#1 #2)\a@rgx\a@rgy
\s@etcsn \a@rgx {\the\x@pix}%
\s@etcsn \a@rgy {\the\y@pix}}
\def\savepos (#1 #2)(#3 #4){\getpos (#1 #2)\a@rgx\a@rgy
\coordtopix \a@rgx \t@pixa
\advance \t@pixa by \x@segoffpix
\coordtopix \a@rgy \t@pixb
\advance \t@pixb by \y@segoffpix
\getsympos (#3 #4)\a@rgx\a@rgy
\s@etcsn \a@rgx {\the\t@pixa}%
\s@etcsn \a@rgy {\the\t@pixb}}
% ===== Line parameters
% The following parameters apply to subsequent lines. Each of these
% commands invokes a stroke to draw the previous line segments,
% establishes the current point and then changes the line parameter.
% The parameters are kept local by the PostScript gsave/grestore
% mechanism. We use \writetx here, instead of \writeps, since we
% do not want to flush any moves.
\def\linewd #1 {\coordtopix {#1}\t@pixa
\f@lushbs
\writetx {\the\t@pixa\space sl}}
\def\setgray #1 {\f@lushbs
\writetx {#1 sg}}
\def\lpatt (#1){\listtopix (#1)\p@ixlist
\f@lushbs
\writetx {[\p@ixlist] sd}}
% ===== Line drawing
% PostScript uses the concept of a path consisting of line segments.
% In this interface to PostScript, paths are continuous across the
% beginning of segments. Paths terminate at the end of a segment with
% an implicit move. In addition, paths are both terminated and started
% with a move. There is a current point at all times, starting with
% initial position (0,0).
\def\lvec (#1 #2){\getpos (#1 #2)\a@rgx\a@rgy
\s@etpospix \a@rgx \a@rgy
\writeps {\the\x@pix\space \the\y@pix\space lv}}
\def\rlvec (#1 #2){\getpos (#1 #2)\a@rgx\a@rgy
\r@elpospix \a@rgx \a@rgy
\writeps {\the\x@pix\space \the\y@pix\space lv}}
\def\move (#1 #2){\getpos (#1 #2)\a@rgx\a@rgy
\s@etpospix \a@rgx \a@rgy
\s@avemove \x@pix \y@pix}
\def\rmove (#1 #2){\getpos (#1 #2)\a@rgx\a@rgy
\r@elpospix \a@rgx \a@rgy
\s@avemove \x@pix \y@pix}
% ===== Circles, ellipses and arcs
% Note that arcs do not update the size of the drawing.
% \lcir, stroked circle
% r:#1 - radius
% \fcir, filled circle
% f:#1 - fill gray level, 0 is black, 1 is white
% r:#2 - radius
% \ellip, stroked ellipse
% rx:#1 - x radius
% ry:#2 - y radius
% \fellip, filled ellipse
% f:#1 - fill gray level, 0 is black, 1 is white
% rx:#1 - x radius
% ry:#2 - y radius
% \larc, stroked counterclockwise arc, with the present position being
% the center of the arc. Only the arc is drawn (not the line
% joining the center to the beginning of the arc)
% r:#1 - radius
% sd:#2 - start angle (degrees)
% ed:#3 - end angle (degrees)
\def\lcir r:#1 {\coordtopix {#1}\t@pixa
\writeps {\the\t@pixa\space cr}%
\r@elupd \t@pixa \t@pixa
\r@elupd {-\t@pixa}{-\t@pixa}}
\def\fcir f:#1 r:#2 {\coordtopix {#2}\t@pixa
\writeps {\the\t@pixa\space #1 fc}%
\r@elupd \t@pixa \t@pixa
\r@elupd {-\t@pixa}{-\t@pixa}}
\def\lellip rx:#1 ry:#2 {\coordtopix {#1}\t@pixa
\coordtopix {#2}\t@pixb
\writeps {\the\t@pixa\space \the\t@pixb\space el}%
\r@elupd \t@pixa \t@pixb
\r@elupd {-\t@pixa}{-\t@pixb}}
\def\fellip f:#1 rx:#2 ry:#3 {\coordtopix {#2}\t@pixa
\coordtopix {#3}\t@pixb
\writeps {\the\t@pixa\space \the\t@pixb\space #1 fe}%
\r@elupd \t@pixa \t@pixb
\r@elupd {-\t@pixa}{-\t@pixb}}
\def\larc r:#1 sd:#2 ed:#3 {\coordtopix {#1}\t@pixa
\writeps {\the\t@pixa\space #2 #3 ar}}
% ===== Fill commands
% The form here completes a path with a closepath, applies the fill,
% starts a newpath and moves to the current point. The gray level has
% 0 as black and 1 as white. The current path is terminated.
\def\ifill f:#1 {\writeps {#1 fl}} % Fill only
\def\lfill f:#1 {\writeps {#1 fp}} % Stroke and fill
% ===== Text
% TeX text superimposed on the drawing
% \htext (x y){text} or \htext {text}
% \vtext (x y){text} or \vtext {text}
% \rtext td:angle (x y){text} or \rtext td:angle {text}
% \textref h:#1 v:#2
% The TeX text (or whatever) is placed in an \hbox. The box is rotated
% for vertical text. The text is placed on the drawing at the specified
% location (coordinates specified) or the current location (coordinates
% not specified). The text reference point is placed at that location.
% For the purposes of determining the drawing size, the text box is of
% zero size.
% Horizontal text
% Check if the argument starts with a left parenthesis
\def\htext #1{\def\testit {#1}%
\ifx \testit\l@paren
\let\t@cmd=\h@move
\else
\let\t@cmd=\h@text
\fi
\t@cmd {#1}}
% Rotated text
\def\rtext td:#1 #2{\def\testit {#2}%
\ifx \testit\l@paren
\let\t@cmd=\r@move
\else
\let\t@cmd=\r@text
\fi
\t@cmd td:#1 {#2}}
% Vertical text
\def\vtext {\rtext td:90 }
% Text reference point
% h:#1 text horizontal reference point - L, C or R
% v:#2 text vertical reference point - T, C or B
\def\textref h:#1 v:#2 {\ifx #1R%
\edef\l@stuff {\hss}\edef\r@stuff {}%
\else
\ifx #1C%
\edef\l@stuff {\hss}\edef\r@stuff {\hss}%
\else % default L
\edef\l@stuff {}\edef\r@stuff {\hss}%
\fi
\fi
\ifx #2T%
\edef\t@stuff {}\edef\b@stuff {\vss}%
\else
\ifx #2C%
\edef\t@stuff {\vss}\edef\b@stuff {\vss}%
\else % default B
\edef\t@stuff {\vss}\edef\b@stuff {}%
\fi
\fi}
% ===== Arrow vectors
\def\avec (#1 #2){\getpos (#1 #2)\a@rgx\a@rgy
\s@etpospix \a@rgx \a@rgy
\writeps {\the\x@pix\space \the\y@pix\space (\a@type) %
\the\a@lenpix\space \the\a@widpix\space av}}
\def\ravec (#1 #2){\getpos (#1 #2)\a@rgx\a@rgy
\r@elpospix \a@rgx \a@rgy
\writeps {\the\x@pix\space \the\y@pix\space (\a@type) %
\the\a@lenpix\space \the\a@widpix\space av}}
% Arrowhead size
% l:#1 - length of the arrowhead
% w:#2 - width of the base of the arrowhead
\def\arrowheadsize l:#1 w:#2 {\coordtopix{#1}\a@lenpix
\coordtopix{#2}\a@widpix}
% Arrowhead type
% t:#1 - arrowhead type, F filled triangle (using current gray level)
% T empty closed triangle
% W white filled triangle
% V Vee shape, at the end of the vector
% H (or other character) Vee shape, vector stops
% short of the Vee
\def\arrowheadtype t:#1 {\edef\a@type{#1}}
% ===== Bezier curve
% The initial point is assumed to be the current point. Only the last
% coordinate affects the size of the plot.
\def\clvec (#1 #2)(#3 #4)(#5 #6)%
{\getpos (#1 #2)\a@rgx\a@rgy
\coordtopix \a@rgx\t@pixa
\advance \t@pixa by \x@segoffpix
\coordtopix \a@rgy\t@pixb
\advance \t@pixb by \y@segoffpix
\getpos (#3 #4)\a@rgx\a@rgy
\coordtopix \a@rgx\t@pixc
\advance \t@pixc by \x@segoffpix
\coordtopix \a@rgy\t@pixd
\advance \t@pixd by \y@segoffpix
\getpos (#5 #6)\a@rgx\a@rgy
\s@etpospix \a@rgx \a@rgy
\writeps {\the\t@pixa\space \the\t@pixb\space
\the\t@pixc\space \the\t@pixd\space
\the\x@pix\space \the\y@pix\space cv}}
% ===== Draw the bounding box
\def\drawbb {\bsegment
\drawdim bp
\linewd 0.24 % line width 1/300 inch = 0.24 bp
\setunitscale {\p@sfactor}
\writeps {\the\xminpix\space \the\yminpix\space mv}%
\writeps {\the\xminpix\space \the\ymaxpix\space lv}%
\writeps {\the\xmaxpix\space \the\ymaxpix\space lv}%
\writeps {\the\xmaxpix\space \the\yminpix\space lv}%
\writeps {\the\xminpix\space \the\yminpix\space lv}%
\esegment}
% ===============================================================
% ===== Utility macros used by TeXdraw ==========================
% ===== Decode coordinates
% Get coordinates
% This macro is used to get two arguments separated by a blank, with
% possible leading and trailing blanks. Symbolic coordinates are
% converted to user coordinates.
% (#1 #2) - coordinates
% #3 - macro name to receive the x-coordinate value
% #4 - macro name to receive the y-coordinate value
\def\getpos (#1 #2)#3#4{\g@etargxy #1 #2 {} \\#3#4%
\c@heckast #3%
\ifa@st
\g@etsympix #3\t@pixa
\advance \t@pixa by -\x@segoffpix
\pixtocoord \t@pixa #3%
\fi
\c@heckast #4%
\ifa@st
\g@etsympix #4\t@pixa
\advance \t@pixa by -\y@segoffpix
\pixtocoord \t@pixa #4%
\fi}
% Get symbolic coordinate names
% (#1 #2) - symbolic coordinates
% #3 - macro name to receive the symbolic x coordinate name
% #4 - macro name to receive the symbolic y coordinate name
\def\getsympos (#1 #2)#3#4{\g@etargxy #1 #2 {} \\#3#4%
\c@heckast #3%
\ifa@st \else
\t@xderror {TeXdraw: invalid symbolic coordinate}%
\fi
\c@heckast #4%
\ifa@st \else
\t@xderror {TeXdraw: invalid symbolic coordinate}%
\fi}
% ===== Convert a list of values to pixel values
% (#1) - blank separated list of values in user coordinates
% #2 - macro name to receive the blank separated list of pixel values
\def\listtopix (#1)#2{\def #2{}%
\edef\l@ist {#1 }% % append a blank to the string
\m@oretrue
\loop
\expandafter\g@etitem \l@ist \\\a@rgx\l@ist
\a@pppix \a@rgx #2%
\ifx \l@ist\empty
\m@orefalse
\fi
\ifm@ore
\repeat}
% ===== Real multiplication
% This function uses the property that a box dimension may be scaled by
% a real value. The values are converted to dimensions in units of pt.
% This choice gives us a reasonable dynamic range. The final step is to
% clean off the "pt" on the resulting dimension. Note that these are fixed
% point operations with each operand represented to an accuracy of about 5
% decimal places.
% Note we must use magnified points not "true" points, since the answer is
% expressed in magnified points. The result will be calculated in the same
% manner no matter what the magnification is.
% #1 and #2 are multiplicands
% #3 macro name to capture the real result
\def\realmult #1#2#3{\dimen0=#1pt
\dimen2=#2\dimen0
\edef #3{\expandafter\c@lean\the\dimen2}}
% ===== Divide integers, real result
% #1 integer numerator value
% #2 integer denominator (divisor) value
% #3 macro name to capture the real result
\def\intdiv #1#2#3{\t@counta=#1
\t@countb=#2
% Limitations: #1 must be negatable, i.e. it must not be the largest
% magnitude negative number
% #2 must be able to be multiplied by 2 without overflow
% Calculate a*65536/b where the factor 65536 converts from pt to sp.
% This operation can also be interpretated as an extended precision
% numerator divided by the denominator. The scheme used is basically a
% long division, except that it is bootstrapped by an integer divide.
% The computations are carried out with positive numerator and
% denominator, with the appropriate restoration of sign at the end.
% \t@counta == remainder, r, initially set to a
% \t@countb == denominator, b
% \t@countc == quotient, q
% \t@countd == +1, a and b have the same sign
% -1, a and b have opposite signs
% \t@counte == temporary register
\ifnum \t@countb<0
\t@counta=-\t@counta
\t@countb=-\t@countb
\fi
\t@countd=1 % record the sign
\ifnum \t@counta<0
\t@counta=-\t@counta
\t@countd=-1
\fi
% % q=a/b, r=a-q*b
\t@countc=\t@counta \divide \t@countc by \t@countb
\t@counte=\t@countc \multiply \t@counte by \t@countb
\advance \t@counta by -\t@counte
\t@counte=-1
\loop
\advance \t@counte by 1
\ifnum \t@counte<16 % loop 16 times
\multiply \t@countc by 2 % q=2q
\multiply \t@counta by 2 % r=2r
\ifnum \t@counta<\t@countb \else % if ( r >= b )
\advance \t@countc by 1 % q=q+1
\advance \t@counta by -\t@countb % r=r-b
\fi
\repeat
\divide \t@countb by 2 % rounding
\ifnum \t@counta<\t@countb % if ( r >= b/2 ) q=q+1
\advance \t@countc by 1
\fi
\ifnum \t@countd<0 % restore the sign
\t@countc=-\t@countc
\fi
\dimen0=\t@countc sp % express as a dimension
\edef #3{\expandafter\c@lean\the\dimen0}}
% ===============================================================
% ===== Internal TeXdraw macros =================================
% ===== Macros for converting between dimensions and units
% Convert drawing units (coordinate value, scaled by the unit scale and
% segment scale) to pixels. We use rounding to get more accurate results.
% #1 dimension in drawing units
% #2 count in pixels (returned into a count)
\def\coordtopix #1#2{\dimen0=#1\d@dim
\dimen2=\d@sc\dimen0
\t@counta=\dimen2 % scaled dimension in sp
\t@countb=\s@ppix
\divide \t@countb by 2
\ifnum \t@counta<0 % rounding
\advance \t@counta by -\t@countb
\else
\advance \t@counta by \t@countb
\fi
\divide \t@counta by \s@ppix
#2=\t@counta}
% Convert from absolute pixels to relative scaled coordinates
% #1 - input integer pixel value
% #2 - macro name to receive the character string corresponding to the
% floating point coordinate value
\def\pixtocoord #1#2{\t@counta=#1%
\multiply \t@counta by \s@ppix
\dimen0=\d@sc\d@dim
\t@countb=\dimen0
\intdiv \t@counta \t@countb #2}
% Convert pixels to TeX dimensions.
% #1 - input integer pixel value
% #2 - returned dimension (returned into a dimension register)
\def\pixtodim #1#2{\t@countb=#1%
\multiply \t@countb by \s@ppix
#2=\t@countb sp\relax}
% Convert pixels to (integer) bp units
% #1 - input pixel value
% #2 - integer value, returned as a macro definition
\def\pixtobp #1#2{\dimen0=\p@sfactor pt
\t@counta=\dimen0
\multiply \t@counta by #1%
\ifnum \t@counta < 0 % rounding
\advance \t@counta by -32768
\else
\advance \t@counta by 32768
\fi
\divide \t@counta by 65536
\edef #2{\the\t@counta}}
% ===== Allocations for registers and counts
% == Temporary count registers
\newcount\t@counta \newcount\t@countb % Use at lowest levels
\newcount\t@countc \newcount\t@countd
\newcount\t@counte
\newcount\t@pixa \newcount\t@pixb % Use for pixel values
\newcount\t@pixc \newcount\t@pixd
% == Temporary dimension registers
\newdimen\t@xpos \newdimen\t@ypos
% == Position and parameter registers
% The minimum and maximum extent in the X and Y direction in pixel units
% (updated globally to reach outside segments)
\newcount\xminpix \newcount\xmaxpix
\newcount\yminpix \newcount\ymaxpix
% == Arrowhead parameters
\newcount\a@lenpix \newcount\a@widpix
% == Absolute pixel positions
\newcount\x@pix \newcount\y@pix
\newcount\x@segoffpix \newcount\y@segoffpix
\newcount\x@savepix \newcount\y@savepix
% == Conversion factor
\newcount\s@ppix % sp/pixel
% == Pending segments count
\newcount\d@bs
% == Counter to form unique file names
\newcount\t@xdnum
\global\t@xdnum=0
% == TeXdraw box
\newbox\t@xdbox
% == Output stream number for the PostScript file
\newwrite\drawfile
% == \newif
\newif\ifm@pending
\newif\ifp@ath
\newif\ifa@st
\newif\ifm@ore
\newif \ift@extonly
\newif\ifp@osinit
% == \newtoks
\newtoks\everytexdraw
% ===== Character definitions
\def\l@paren{(}
\def\a@st{*}
% ===== Special character macros
% Need to be able to insert "%", "{" and "}" characters into the
% PostScript file.
% Define macros which have these characters with category "other".
% We will assume that these characters have the standard meanings -
% after all, we use comments and braces in this code.
\catcode`\%=12
\def\p@b {%!} \def\p@p {%%}
\catcode`\%=14
\catcode`\{=12 \catcode`\}=12 \catcode`\u=1 \catcode`\v=2
\def\l@br u{v \def\r@br u}v
\catcode `\{=1 \catcode`\}=2 \catcode`\u=11 \catcode`\v=11
% ===== Pixel conversion factors
% The position is kept as an integer value (count). It is set to a
% resolution corresponding to 300 units/inch. We refer to them as pixels,
% but in fact the resolution is just that: movements are quantized to lie
% on a grid with that resolution.
% Using pixel units which correspond to the actual resolution of the device
% has advantages in that all horizontal and vertical lines then will be
% drawn with the same line thickness. In addition the coordinates are
% then integer values (no decimal point or leading zeros) which leads
% to a more compact PostScript file.
% The following macro sets the conversion from PostScript units (bp) to the
% integer units (pixels). The file inclusion \special environment in the
% PostScript driver restores the context to default PostScript values
% (bp or 72/in and origin in the lower lefthand corner). A scaling value
% of 0.24 converts to 300/inch. Note that the PostScript commands written
% to the temporary PostScript file do not depend on the TeX magnification
% in effect. Magnification should be handled by the dvi to PostScript
% driver at the time that the file is included in the output.
% Calculate the conversion factors
% Let s@ppix = sp/pixel = u / p, where u = sp/unit and p = pix/unit (both
% integer values).
% We calculate s@ppix as
% s@ppix = [ (u+0.5p)/p ]
% We also calculate the PostScript scale factor bp/pixel
% Let b = sp/bp. We want p@sfactor = s@ppix/b. For 300 pixels/inch, this
% gives p@sfactor=0.24. Using rounding
% p@sfactor = [ (s@ppix+0.5b)/b ] .
% To carry out the arithmetic, we will operate in sp units (integers) and
% generate the answer in pt units (multiplying by sp/pt). This result will
% expressed as a character string representing a real number after the "pt"
% designator is stripped off.
{\catcode`\p=12 \catcode`\t=12
\gdef\c@lean #1pt{#1}}
\def\sppix#1/#2 {\dimen0=1#2 \s@ppix=\dimen0
\t@counta=#1%
\divide \t@counta by 2
\advance \s@ppix by \t@counta
\divide \s@ppix by #1% % \s@ppix available
\t@counta=\s@ppix
\multiply \t@counta by 65536 % 1 pt = 65536 sp
\advance \t@counta by 32891 % 0.5 bp = 32890.88 sp
\divide \t@counta by 65782 % 1 bp = 65781.76 sp
\dimen0=\t@counta sp
\edef\p@sfactor {\expandafter\c@lean\the\dimen0}}
% ===== Low level coordinate decoding macros
% Get two values, separated by a blank
% Invoke as \g@etargxy <stuff> {} \\\ma\mb
\def\g@etargxy #1 #2 #3 #4\\#5#6{\def #5{#1}%
\ifx #5\empty
\g@etargxy #2 #3 #4 \\#5#6% leading blank
\else
\def #6{#2}%
\def\a@rg {#3}%
\ifx \a@rg\empty \else
\t@xderror {TeXdraw: invalid coordinate}%
\fi
\fi}
% Check for a leading asterisk
% Sets \a@stfalse or \a@sttrue, test with \ifa@st
\def\c@heckast #1{\expandafter
\c@heckastll #1\\}
\def\c@heckastll #1#2\\{\def\testit {#1}%
\ifx \testit\a@st
\a@sttrue
\else
\a@stfalse
\fi}
% Decode a symbolic coordinate
% Pixel value returned to a count
\def\g@etsympix #1#2{\expandafter
\ifx \csname #1\endcsname \relax
\t@xderror {TeXdraw: undefined symbolic coordinate}%
\fi
#2=\csname #1\endcsname}
% Set a macro named #1 to have value #2
\def\s@etcsn #1#2{\expandafter
\xdef\csname#1\endcsname {#2}}
% ===== Low level list decoding macros
% Pick off the first item -> #3, rest of string -> #4
\def\g@etitem #1 #2\\#3#4{\edef #4{#2}\edef #3{#1}}
\def\a@pppix #1#2{\edef\a@rg {#1}%
\ifx \a@rg\empty \else
\coordtopix {#1}\t@pixa
\ifx #2\empty
\edef #2{\the\t@pixa}%
\else
\edef #2{#2 \the\t@pixa}%
\fi
\fi}
% ===== Macros for updating the position
% Calculate the position in pixels and update the maximum excursions
\def\s@etpospix #1#2{\coordtopix {#1}\x@pix
\advance \x@pix by \x@segoffpix
\coordtopix {#2}\y@pix
\advance \y@pix by \y@segoffpix
\u@pdateminmax \x@pix \y@pix}
\def\r@elpospix #1#2{\coordtopix {#1}\t@pixa
\advance \x@pix by \t@pixa
\coordtopix {#2}\t@pixa
\advance \y@pix by \t@pixa
\u@pdateminmax \x@pix \y@pix}
\def\r@elupd #1#2{\t@counta=\x@pix
\advance\t@counta by #1%
\t@countb=\y@pix
\advance\t@countb by #2%
\u@pdateminmax \t@counta \t@countb}
\def\u@pdateminmax #1#2{\ifnum #1>\xmaxpix
\global\xmaxpix=#1%
\fi
\ifnum #1<\xminpix
\global\xminpix=#1%
\fi
\ifnum #2>\ymaxpix
\global\ymaxpix=#2%
\fi
\ifnum #2<\yminpix
\global\yminpix=#2%
\fi}
% ===== Save moves / flush moves
% A TeXdraw segment which generates only TeX text uses only move, begin
% segment and end segment commands. The goal is to avoid writing out
% empty segments for such cases. To this end, moves are held back and
% only written out if necessary to set the position or terminate a path.
% Also in this way, a TeXdraw drawing which generates only TeX text will
% not generate a PostScript file.
% Two flags are used. Both flags are local to a segment.
% - move pending: Set when a move has been invoked but the move command
% has not been written out to the PostScript file.
% - path in progress: Set when a PostScript path has been started but the
% path has not been terminated and stroked.
% (1) Moves are kept back. Using TeX's groups, a local flag and local
% position registers are used to keep track of whether the latest
% move applicable to a given segment has been written out or not. In
% effect there is a stack of pending moves, one for each level of
% segment nesting.
% (2) At the beginning of a segment, if a PS path is in progress and a
% a move is pending, the move is written out, terminating the path
% and stroking the path. This is done to ensure that the path is
% stroked before lines and/or fills are executed in the segment.
% (3) At the beginning of a segment, if a PS path is not in progress,
% any pending moves are kept back. Effectively, the move will be
% transferred into the segment. It will be written out only when
% the position needs to be updated for some other command. Such
% moves which are transferred into segments may have to be repeated
% outside the segment. The move pending flag will be restored to
% the value outside the segment on exit from the segment.
% (4) A begin segment command is not written out, but instead a global
% segment backlog counter is incremented. The backlog of begin
% segment commands is written out when a drawing command is
% encountered.
% The effect of the above on the TeXdraw commands is as follows.
% (a) move:
% - set the current position
% - record the position of the saved move
% - set the move pending flag
% (b) begin segment:
% - if a path is in progress
% - if a move is pending
% - if there is a backlog of segments
% - write out enough begin segments to clear the backlog
% - write out the pending move
% - reset the move pending flag (local to the containing segment,
% but affects inferior segments)
% - reset the path in progress flag
% - increment the segment backlog counter
% - begin a group
% (c) end segment:
% - end a group
% - if there is no backlog of segments
% - write an end segment command
% - if there is a backlog of segments
% - decrement the backlog counter, thereby omitting an empty
% empty segment.
% - the move pending flag and path in progress flag are automatically
% restored on leaving the TeX group
% (d) text:
% - create a text box
% (e) line parameters:
% - if there is a backlog of segments
% - write out enough begin segments to clear the backlog
% - clear the path in progress flag
% - write the PS command changing the line parameter
% (f) other drawing commands:
% - update the current position
% - if there is a backlog of segments
% - write out enough begin segments to clear the backlog
% - if there is a pending move
% - write out the pending move
% - reset the move pending flag (local to this segment, but affects
% inferior segments)
% - set the path in progress flag
% - write the drawing command
% Notes:
% (1) The es PS command strokes the path at the end of a segment to
% ensure that the correct line parameters are used for the segment.
% The path before the corresponding bs command is restored and
% continued.
% (2) The \f@lushbs and \f@lushmove commands must be invoked before each
% drawing command written to the PS file. The macro \writeps includes
% these operations.
% Another awkward business has to do with initialization. We want a
% default (0 0) initial position so that the user can draw vectors
% immediately. However, if the user specifies another move before
% beginning to draw, that position should be the initial position. The
% importance of this initial position is that the determination of the
% maximum excursion must take this value into account. We handle the
% initialization in the \s@avemove and \f@lushmove macros. The macro
% \ifp@osinit indicates whether the next move should be captured as the
% initial values for \xminpix, \yminpix, \xmaxpix, and \ymaxpix. However,
% if a \f@lushmove is invoked, then we assume that the appropriate initial
% values have already been set. The "mv" command in PostScript is defined
% to stroke the current path (if any) and move to the pixel coordinates
% specified.
% Note that \m@pendingtrue and \m@pendingfalse define the flag locally.
% In addition, \x@savepix and \y@savepix are local variables. We make
% use of the fact that the values of the flag and positions propagate
% down to inferior segments but not up to superior segments. This
% behaviour Is consistent with the gsave/grestore operation on the
% PostScript side.
\def\s@avemove #1#2{\x@savepix=#1\y@savepix=#2%
\m@pendingtrue
\ifp@osinit \else
\global\p@osinittrue
\global\xminpix=\x@savepix \global\yminpix=\y@savepix
\global\xmaxpix=\x@savepix \global\ymaxpix=\y@savepix
\fi}
\def\f@lushmove {\global\p@osinittrue
\ifm@pending
\writetx {\the\x@savepix\space \the\y@savepix\space mv}%
\m@pendingfalse
\p@athfalse
\fi}
% ===== Flush begin segment
% \f@lushbs flushes any saved up \bsegments. Some of these may be
% redundant, but we cannot know without looking ahead beyond the
% \esegment.
\def\f@lushbs {\loop
\ifnum \d@bs>0
\writetx {bs}%
\global\advance \d@bs by -1
\repeat}
% ===== Internal text macros
% Horizontal text, use only 3 levels of box nesting here
\def\h@move #1#2 #3)#4{\move (#2 #3)%
\h@text {#4}}
\def\h@text #1{\pixtodim \x@pix \t@xpos
\pixtodim \y@pix \t@ypos
\vbox to 0pt{\normalbaselines
\t@stuff
\kern -\t@ypos
\hbox to 0pt{\l@stuff
\kern \t@xpos
\hbox {#1}%
\kern -\t@xpos
\r@stuff}%
\kern \t@ypos
\b@stuff\relax}}
% Rotated text
% Uses 5 levels of box nesting here (so that the text reference point
% is that <before> rotation). This was done so that the reference point
% definition makes sense with arbitrary angle rotation. The text is
% rotated with respect to the text reference point. The result is zero
% sized. These macros generate in-line PostScript.
% #1 - rotation angle in degrees
% #2 - text to be rotated
\def\r@move td:#1 #2#3 #4)#5{\move (#3 #4)%
\r@text td:#1 {#5}}
\def\r@text td:#1 #2{\vbox to 0pt{\pixtodim \x@pix \t@xpos
\pixtodim \y@pix \t@ypos
\kern -\t@ypos
\hbox to 0pt{\kern \t@xpos
\rottxt {#1}{\z@sb {#2}}%
\hss}%
\vss}}
\def\z@sb #1{\vbox to 0pt{\normalbaselines
\t@stuff
\hbox to 0pt{\l@stuff \hbox {#1}\r@stuff}%
\b@stuff}}
% ===== Rotate text, in-line PostScript code
\ifx \rotatebox\@undefined
\def\rottxt #1#2{\bgroup
\special {ps: gsave currentpoint currentpoint translate
#1\space neg rotate
neg exch neg exch translate}%
#2%
\special {ps: currentpoint grestore moveto}%
\egroup}
\else
\let\rottxt=\rotatebox
\fi
% ===== Error message
% If not defined, use the plain TeX errmessage macro
\ifx \t@xderror\@undefined
\let\t@xderror=\errmessage
\fi
% ===== Default values
% These are reset each time TeXdraw is invoked
\def\t@exdrawdef {\sppix 300/in % 300 pixels/inch
\drawdim in % drawing units are inches
\edef\u@nitsc {1}% % unit scale 1 (has to be set
% before invoking \setsegscale)
\setsegscale 1 % segment scale 1
\arrowheadsize l:0.16 w:0.08
\arrowheadtype t:T
\textref h:L v:B }
% ===============================================================
% ===== PostScript file macros ==================================
% ===== Include the TeXdraw graphics
% The drawing in a box of appropriate size will be placed such that its
% lower left hand corner will be at the current TeX position.
\ifx \includegraphics\@undefined
\def\t@xdinclude [#1,#2][#3,#4]#5{%
\begingroup % keep definitions local
\message {<#5>}%
\leavevmode
\t@counta=-#1% % integer bounding box coordinates
\t@countb=-#2%
\setbox0=\hbox{%
\special {PSfile="#5"\space
hoffset=\the\t@counta\space voffset=\the\t@countb}}%
\t@ypos=#4 bp%
\advance \t@ypos by -#2 bp%
\t@xpos=#3 bp%
\advance \t@xpos by -#1 bp%
\dp0=0pt \ht0=\t@ypos \wd0=\t@xpos
\box0%
\endgroup}
\else
\let\t@xdinclude=\includegraphics
\fi
% Leave space without including a PS file
\def\t@xdempty [#1,#2][#3,#4]{%
\begingroup
\leavevmode
\setbox0=\hbox{}%
\t@ypos=#4 bp%
\advance \t@ypos by -#2 bp%
\t@xpos=#3 bp%
\advance \t@xpos by -#1 bp%
\dp0=0pt \ht0=\t@ypos \wd0=\t@xpos
\box0%
\endgroup}
% ===== Write to the PostScript file
% Macro to write PostScript commands to the temporary PostScript file
% To decrease the size of the PostScript file, moves are kept back to
% allow redundant multiple moves to be removed. In addition empty gsave/
% grestore pairs are not written. The PostScript file is not opened if
% TeXdraw has not generated any PostScript commands, i.e. it has produced
% only TeX text.
% \writeps : flushes the pending move to make sure things are positioned
% correctly and flushes pending begin segments before calling
% \writetx to write to the PostScript file
% \writetx : writes directly to the PostScript file. This version is used
% only for those commands which just change line parameters
% without drawing. This routine opens the file and writes the
% PS file header the first time it is called.
% \p@swr : lowest level direct write to the PostScript file
\def\writeps #1{\f@lushbs
\f@lushmove
\p@athtrue
\writetx {#1}}
\def\writetx #1{\p@sopen
\ifx\p@sfile\p@sundef \else
\p@swr {#1}%
\fi}
\def\p@swr #1{\immediate\write\drawfile {#1}}
% ===== Open/Close a PostScript file
% Open a PostScript file, write the definitions used by TeXdraw.
\xdef\p@sundef{UnDeFiNeD}
\def\p@sopen {%
\ifx\p@sfile\p@sundef
\p@sopenI
\fi
}
% The code has a hook to avoid generating the PS file under certain
% circumstances. The amsmath package sometimes sets an expression twice,
% once to measure it and again to actually typeset it. In the first case,
% \ifmeasuring@ is set to true. For that setting, the PS file is not
% generated.
\def\p@sopenI {%
\ifx\ifmeasuring@\iftrue \else % \ifmeasuring@ undefined or false
\global\advance \t@xdnum by 1
\ifnum \t@xdnum<10
\xdef \p@sfile{\jobname.ps\the\t@xdnum}%
\else
\xdef \p@sfile{\jobname.p\the\t@xdnum}%
\fi
\t@xdopen \p@sfile
\fi
}
\def\p@sclose {
\ifx\p@sfile\p@sundef \else
\t@xdclose
\fi
}
\def\t@xdopen #1{%
\immediate\openout\drawfile=#1%
\p@swr {\p@b PS-Adobe-3.0 EPSF-3.0}%
\p@swr {\p@p BoundingBox: (atend)}%
\p@swr {\p@p Title: TeXdraw drawing: #1}%
\p@swr {\p@p Pages: 1}%
\p@swr {\p@p Creator: \TeXdrawId}%
\p@swr {\p@p CreationDate: \the\year/\the\month/\the\day}%
\p@swr {50 dict begin}%
\p@swr {/mv {stroke moveto} def}%
\p@swr {/lv {lineto} def}%
\p@swr {/st {currentpoint stroke moveto} def}%
\p@swr {/sl {st setlinewidth} def}%
\p@swr {/sd {st 0 setdash} def}%
\p@swr {/sg {st setgray} def}%
\p@swr {/bs {gsave} def /es {stroke grestore} def}%
\p@swr {/fl \l@br gsave setgray fill grestore}%
\p@swr { currentpoint newpath moveto\r@br\space def}%
\p@swr {/fp {gsave setgray fill grestore st} def}%
\p@swr {/cv {curveto} def}%
\p@swr {/cr \l@br gsave currentpoint newpath 3 -1 roll 0 360 arc}%
\p@swr { stroke grestore\r@br\space def}%
\p@swr {/fc \l@br gsave setgray currentpoint newpath}%
\p@swr { 3 -1 roll 0 360 arc fill grestore\r@br\space def}%
\p@swr {/ar {gsave currentpoint newpath 5 2 roll arc stroke grestore} def}%
\p@swr {/el \l@br gsave /svm matrix currentmatrix def}%
\p@swr { currentpoint translate scale newpath 0 0 1 0 360 arc}%
\p@swr { svm setmatrix stroke grestore\r@br\space def}%
\p@swr {/fe \l@br gsave setgray currentpoint translate scale newpath}%
\p@swr { 0 0 1 0 360 arc fill grestore\r@br\space def}%
\p@swr {/av \l@br /hhwid exch 2 div def /hlen exch def}%
\p@swr { /ah exch def /tipy exch def /tipx exch def}%
\p@swr { currentpoint /taily exch def /tailx exch def}%
\p@swr { /dx tipx tailx sub def /dy tipy taily sub def}%
\p@swr { /alen dx dx mul dy dy mul add sqrt def}%
\p@swr { /blen alen hlen sub def}%
\p@swr { gsave tailx taily translate dy dx atan rotate}%
\p@swr { (V) ah ne {blen 0 gt {blen 0 lineto} if} {alen 0 lineto} ifelse}%
\p@swr { stroke blen hhwid neg moveto alen 0 lineto blen hhwid lineto}%
\p@swr { (T) ah eq {closepath} if}%
\p@swr { (W) ah eq {gsave 1 setgray fill grestore closepath} if}%
\p@swr { (F) ah eq {fill} {stroke} ifelse}%
\p@swr { grestore tipx tipy moveto\r@br\space def}%
\p@swr {\p@sfactor\space \p@sfactor\space scale}%
\p@swr {1 setlinecap 1 setlinejoin}%
\p@swr {3 setlinewidth [] 0 setdash}%
\p@swr {0 0 moveto}%
}
% Notes:
% - mv (move to) This command includes a stroke before the moveto. The
% stroke terminates a path and the move begins another path.
% - bs (begin segment) encloses a segment in a gsave/grestore to keep
% changes to line parameters local.
% - es (end segment) does a "stroke grestore" to make sure lines inside
% the segment use the line parameters local to that segment
% - ar (arc) The path is generated and stroked inside a gsave/grestore,
% leaving the current path intact.
% - cr (circle) The path is generated and stroked inside a gsave/grestore,
% leaving the current path intact.
% - fc (filled circle) The path is generated and filled inside a gsave/
% grestore, keeping the fill level local to the circle. The current
% path is left intact.
% - el (ellipse) The path is generated and stroked inside a gsave/grestore,
% leaving the current path intact. The elliptical path is defined
% with different x and y scaling, then stroked with default scaling
% to give a constant line thickness.
% - fe (filled ellipse) The path is generated and filled inside a gsave/
% grestore, leaving the current path intact.
% - fl (fill) The current path is closed and filled inside a gsave/restore,
% keeping the fill level local. A newpath terminates the path.
% - fp (fill path) The current path is closed and then filled inside a
% gsave/grestore. Finally the closed path is stroked, implicitly
% terminating the path.
% - av (arrow vector) The arrow vector is drawn inside a gsave/grestore.
% The line width and type are those currently in effect. After the
% grestore, the current path is continued with a move to the tip of
% the vector.
% ===== Close the PostScript file
% Write a trailer with the BoundingBox, close the file. Note that the
% BoundingBox may be larger than the commands in the PostScript file
% indicate. This is due to the fact that multiple move commands in
% a row are collapsed into a single move. The BoundingBox information
% includes the effect of the moves which were expunged.
\def\t@xdclose {%
\bgroup
\p@swr {stroke end showpage}%
\p@swr {\p@p Trailer:}%
\pixtobp \xminpix \l@lxbp \pixtobp \yminpix \l@lybp
\pixtobp \xmaxpix \u@rxbp \pixtobp \ymaxpix \u@rybp
\p@swr {\p@p BoundingBox: \l@lxbp\space \l@lybp\space
\u@rxbp\space \u@rybp}%
\p@swr {\p@p EOF}%
\egroup
\immediate\closeout\drawfile
}
% ===============================================================
\catcode`\@=\catamp
