%% $Id$ %% %% Xy-pic ``Necula extensions'' option. %% Copyright (c) 1998 George C. Necula %% %% This file is part of the Xy-pic package for graphs and diagrams in TeX. %% See the companion README and INSTALL files for further information. %% Copyright (c) 1991-1998 Kristoffer H. Rose %% %% The Xy-pic package is free software; you can redistribute it and/or modify %% it under the terms of the GNU General Public License as published by the %% Free Software Foundation; either version 2 of the License, or (at your %% option) any later version. %% %% The Xy-pic package is distributed in the hope that it will be useful, but %% WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY %% or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License %% for more details. %% %% You should have received a copy of the GNU General Public License along %% with this package; if not, write to the Free Software Foundation, Inc., %% 675 Mass Ave, Cambridge, MA 02139, USA. %% \ifx\xyloaded\undefined \input xy \fi \xyprovide{necula}{Necula's extensions}{\stripRCS$Revision: 0.0 $}% {George C. Necula}{necula@cs.cmu.edu}% {School of Computer Science, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213-3891, USA} \DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \paragraph*{Header:}\leavevmode \DOCHEADER \DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% This option contains two extensions of the \Xy-pic kernel: A way to expand \TeX\ macros in object s, and a way to specify arbitrary polygons as the of an object. \DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Expansion} The special syntax ??c![e|]|||| is introduced in an object ??w![]s and ??w![]inates. It expands the given \TeX\ (with |\edef|) before reinterpretation as a of , respectively. \DOCMODE( \def\expandbeforenext@#1{% \DN@ e|##1|{\edef\tmp@{##1}\expandafter\xyFN@\expandafter#1\tmp@}% } \xylet@\xy@oldOBJECT@=\OBJECT@ \xydef@\xy@newOBJECT@{% \ifx \space@\next \expandafter\DN@\space{\xyFN@\xy@newOBJECT@}%gobble spaces \else\ifx e\next \expandbeforenext@\OBJECT@ \else \DN@{\xy@oldOBJECT@}\fi\fi \next@}% \let\OBJECT@=\xy@newOBJECT@ \xylet@\xy@oldCOORD@=\COORD@ \xydef@\xy@newCOORD@{% \ifx \space@\next \expandafter\DN@\space{\xyFN@\xy@newCOORD@}%gobble spaces \else\ifx e\next \expandbeforenext@\COORD@ \else \DN@{\xy@oldCOORD@}\fi\fi \next@}% \let\COORD@=\xy@newCOORD@ \DOCMODE) This code may become part of the \Xy-pic kernel at a certain point. \DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Polygon shapes} A polygon is specified as % \begin{defs1} % ??c![[P:]|,|\dots|,||]| % \end{defs1} \noindent\unskip % where |[P:|$p_1$|,|\dots|,|$p_n$|]| denotes the shape obtained by tracking the edge with each $p_i$ a position relative to the object reference point. s and s can be used directly; otherwise use |-p| to get the relative position. \NOTE: Do not use |{}| or |[]| in the itions. \BUG: The algorithm assumes that the reference point is always inside the polygon. It is possible to frame polygons is also possible. \DOCMODE( % Define the polygon as a stylechar so that it is deferred \xydefcsname@{*stylechar@P@}#1{\Pshape@#1@} \xynew@{count}\c@poly@count \c@poly@count=\z@ % Polygon identifiers \xydef@\Pshape@:#1@{% Strip the mandatory : \addtotoks@{% % \xy@showthe c{Before parse}\xy@showthe p{Before parse}% % \xy@showdim{Before parse}% \def\poly@list{@}% \poly@parse #1,\relax,%Sets the poly@list \def\poly@cache{}% \edef\poly@id{\the\c@poly@count}% \global\advance\c@poly@count\@ne \poly@setEdge % Save the old values of Lc for shifting \edef\poly@saveLcshape{\the\L@c}% \polygonEdge@Outer% Set U,R,D,L \poly@setEdge % Now shift the object to keep it centered \dimen@=\poly@saveLcshape\advance\dimen@-\L@c \advance\R@p -\dimen@ % \xy@showthe c{After parse}% }} % Set the edge % A polygonal edge is represented as \polygonEdge x1,y1;x2,y2;...;xn,yn@id@ % where xi,yi define the vertices of the polygonal edge as displacement from % the object reference point (xn=x1,yn=y1), and id is a numerical id used for % caching the result of the last intersection operation. The cached values for % polygon id are stored in the global macro poly@cache. \xydef@\poly@setEdge{\expandafter\poly@setEdge@\poly@list\poly@id} \xydef@\poly@setEdge@#1@#2{\Edge@c={\polygonEdge#1@#2@}% \expandafter\xdef\csname poly@cache#2% \endcsname{\poly@cache}} % Define the polygon framing operations \xydefcsname@{frm[P]{-}}{\expandafter\draw@polyframe\the\Edge@c{-}} \xydefcsname@{frm[P]{.}}{\expandafter\draw@polyframe\the\Edge@c{.}} \xydefcsname@{frm[P]{=}}{\expandafter\draw@polyframe\the\Edge@c{=}} \xydef@\draw@polyframe\polygonEdge#1@#2@#3{% \def\poly@dir{#3}% \def\poly@list{#1@}% \def\poly@id{#2}% \edef\poly@cache{\csname poly@cache\poly@id\endcsname}% \draw@polygon} % A polygon is maintained as a list of relative positions, as follows: % poly@list = Xdimen_0,Ydimen_0;...;Xdimen_n,Ydimen_n @ % The list is closed, i.e., the first and last element coincide % Each polygon has an id storred in \poly@id % Each polygon caches the result of the last intersection operation % as d@x,d@y,x1,y1,x2,y2 where the first two values define the slope % and the two sets of points are the two intersection points % These values are storred in \poly@cache. % % % Helper function for dealing with polygon lists % Map over a polygon list. Make sure you define % \let\poly@map@next=\poly@map before. Then, you can define % \let\poly@map@next=\poly@map@stop if you want to stop the traversal \xydef@\poly@empty{} \xydef@\poly@map#1#2,#3;#4@{% #1{#2}{#3}% \def\tmp@{#4}% \ifx \poly@empty\tmp@ \else \poly@map@next#1#4@% \fi } \xydef@\poly@map@stop#1@{} \xydef@\poly@mapExpand#1#2{% \edef\tmp@{\noexpand\poly@map\noexpand #1#2}% \tmp@} % Parse a polygon definition \xydef@\poly@parse #1,{% \ifx #1\relax %Done. Copy the head of the list at its end \poly@close \let\next@=\relax \else % Save everything \save@ % Process the position using POS \POS #1% % Now add the new c to the list \edef\tmp@{{\the\X@c}{\the\Y@c}}% \expandafter\poly@append\tmp@ \restore \let\next@=\poly@parse % continue parsing \fi \next@ } % Append to the list of polygon points \xydef@\poly@append#1#2{\expandafter\poly@append@\poly@list{#1,#2;}} \xydef@\poly@append@#1@#2{\global\def\poly@list{#1#2@}} % Close the polygon \xydef@\poly@close{\expandafter\poly@close@\poly@list} \xydef@\poly@close@#1,#2;#3@{\poly@append{#1}{#2}} % Draw a polygon at the current location \xydef@\draw@polygon{% First separate the head % \W@{Drawing polygon \poly@list}\xy@showthe c{ Centered at}% \save@ % Set the origin to point at the reference point \X@origin=\X@c \Y@origin=\Y@c \poly@setp % Set p at the beginning of the polygon and set poly@rest % Zero the edges \U@c=\z@\R@c=\z@\D@c=\z@\L@c=\z@\U@p=\z@\R@p=\z@\D@p=\z@\L@p=\z@ \Edge@c={\zeroEdge}\Edge@p={\zeroEdge}% \let\poly@map@next=\poly@map \poly@mapExpand\poly@drawseg\poly@rest \restore } % Set p to the first element. Requires the origin to be % at the reference point \xydef@\poly@setp{\expandafter\poly@setp@\poly@list} \xydef@\poly@setp@#1,#2;#3@{% \X@p=#1\advance\X@p\X@origin \Y@p=#2\advance\Y@p\Y@origin% \global\def\poly@rest{#3@}} \xydef@\poly@drawseg#1#2{% \dimen@=#1\X@c=\the\dimen@\advance\X@c \X@origin \dimen@=#2\Y@c=\the\dimen@\advance\Y@c \Y@origin % \W@{Next segment is at offset #1,#2 and absolute \the\X@c,\the\Y@c}% \expandafter\connect@\expandafter\dir\poly@dir% \X@p=\X@c\Y@p=\Y@c} % Polygonal edge % Requires c to be the reference point \xydef@\polygonEdge#1@#2@#3{% \def\poly@list{#1@}% \def\poly@id{#2}% \edef\poly@cache{\csname poly@cache\poly@id\endcsname}% \ifcase#3\relax \DN@{\polygonEdge@Inters % \ifpoly@badinters % \xyerror@{Could not find intersection for polygon}\fi }%0 \or \DN@{\polygonEdge@Under}%1 \or \DN@{\polygonEdge@Dist}%2 \or \DN@{\rectangleProp@}%3 I do not understand Prop! \or \DN@{\polygonEdge@Inner}%4 \or \DN@{\polygonEdge@Outer}%5 \else \DN@{}\fi \next@} \newif\ifpoly@badinters \xydef@\polygonEdge@Inters{% % \W@{Edge intersection with (\the\X@c, \the\Y@c) -> (\the\X@p,\the\Y@p)}% % \W@{ for polygon: \poly@id}% % \W@{ with list: \poly@list}% % \W@{ with cache: \poly@cache}% % Check the cache first \ifx\poly@cache\poly@empty \poly@intersdoit \else \expandafter\poly@intersprobecache\poly@cache @% \fi % \xy@showthe c{Inters res}% } % % Redefine poly@cachehit to poly@cachehitdisable to diable polygon caching \xydef@\poly@cachehit#1#2{% % \W@{ intersection point found in cache}% \X@c=#1\Y@c=#2} \xydef@\poly@cachehitdisable#1#2{\poly@intersdoit} %\let\poly@cachehit=\poly@cachehitdiasable% Uncomment this line to disable $ % Probes the cache % \xydef@\poly@intersprobecache#1,#2,#3,#4,#5@{% \dimen@=#1\advance\dimen@-\d@X \ifdim\zz@\dimen@ \dimen@=#2\advance\dimen@-\d@Y \ifdim\zz@\dimen@ \poly@cachehit{#3}{#4} \else \poly@intersdoit \fi \else \poly@intersdoit \fi } % Computes the intersection between the line cp and the edge. % Both intersection points are stored in the cache, the one in the % direction towards p first. \xydef@\poly@intersdoit{% % \W@{ intersection not in cache. Computing it}% % Save A@ and B@ because we cannot change them \edef\polyoldA@{\the\A@}\edef\polyoldB@{\the\B@}% % Initialize the intersection points \def\poly@intersneg{}\def\poly@interspos{}% \save@ \poly@setorigin % Set origin at the beginning of the polygon and % set poly@rest \def\zeroDivide@{\poly@badinterstrue}% Handle the division by zero except. \let\poly@map@next=\poly@map \poly@mapExpand\poly@interseg\poly@rest \ifx\poly@intersneg\poly@empty \poly@badinterstrue \else \ifx\poly@interspos\poly@empty \poly@badinterstrue \else \poly@badintersfalse \fi \fi \restore \A@=\polyoldA@\B@=\polyoldB@ % Restore A@ and B@ \ifpoly@badinters \else \edef\tmp@{\poly@interspos,\poly@intersneg @}% \expandafter\poly@intersfinish\tmp@ \fi } \xydef@\poly@intersfinish#1,#2,#3@{% \X@c=#1\Y@c=#2\relax \xdef\poly@cache{\the\d@X,\the\d@Y,#1,#2,#3}% \poly@setEdge } % Set origin to the first point. Define poly@rest % Requires c to be set to the reference point \xydef@\poly@setorigin{\expandafter\poly@setorigin@\poly@list} \xydef@\poly@setorigin@#1,#2;#3@{% \X@origin=#1\advance\X@origin\X@c \Y@origin=#2\advance\Y@origin\Y@c% \global\def\poly@rest{#3@}} % % Compute one intersection with a given edge % c is set to the reference point, p is set to the end of the ray % origin is set to the start of the segment \xydef@\poly@interseg#1#2{% % Default is no intersection % \W@{ Intersection with edge (\the\X@origin,\the\Y@origin) -> (#1,#2)}% % Compute the absolute values \dimen@=#1\advance\dimen@\X@c \edef\poly@saveXcinters{\the\dimen@}% \dimen@=#2\advance\dimen@\Y@c \edef\poly@saveYcinters{\the\dimen@}% \save@ \poly@badintersfalse % Set R@c and U@c to the distance to end of segment \R@c=\poly@saveXcinters \advance\R@c -\X@origin \U@c=\poly@saveYcinters \advance\U@c -\Y@origin % Now call intersect to set X@c and Y@c to the intersection point \intersect@ \A@=\X@c \B@=\Y@c % Save result \restore \ifpoly@badinters % \W@{ \space failed after intersect}% \else % \W@{ \space after intersect@ (\the\A@,\the\B@)}% % Verify that it is on the segment from origin to (#1, #2) \poly@isonseg\X@origin\Y@origin\A@\B@\poly@saveXcinters\poly@saveYcinters \ifpoly@badinters % \W@{ \space failed after seg check}% \else % Verify that (A,B) is on the ray from c to p \poly@isonray\X@c\Y@c\A@\B@\X@p\Y@p \ifpoly@badinters % It is on the negative ray % \W@{ \space a negative intersection}% \edef\poly@intersneg{\the\A@,\the\B@}% \else % \W@{ \space a positive intersection}% \edef\poly@interspos{\the\A@,\the\B@}% \fi \fi \fi % Set the origin to the start of the next segment \X@origin=\poly@saveXcinters\Y@origin=\poly@saveYcinters } % % Computes the distance from reference point to the intersection % \xydef@\polygonEdge@Dist{\xyerror@{Dist is not yet implemented for polygons}} % % Checks that #1 <= #2 <= #3 or that #3 <= #2 <= #1 % Sets ifpoly@badinters otherwise % ifpoly@closedrange decides whether the second inequality is also checked % All checks are done with a precision of 100*almostz@ =~ 5000sp = 0.08pt \newif\ifpoly@closedrange \xydef@\poly@isinrange#1#2#3{% \ifpoly@badinters \else \dimen@=#1\dimen@i=#2\dimen@ii=#3\relax % \W@{check if in \ifpoly@closedrange closed\else open\fi\space % range 1=\the\dimen@,2=\the\dimen@i,3=\the\dimen@ii}% \advance\dimen@ii -\dimen@ \advance\dimen@i -\dimen@ \ifdim\dimen@ii<0pt\relax \ifdim\dimen@i>100\almostz@ \poly@badinterstrue \fi \dimen@i=-\dimen@i \dimen@ii=-\dimen@ii \else \ifdim\dimen@i<-100\almostz@\relax \poly@badinterstrue \fi \fi \ifpoly@closedrange \advance\dimen@ii 100\almostz@ \ifdim\dimen@i>\dimen@ii \poly@badinterstrue \fi \fi % \ifpoly@badinters \W@{ failed}\else\W@{ succeeded}\fi \fi} % % Checks that (#3,#4) is on a segment defined by (#1,#2)->(#5,#6) \xydef@\poly@isonseg#1#2#3#4#5#6{% % Check X first \poly@closedrangetrue \poly@isinrange{#1}{#3}{#5}% \poly@isinrange{#2}{#4}{#6}% } % % Checks that (#3,#4) is on a ray defined by (#1,#2)->(#5,#6) \xydef@\poly@isonray#1#2#3#4#5#6{% % Check X first \poly@closedrangefalse \poly@isinrange{#1}{#3}{#5}% \poly@isinrange{#2}{#4}{#6}% } % % Test whether (Xp,Yp) is inside the polygon (or on the edge) % Sets \ifInside@ accordingly \xydef@\polygonEdge@Under{% % \W@{}\W@{Edge Under with c=(\the\X@c,\the\Y@c) and p=(\the\X@p,\the\Y@p)}% % \W@{ for polygon: \poly@list}% % Save A@ and B@ \edef\polysaveA@under{\the\A@}\edef\polysaveB@under{\the\B@}% % Save X@c and Y@c \edef\poly@saveXcUnder{\the\X@c}\edef\poly@saveYcUnder{\the\Y@c}% % Compute the intersection \polygonEdge@Inters \ifpoly@badinters% p is very close to c \Inside@true \else \A@=\X@c\B@=\Y@c % Restore c \X@c=\poly@saveXcUnder\Y@c=\poly@saveYcUnder % Now verify that the intersection point is on the ray c->p \poly@isonseg\X@c\Y@c\X@p\Y@p\A@\B@ \ifpoly@badinters \Inside@false \else \Inside@true\fi \A@=\polysaveA@under\B@=\poly@saveB@under \fi % \ifInside@\W@{->inside}\else\W@{->outside}\fi } % % Compute the inner rectangle % \xydef@\polygonEdge@Inner{% % \W@{}\W@{Edge Inner with (\the\X@c, \the\Y@c) -> (\the\X@p,\the\Y@p)}% % \W@{ for polygon: \poly@list}% % \W@{ with cache: \poly@cache}% % Save everything except c \enter@{\basefromthebase@ \pfromthep@ \DirectionfromtheDirection@}% % Save c in Lc,Dc \L@c=\X@c \D@c=\Y@c % Compute the two intersection points \polygonEdge@Inters \ifpoly@badinters \czeroEdge@ \else % Save the result in Rc,Uc and in X@c,Y@c \expandafter\poly@getinterspoints\poly@cache @% % Now compute the inner rectangle centered \ifdim\X@c>\R@c \L@c=\R@c \R@c=\X@c \else \L@c=\X@c \fi \X@c=0.5\L@c \advance\X@c 0.5\R@c \advance\R@c -\X@c \L@c=\R@c \ifdim\Y@c>\U@c \D@c=\U@c \U@c=\Y@c \else \D@c=\Y@c \fi \Y@c=0.5\D@c \advance\Y@c 0.5\U@c \advance\U@c -\Y@c \D@c=\U@c \Edge@c={\rectangleEdge}% \fi \leave@ % \xy@showthe c{After inner}% } \xydef@\poly@getinterspoints#1,#2,#3,#4,#5,#6@{% \R@c=#3\U@c=#4\X@c=#5\Y@c=#6} % % Compute the outer rectangle (set Uc,Dc,Lc,Rc and Edgec). % Does not change Xc,YC % \xydef@\polygonEdge@Outer{% % \W@{Computing outer for \poly@list}\xy@showthe c{Before outer}% % Save everything except c \enter@{\basefromthebase@ \pfromthep@ \DirectionfromtheDirection@}% \czeroEdge@ % Zero out c \let\poly@map@next=\poly@map \poly@mapExpand\poly@findextent\poly@list \Edge@c={\rectangleEdge}% \leave@ % \xy@showthe c{After outer} } \xydef@\poly@findextent#1#2{% % \xy@showthe c{Before find extent}% % \W@{ extx=#1, exty=#2}% \dimen@=#1\dimen@=\the\dimen@% it fails if I remove the second assign \ifdim\dimen@>\R@c \R@c=\dimen@ \fi \ifdim -\dimen@>\L@c \L@c=-\dimen@ \fi \dimen@=#2\dimen@=\the\dimen@% it fails if I remove the second assign \ifdim\dimen@>\U@c \U@c=\dimen@ \fi \ifdim -\dimen@>\D@c \D@c=-\dimen@ \fi % \xy@showthe c{ After extent}% } % Change to account for polynomial shapes, in addition to circular ones % \xydef@\Fshape@#1:{\def\whichframe@@{{#1}}\let\whichoptions@@=\empty \DN@{{}}\ifx\whichframe@@\next@ \def\whichframe@@{{-}}\fi \expandafter\xyFN@\expandafter\Fshape@whichframe\the\Edge@c} \xydef@\Fshape@whichframe{% \ifx\next\circleEdge \edef\whichframe@@{[o]\whichframe@@}% \DN@##1{\xyFN@\Fshape@i}% \else \ifx\next\polygonEdge \edef\whichframe@@{[P]\whichframe@@}% \DN@\polygonEdge##1@##2@{\xyFN@\Fshape@i}% \else \DN@##1{\xyFN@\Fshape@i}% \fi\fi \next@ } \xyendinput \DOCMODE) \DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \BUG: This code should be merged with the `frame' and `poly' options. The example at the end of \S??g[:smart] illustrates the extensions. \DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \DOCMODE( % $Log$ % Received from George. \DOCMODE) \DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Tell Emacs that this is a LaTeX document and how it is formatted: % Local Variables: % mode:latex % fill-prefix:"\t" % fill-column:77 % paragraph-separate:"^[ \t\f]*$\\|^[^\t]\\|\\\\\\\\\\|\\$\\$\\|[^\n\\\\][%&]" % paragraph-start:"^[ \t\f]*$\\|^[^\t]\\|\\\\\\\\\\|\\$\\$\\|[^\n\\\\][%&]" % End: