path: root/Master/texmf-dist/source/generic/xypic/xynecula.doc

%% $Id$
%%
%% Xy-pic ``Necula extensions'' option.
%% Copyright (c) 1998	         George C. Necula	<necula@cs.cmu.edu>
%%
%% 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  <krisrose@ens-lyon.fr>
%%
%% 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 <modifier>s, and a way to specify
	arbitrary polygons as the <shape> of an object.

\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsection{Expansion}

	The special syntax ??c![e|]<macros>|||| is introduced in
	an object ??w![<modifier>]s and ??w![<coord>]inates.  It
	expands the given \TeX\ <macros> (with |\edef|) before
	reinterpretation as a <modifier> of <coord>, 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 <shape> is specified as
%
\begin{defs1}
%
 ??c![[P:]<pos>|,|\dots|,|<pos>|]|
%
\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. <vector>s and <corner>s can be used
	directly; otherwise use |-p| to get the relative position.

        \NOTE: Do not use |{}| or |[]| in the <pos>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<id>.
\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<id>.
%
%
% 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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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