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-%% $Id: xyarrow.doc,v 3.5 1997/05/28 13:05:01 krisrose Exp $
-%%
-%% Xy-pic ``Arrows and Paths'' feature.
-%% Copyright (c) 1991-1997 Kristoffer H. Rose <krisrose@brics.dk>
-%%
-%% 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) 1991-1997 Kristoffer H. Rose <krisrose@brics.dk>
-%%
-%% 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{arrow}{Arrow and Path feature}{\stripRCS$Revision: 3.5 $}%
- {Kristoffer H.~Rose}{krisrose@brics.dk}%
- {BRICS/Computer Science, University of Aarhus, Ny Munkegade, building 540,
- DK--8000 Aarhus~C}
-
-\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
- This feature provides \Xy-pic with the arrow paradigm presented
- in~\cite{R92:HowTPDAT}.
-
- \NOTE: |\PATH| command incompatibly changed for version 3.3 (the
- |\ar| command is unaffected).
-
- The basic concept introduced is the "path": a connection that
- "starts" from $c$ (the current object), "ends" at a specified object,
- and may be split into several "segments" between intermediate
- specified objects that can be individually labelled, change style,
- have breaks, etc.
-
- \S??[path] is about the |\PATH| primitive, including the syntax of
- paths, and \S??[arrow] is about the |\ar| customisation of paths to
- draw arrows using \Xy-pic directional objects.
-
-\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\paragraph*{Header:}\leavevmode
-\DOCHEADER
-\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-
-\subsection{Paths}
-??=[path]
-
-\DOCMODE(
-\message{path,}
-\DOCMODE)
-
- The fundamental commands of this feature are ??c![\PATH] and
- ??c![\afterPATH] that will parse the <path> according to the grammar
- in figure~??[f.path] with notes below.
-
-\begin{figure*}[tb]
-\begin{syntax}
-%
- \multispan{3}{{\tt\string\PATH} <path>\hfil}
- & interpret <path>
-\cr
-%
- \multispan{3}{{\tt\string\afterPATH\string{<decor>\string}} <path>\hfil}
- & interpret <path> and then run <decor>
-\cr
-\noalign{\nobreak\smallskip\nobreak\hrule\nobreak\smallskip\nobreak}
-%
- <path>
- &\iss & ??c![~] <action> |{| <stuff> |}| <path>
- & set ??!^[<action>] to <stuff>
-\cr
- &\orr & ??c![~] <which> |{| <labels> |}| <path>
- & add ??!^[<labels> prefix for some segments]
-\cr
- &\orr & ??c![~] |{| <stuff> |}| <path>
- & set ??!^[failure continuation] to <stuff>
-\cr
- &\orr & ??c!['] <segment> <path>
- & make ??!^[straight segment]
-\cr
- &\orr & ??c![`] <turn> <segment> <path>
- & make ??!^[turning segment]
-\cr
- &\orr & <segment>
- & make ??!^[last segment]
-\cr
-\noalign{\smallskip}
-%
- <turn>
- &\iss & <diag> <turnradius>
- & ??!^[1/4 turn] starting in <diag>
-\cr
- &\orr & <cir> <turnradius>
- & ??!^[explicit turn]
-\cr
-%
- <turnradius>
- &\iss & <empty>
- & use default turn radius
-\cr
- &\orr & ??c![/] <dimen>
- & set "turnradius" to <dimen>
-\cr
-\noalign{\smallskip}
-%
- <segment>
- &\iss & <path-pos> <slide> <labels>
- & ??!^[segment] with <slide> and <labels>
-\cr
-\noalign{\smallskip}
-%
- <slide>
- &\iss & <empty> \orr\ ??c![<] <dimen> ??c![>]
- & optional ??!^[slide]: <dimen> in the ``above'' direction
-\cr
-\noalign{\smallskip}
-%
- <labels>
- &\iss & ??c![^] <anchor> <it> <alias> <labels>
- & ??!^[label with <it>] "above" <anchor>
-\cr
- &\orr & ??c![_] <anchor> <it> <alias> <labels>
- & ??!^[label with <it>] "below" <anchor>
-\cr
- &\orr & ??c![|] <anchor> <it> <alias> <labels>
- & ??!^[break with <it>] at <anchor>
-\cr
- &\orr & <empty>
- & no more labels
-\cr
-\noalign{\smallskip}
-%
- <anchor>
- &\iss & ??c![-] <anchor> \orr\ <place>
- & label/break placed relative to the <place> where ??c![-] is a synonym
- for ??c![<>(.5)]
-\cr
-\noalign{\smallskip}
-%
- <it>
- &\iss & <digit>\orr<letter>\orr|{|<text>|}|\orr<cs>
- & <it> is a ??!^[default label]
-\cr
- &\orr & ??c![*] <object>
- & <it> is an <object>
-\cr
- &\orr & ??c![@] <dir>
- & <it> is a <dir>ectional
-\cr
- &\orr & |[| <shape> |]| <it>
- & use |[|<shape>|]| for <it>
-\cr
-\noalign{\smallskip}
-%
- <alias>
- &\iss & <empty> \orr\ ??c![=]|"|<id>|"|
- & optional ??!^[name for label object]
-\cr
-\end{syntax}
-\caption{\protect<path>s}
-??=[f.path]
-\end{figure*}
-
-\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\paragraph*{Parsing:}
-
- |\afterPATH| sets up |\afterPATH@| and initialise all the actions
- (see note~??[<action>] below) before invoking the actual <path>
- parser. |\PATH| is just a dummy interface.
-
-\DOCMODE(
-\xydef@\PATH{\afterPATH{}}
-
-\xylet@\afterPATH@=\empty
-
-\xydef@\afterPATH#1{\save
- \DN@##1{\def\afterPATH@{\restore \def\afterPATH@{##1}#1}}%
- \expandafter\next@\expandafter{\afterPATH@}%
- \let\PATHfail@@=\empty
- \let\PATHbefore@@=\empty
- \let\PATHafter@@=\empty
- \let\PATHlabelsevery@@=\empty
- \let\PATHlabelsnext@@=\empty
- \let\PATHlabelslast@@=\empty
- \xy@{\afterPATH{#1}}{\def\PATHslide@@{\z@}}%
- \def\PATHcontinue@@{\xyFN@\PATH@}%
- \xyFN@\PATH@}
-\DOCMODE)
-
- |\PATH@| is the parser for <path>: it eats the <path> until it fails
- and then calls the `failure continuation' which will eventually
- become |\empty| which ends the parsing. \HACK: The
- `|\ifPATHsingle@|' switch switches the <segment> parsing "off"; this
- is used by the graph feature to parse stand-alone <slide> <labels>
- sequences.
-
-\DOCMODE(
-\xynew@{if}\ifPATHsingle@
-
-\xydef@\PATH@{%
- \ifx \space@\next \expandafter\DN@\space{\xyFN@\PATH@}%
- \else\ifPATHsingle@ \let\next@=\PATH@single
- \else \let\next@=\PATH@normal \fi\fi \next@}
-
-\xydef@\PATH@normal{%
- \ifx ~\next \DN@ ~{\xyFN@\PATHsetting@}%
- \else \addRQ@\ifx \next \addRQ@\DN@{\xy@'{}\xyFN@\PATHstraight@}%
- \else \addLQ@\ifx \next \addLQ@\DN@{\xy@`{}\xyFN@\PATHturn@}%
- \else\ifx \PATHfail@@\PATH@x \DN@{\xyFN@\PATHfinal@}%
- \else
- \DNii@{\let\PATHfail@@=\PATH@x \xyFN@\PATH@}%
- \DN@{\expandafter\nextii@\PATHfail@@}%
- \fi\fi\fi\fi \next@}
-\DOCMODE)
-
- |\PATHsetting@| just reads an <action> or <which> determining which
- action stuff to set and then does it---we treat the failure
- continuation as an action here even though it is not, strictly
- speaking. The four actions are explained in the appropriate notes
- below.
-
-\DOCMODE(
-\xylet@\PATHfail@@=\empty
-
-\xylet@\PATHbefore@@=\empty
-\xylet@\PATHafter@@=\empty
-
-\xylet@\PATHlabelsevery@@=\empty
-\xylet@\PATHlabelsnext@@=\empty
-\xylet@\PATHlabelslast@@=\empty
-
-\xydef@\PATHsetting@{%
- \ifx \space@\next \expandafter\DN@\space{\xyFN@\PATHsetting@}%
- \else\ifx \bgroup\next
- \DN@##1{\xy@{~{##1}}{}\def\PATHfail@@{##1}\xyFN@\PATH@}%
- \else \addEQ@\ifx \next
- \addEQ@\DN@##1{\xy@{~={##1}}{}\def\PATHbefore@@{##1}\xyFN@\PATH@}%
- \else \addLT@\ifx \next
- \addLT@\DN@##1{\xy@{~<{##1}}{}\def\PATHlabelsnext@@{##1}\xyFN@\PATH@}%
- \else \addGT@\ifx \next
- \addGT@\DN@##1{\xy@{~>{##1}}{}\def\PATHlabelslast@@{##1}\xyFN@\PATH@}%
- \else \addPLUS@\ifx \next
- \addPLUS@\DN@##1{\xy@{~+{##1}}{}\def\PATHlabelsevery@@{##1}\xyFN@\PATH@}%
- \else \ifx /\next
- \DN@/##1{\xy@{~/{##1}}{}\def\PATHafter@@{##1}\xyFN@\PATH@}%
- \else \addDASH@\ifx \next
- \xywarning@{Obsolete `-' PATH <action> translated to `='.}%
- \addDASH@\DN@##1{\xy@{~-{##1}}{}\def\PATHbefore@@{##1}\xyFN@\PATH@}%
- \else
- \xyerror@{Unknown \string~ setting: \meaning\next}%
- {See the Xy-pic arrow feature documentation for help.}%
- \fi\fi\fi\fi\fi\fi\fi\fi \next@}
-\DOCMODE)
-
- Next the setup for straight segments including the last: they set
- |\PATHinit@@| to initialise, \ie, slide, |\PATHextra@@| to do what is
- needed after the ??c![=] action, and finally |\PATHpost@@| is set to
- any operations to be done after the entire segment is typeset but
- before the next is read. |\PATHcontinue@@| is used internally to
- distinguish the ordinary segments from the last.
-
-\DOCMODE(
-\xylet@\PATHinit@@=\empty
-
-\xylet@\PATHextra@@=\empty
-\xylet@\PATHpost@@=\empty
-\xylet@\PATHcontinue@@=\empty
-
-\xydef@\PATHstraight@{%
- \def\PATHinit@@{\PATHinitstraight@}%
- \let\PATHextra@@=\empty
- \let\PATHpost@@=\empty
- \let\PATHlabelsextra@@=\relax
- \xy@@\pfromc@ \PATHafterPOS{\xyFN@\PATHsegment@}}
-
-\xydef@\PATHfinal@{%
- \def\PATHinit@@{\PATHinitstraight@}%
- \def\PATHextra@@{\let\PATHcontinue@@=\afterPATH@}%
- \let\PATHpost@@=\empty
- \let\PATHlabelsextra@@=\PATHlabelsextralast@
- \xy@@\pfromc@ \PATHafterPOS{\xyFN@\PATHsegment@}}
-
-\xydef@\PATHlabelsextralast@{\let\PATHlabelsextra@@=\relax
- \expandafter\xyFN@\expandafter\PATHlabels@\PATHlabelslast@@}
-
-\xydef@\PATHinitstraight@{\xy@@{\setupDirection@ \dimen@=\PATHslide@@
- \dimen@ii=-\sinDirection\dimen@
- \ifPATHomitslide@@\else\advance\X@p\dimen@ii\fi \advance\X@c\dimen@ii
- \dimen@ii= \cosDirection\dimen@
- \ifPATHomitslide@@\else\advance\Y@p\dimen@ii\fi \advance\Y@c\dimen@ii
- \PATHomitslide@@false \resetupDirection@}}
-\DOCMODE)
-
- Setup for turning segments is in note~??[turning segment].
-
- A <segment> is interpreted as follows after $p$ has been set to the
- previous end object, $c$ to the <pos> given at the start of the
- segment, and |\PATHslide@@| to the slide:
-
-\DOCMODE(
-\xydef@\PATHslide@@{\z@}
-\xynew@{if}\ifPATHomitslide@@
-
-\xydef@\PATHsegment@{%
- \addLT@\ifx\next
- \addGT@{\addLT@\DN@##1}{%
- \xy@{<##1>}{\dimen@=##1\relax \edef\PATHslide@@{\the\dimen@}}%
- \xyFN@\PATHsegment@@}%
- \else \let\next@=\PATHsegment@@
- \fi \next@}
-\DOCMODE)
-
-\begin{enumerate}
-\item
- Expand |\PATHinit@@| (for straight segments this just sets up the
- direction and applies the <slide>).
-\item
- Expand |\PATHaction={|<stuff>|}| as set using |~={|<stuff>|}|.
-\item
- Sets |\PATHcontinue@@| to any continuation set with |~{|<stuff>|}|).
-\item
- Construct list of <labels> specified by the user through |~|<which>
- setup. Those applicable to the present segment are inserted before
- the user's <labels> in the sequence |<>=|.
-\item
- Store $p,c$ as "start","end" of segment.
-\item
- Interpret <labels> (see below), including the ones added by the
- |~|<when>\dots\ <setup>.
-\end{enumerate}
-%
- |\PATHsegment@@| performs this except the last two points:
-
-\DOCMODE(
-\xydef@\PATHsegment@@{\PATHinit@@ \addEQ@\PATHaction@\PATHbefore@@ \PATHextra@@
- \expandafter\toks@\expandafter{\PATHlabelsnext@@}\let\PATHlabelsnext@@=\empty
- \expandafter\addtotoks@\expandafter{\PATHlabelsevery@@}%
- \expandafter\def\expandafter\PATHlabels@@\expandafter{\the\toks@}%
- \toks@={}\expandafter\xyFN@\expandafter\PATHlabels@\PATHlabels@@}
-\DOCMODE)
-
- |\PATHlabels@| parses all <labels> of a <segment>. This sets
- |\PATHlabelit@@| to the operation building the label in question.
- Then some parsing stores the tokens ??c![<>(.5)] for each ??c![-] in
- the <anchor> and finally passes control to the kernel <place> parser
- with these tokens as the head. This then in turn calls |\PATHit@|
- that parses <it> and applies the chosen operation. After the last we
- continue with the accumulated subsegment actions.
-
-\DOCMODE(
-\xylet@\PATHlabelit@@=\empty
-
-\xydef@\PATHlabels@{%
- \ifx \space@\next \expandafter\DN@\space{\xyFN@\PATHlabels@}%
- \else \ifx ^\next
- \DN@##1{\xy@^{}\let\PATHlabelit@@=\PATHlabelabove@@
- \DNii@{}\xyFN@\PATHanchor@}%
- \else \ifx _\next
- \DN@##1{\xy@_{}\let\PATHlabelit@@=\PATHlabelbelow@@
- \DNii@{}\xyFN@\PATHanchor@}%
- \else \ifx |\next
- \DN@##1{\xy@|{}\let\PATHlabelit@@=\PATHlabelbreak@
- \DNii@{}\xyFN@\PATHanchor@}%
- \else \let\next@=\PATHfinishsegments@ \fi\fi\fi\fi \next@}
-
-\xydef@\PATHanchor@{\begingroup \toks@={}\PATHanchor@i}
-
-\xydef@\PATHanchor@i{%
- \ifx \space@\next \expandafter\DN@\space{\xyFN@\PATHanchor@i}%
- \else\addDASH@\ifx \next
- \addDASH@\DN@{\expandafter\addtotoks@\expandafter{\PATHanchor@toks}%
- \xyFN@\PATHanchor@i}%
- \else
- \DNii@##1{\endgroup\afterPLACE{\xyFN@\PATHit@}##1}%
- \DN@{\expandafter\nextii@\expandafter{\the\toks@}}%
- \fi\fi \next@}
-
-{\xyuncatcodes \gdef\next{<>(.5)}}
-\xylet@\PATHanchor@toks=\next
-
-\xylet@\PATHitshapes@@=\empty
-
-\xydef@\PATHit@{\let\PATHitshape@@=\empty \xyFN@\PATHit@i}
-
-\xydef@\PATHit@i{%
- \ifx \space@\next \expandafter\DN@\space{\xyFN@\PATHit@i}%
- \else \ifx *\next \DN@*##1##{\PATHlabelit@@{!C##1}}%
- \else \addAT@\ifx\next \addAT@\DN@##1##{\PATHlabelit@@{\dir##1}}%
- \else \ifx [\next \DN@[##1]{%
- \expandafter\def\expandafter\PATHitshape@@\expandafter{\PATHitshape@@[##1]}%
- \xyFN@\PATHit@i}%
- \else \DN@{\PATHlabelit@@{}}%
- \fi\fi\fi\fi \next@}
-\DOCMODE)
-
- The individual operations bound to |\PATHlabelit@@| are discussed as
- appropriate in the notes.
-
- After the last break and label we typeset the last piece of the
- connection.
-
-\DOCMODE(
-\xydef@\PATHfinishsegments@{%
- \ifx\PATHlabelsextra@@\relax \expandafter\PATHfinishsegments@i
- \else
- \expandafter\PATHlabelsextra@@ \fi}
-
-\xydef@\PATHfinishsegments@i{%
- \xy@@{\Clast@@}\the\toks@ \toks@={}%
- \xy@@\setupDirection@
- \PATHpost@@ \PATHaction@/\PATHafter@@
- \PATHcontinue@@}
-\DOCMODE)
-
- \BUG: The order of the breaks determines the order of the
- subsegments. This is maybe a feature.
-
-\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\begin{notes}
-
-\note??=[<action>]
-%
- An <action> can be either of the characters |=/|. The associated
- <stuff> is saved and used to call
-$$
- ??c![\PATHaction]<action>|{|<stuff>|}|
-$$
- "before" and "after" each segment (including all <labels>) for
- ??c![=] and ??c![/], respectively.
-
- The default ??c![\PATHaction] macro just expands to ``??c![\POS]
- <stuff> |\relax|'' thus <stuff> should be of the form <pos> <decor>.
- The user can redefine this---in fact the ??c![\ar] command described
- in \S??[arrow] below is little more than a special ??c![\PATHaction]
- command and a clever defaulting mechanism.
-
-\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
- Here is the default ??c![\PATHaction]:
-
-\DOCMODE(
-\xydef@\PATHaction@default#1#2{\xy@{PATHaction#1{#2}}{}\POS#2\relax}
-\xylet@\PATHaction=\PATHaction@default
-\DOCMODE)
-
- It is called using |\PATHaction@| to expand the action control
- sequences back to their <stuff> first:
-
-\DOCMODE(
-\xydef@\PATHaction@#1#2{\expandafter\PATHaction\expandafter#1\expandafter{#2}}
-\DOCMODE)
-
-\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\note??=[<labels> prefix for some segments]
-%
- It is possible to include a number of default <labels> "before" the
- <labels> of the actual <segment> are interpreted, using
- |~|<which>|{|<labels>|}|. The specified <which> determines for which
- segments the indicated <labels> should be prefixed as follows:
-$$
-\begin{tabular}{\otherbar c\otherbar l\otherbar}
-\hline
- <which> & applied to\dots \\
-\hline
- ??c![<] & next segment only \\
- ??c![>] & last segment only \\
- ??c![=] & every segment \\
-\hline
-\end{tabular}
-$$
- (when several apply to the same segment they are inserted in the
- sequence |<>+|).
-
- This is useful to draw connections with a `center marker' in
- particular with arrows, \eg, the `mapsto' example explained below can
- be changed into a `breakto' example: typing
-%
-\begin{code}
-\xy*+{0}\PATH
- ~={**\dir{-}}
- ~>{|>*\dir{>}}
- ~+{|*\dir{/}}
- '(10,1)*+{1} '(20,-2)*+{2} (30,0)*+{3}
-\endxy
-\end{code}
-\displaycode
-\noindent\unskip
-%
- will typeset
-$$
- \docode
-$$
- Note, however, that what goes into |~+{|\dots|}| is <labels> and thus
- not a <pos> -- it is not an action in the sense explained above.
-
-\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\note??=[failure continuation]
-%
- Specifying |~{|<stuff>|}| will set the ``failure continuation'' to
- <stuff>. This will be inserted when the last <segment> is
- expected---it can even replace it or add more <segment>s, \ie,
-%
-\begin{code}
-\xy *+{0} \PATH ~={**\dir{-}}
- ~{'(20,-2)*+{2} (30,0)*+{3}} '(10,1)*+{1}
-\endxy
-\end{code}
-\displaycode
-%
- is equivalent to
-%
-\begin{code}
-\xy *+{0} \PATH ~={**\dir{-}}
- '(10,1)*+{1} '(20,-2)*+{2} (30,0)*+{3}
-\endxy
-\end{code}
-\displaycode
-%
- typesetting
-$$
- \docode
-$$
- because when |\endxy| is seen then the parser knows that the next
- symbol is neither of the characters |~'`| and hence that the last
- <segment> is to be expected. Instead, however, the failure
- continuation is inserted and parsed, and the <path> is finished by
- the inserted material.
-
- Failure continuations can be nested:
-%
-\begin{code}
-\xy *+{0} \PATH ~={**\dir{-}}
- ~{~{(30,0)*+{3}}
- '(20,-2)*+{2}} '(10,1)*+{1}
-\endxy
-\end{code}
-\displaycode
-%
- will also typeset the connected digits.
-
-\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\note??=[straight segment]
-%
- A ``straight segment'' is interpreted as follows:
-%
-\begin{enumerate}
-\item
- First $p$ is set to the end object of the previous segment (for the
- first segment this is $c$ just before the path command) and $c$ is
- set to the <pos> starting the <segment>, and the current <slide> is
- applied.
-\item
- Then the |=| and |<| "segment actions" are expanded (in that
- sequence) and the |<| action is cleared. The resulting $p$ and $c$
- become the "start" and "end" object of the segment.
-\item
- Then all <labels> (starting with the ones defined as described in
- note~??[<labels> prefix for some segments] below).
-\end{enumerate}
-
-\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- The code expanding the actions is part of the parsing above.
-\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\note??=[segment]
-%
- A "segment" is a part of a <path> between a previous and a new
- "target" given as a <path-pos>: normally this is just a <pos> as
- described in~\S??g[xy.doc:pos] but it can be changed to something
- else by changing the control sequence ??c![\PATHafterPOS] to be
- something other than ??c![\afterPOS].
-
-\DOCMODE(
-\xylet@\PATHafterPOS@default=\afterPOS
-\xylet@\PATHafterPOS=\PATHafterPOS@default
-\DOCMODE)
-
-\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\note??=[turning segment]??=[1/4 turn]??=[explicit turn]
-%
- A "turning" segment is one that does not go all the way to the given
- <pos> but only as far as required to make a turn towards it. The $c$
- is set to the actual turn object after a turning segment such that
- subsequent turning or other segments will start from there, in
- particular the last segment (which is always straight) can be used to
- finish a winding line.
-
- What the turn looks like is determined by the <turn> form:
-%
-\begin{description}
-
-\item[<empty>]
- Nothing between the ??c![`] and the <pos> is interpreted the same as
- giving just the <diag> last used "out" of a turn.
-
-\item[<diag>]
- Specifying a single <diag> $d$ is the same as specifying either of
- the <cir>cles $d$??c![^] or $d$??c![_], depending on whether the specified
- <pos> has its center `above' or `below' the line from $p$ in the
- <diag>onal direction.
-
-\item[<cir>]
- When a full explicit <cir>cle is available then the corresponding
- <cir>cle object is placed such that its ingoing direction is a
- continuation of a straight connection from $p$ and the outgoing
- direction points such that a following straight (or last) segment
- will connect it to $c$ (with the same slide).
-
-\end{description}
-%
- Here is an example using all forms of <turn>s:
-%
-\begin{code}
-\xy <4pc,0pc>:(0,0)
- *+\txt{base}="base"
- \PATH ~={**\dir{-}?>*\dir{>}}
- `l (-1,-1)*{A} ^a
- ` (1,-1)*{B} ^b
- `_ul (1, 0)*{C} ^c
- `ul^l "base" ^d
- "base" ^e
-\endxy
-\end{code}
-$$
-\docode
-$$
- was typeset by
-%
-\displaycode
-
- \BUG: Turns are only really resonable for paths that use straight
- lines like the one above.
-
- \NOTE: Always write a valid <pos> after a <turn>, otherwise any
- following ??c![^] or ??c![_] labels can confuse the parser. So if
- you intend the |^r| in |`^r| to be a label then write |`,^r|, using a
- dummy ??c![,] <pos>ition.
-
-\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
- We need to keep track of the current "in" and "out" <diag>
- directions as well as the current radius.
-
-\DOCMODE(
-\xydef@\PATHlastout@@{3}
-\DOCMODE)
-
- The startup routine is just a selection of the two kinds of <turn>:
-
-\DOCMODE(
-\xydef@\PATHturn@{\afterCIRorDIAG\PATHturn@cir\PATHturn@diag}
-\DOCMODE)
-
- In both cases the trick is to set up a |\PATHinit@@| method that
- typesets the right circle segment at the right location. The
- simplest one is when there is a full <cir> available because that
- should just be used directly. The only complication is that we
- forbid $180^\circ$ turns:
-
-\DOCMODE(
-\xydef@\PATHturn@cir{\toks@={\xy@@{%
- \count@=\CIRin@@ \ifnum\count@<4\else\advance\count@-4\fi
- \count@@=\CIRout@@ \ifnum\count@@<4\else\advance\count@@-4\fi
- \ifnum\count@=\count@@ \xyerror@{<turn> cannot be half or full}{%
-You asked for a <turn>ed segment with parallel in- and out-direction.^^J%
-This is not allowed because it is not possible to position it uniquely.}\fi}}%
- \edef\next@{{\CIRin@@}{\expandafter\noexpand\CIRorient@@}{\CIRout@@}}%
- \expandafter\PATHturn@i\next@}
-\DOCMODE)
-
- "Procedure for <diag> turns": Builds initial part of |\PATHinit@@|
- that computes the missing "orient" and "out" from "in" and the $c$
- passed through the segment. This initial segment should set
- "orient" as follows:
-$$
- \xy <9mm,0mm>: <0mm,4mm>::
- ,(1,1) *+\dir{*}!D *!LU{p}
- ,(0,0);(4,4)**\dir{-}
- ?< *!/+\jot/\composite{{.}*!/+\jot/{.}*!/+2\jot/{.}}
- ?> *!/-\jot/\composite{{.}*!/-\jot/{.}*!/-2\jot/{.}}
- ?(.6)*!/1ex/\dir{>} *^!/-1ex/{|^|} *_!/-1ex/{|_|}
- \endxy
-$$
- \ie, as the sign of the inner product $\vec{pc} \cdot \hat{"in"}$,
- and set "out" as for the <cir>cle "in" "orient".
-
-\DOCMODE(
-\xydef@\PATHturn@diag{\toks@={\xy@@{%
- \setupDirection@ \count@=\CIRin@@ \dimen@=\xydashl@ \ABfromdiag@
- \ifdim \sinDirection\A@>\cosDirection\B@ \def\CIRorient@@{\CIRacw@}%
- \advance\count@\ifnum\count@<6 \tw@ \else -6\fi
- \else \def\CIRorient@@{\CIRcw@}%
- \advance\count@\ifnum\count@>\@ne -\tw@ \else 6\fi
- \fi
- \edef\CIRout@@{\the\count@}}}%
- \edef\next@{{\CIRin@@}{}{}}%
- \expandafter\PATHturn@i\next@}
-\DOCMODE)
-
- |\PATHturn@i| is where |\PATHinit@@| is defined to do the following:
-%
-\begin{itemize}
-
-\item[{??_[turni1]}]
- Setup the default "in", "orient", and "out" as defined by the call
- from the above macros. Set "radius" parameter to the current
- "turnradius" value. The commands in |\toks@| are run to do any
- last-minute fixing of the defaults.
-
-\item[{??_[turni2]}]
- The segment will leave $p$ in direction "in" and pretend to be
- meeting $c$ in direction "out". Thus the center of the <cir>cle
- object to be used for the actual <turn> object is located at the
- intersection of the line through $p+"radius"\hat{v}_"in"$ in
- direction $\vec{v}_"in"$ and the line through
- $c+"radius"\hat{v}_"out"$ in direction $\vec{v}_"out"$. Here we
- compute $p+R\hat{v}_"in"$ using $R="radius"$ if this is the initial
- turn and $R="radius"\pm"slide"$ if it is a continuation turn.
-
-\item[{??_[turni2b]}]
- Save $p$ and "base" for later.
-
-\item[{??_[turni3]}]
- Compute $c+"radius"\hat{v}_"out"$ and use the kernel |\intersect@|
- primitive to compute the turn circle segment center.
-
-\item[{??_[turni3b]}]
- However, if the intersection point lies on the `wrong side' of $p$,
- \ie, if $\vec{pc} \cdot "in"$ is negative, then we should not use the
- intersection point but the point as close to $p$ as possible because
- the connection from $p$ to the turn should at least have zero
- length---in fact we set it to have 8sp length to make sure that a
- sugsegment is typeset!
-
-\item[{??_[turni4]}]
- Modify "radius" to use for the actual circle segment by the "slide":
- either positively (for "orient" ??c![_]) or negatively (for "orient"
- ??c![^]), and drop the circle segment (bypassing |\cir| to use the
- internal settings from above).
-
-\item[{??_[turni5]}]
- Store in |\PATHpostpos@@| the true end of the circle segment and code
- to prevent the application of the "slide" for the start of the next
- <segment>.
-
-\item[{??_[turni6]}]
- Move $c$ to true beginning of the circle segment.
-
-\item[{??_[turni7]}]
- Restore saved $p$ and "base", and slide $p$ finally.
-
-\end{itemize}
-
-\DOCMODE(
-\xylet@\PATHpostpos@@=\empty
-
-\xydef@\PATHturn@i#1#2#3{%
- \DN@##1{\def\PATHinit@@{\xy@@{%
- \def\CIRin@@{#1}\def\CIRorient@@{#2}\def\CIRout@@{#3}%?*[turni1]
- \ifnum\CIRin@@=8 \let\CIRin@@=\PATHlastout@@ \fi
- \R@=\turnradius@
- ##1\relax}%
- \xy@@{\count@=\CIRin@@ %?*[turni2]
- \ifPATHomitslide@@ \dimen@=-\PATHslide@@
- \ABfromdiag@ \advance\X@p-\B@ \advance\Y@p\A@ \fi
- \enter@{\pfromthep@ \basefromthebase@}}%?*[turni2b]
- \xy@@{\dimen@=\expandafter\ifx\CIRorient@@\CIRcw@-\fi\R@
- \ABfromdiag@ \advance\X@p-\B@ \advance\Y@p\A@
- \X@origin=\X@p \Y@origin=\Y@p}%?*[turni3]
- \xy@@{\dimen@=\xydashl@ \ABfromdiag@ \R@c=\A@ \U@c=\B@
- \count@=\CIRout@@
- \dimen@=\expandafter\ifx\CIRorient@@\CIRcw@-\fi\R@
- \ABfromdiag@ \advance\X@c-\B@ \advance\Y@c\A@
- \dimen@=\xydashl@ \X@p=\X@c \Y@p=\Y@c
- \ABfromdiag@ \advance\X@p-\A@ \advance\Y@p-\B@
- \intersect@
- \count@=\CIRin@@ \dimen@=\p@ \ABfromdiag@}%?*[turni3b]
- \xy@@{\edef\next@{\expandafter\removePT@\the\A@}%
- \edef\nextii@{\expandafter\removePT@\the\B@}%
- \A@=\X@c \advance\A@-\X@origin \B@=\Y@c \advance\B@-\Y@origin
- \ifdim \next@\A@<-\nextii@\B@
- \dontleave@ \cfromp@
- \count@=\CIRin@@ \advance\count@\ifnum\count@<4 +4\else -4\fi
- \dimen@=\xydashl@ \Directionfromdiag@
- \the\Edge@c\z@
- \count@=\CIRin@@ \dimen@=\expandafter\ifx\CIRorient@@\CIRcw@-\fi\R@
- \ABfromdiag@ \advance\X@c-\B@ \advance\Y@c\A@
- \dimen@=5sp \ABfromdiag@ \advance\X@c\A@ \advance\Y@c\B@
- \fi
- \dimen@ii=\expandafter\ifx\CIRorient@@\CIRacw@-\fi\PATHslide@@ %?*[turni4]
- \advance\R@\dimen@ii
- \drop@\literal@{\hbox\bgroup\cir@i}}%
- \xy@@{\X@p=\X@c \Y@p=\Y@c %?*[turni5]
- \count@=\CIRout@@
- \dimen@=\expandafter\ifx\CIRorient@@\CIRacw@-\fi\R@c
- \ABfromdiag@ \advance\X@p-\B@ \advance\Y@p\A@
- \edef\PATHpostpos@@{\X@c=\the\X@p \Y@c=\the\Y@p \noexpand\czeroEdge@
- \noexpand\PATHomitslide@@true}}%
- \xy@@{\count@=\CIRin@@ %?*[turni6]
- \dimen@=\expandafter\ifx\CIRorient@@\CIRacw@-\fi\R@c
- \ABfromdiag@ \advance\X@c-\B@ \advance\Y@c\A@ \czeroEdge@}%
- \xy@@{\leave@ %?*[turni7]
- \count@=\CIRin@@ \dimen@=\PATHslide@@
- \ABfromdiag@ \advance\X@p-\B@ \advance\Y@p\A@
- \edef\PATHlastout@@{\CIRout@@}%
- \count@=\CIRout@@ \dimen@=\xydashl@ \Directionfromdiag@}}}%
- \expandafter\next@\expandafter{\the\toks@}\toks@={}%
- \let\PATHextra@@=\empty
- \def\PATHpost@@{\xy@@\PATHpostpos@@}%
- \let\PATHlabelsextra@@=\relax
- \xyFN@\PATHturn@ii}
-\DOCMODE)
-
- The final macro takes care of the v2.6 format for changing
- "turnradius": using ??c![/]<dimen> right after the <turn>.
-
-\DOCMODE(
-\xydef@\PATHturn@ii{%
- \ifx /\next
- \DN@ /{\afterassignment\nextii@\dimen@=}%
- \DNii@{%
- \edef\next@{\noexpand\xy@@{\edef\noexpand\turnradius@{\the\dimen@}}}\next@
- \xy@@\pfromc@ \PATHafterPOS{\xyFN@\PATHsegment@}}%
- \else \DN@{\xy@@\pfromc@ \PATHafterPOS{\xyFN@\PATHsegment@}}\fi
- \next@}
-\DOCMODE)
-
- This just stores a <diag> vector of the specified lenght in
- $|<|A|,|B|>|$ thus acting as an optimised version of
- |\Directionfromdiag@|:
-
-\DOCMODE(
-\xydef@\ABfromdiag@{\ifcase\count@\relax
- \A@=-.7071\dimen@ \B@=-.7071\dimen@ \or \A@=\z@ \B@=-\dimen@
- \or \A@=+.7071\dimen@ \B@=-.7071\dimen@ \or \A@=\dimen@ \B@=\z@
- \or \A@=+.7071\dimen@ \B@=+.7071\dimen@ \or \A@=\z@ \B@=+\dimen@
- \or \A@=-.7071\dimen@ \B@=+.7071\dimen@ \or \A@=-\dimen@ \B@=\z@
- \else\xybug@{impossible <diag>?}\fi}
-\DOCMODE)
-
-\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
- The default used for "turnradius" can be set by the operation
-%
-\begin{defs1}
- ??c![\turnradius] <add op> |{|<dimen>|}|\cr
-\end{defs1}
-\noindent\unskip
-%
- that works like the kernel ??c![\objectmargin] etc. commands; it defaults
- to 10pt.
-
-\DOCMODE(
-\xydef@\turnradius@{10pt}
-
-\xydef@\turnradius{\afterADDOP{\Addop@@\turnradius@}}
-\DOCMODE)
-
-\begin{exercise}
- Typeset
-\begin{code}
-\xy *+{A}*\cir<10pt>{}="me"
- \PATH `ul^ur,"me" "me" |>*:(1,-.25)\dir{>}
-\endxy
-\end{code}
-$$\docode$$
-%
- using <turn>s.
-%
-\answertext{Here is what the author did:??c[\cir]}
-\answercode
-\answertext\displaycode
-\answertext{The trick is getting the arrow head right: the |:| modifier to
- the explicit {\tt\string\dir} <object> does that.}
-\end{exercise}
-
-\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\note??=[last segment]
-%
- The last segment is exactly as a straight one except that the ??c![>]
- action (if any) is executed (and cleared) just after the ??c![<]
- action.
-
-\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- (The code implementing this is merged with the parsing.)
-\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\note??=[slide]
-%
- ``Sliding'' a segment means moving each of the $p,c$ objects in the
- direction perpendicular to the current direction at each.
-
-\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- (The code implementing this is merged with the parsing, using the
- |\PATHslide@@| control sequence to hold the current slide.)
-
-\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\note??=[label with <it>]
-%
- Labelling means that <it> is dropped relative to the current segment
- using a ??c![?] <pos>ition. This thus depends on the user setting up
- a connection with a ??c![**] <pos> as one of the actions---typically
- the~??c![=] action is used for this (see note~??[straight segment]
- for the details). The only difference between ??c![^] and ??c![_] is
- that they shift the label in the ??c![^] respectively ??c![_]
- direction; for straight segments it is placed in the ``superscript''
- or ``subscript'' position.
-
-\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
- The operations used by |\PATHlabels@| to put labels above and below
- (with ??c![^] and ??c![_]) are trivial, taking two arguments and
- placing the label immediately; for convenience the |\drop| head are
- named separately such that they may be redefined:
-
-\DOCMODE(
-\xydef@\PATHlabelabove@#1#2{\droplabel@\belowDirection@{#1}{#2}%
- \let\afteraliases@@=\empty \xyFN@\PATHlabelalias@}
-
-\xydef@\PATHlabelbelow@#1#2{\droplabel@\aboveDirection@{#1}{#2}%
- \let\afteraliases@@=\empty \xyFN@\PATHlabelalias@}
-
-\xylet@\PATHlabelabove@@=\PATHlabelabove@
-\xylet@\PATHlabelbelow@@=\PATHlabelbelow@
-
-\xydef@\droplabel@#1#2#3{\xy@@{\enter@\DirectionfromtheDirection@}%
- \DN@{#2}\ifx\next@\empty
- \expandafter\xy@@ix@\expandafter{\PATHitshape@@\labelbox{#3}}%
- \else \expandafter\xy@@ix@\expandafter{\PATHitshape@@#2{#3}}\fi
- \xy@@{\setbox\z@=\expandafter\object\the\toks9 %
- \advance\L@c\labelmargin@ \advance\R@c\labelmargin@
- \advance\D@c\labelmargin@ \advance\U@c\labelmargin@
- \setboxz@h{\kern\labelmargin@\boxz@\kern\labelmargin@}%
- \A@=\X@c \B@=\Y@c #1\xydashl@ \the\Edge@c\thr@@
- \advance\A@-\X@c \advance\B@-\Y@c \advance\X@c 2\A@ \advance\Y@c 2\B@
- \ht\z@=\U@c \dp\z@=\D@c \dimen@=\L@c \advance\dimen@\R@c \wd\z@=\dimen@
- \setbox\lastobjectbox@=\hbox{\X@c=\L@c \Y@c=\z@ \Drop@@}%
- \drop@{\box\lastobjectbox@}{}%
- \leave@}}
-
-\xydef@\PATHlabelbreak@#1#2{%
- \DN@{#1}\ifx\next@\empty \drop\labelbox{#2}\else \drop#1{#2}\fi
- \def\afteraliases@@{\xy@@\Cbreak@@}\xyFN@\PATHlabelalias@}
-\DOCMODE)
-
- These emulate the effect of the <modifier>s |!C|
- |+<|2"labelmargin"|>| <perp> |!P| <unperp> where <perp>,<unperp> are
- |^|,|_| for |^|-labels and |_|,|^| for |_|-labels. The last hack
- using |\lastobjectbox@| aims at both setting that right and setting
- the label as an object (such that modifiers take effect) even though
- its placement is peculiar.
-
-\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
- Labels will be separated from the connection by the "label"\-"margin"
- that you can set with the operation
-%
-\begin{defs1}
- ??c![\labelmargin] <add op> |{|<dimen>|}|
-\end{defs1}
-\noindent\unskip
-%
- that works like the kernel ??c![\objectmargin] command; in fact
- "labelmargin" defaults to use "objectmargin" if not set.
-
-\DOCMODE(
-\xylet@\labelmargin@=\objectmargin@
-
-\xydef@\labelmargin{\afterADDOP{\Addop@@\labelmargin@}}
-\DOCMODE)
-
-\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\note??=[break with <it>]??=[piece]
-%
- Breaking means to ``slice a hole'' in the connection and insert <it>
- there. This is realized by typesetting the connection in question in
- "subsegments", one leading to the break and one continuing after the
- break as described in notes~??[<action>] and~??[straight segment].
-
- The special control sequence ??c![\hole] is provided to make it easy to
- make an empty break.
-
-\DOCMODE(
-\xydef@\hole{\hbox{\dimen@=\objectmargin@ \kern2\dimen@
- \vrule height\dimen@ depth\dimen@ width\z@}}
-\DOCMODE)
-
-\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
- Subsegments are typeset using the `|\Cbreak@@|' method.
-
-\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\note??=[default label]
-%
- Unless <it> is a full-fledged <object> (by using the ??c![*] form),
- it is typeset using a ??c![\labelbox] object (initially similar to
- ??c![\objectbox] of basic \Xy-pic but using ??c![\labelstyle] for the
- style).
-
- \REMARK: You can only omit the |{}|s around single letters, digits,
- and control sequences.
-
-\DOCMODE(
-\xylet@\labelstyle=\scriptstyle
-\xydef@\labelbox#1{\hbox{$\m@th\labelstyle{#1}$}}
-\DOCMODE)
-
-\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\note??=[name for label object]
-%
- A label is an object like any other in the \Xy-picture. Inserting an
- <alias> ??c![=]|"|<id>|"| saves the label object as |"|<id>|"| for
- later reference.
-
-\begin{exercise}
- Typeset
-%
-\begin{code}
-\xy(0,0)
- \ar @{-->} (30,7) ^A="a"
- \POS(10,12)*+\txt{label} \ar "a"
-\endxy
-\end{code}
-$$\docode$$
-%
-\answercode
-\answertext{The author did \displaycode}
-\end{exercise}
-
-\DOCMODE(
-\xydef@\PATHlabelalias@{%
- \ifx \space@\next \expandafter\DN@\space{\xyFN@\PATHlabelalias@}%
- \else \addEQ@\ifx \next
- \addEQ@\DN@"##1"{\savealias@{##1}\xyFN@\PATHlabelalias@}%
- \else \DN@{\afteraliases@@\PATHlabels@}\fi\fi \next@}
-
-\xylet@\afteraliases@@=\empty
-
-%{\xyuncatcodes \gdef\next#1{\POS!C="#1"\relax}}
-\xydef@\savealias@#1{\xy@@{\enter@\cfromthec@
- \advance\X@c-\L@c \advance\L@c\R@c \L@c=.5\L@c \R@c=\L@c \advance\X@c\L@c
- \advance\Y@c-\D@c \advance\D@c\U@c \D@c=.5\D@c \U@c=\D@c \advance\Y@c\D@c
- \idfromc@{#1}\leave@}}
-\DOCMODE)
-
-\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\end{notes}
-
-\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-
-\subsection{Arrows}
-??=[arrow]
-
-\begin{figure*}[tb]
-\vfil
-\begin{syntax}
-%
- \multispan{3}{{\tt\string\ar} <arrow> <path>\hfil}
- & make <arrow> along <path>
-\cr
-\noalign{\nobreak\smallskip\nobreak\hrule\nobreak\smallskip\nobreak}
-%
- <arrow>
- &\iss & <form>\star
- & <arrow> has the <form>s
-\cr
-\noalign{\smallskip}
-%
- <form>
- &\iss & ??c![@] <variant>
- & use <variant> of arrow
-\cr
- &\orr & ??c![@] <variant> |{| <tip> |}|
- & ??!^[build arrow] using <variant> of a standard stem and <tip> for
- the head
-\cr
- &\orr & ??c![@] <variant> |{| <tip> <conn> <tip> |}|
- & ??!^[build arrow] using <variant> of <tip>, <conn>, <tip>
- as arrow tail, stem, and head (in that order)
-\cr
- &\orr & ??c![@] <connchar>
- & change stem to the indicated <connchar>
-\cr
- &\orr & ??c![@!]
- & dash the arrow stem by doubling it
-\cr
- &\orr & ??c![@/] <direction> <dist> |/|
- & ??!^[curve] arrow the <dist>ance towards <direction>
-\cr
- &\orr & ??c![@(] <direction> |,| <direction> |)|
- & curve to fit with ??!^[in-out directions]
-\cr
- &\orr & ??c![@`] |{| <control point list> |}|
- & ??!^[curve setup] with explicit control points
-\cr
- &\orr & |@[| <shape> |]|
- & add |[|<shape>|]| to ??!^[object <modifier>s] for all objects
-\cr
- &\orr & ??c![@*] |{| <modifier>\star\ |}|
- & add ??!^[object <modifier>s] for all objects
-\cr
- &\orr & ??c![@<] <dimen> |>|
- & ??!^[slide arrow] the <dimen>
-\cr
- &\orr & ??c![|] <anchor> <it>
- & break each segment at <anchor> with <it>
-\cr
- &\orr & ??c![^] <anchor> <it> \orr\ ??c![_] <anchor> <it>
- & label each segment at <anchor> with <it>
-\cr
- &\orr & ??c![@?]
- & ??!^[reverse meaning of above and below]
-\cr
-\noalign{\smallskip}
-%
- <variant>
- &\iss & <empty> \orr\ ??c![^] \orr\ ??c![_] & \cr
- & & \orr\ ??c![0] \orr\ ??c![1] \orr\ ??c![2] \orr\ ??c![3]
- & <variant>: plain, above, below, double, or triple
-\cr
-\noalign{\smallskip}
-%
- <tip>
- &\iss & <tipchar>\star
- & directional named as the sequence of <tipchar>s
-\cr
- &\orr & <dir>
- & ??!^[any <dir>ectional]
-\cr
-\noalign{\smallskip}
-%
- <tipchar>
- &\iss & |<|\orr|>|\orr|(|\orr|)|\orr||||\orr|'|\orr|`|\orr|+|\orr|/|
- & recognised tip characters
-\cr
- &\orr & <letter> \orr\ <space>
- & more tip characters
-\cr
-\noalign{\smallskip}
-%
- <conn>
- &\iss & <connchar>\star
- & directional named as the sequence of <connchar>s
-\cr
- &\orr & <dir>
- & ??!^[any <dir>ectional]
-\cr
-\noalign{\smallskip}
-%
- <connchar>
- &\iss & |-|\orr|.|\orr|~|\orr|=|\orr|:|
- & recognised connector characters
-\cr
-\end{syntax}
-\caption{\protect<arrow>s.}??=[f.arrow]
-\vfil
-\end{figure*}
-
-\DOCMODE(
-\message{\string\ar,}
-\DOCMODE)
-
- Arrows are paths with a particularly easy syntax for setting up
- arrows with "tail", "stem", and "head" in the style
- of~\cite{R92:HowTPDAT}. This is provided by a single <decor>ation
- the syntax of which is described in figure~??[f.arrow] (with the
- added convention that a raised `\star' means 0 or more repetitions of
- the preceeding nonterminal).
-
-\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\paragraph*{Parsing:}
-
- The ??c![\ar] command effectively translates the <arrow> into a
- ??c![\PATH] command that initialises the tail, stem, and head of it as
- required to get the desired <arrow>.
-
- The translation of the <arrow> is saved in the following variables:
-
-\DOCMODE(
-\xylet@\arvariant@@=\empty
-\xylet@\arstemprefix@@=\empty
-\xylet@\artail@@=\empty
-\xylet@\arstem@@=\empty
-\xylet@\arhead@@=\empty
-\xylet@\armodifiers@@=\empty
-\xylet@\arlabels@@=\empty
-\xylet@\arafterPOS@@=\empty
-\xylet@\arinit@@=\empty
-\xylet@\arexit@@=\empty
-
-\xylet@\arcomponent@@=\relax
-\xylet@\arcomponenttype@@=\relax
-
-\xylet@\afterar@@=\relax
-\DOCMODE)
-
- ??c![\ar] stores the defaults; it loads an intermediate command to
- avoid problems when used as first command in compiled matrix
- entry\dots
-
-\DOCMODE(
-\xydef@\ar{\relax\arSAFE}
-
-\xydef@\arSAFE{%
- \let\arvariant@@=\empty
- \def\arstemprefix@@{\dir}%
- \edef\artail@@{\arvariant@@{}}%
- \edef\arstem@@{\arvariant@@{-}}%
- \edef\arhead@@{\arvariant@@{>}}%
- \def\armodifiers@@{}%
- \def\arafterPOS@@{}%
- \def\arlabels@@{}%
- \def\arinit@@{}%
- \def\arexit@@{}%
- \let\PATHlabelabove@@=\PATHlabelabove@
- \let\PATHlabelbelow@@=\PATHlabelbelow@
- \xyFN@\ar@}
-\DOCMODE)
-
- |\ar@| is where we parse the sequence of <form>s and continue with
- typesetting the arrow afterwards.
-
-\DOCMODE(
-\xydef@\ar@{%
- \ifx \space@\next \expandafter\DN@\space{\xyFN@\ar@}%
- \else \addAT@\ifx\next \addAT@\DN@{\xyFN@\ar@form}%
- \else\ifx |\next
- \DN@ |{\ar@anchor|}%
- \else\ifx ^\next
- \DN@ ^{\ar@anchor^}%
- \else\ifx _\next
- \DN@ _{\ar@anchor_}%
- \else \let\next@=\ar@x \fi\fi\fi\fi\fi \next@}
-\DOCMODE)
-
- \NOTE: Makes use of the "new compilation principle" to parse a
- <place> vacuously\dots
-
-\DOCMODE(
-\xydef@\addtoarinit@#1{%
- \expandafter\def\expandafter\arinit@@\expandafter{\arinit@@ #1}}
-
-\xydef@\addtoarlabels@#1{%
- \expandafter\def\expandafter\arlabels@@\expandafter{\arlabels@@ #1}}
-
-\xydef@\ar@anchor#1{\begingroup
- \def\PATHlabelit@@##1##2{%
- \DN@{##1}\ifx\next@\empty
- \DN@####1{\expandafter\endgroup\expandafter\addtoarlabels@
- \expandafter{\the\toks@####1{##2}}\xyFN@\ar@}%
- \else
- \DN@####1{\expandafter\endgroup\expandafter\addtoarlabels@
- \expandafter{\the\toks@*!C####1##1{##2}}\xyFN@\ar@}\fi
- \expandafter\next@\expandafter{\PATHitshape@@}}%
- \toks@={#1}%
- \def\xy@##1##2{\addtotoks@{##1}}\change@oxy@\xy@ \let\xy@@ix@=\eat@
- \DNii@{}\xyFN@\PATHanchor@}
-\DOCMODE)
-
- |\ar@form| handles one <form>:
-
-\DOCMODE(
-\xydef@\ar@form{%
- \ifx \space@\next \expandafter\DN@\space{\xyFN@\ar@form}%
- \else\ifx ^\next \DN@ ^{\xyFN@\ar@style}\edef\arvariant@@{\string^}%
- \else\ifx _\next \DN@ _{\xyFN@\ar@style}\edef\arvariant@@{\string_}%
- \else\ifx 0\next \DN@ 0{\xyFN@\ar@style}\def\arvariant@@{0}%
- \else\ifx 1\next \DN@ 1{\xyFN@\ar@style}\def\arvariant@@{1}%
- \else\ifx 2\next \DN@ 2{\xyFN@\ar@style}\def\arvariant@@{2}%
- \else\ifx 3\next \DN@ 3{\xyFN@\ar@style}\def\arvariant@@{3}%
- \else\ifx \bgroup\next \let\next@=\ar@style
- \else\ifx [\next \DN@[##1]{\ar@modifiers{[##1]}}%]
- \else\ifx *\next \DN@ *{\ar@modifiers}%
- \else\addLT@\ifx\next \let\next@=\ar@slide
- \else\ifx /\next \let\next@=\ar@curveslash
- \else\ifx (\next \let\next@=\ar@curveinout %)
- \else\addRQ@\ifx\next \addRQ@\DN@{\ar@curve@}%
- \else\addLQ@\ifx\next \addLQ@\DN@{\xyFN@\ar@curve}%
- \else\addDASH@\ifx\next \addDASH@\DN@{\defarstem@-\xyFN@\ar@}%
- \else\addEQ@\ifx\next \addEQ@\DN@{\def\arvariant@@{2}\defarstem@-\xyFN@\ar@}%
- \else\addDOT@\ifx\next \addDOT@\DN@{\defarstem@.\xyFN@\ar@}%
- \else\ifx :\next \DN@:{\def\arvariant@@{2}\defarstem@.\xyFN@\ar@}%
- \else\ifx ~\next \DN@~{\defarstem@~\xyFN@\ar@}%
- \else\ifx !\next \DN@!{\dasharstem@\xyFN@\ar@}%
- \else\ifx ?\next \DN@?{\ar@upsidedown\xyFN@\ar@}%
- \else \let\next@=\ar@error
- \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi \next@}
-
-\xydef@\defarstem@#1{\edef\arstem@@{\arvariant@@{\string#1}}%
- \DNii@##1##{\next@}%
- \edef\next@##1{\def\noexpand\artail@@{\arvariant@@{##1}}}%
- \expandafter\nextii@\artail@@
- \edef\next@##1{\def\noexpand\arhead@@{\arvariant@@{##1}}}%
- \expandafter\nextii@\arhead@@}
-
-\xydef@\dasharstem@{%
- \DN@##1##{\nextii@{##1}}\DNii@##1##2{\def\arstem@@{##1{##2##2}}}%
- \expandafter\next@\arstem@@}
-
-\xydef@\ar@error#1{\xyerror@{Illegal <form>ation (\meaning\next)}{}%
- \xyFN@\ar@}
-\DOCMODE)
-
- |\ar@i| sets the remaining defaults and then allows |\ar@ii|-|iv| to
- pick up any tail, stem, and head using a {|$|} as terminator.%$
-
-\DOCMODE(
-\xydef@\ar@style{%
- \ifx \bgroup\next \def\artail@@{{}}%
- \edef\arstem@@{\arvariant@@{-}}\edef\arhead@@{\arvariant@@{>}}%
- \expandafter\ar@i
- \else \resetvariant@\artail@@ \resetvariant@\arstem@@ \resetvariant@\arhead@@
- \expandafter\xyFN@\expandafter\ar@ \fi}
-
-\xydef@\resetvariant@#1{%
- \DN@##1##{\DN@{##1}\ifx\next@\empty
- \DN@{\expandafter\nextii@\expandafter{\arvariant@@}}%
- \else \DN@{\nextii@{##1}}\fi \next@}%
- \DNii@##1##2{\def#1{##1{##2}}}%
- \expandafter\next@#1}
-
-\xydef@\ar@i#1{\DN@{#1}%
- \ifx\next@\empty \edef\arstem@@{\arvariant@@{}}\edef\arhead@@{\arvariant@@{}}%
- \DN@{\xyFN@\ar@}%
- \else
- \let\arcomponent@@=\ar@ii \let\arcomponenttype@@=\artip@
- \DN@{\xyFN@\arcomponent@#1$}%
- \fi \next@}
-
-\xydef@\ar@ii{\ifx $\next \let\next@=\ar@iv
- \else \expandafter\def\expandafter\artail@@\expandafter{\the\toks@}%
- \let\arcomponent@@=\ar@iii \let\arcomponenttype@@=\arconn@
- \DN@{\xyFN@\arcomponent@}\fi \next@}
-
-\xydef@\ar@iii{%
- \expandafter\def\expandafter\arstem@@\expandafter{\the\toks@}%
- \resetvariant@\artail@@
- \let\arcomponent@@=\ar@iv \let\arcomponenttype@@=\artip@
- \xyFN@\arcomponent@}
-
-\xydef@\ar@iv{%
- \expandafter\def\expandafter\arhead@@\expandafter{\the\toks@}%
- \ifx $\next \DN@ ${\xyFN@\ar@}%
- \else \xyerror@{illegal <arrow>: \meaning\next\space not valid}{}\fi \next@}
-\DOCMODE)
-
- |\ar@x| is the final macro that passes control to the <path>
- interpreter. It is a bit clumsy because we must pass the right
- character tokens; it could definitely be more efficient by calling
- <path> internals directly\dots
-
-\DOCMODE(
-\xydef@\ar@x{%
- \let\arsavedPATHafterPOS@@=\PATHafterPOS \let\PATHafterPOS=\arafterPOS@
- \toks@={\ar@PATH}%
- \expandafter\addtotoks@\expandafter{\expandafter{\artail@@}}%#1
- \expandafter\addtotoks@\expandafter{\expandafter{\arstem@@}}%#2
- \expandafter\addtotoks@\expandafter{\expandafter{\arstemprefix@@}}%#3
- \expandafter\addtotoks@\expandafter{\expandafter{\arhead@@}}%#4
- \expandafter\addtotoks@\expandafter{\expandafter{\armodifiers@@}}%#5
- \expandafter\addtotoks@\expandafter{\expandafter{\arinit@@}}%#6
- \expandafter\addtotoks@\expandafter{\expandafter{\arexit@@}}%#7
- \expandafter\addtotoks@\expandafter{\expandafter{\arlabels@@}}%#8
- \addtotoks@{\afterar@@}%#9
- \expandafter\DNii@\expandafter{\the\toks@}\toks@={}%
-%
-%{\let\x=\expandafter \x\x\x\DNii@\x\x\x{\nextii@}\W@{RUN: \codeof\nextii@}}%
-%
- \nextii@}
-
-{\xyuncatcodes \gdef\next#1#2#3#4#5#6#7#8#9{%
- \def\next{%
- \afterPATH{#9}%
- ~={#6\preconnect#5#3#2}%
- ~/{#7}%
- ~<{|<*h#5\dir#1}%
- ~>{|>*h#5\dir#4}%
- ~+{#8}%
- }%
- \next}}
-
-\xylet@\ar@PATH=\next
-
-\xydef@\arafterPOS@#1{%
- \arsavedPATHafterPOS@@{\let\PATHafterPOS=\arsavedPATHafterPOS@@
- \DN@{#1}\expandafter\next@\arafterPOS@@}}%
-
-\xylet@\arsavedPATHafterPOS@@=\relax
-\DOCMODE)
-
- <tip>s and <conn>ectors are interpreted by these that leave any
- <variant> in |\toks@ii| and the sequence of <tipchar>s or <connchar>s
- characters in |\toks@|:
-
- The work is really done in |\arcomponent@| that builds |\toks@|
- with something conforming to the |\arcomponenttype@@| and then
- passes control to |\arcomponent@@|:
-
-\DOCMODE(
-\xydef@\arcomponent@{%
- \ifx ^\next \toks@ii={^}\DN@ ^{\xyFN@\arcomponent@i}%
- \else\ifx _\next \toks@ii={_}\DN@ _{\xyFN@\arcomponent@i}%
- \else\ifx 1\next \toks@ii={1}\DN@ 1{\xyFN@\arcomponent@i}%
- \else\ifx 2\next \toks@ii={2}\DN@ 2{\xyFN@\arcomponent@i}%
- \else\ifx 3\next \toks@ii={3}\DN@ 3{\xyFN@\arcomponent@i}%
- \else\ifx \bgroup\next \expandafter\toks@ii\expandafter{\arvariant@@}%
- \let\next@=\arcomponent@i
- \else\ifx *\next \DN@*##1##{\arcomponent@ii{##1}}%
- \else \expandafter\toks@ii\expandafter{\arvariant@@}\toks@={}%
- \let\next@=\arcomponenttype@@
- \fi\fi\fi\fi\fi\fi\fi
- \next@}
-
-\xydef@\arcomponent@i#1{\toks@={#1}\arcomponent@x}
-
-\xydef@\arcomponent@ii#1#2{\toks@={*#1{#2}}\xyFN@\arcomponent@@}
-
-\xydef@\artip@{%
- \addGT@\ifx\next \addGT@\addtotoks@ \addGT@\DN@{\xyFN@\artip@}%
- \else\addLT@\ifx\next \addLT@\addtotoks@ \addLT@\DN@{\xyFN@\artip@}%
- \else\ifx (\next \addtotoks@(\DN@({\xyFN@\artip@}%
- \else\ifx )\next \addtotoks@)\DN@){\xyFN@\artip@}%
- \else\ifx |\next \addtotoks@|\DN@|{\xyFN@\artip@}%
- \else\addLQ@\ifx\next \addLQ@\addtotoks@ \addLQ@\DN@{\xyFN@\artip@}%
- \else\addRQ@\ifx\next \addRQ@\addtotoks@ \addRQ@\DN@{\xyFN@\artip@}%
- \else\addPLUS@\ifx \next \addPLUS@\addtotoks@ \addPLUS@\DN@{\xyFN@\artip@}%
- \else\ifx /\next \addtotoks@/\DN@/{\xyFN@\artip@}%
- \else\ifcat A\noexpand\next \DN@##1{\addtotoks@{##1}\xyFN@\artip@}%
- \else\ifx\space@\next \addtotoks@{ }\expandafter\DN@\space{\xyFN@\artip@}%
- \else \let\next@=\arcomponent@x
- \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi \next@}
-
-\xydef@\arconn@{%
- \addDASH@\ifx\next \addDASH@\addtotoks@ \addDASH@\DN@{\xyFN@\arconn@}%
- \else\addEQ@\ifx\next \addEQ@\addtotoks@ \addEQ@\DN@{\xyFN@\arconn@}%
- \ifx\arvariant@@\empty \def\arvariant@@{2}\fi
- \else\addDOT@\ifx\next \addDOT@\addtotoks@ \addDOT@\DN@{\xyFN@\arconn@}%
- \else\ifx :\next \addtotoks@:\DN@:{\xyFN@\arconn@}%
- \ifx\arvariant@@\empty \def\arvariant@@{2}\fi
- \else\ifx ~\next \addtotoks@~\DN@~{\xyFN@\arconn@}%
- \else \let\next@=\arcomponent@x
- \fi\fi\fi\fi\fi \next@}
-
-\xydef@\arcomponent@x{%
- \DN@##1{\toks@=\expandafter{\the\toks@ii{##1}}}%
- \expandafter\next@\expandafter{\the\toks@}%
- \xyFN@\arcomponent@@}
-\DOCMODE)
-
-\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\begin{notescontd}
-
-\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\note??=[build arrow]
-
- Building an <arrow> is simply using the specified directionals (using
- ??c![\dir] of~\S??g[xy.doc:objectlib.directionals]) to build a path:
- the first <tip> becomes the "??w![arrow tail]" of the arrow, the
- <conn>ection in the middle becomes the "??w![arrow stem]", and the
- second <tip> becomes the "??w![arrow head]". If a <variant> is given
- before the |{| then that variant ??c![\dir] is used for all three.
- For example,
-%
-\begin{code}
-\xy\ar @^{(->} (20,7)\endxy
-\end{code}
-\displaycode
-%
- typesets
-%
-$$\docode$$
-
-\begin{exercise}
- Typeset these arrows:
-%
-\begin{code}
-\xy ;<1pc,0pc>:
- \POS(0,0)*+{A}
- \ar +(-2,3)*+{A'}*\cir{}
- \ar @2 +( 0,3)*+{A''}*\cir{}
- \ar @3 +( 2,3)*+{A'''}*\cir{}
- \POS(6,0)*+{B}
- \ar @1{||.>>} +(-2,3)*+{B'}*\cir{}
- \ar @2{||.>>} +( 0,3)*+{B''}*\cir{}
- \ar @3{||.>>} +( 2,3)*+{B'''}*\cir{}
-\endxy
-\end{code}
-$$\docode$$
-%
-\answertext{Here is the entire \Xy-picture of the exercise:}
-\answercode
-\answertext\displaycode
-\answertext{The first batch use the default |{->}| specification.}
-\end{exercise}
-
- The above is a flexible scheme when used in conjunction with the
- kernel ??c![\newdir] to define all sorts of arrowheads and -tails. For
- example,
-%
-\begin{code}
-\newdir{|>}{!/4.5pt/\dir{|}
- *:(1,-.2)\dir^{>}
- *:(1,+.2)\dir_{>}}
-\end{code}
-\displaycode
-\gdocode
-%
- defines a new arrow tip that makes
-%
-\begin{code}
-\xy (0,0)*+{A}
- \ar @{=|>} (20,3)*+{B}
-\endxy
-\end{code}
-\displaycode
-%
- typeset
-%
-$$\docode$$
-%
- Notice that the fact that the directional uses only <tipchar>
- characters means that it blends naturally with the existing tips.
-
-\begin{exercise}
- Often tips used as `tails' have their ink on the wrong side of the
- point where they are placed. Fortunately space is also a <tipchar>
- so we can define |\dir{ >}| to generate a `tail' arrow. Do this such
- that
-%
-\begin{code}
-\xy (0,0)*+{A}="a", (20,3)*+{B}="b"
- \ar @{>->} "a";"b" < 2pt>
- \ar @{ >->} "a";"b" <-2pt>
-\endxy
-\end{code}
-\displaycode
-%
- typesets
-%
-$$
- \newdir{ >}{{}*!/-5pt/\dir{>}}
- \docode
-$$
-%
-\begin{code}
-\newdir{ >}{{}*!/-5pt/\dir{>}}
-\end{code}
-\answercode
-\answertext{The author used \displaycode}
-\end{exercise}
-
-\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\note??=[any <dir>ectional]
-
- Specifying a <dir> as a <tip> or <conn> means that ??c![\dir]<dir> is
- used for that <tip> or <conn>. For example,
-%
-\begin{code}
-\xy\ar @{<^{|}>} (20,7)\endxy
-\end{code}
-\displaycode
-%
- typesets
-%
-$$\docode$$
-%
- When using this you must specify a |{}| dummy <dir>ectional in order
- to ignore one of the tail, stem, or tip components, \eg,
-%
-\begin{code}
-\xy\ar @{{}{+}>} (20,7)\endxy
-\end{code}
-\displaycode
-%
- typesets
-%
-$$\docode$$
-%
- In particular ??c![*]<object> is a <dir> so any <object> can be used
- for either of the tail, stem, or head component:
-%
-\begin{code}
-\xy\ar @{*{x}*{y}*{z}} (20,7)\endxy
-\end{code}
-\displaycode
-%
- typesets
-%
-$$\docode$$
-%
- \NOTE: A |*| introduces an <object> whereas the directional
- `$\xy*+!<0pt,-\jot>\dir{*}\endxy$' is typeset by the <dir> |{*}|.
-
-\begin{exercise}
- Typeset
-\begin{code}
-\xy
- \ar @{>>*\composite{\dir{x}*\dir{+}}<<}
- (20,7)
-\endxy
-\end{code}
-$$\docode$$
- using only one |\ar| command.
-%
-\answertext{The author used}
-\answercode
-\answertext\displaycode
-\end{exercise}
-
-\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\note??=[curve]
-%
- "Curving" the arrow using $??c![/]d\ell|/|$, where $d$ is a
- <direction> and $\ell$ a <dimen>sion, makes the stem a curve which is
- similar to a straight line but has had it's center point `dragged'
- the distance~$\ell$ in~$d$:
-%
-\begin{code}
-\xy
- \POS (0,10) *\cir<2pt>{} ="a"
- , (20,-10)*\cir<2pt>{} ="b"
- \POS"a" \ar @/^1ex/ "b"|\uparrow
- \POS"a" \ar @/_1ex/ "b"|\downarrow
-%
- \POS (20,10) *\cir<2pt>{} ="a"
- , (40,-10)*\cir<2pt>{} ="b"
- \POS"a" \ar @/u1ex/ "b"|u
- \POS"a" \ar @/d1ex/ "b"|d
-\endxy
-\end{code}
-$$\docode$$
-%
- was typeset by
-%
-\displaycode
-%
- $\ell$ defaults to |.5pc| if omitted.
-
- This is really just a shorthand for curving using the more general
- form described next: $??c![@/]d\ell|/|$ is the same as |@`{{**{}
- ?+/|$d~2\ell~$|/}}| which makes the (quadratic) curve pass through
- the point defined by the <pos> |**{} ?+/|$d\ell$|/|.
-
-\DOCMODE(
-\xydef@\ar@curveslash/#1/{\expandafter\ar@curve@\ar@slashing{#1}}
-
-\xydef@\ar@slashing#1{{\xy@{**{} ?+/#1/+/#1/ @+c}{\setupDirection@
- \vfromslide@{#1}%
- \X@c=2\X@c \advance\X@c\X@p \advance\X@c.5\d@X
- \Y@c=2\Y@c \advance\Y@c\Y@p \advance\Y@c.5\d@Y
- \czeroEdge@
- \spushc@}}}
-\DOCMODE)
-
-\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\note??=[in-out directions]
-%
- Using ??c![@(]$d_2$|,|$d_2$|)| where $d_1,d_2$ are simple
- <direction>s (as described in note~??g[xy.doc:<direction>] except it
- is not possible to use |()|s) will typeset the arrow curved such that
- it leaves the source in direction $d_1$ and enters the target from
- direction~$d_2$.
-
-\begin{exercise}
- Typeset
-%
-\begin{code}
-\xy *{\circ}="b" \ar@(ur,ul) c
- \ar@{.>}@(dr,ul) (20,0)*{\bullet}
-\endxy
-\end{code}
-$$\docode$$
-\answercode
-\answertext{The author used \displaycode\noindent Note that it is essential
- that the curving specification comes after the arrow style.}
-\end{exercise}
-
-\DOCMODE(
-{\xyuncatcodes \catcode`\#=6 %
- \gdef\next(#1,#2){{+/#1 3pc/,p+/#2 3pc/}}}
-\xylet@\ar@curveinout@=\next
-
-\xydef@\ar@curveinout{\expandafter\ar@curve@load\ar@curveinout@}
-\DOCMODE)
-
- \TODO: implement this efficiently and properly get rid of the no-|()|
- restriction!
-
-\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\note??=[curve setup]
-%
- The final curve form is the most general one: |@`{|<control point
- lists>|}| sets the control points explicitly to the ones in the
- <control point lists> (where they should be separated by~|,|). See
- the curve extension described in~\S??g[:curve] for the way the
- control points are used; when the control points list is parsed $p$
- is the source and $c$ the target of the arrow.
-
-\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
- Curving simply uses ??c![\crvi] instead of ??c![\dir]. The
- only tricky bit is to put the control points on the stack
- right.
-
-\DOCMODE(
-\xydef@\ar@curve{%
- \ifx \space@\next \expandafter\DN@\space{\xyFN@\ar@curve}%gobble spaces
- \else\ifx \bgroup\next \let\next@=\ar@curve@load
- \else\ifx "\next \DN@"##1"{\ar@curve@{"##1"}}%
- \else \xyerror@{@= <form> must be followed by \string"<id>\string" or
- {<control point list>}}{}%
- \fi\fi\fi \next@}
-
-{\xyuncatcodes \gdef\next#1#2{\def#1##1{#2{;@={##1}}}}}
-\next\ar@curve@load\ar@curve@
-
-\xydef@\ar@curve@#1{\curve@check
- \setcurvearinit@{#1}\setcurvearexit@\arexit@@
- \def\arstemprefix@@{\crvi}\xyFN@\ar@}
-
-{\xyuncatcodes \gdef\next#1{\save @(,#1\restore}}
-\xylet@\setcurvearinit@i=\next
-\xydef@\setcurvearinit@#1{%
- \expandafter\addtoarinit@\expandafter{\setcurvearinit@i{#1}}}
-
-{\xyuncatcodes \gdef\next#1{\def#1{\POS @i @) }}}
-\xylet@\setcurvearexit@=\next
-
-\xydef@\curve@check{%
- \xyerror@{Forms @/.../, @(...), and @`{...}, only available when curve
- extension loaded}{}}
-\xywithoption{curve}{\let\curve@check=\relax}
-\DOCMODE)
-
- \TODO: The parsing is trivial and should be extended to include more
- exotic control point forms.
-
-\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\note??=[object <modifier>s]
-%
- |@[|\dots|]| and |@*{|\dots|}| formations define what object
- <modifier>s should be used when building objects that are part of the
- arrow. This is mostly useful in conjunction with extensions that
- define additional |[|<shape>|]| modifiers, \eg, if a |[red]|
- <modifier> changes the colour of an object to red then |@[red]|
- will make the entire arrow red; similarly if it is desired to make
- and entire arrow invisible then |@*{i}| can be used.
-
-\DOCMODE(
-\xydef@\ar@modifiers#1{%
- \expandafter\def\expandafter\armodifiers@@\expandafter{\armodifiers@@#1}%
- \xyFN@\ar@}
-\DOCMODE)
-
-\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\note??=[slide arrow]
-%
- ??c![@<]$D$|>| will slide (each segment of) the arrow the dimension $D$
- as explained in note~??[slide].
-
-\DOCMODE(
-{\xyuncatcodes \catcode`\#=6 \catcode`\@=11 %
- \gdef\next<#1>{\def\arafterPOS@@{<#1>}\xyFN@\ar@}}
-\xylet@\ar@slide=\next
-\DOCMODE)
-
-\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\note??=[reverse meaning of above and below]
-%
- ??c![@?] reverse the meaning of `above' and `below' for this particular
- arrow.
-
-\DOCMODE(
-\xydef@\ar@upsidedown{\let\next=\PATHlabelabove@@
- \let\PATHlabelabove@@=\PATHlabelbelow@@ \let\PATHlabelbelow@@=\next}
-\DOCMODE)
-
-\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\end{notescontd}
-
- All the features of <path>s described above are available for arrows.
-
-\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-
-\subsection*{End \& log}
-
-\DOCMODE(
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-% $Log: xyarrow.doc,v $
-% Revision 3.5 1997/05/28 13:05:01 krisrose
-% Fixed missing breaks bug.
-%
-% Revision 3.4 1997/05/18 01:14:25 krisrose
-% Essential bugfixes.
-%
-% Revision 3.3 1996/12/19 03:31:56 krisrose
-% Maintenance release
-%
-% Revision 3.2 1995/09/19 18:22:27 kris
-% Bug fix release.
-%
-% Revision 3.1 1995/09/05 20:31:32 kris
-% Releasing!
-%
-% Revision 3.0 1995/07/07 20:14:21 kris
-% Major release w/new User's Guide!
-%
-% Revision 2.13 1995/07/04 15:11:17 kris
-% Ready to release v3?
-%
-% Revision 2.12 1994/10/25 11:34:25 kris
-% Interim release just before v3 [works with AMS-LaTeX 1.2]...
-%
-% Revision 2.11 1994/07/05 10:37:32 kris
-% Third 3beta release [bug fixes].
-% Experimental graph feature included (for ECCT-94 presentation).
-%
-% Revision 2.10 1994/06/15 12:55:07 kris
-% Second 3beta release: bug fixes.
-%
-% Revision 2.9 1994/06/09 14:59:19 kris
-% Release 3beta.
-%
-% Revision 2.8 1994/04/08 04:30:00 kris
-% Second (bug fix) 3alpha release.
-%
-% Revision 2.7 1994/03/08 10:25:18 kris
-% Release 3alpha.
-%
-% Revision 2.6.9.1 1994/03/07 04:22:46 kris
-% Last internal 3alpha and pre-2.7 release.
-%
-% NEW for version 2.7 based of path and arrow code in xypic.doc 2.6.1.1.
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