%% xyarc.tex from $Id: xyarc.doc,v 3.3 1996/12/18 14:21:23 ross Exp $
%%
%% Xy-pic ``Circles, Ellipses and Arcs'' feature.
%% Copyright (c) 1995-1996 Ross Moore <[email protected]>
%%
%% 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) 1991-1996 Kristoffer H. Rose <[email protected]>
%%
%% 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{arc}{Circle, Ellipse and Arc feature}{\stripRCS$Revision: 3.3 $}%
{Ross Moore}{[email protected]}%
{Mathematics Department, Macquarie University, NSW~2109, Australia}
\xyrequire{curve}
\xycatcodes
\xydef@\ellipse#1#{\xy@{ELLIPSE}{\hbox\bgroup\save@}%
\let\endarc@=\endellipse@@ \xyFN@\preARC@ #1@}
\xydef@\endellipse@@{\xy@{endELLIPSE}{\leave@\origDirection@
\edef\next@{\egroup \X@min=\the\X@min \X@max=\the\X@max
\Y@min=\the\Y@min \Y@max=\the\Y@max }\next@}\let\bstartPLACE@=\relax}
\xydef@\preARC@{%
\ifx\next\space@ \expandafter\DN@\space{\xyFN@\preARC@}%
\else\ifx\next @\DN@{\xy@{ellipseARC}\ellipticARC@ \arc@}%
\else\ifx\next ~\DN@~##1{\tildeARC@{##1}}%
\else\DN@{\xy@{ellipticARC}\ellipticARC@ \arc@}%
\fi\fi\fi \next@ }
\xydef@\arc@#1@#2{\xy@{arcSTYLE}{\def\arcSTYLE{#2}}\arc@i
\DNii@{#1}%
\ifx\nextii@\empty \DN@{\fullCircle@}%
\else \DN@{_}%
\ifx\next@\nextii@ \xy@{_}{\def\arcOrient@@{_}}%
\let\arcOrient@@=\next@ \DN@{\fullCircle@}%
\else \DN@{^}%
\ifx\next@\nextii@ \xy@{^}{\def\arcOrient@@{^}}%
\let\arcOrient@@=\next@ \DN@{\fullCircle@}%
\else \DN@{\def\afterARCextents@@{%
\xy@{aftARCext}{\let\doCircleArc@=\doCircleArc@@}%
\ellipseArc@
\xy@{doCircARCs}{\leave@ \doCircleArcs@}\endarc@ }%
\xyFN@\getarcparams@#1@}\fi\fi\fi
\next@ }
\xydef@\arc@i{\xy@{ARCi}{%
\save@\idfromc@{0@c}\cfromp@\idfromc@{0@p}%
\enter@\cplusthec@ \enter@\relax\begingroup\vfromslide@i{}@\czeroEdge@
\leave@\idfromc@{0@m}\leave@ \zeroDivideLimit@{50}%
\edef\origDirection@{\Direction=\the\Direction
\relax\noexpand\imposeDirection@}%
\let\startDirection@=\origDirection@ \def\startDirection@@{}%
\def\endDirection@{}\def\endDirection@@{}\def\arcOrient@@{^}}%
\def\arcOrient@@{^}\let\processDirections@=\checkstartDirection@
\def\arcRadius@{}\def\ellipseRatio@{}\def\arcScale@{\arcScale@@}}
\message{circles,}
\xydef@\fullCircle@{\xy@{fullCIRC}{\let\endDirection@=\relax
\let\doCircleArc@=\doMergeEndArc@@}\circleArc@ }%
\xydef@\getarcparams@{%
\ifx\space@\next \expandafter\DN@\space{\xyFN@\getarcparams@}%
\else\addLT@\ifx \next \xy@{<}{}%
\addGT@{\addLT@\DN@##1}{\splitRadius@dim##1,,@}%
\else\ifx\next (\DN@({\xyFN@\checkRadOpen@}%
\else\ifx\next @\xy@{@}{}\DN@ @{\fullEllipse@}%
\else \addLQ@\ifx \next \addLQ@\DN@{\xy@`{}\ARCturn@}%
\else \DN@{\getarcExtents@}%
\fi\fi\fi\fi\fi \next@ }
\xydef@\checkRadOpen@{%
\ifx\next *\DN@{\xyFN@\getarcExtents@ (}%
\else \xy@{(}{}\DN@##1){\splitRadius@##1,,@}%
\fi \next@ }
\xydef@\fixedRadiusArc@{%
\xy@{fixRadArc}{\save@ \idfromc@{0@0}\cfromp@\idfromc@{0@c}\leave@}%
\xyFN@\fixedRadiusArc@i }
\xydef@\fixedRadiusArc@i{%
\ifx\next\space@ \expandafter\DN@\space{\xyFN@\fixedRadiusArc@i}%
\else\ifx\next @\xy@{@}{}\DN@ @{\fullEllipse@}%
\else\DN@{\let\processDirections@=\processArcDirections@
\def\afterARCextents@@{\xy@{aftARCext}{\let\doCircleArc@=\doCircleArc@@
\ellipseSector@}}\xyFN@\getarcExtents@}%
\fi\fi \next@ }
\xydef@\arcScale@@{\xy@{arcSCALE@@}{\save@
\cfromid@{0@0}\pfromc@\cfromid@{0@p}\setbase@\X@p\Y@p\X@c\Y@c}}
\xydef@\arcScale@dim#1{\xy@{arcSCALEdim}{\save@\cfromid@{0@0}\pfromc@
\cfromid@{0@p}\setupDirection@\cfromp@ \enter@\cplusthec@
\enter@\relax\begingroup\vfromslide@i#1@\leave@
\setbase@\X@p\Y@p\X@c\Y@c \idfromc@{0@p}}}
\xydef@\ellipseScale@dim#1{\xy@{ellSCALEdim}{\setupDirection@\cfromp@
\enter@\cplusthec@ \aboveDirection@\xydashl@ \vfromslide@{#1}\leave@
\setbase@@\X@c\Y@c}}
\xydef@\ellipseScale@#1{\xy@{ellSCALE@}%
{\vfromcartesian@@0,#1@\setbase@@\X@c\Y@c}}
\xydef@\splitRadius@dim#1,#2,#3@{%
\DN@{#1}\ifx\next@\empty\dimen@=\z@\else\dimen@=#1\relax%\splinetracing
\expandafter\def\expandafter\arcRadius@
\expandafter{\arcScale@dim{#1}}\fi
\DN@{#2}\ifx\next@\empty\dimen@ii=\z@\def\ellipseRatio@{}%
\else\dimen@ii=#2\relax \expandafter
\def\expandafter\ellipseRatio@\expandafter{\ellipseScale@dim{#2}}%
\fi \fixedRadiusArc@ }
\xydef@\splitRadius@#1,#2,#3@{%
\DN@{#1}\ifx\next@\empty\dimen@=\z@\else\dimen@=#1\p@\relax\fi
\DN@{#2}\ifx\next@\empty\dimen@ii=\z@\else\dimen@ii=#2\p@\relax\fi
\ifdim\dimen@=\z@ \ifdim\dimen@ii=\z@\else \expandafter
\def\expandafter\ellipseRatio@\expandafter{\ellipseScale@{#2}}\fi
\else
\ifdim\dimen@ii=\z@
\def\arcScale@{\xy@{arcSCALE@}{\save@\cfromid@{0@0}%
\X@origin=\X@c \Y@origin=\Y@c
\X@xbase=#1\X@xbase \Y@xbase=#1\Y@xbase
\X@ybase=#1\X@ybase \Y@ybase=#1\Y@ybase
\advance\X@c\X@xbase \advance\Y@c\Y@xbase \czeroEdge@
\idfromc@{0@p}\idfromc@{0@c}}}%
\else
\def\arcScale@{\xy@{arcSCALE@}{\save@\cfromid@{0@0}%
\X@origin=\X@c \Y@origin=\Y@c
\X@xbase=#1\X@xbase \Y@xbase=#1\Y@xbase
\X@ybase=#2\X@ybase \Y@ybase=#2\Y@ybase
\advance\X@c\X@xbase \advance\Y@c\Y@xbase \czeroEdge@
\idfromc@{0@p}\idfromc@{0@c}}}%
\fi
\fi \fixedRadiusArc@ }
\xydef@\baseOrient@{\DN@{_}\ifx\next@\arcOrient@@
\X@ybase=-\X@ybase \Y@ybase=-\Y@ybase \fi }
\message{ellipses,}
\xydef@\fullEllipse@{\xy@{fullELLIPSE}%
{\def\startDirection@{}\let\doCircleArc@=\doMergeEndArc@@}%
\ellipseArc@
\xy@{doCIRCarcs}{\leave@ \doCircleArcs@}\endarc@ }
\xydef@\ellipseArc@{%
\arcScale@ \arcRadius@ \ellipseRatio@
\xy@{arcCONTROLS}{\baseOrient@ \arcControls@ \let\bstartPLACE@=\relax }}
\xydef@\cubicARCcontrols@@{\czeroEdge@
\vfromcartesian@@0,1@\idfromc@{1@c}%
\vfromcartesian@@-1,0@\idfromc@{2@c}%
\vfromcartesian@@0,-1@\idfromc@{3@c}%
\vfromcartesian@@1,\arcparam@ @\idfromc@{1@m}%
\vfromcartesian@@\arcparam@,1@\idfromc@{2@m}%
\vfromcartesian@@-\arcparam@,1@\idfromc@{3@m}%
\vfromcartesian@@-1,\arcparam@ @\idfromc@{4@m}%
\vfromcartesian@@-1,-\arcparam@ @\idfromc@{5@m}%
\vfromcartesian@@-\arcparam@,-1@\idfromc@{6@m}%
\vfromcartesian@@\arcparam@,-1@\idfromc@{7@m}%
\vfromcartesian@@1,-\arcparam@ @\idfromc@{8@m}%
}
\xydef@\doCircleArc@@#1#2{\save@ \ifcase#2\relax
\doCircleArc@@@{0@p}{1@m}{2@m}{1@c}{#1}\or
\doCircleArc@@@{1@c}{3@m}{4@m}{2@c}{#1}\or
\doCircleArc@@@{2@c}{5@m}{6@m}{3@c}{#1}\or
\doCircleArc@@@{3@c}{7@m}{8@m}{0@p}{#1}\or
\doCircleArc@@@{0@p}{1@m}{2@m}{1@c}{#1}\or
\doCircleArc@@@{1@c}{3@m}{4@m}{2@c}{#1}\or
\doCircleArc@@@{2@c}{5@m}{6@m}{3@c}{#1}\or
\doCircleArc@@@{3@c}{7@m}{8@m}{0@p}{#1}\fi \leave@ }
\xydef@\doCircleArc@@@#1#2#3#4#5{%
\cfromid@{#1}\pfromc@\senter@
\cfromid@{#2}\spushc@\cfromid@{#3}\spushc@\cfromid@{#4}%
\connect@\crvs{#5}\relax\sinit@\sleave@}
\xydef@\doMergeEndArc@@#1#2{\save@\ifcase#2\relax
\doMergeEnd@@@{0@p}{1@m}{2@m}{1@c}{#1}\relax\or
\doMergeEnd@@@{1@c}{3@m}{4@m}{2@c}{#1}\relax\or
\doMergeEnd@@@{2@c}{5@m}{6@m}{3@c}{#1}\relax\or
\doMergeEnd@@@{3@c}{7@m}{8@m}{0@p}{#1}@\fi \leave@ }
\xydef@\doMergeEnd@@@#1#2#3#4#5#6{%
\cfromid@{#1}\pfromc@\senter@
\cfromid@{#2}\spushc@\cfromid@{#3}\spushc@\cfromid@{#4}%
\ifx#6\relax
\L@c=.1\p@ \R@c=\L@c \U@c=\L@c \D@c=\L@c \Edge@c={\rectangleEdge}\fi
\enter@\cmergethec@\cfromid@{0@c}\leave@
\enter@\cmergethec@\cfromcontrols@{#1}{#2}{#3}{#4}\leave@
\connect@\crvs{#5}\relax
\sinit@\sleave@}
\xydef@\doMergeStartArc@#1#2{\save@\ifcase#2\relax
\doMergeStart@@{0@p}{1@m}{2@m}{1@c}{#1}@\or
\doMergeStart@@{1@c}{3@m}{4@m}{2@c}{#1}\relax\or
\doMergeStart@@{2@c}{5@m}{6@m}{3@c}{#1}\relax\or
\doMergeStart@@{3@c}{7@m}{8@m}{0@p}{#1}\relax\fi \leave@ }
\xydef@\doMergeStart@@#1#2#3#4#5#6{%
\cfromid@{#1}\ifx#6\relax
\L@c=.1\p@ \R@c=\L@c \U@c=\L@c \D@c=\L@c \Edge@c={\rectangleEdge}\fi
\enter@\cmergethec@\cfromid@{0@x}\leave@
\enter@\cmergethec@\cfromcontrols@{#4}{#3}{#2}{#1}\leave@
\pfromc@
\senter@ \cfromid@{#2}\spushc@\cfromid@{#3}\spushc@\cfromid@{#4}%
\connect@\crvs{#5}\relax\sinit@\sleave@}
\xydef@\doMergeBothArc@#1#2{\save@\ifcase#2\relax
\doMergeBoth@@{0@p}{1@m}{2@m}{1@c}{#1}@\or
\doMergeBoth@@{1@c}{3@m}{4@m}{2@c}{#1}\relax\or
\doMergeBoth@@{2@c}{5@m}{6@m}{3@c}{#1}\relax\or
\doMergeBoth@@{3@c}{7@m}{8@m}{0@p}{#1}\relax\fi \leave@ }
\xydef@\doMergeBoth@@#1#2#3#4#5#6{%
\cfromid@{#1}\ifx#6\relax
\L@c=.1\p@ \R@c=\L@c \U@c=\L@c \D@c=\L@c \Edge@c={\rectangleEdge}\fi
\enter@\cmergethec@\cfromid@{0@x}\leave@
\enter@\cmergethec@\cfromcontrols@{#4}{#3}{#2}{#1}\leave@
\pfromc@
\senter@ \cfromid@{#2}\spushc@\cfromid@{#3}\spushc@\cfromid@{#4}%
\enter@\cmergethec@\cfromid@{0@c}\leave@
\enter@\cmergethec@\cfromcontrols@{#1}{#2}{#3}{#4}\leave@
\connect@\crvs{#5}\relax\sinit@\sleave@}
\xydef@\doMergeEndArc@#1#2{\count@@=#2\relax
\ifnum\count@@>\thr@@ \advance\count@@-4\fi\relax
\doMergeEndArc@@{#1}\count@@ }
\xydef@\doStraightArc@@#1{\xy@{STRAITarc}{\save@
\cfromid@{0@p}\pfromc@\cfromid@{0@c}%
\senter@\connect@\crvs{#1}\sinit@\sleave@\leave@}}
\xydef@\cfromcontrols@#1#2#3#4{\bgroup
\cfromid@{#1}\L@p=\X@c \U@p=\Y@c
\cfromid@{#4}\R@p=\X@c \D@p=\Y@c
\cfromid@{#3}\A@=\X@c \B@=\Y@c \cfromid@{#2}%
\ifdim\R@p>\L@p \ifdim\A@>\R@p \R@p=\A@
\ifdim\X@c>\R@p \R@p=\X@c\fi\fi
\else \ifdim\A@<\R@p \R@p=\A@
\ifdim\X@c<\R@p \R@p=\X@c\fi\fi
\fi
\ifdim\D@p>\U@p \ifdim\B@>\D@p \D@p=\B@
\ifdim\Y@p>\D@p \D@p=\Y@p\fi\fi
\else \ifdim\B@<\D@p \D@p=\B@
\ifdim\Y@p<\D@p \D@p=\Y@p\fi\fi
\fi
\edef\next@{\egroup \X@c=\the\R@p \Y@c=\the\D@p}\next@ }
\xydef@\doCircleArcs@{\save@
\cfromid@{0@0}\pfromc@\cfromid@{0@p}\setupDirection@
\startDirection@ \edef\startDirection@@{\the\Direction}%
\cfromid@{1@c}\setupDirection@ \edef\quadDirection@{\the\Direction}\relax
\count@=\quadDirection@ \relax\def\nextii@{^}%
\let\preDirection@@=\startDirection@@
\ifx\nextii@\arcOrient@@
\ifnum\quadDirection@>\startDirection@@ \relax
\else \advance\count@ by8192 \relax\edef\quadDirection@{\the\count@}\fi
\ifx\endDirection@@\empty
\ifx\endDirection@\relax
\bgroup\cfromid@{0@c}\setupDirection@
\edef\next@{\egroup \count@@=\the\Direction}\next@ \relax
\ifnum\count@@<\startDirection@@ \advance\count@@ 8192 \fi
\edef\endDirection@@{\the\count@@}%
\else
\count@@=\startDirection@@
\advance\count@@ by8192 \edef\endDirection@@{\the\count@@}%
\fi
\else
\count@@=\endDirection@@ \relax\ifnum\count@@<\startDirection@@ \relax
\advance\count@@ by8192 \edef\endDirection@@{\the\count@@}\fi
\fi
\ifnum\endDirection@@>\quadDirection@
\DN@{\expandafter\doCircleArc@@\expandafter{\arcSTYLE}{0}}%
\else
\DN@{\expandafter\doCircleArc@\expandafter{\arcSTYLE}{0}}%
\fi
\else
\ifnum\count@<\startDirection@@\relax\else\advance\count@ by-8192 \relax
\edef\quadDirection@{\the\count@}\fi
\ifx\endDirection@@\empty
\ifx\endDirection@\relax
\bgroup\cfromid@{0@c}\setupDirection@
\edef\next@{\egroup \count@@=\the\Direction}\next@ \relax
\ifnum\count@@>\startDirection@@ \advance\count@@-8192 \fi
\edef\endDirection@@{\the\count@@}%
\else
\count@@=\startDirection@@
\advance\count@@ by-8192 \edef\endDirection@@{\the\count@@}%
\fi
\else
\count@@=\endDirection@@ \relax \ifnum\count@@>\startDirection@@
\advance\count@@ by-8192 \edef\endDirection@@{\the\count@@}\fi
\fi
\ifnum\endDirection@@<\quadDirection@
\DN@{\expandafter\doCircleArc@@\expandafter{\arcSTYLE}{0}}%
\else \DN@{\expandafter\doCircleArc@\expandafter{\arcSTYLE}{0}}\fi
\fi
\next@ \relax
\count@=\quadDirection@ \relax\def\nextii@{^}\DN@{}%
\ifx\nextii@\arcOrient@@
\count@@=\startDirection@@ \advance\count@@ by4096 \relax
\ifnum \count@<\endDirection@@ \relax
\ifnum\endDirection@@>\count@@
\DN@{\expandafter\doCircleArc@@\expandafter{\arcSTYLE}{1}}%
\else \DN@{\expandafter\doCircleArc@\expandafter{\arcSTYLE}{1}}\fi
\fi
\else
\count@@=\startDirection@@ \advance\count@@ by-4096 \relax
\ifnum \count@>\endDirection@@ \relax
\ifnum\endDirection@@<\count@@
\DN@{\expandafter\doCircleArc@@\expandafter{\arcSTYLE}{1}}%
\else \DN@{\expandafter\doCircleArc@\expandafter{\arcSTYLE}{1}}\fi
\fi\fi
\next@ \relax
\ifx\next@\empty \else \relax
\count@=\startDirection@@ \relax\def\nextii@{^}\DN@{}%
\ifx\nextii@\arcOrient@@ \advance\count@ by4096 \relax
\count@@=\quadDirection@ \advance\count@@ by4096 \relax
\ifnum \count@<\endDirection@@
\ifnum\endDirection@@>\count@@
\DN@{\expandafter\doCircleArc@@\expandafter{\arcSTYLE}{2}}%
\else \DN@{\expandafter\doCircleArc@\expandafter{\arcSTYLE}{2}}\fi
\fi
\else \advance\count@ by-4096 \relax
\count@@=\quadDirection@ \advance\count@@ by-4096 \relax
\ifnum \count@>\endDirection@@ \relax
\ifnum\endDirection@@<\count@@
\DN@{\expandafter\doCircleArc@@\expandafter{\arcSTYLE}{2}}%
\else \DN@{\expandafter\doCircleArc@\expandafter{\arcSTYLE}{2}}\fi
\fi\fi
\next@ \relax
\fi
\ifx\next@\empty \else \relax
\count@=\quadDirection@ \def\nextii@{^}\DN@{}%
\ifx\nextii@\arcOrient@@ \advance\count@ by4096 \relax
\ifnum \count@<\endDirection@@
\DN@{\expandafter\doCircleArc@\expandafter{\arcSTYLE}{3}}\fi
\else \advance\count@ by-4096 \relax
\ifnum \count@>\endDirection@@
\DN@{\expandafter\doCircleArc@\expandafter{\arcSTYLE}{3}}\fi
\fi \next@ \relax
\fi
\leave@ }
\message{elliptical arcs,}
\xydef@\arcmagic@@{0.5517847}
\xylet@\arcmagic=\arcmagic@@
\xydef@\tildeARC@#1{%
\if q#1\DN@{\xy@{quadARC}\quadARC@ \arc@}%
\else\if c#1\DN@{\xyFN@\cubicARC@i}%
\else\if e#1\DN@{\xy@{ellipticARC}\ellipticARC@ \arc@}%
\else\if i#1\DN@{\xy@{interpARC}\interpARC@ \arc@}%
\else\if p#1\DN@{\xy@{cuspidalARC}\cuspidalARC@ \arc@}%
\else\xywarning@{unknown arc type: #1 }%
\DN@{\xy@{ellipticARC}\ellipticARC@ \arc@}%
\fi\fi\fi\fi\fi \next@ }
\xydef@\cubicARC@i{%
\ifx\next\space@ \expandafter\DN@\space{\xyFN@\cubicARC@i}%
\else\ifx\next (\DN@(##1){\xy@{cubicARC(##1)}{\cubicARC@{##1}}\arc@}%
\else \DN@{\xy@{cubicARC(1)}{\cubicARC@{1}}\arc@}%
\fi\fi \next@ }
\xydef@\ellipticARC@{\let\arcControls@=\cubicARCcontrols@@
\edef\arcparam@{\arcmagic@@}}
\xydef@\cubicARC@#1{\let\arcControls@=\cubicARCcontrols@@
\dimen@=#1\p@ \edef\arcparam@{\expandafter\removePT@\the\dimen@}}
\xydef@\quadARC@{\let\arcControls@=\cubicARCcontrols@@
\def\arcparam@{.66667}}
\xydef@\cuspidalARC@{\let\arcControls@=\cubicARCcontrols@@
\def\arcparam@{2}}
\xydef@\interpARC@{\let\arcControls@=\cubicARCcontrols@@
\def\arcparam@{1.33333}}
\xydef@\ARCturn@{\xy@@\bgroup\afterCOORD{%
\xy@@{\edef\next@{\egroup \A@=\the\X@c \B@=\the\Y@c}\next@}\ARCturn@@}}
\xydef@\ARCturn@@#1@{\DN@{#1}\DNii@{^}%
\ifx\next@\nextii@ \xy@{^}{\def\arcOrient@@{^}}%
\else\DNii@{_}\ifx\next@\nextii@ \xy@{_}{\def\arcOrient@@{_}}%
\else\xy@{}{\def\arcOrient@@{}}\fi\fi
\xy@@\ARCturn@@@ \processDirections@@ }
\xydef@\ARCturn@@@{%
\bgroup\cfromid@{0@p}\X@p=\X@c \Y@p=\Y@c \X@c=\A@ \Y@c=\B@
\setupDirection@ \edef\next@{\egroup\count@=\the\Direction}\next@\relax
\edef\startDirection@@{\the\count@ }%
\bgroup\cfromid@{0@c}\X@p=\A@ \Y@p=\B@
\setupDirection@ \edef\next@{\egroup\count@=\the\Direction}\next@\relax
\edef\endDirection@@{\the\count@}%
\ifx\arcOrient@@\empty
\bgroup\cfromid@{0@p}\X@p=\X@c \Y@p=\Y@c \cfromid@{0@c}%
\setupDirection@ \edef\next@{\egroup\count@@=\the\Direction}\next@\relax
\count@=-\count@@ \advance\count@\startDirection@@ \relax \count@=-\count@
\ifnum\count@>4096 \def\arcOrient@@{_}%
\else\ifnum\count@<-4096 \def\arcOrient@@{^}%
\else\ifnum\count@>\z@ \def\arcOrient@@{^}%
\else\def\arcOrient@@{_}\fi\fi\fi
\fi }
\xydef@\circleArc@{%
\xy@{circARC@}{\cfromid@{0@p}\pfromc@\cfromp@\startDirection@
\arcCenter@\idfromc@{0@0}%
\def\startDirection@{\bgroup
\cfromid@{0@0}\pfromc@\cfromid@{0@p}\setupDirection@
\edef\next@{\egroup \Direction=\the\Direction}\next@
\relax\imposeDirection@}}%
\ifx\endDirection@@\empty
\ifx\arcRadius@\empty \ifx\ellipseRatio@\empty\else
\DN@{\arcScale@@}\ifx\arcScale@\next@\else
\xy@@{\bgroup\cfromid@{0@0}\pfromc@\cfromid@{0@c}\setupDirection@
\edef\next@{\egroup \Direction=\the\Direction}\next@
\edef\endDirection@@{\the\Direction}}\fi\fi\fi\fi
\ellipseArc@ \xy@@{\leave@ \doCircleArcs@}\endarc@ }
\xydef@\arcbisector{%
\cfromid@{0@p}\pfromc@\cfromid@{0@c}\setupDirection@
\advance\X@c\X@p\divide\X@c\tw@
\advance\Y@c\Y@p\divide\Y@c\tw@ \czeroEdge@ \pfromc@
\enter@\cplusthec@ \enter@\relax\begingroup
\aboveDirection@\xydashl@ \vfromslide@i{}@\leave@ }
\xydef@\arcCenter@{%
\cfromid@{0@p}\pfromc@\cfromid@{0@m}\setupDirection@
\cfromp@\enter@\cplusthec@ \enter@\relax\begingroup
\aboveDirection@\xydashl@ \vfromslide@i{}@\leave@\no@@
\arcCenter@i }
\xydef@\arcCenter@i{%
\enter@{\pfromthep@}\setupDirection@ \Creset@@
\let\PLACEedgep@@=\PLACEedgep@ \let\PLACEedgec@@=\PLACEedgec@
\enter@{\pfromthep@\basefromthebase@}\bgroup
\arcbisector \edef\next@{\egroup
\X@c =\the\X@c \Y@c=\the\Y@c \X@p=\the\X@p \Y@p=\the\Y@p }%
\next@ \Cintercept@@ \leave@\leave@ }
\xydef@\getarcExtents@{%
\ifx\space@\next\expandafter\DN@\space{\xyFN@\getarcExtents@}%
\else\ifx\next @\xy@{@}{}\DN@ @{\fullEllipse@}%
\else\DN@{\xy@{arcEXTENTs}{\save@
\def\startDirection@{\Direction=\startDirection@@ \imposeDirection@}}%
\xyFN@\getarcExtents@ii}\fi\fi \next@ }
\xydef@\getarcExtents@ii{%
\ifx\next!\xy@{![[}{}\DN@![[##1]]{\getxyDirection@{##1}\getarcExtents@iv}%
\else\DN@{\getarcExtents@iv}\fi \next@ }
\xydef@\getarcExtents@iv{\afterDIRECTIONorEMPTY
{\xy@{startDIR}{\edef\startDirection@@{\the\Direction}\leave@}%
\xyFN@\getarcOrientation@}%
{\xy@{startDIR}{\edef\startDirection@@{\the\Direction}\leave@}%
\xyFN@\getarcOrientation@}}
\xydef@\getarcOrientation@{%
\ifx\space@\next\expandafter\DN@\space{\xyFN@\getarcOrientation@}%
\else\ifx\next @\xy@{@}{}\DN@{\getEndDirection@x}%
\else\ifx\next,\xy@{,}{}\DN@,{\xyFN@\getarcOrientation@i}%
\else\DN@{\getarcOrientation@i}\fi\fi\fi \next@ }%
\xydef@\getarcOrientation@i{%
\ifx\space@\next\expandafter\DN@\space{\xyFN@\getarcOrientation@i}%
\else\ifx\next @\xy@{@}{}\DN@{\getEndDirection@x}%
\else\ifx\next^{}\DN@##1{\xy@{^}{\def\arcOrient@@{^}}%
\def\arcOrient@@{^}\xyFN@\getEndDirection@}%
\else\ifx\next_\DN@##1{\xy@{_}{\def\arcOrient@@{_}}%
\def\arcOrient@@{_}\xyFN@\getEndDirection@}%
\else\DN@{\xyFN@\getEndDirection@}%
\fi\fi\fi\fi \next@ }
\xydef@\getEndDirection@{%
\ifx\space@\next\expandafter\DN@\space{\xyFN@\getEndDirection@}%
\else\ifx\next,\DN@,{\xy@{,}{}\xyFN@\getEndDirection@}%
\else\addEQ@\ifx\next\addEQ@\DN@{\xy@{=}{\save@\startDirection@}%
\xyFN@\getEqDirection@}%
\else \ifx\next!\DN@![[##1]]{\xy@{
