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+% Copyright 2013 by Till Tantau
+%
+% This file may be distributed and/or modified
+%
+% 1. under the LaTeX Project Public License and/or
+% 2. under the GNU Public License.
+%
+% See the file doc/generic/pgf/licenses/LICENSE for more details.
+
+\ProvidesFileRCS[v\pgfversion] $Header: /cvsroot/pgf/pgf/generic/pgf/modules/pgfmodulebending.code.tex,v 1.18 2013/09/30 18:30:15 tantau Exp $
+
+
+%
+% This file defines commands for drawing bending arrows and lines.
+%
+
+\usepgfmodule{nonlineartransformations}
+\usepgflibrary{curvilinear}
+
+
+% Configuration options for arrow tips:
+
+\pgfkeys{
+ /pgf/arrow keys/flex/.code=\pgfarrowsaddtooptions{\pgf@arrows@the@rigidity#1pt\let\pgf@arrow@flex@mode\pgf@arrow@mode@is@flex},
+ /pgf/arrow keys/flex/.default=1,
+ /pgf/arrow keys/flex'/.code=\pgfarrowsaddtooptions{\pgf@arrows@the@rigidity#1pt\let\pgf@arrow@flex@mode\pgf@arrow@mode@is@flex@prime},
+ /pgf/arrow keys/flex'/.default=1,
+ /pgf/arrow keys/bend/.code=\pgfarrowsaddtooptions{\let\pgf@arrow@flex@mode\pgf@arrow@mode@is@bend}
+}
+
+
+\def\pgf@arrow@mode@is@flex{1}
+\def\pgf@arrow@mode@is@flex@prime{2}
+\def\pgf@arrow@mode@is@bend{3}
+
+\newdimen\pgf@arrows@the@rigidity
+
+%
+%
+% Handle the end of a curve
+%
+%
+
+% First, the preparation. This is, essenatially, setting up the
+% nonlinear transformation
+
+\def\pgf@prep@curveend{
+ \pgftransformreset%
+ \pgfsetcurvilinearbeziercurve{\pgfpointlastonpath}{\pgfpointsecondlastonpath}{\pgfpointthirdlastonpath}{\pgfpointfourthlastonpath}
+}
+
+% Second, the shortening.
+
+\def\pgf@do@shorten@curvedend{%
+ \expandafter\expandafter\expandafter\pgf@do@shorten@curvedend@unpack\expandafter\pgfpointfourthlastonpath\pgfpointthirdlastonpath%
+}
+\def\pgf@do@shorten@curvedend@unpack\pgfqpoint#1#2\pgfqpoint#3#4{%
+ \pgf@process{\pgfcurvilineardistancetotime{\pgf@path@shortening@distance}}%
+ % Compute new curve:
+ \pgfpointcurveattime{\pgf@x}{\pgfpointlastonpath}{\pgfpointsecondlastonpath}{\pgfpointthirdlastonpath}{\pgfpointfourthlastonpath}%
+ % \pgfx/y and \pgf xa/xb already correct. Need to setup remaining vector...
+ \pgf@xb#3%
+ \pgf@yb#4%
+ \pgf@xb\pgf@time@t\pgf@xb%
+ \pgf@yb\pgf@time@t\pgf@yb%
+ \advance\pgf@xb by\pgf@time@s\pgf@xc%
+ \advance\pgf@yb by\pgf@time@s\pgf@yc%
+ \edef\pgfprocessresultsubpathsuffix{%
+ \expandafter\noexpand\pgfsubpathfourthlasttoken{#1}{#2}%
+ \noexpand\pgfsyssoftpath@curvetosupportatoken{\the\pgf@xb}{\the\pgf@yb}%
+ \noexpand\pgfsyssoftpath@curvetosupportbtoken{\the\pgf@xa}{\the\pgf@ya}%
+ \noexpand\pgfsyssoftpath@curvetotoken{\the\pgf@x}{\the\pgf@y}}%
+ \expandafter\expandafter\expandafter\def%
+ \expandafter\expandafter\expandafter\pgfprocessresultpathsuffix%
+ \expandafter\expandafter\expandafter{\expandafter\pgfprocessresultsubpathprefix\pgfprocessresultsubpathsuffix}%
+}
+
+% Third, the drawing
+
+\def\pgf@do@draw@curvedend{%
+ \pgf@do@draw@curved\pgf@end@tip@sequence%
+}
+
+\def\pgf@do@draw@curved#1{%
+ {%
+ \pgftransformreset%
+ \pgf@xb\pgf@arrow@tip@total@length% xb will keep track of the total length
+ \let\pgf@arrow@handle\pgf@draw@curved%
+ \let\pgf@arrow@handle@dot\relax%
+ #1%
+ }%
+}
+
+\def\pgf@draw@curved#1#2{%
+ % Prepare:
+ {%
+ \pgfarrows@getid{#1}{#2}%
+ % Do shift:
+ \expandafter\expandafter\expandafter\pgf@arrow@drawer@rigid@shift\csname pgf@ar@ends@\pgf@arrow@id\endcsname%
+ \expandafter\let\expandafter\pgf@arrow@bending@mode\csname pgf@ar@bending@mode@#1\endcsname%
+ \ifx\pgf@arrow@bending@mode\pgfutil@empty\let\pgf@arrow@flex@mode\pgf@arrow@mode@is@flex\fi%
+ % do swap:
+ {%
+ \csname pgf@ar@saves@\pgf@arrow@id\endcsname%
+ \ifcase\pgf@arrow@flex@mode\relax%
+ \expandafter\expandafter\expandafter\pgf@arrow@drawer@rigid\csname pgf@ar@visual@\pgf@arrow@id\endcsname% like flex
+ \or%
+ \expandafter\expandafter\expandafter\pgf@arrow@drawer@rigid\csname pgf@ar@visual@\pgf@arrow@id\endcsname%
+ \or%
+ \expandafter\expandafter\expandafter\pgf@arrow@drawer@rigid\csname pgf@ar@ends@\pgf@arrow@id\endcsname%
+ \or%
+ \pgf@arrow@drawer@bend%
+ \fi%
+ % hull points inside the above
+ }%
+ \expandafter}%
+ % Transform to next tip:
+ \expandafter\pgf@xb\the\pgf@xb%
+}
+\def\pgf@falsetext{false}
+
+\def\pgf@arrow@drawer@rigid@shift#1#2#3{% tip end, back end, line end, sep
+ % Let xa be the actual back end of the current arrow plus the back end:
+ \advance\pgf@xb by#2%
+ \pgf@xa\pgf@xb%
+ % Update the xb:
+ \pgf@x#1%
+ \advance\pgf@x by\pgfarrowsep%
+ \advance\pgf@xb by-\pgf@x%
+}
+
+
+\def\pgf@arrow@drawer@bend{%
+ \pgftransformnonlinear{\pgf@arrow@bending@mode{\pgf@x}{\pgf@y}}
+ \pgftransformscale{-1}%
+ \pgftransformxshift{-\pgf@xa}%
+ % Do slant:
+ \ifdim\pgfarrows@slant pt=0pt%
+ \else%
+ \pgftransformxslant{\pgfarrows@slant}%
+ \fi%
+ \ifpgfarrowswap%
+ \pgftransformyscale{-1}%
+ \fi%
+ {%
+ \pgf@relevantforpicturesizefalse%
+ \pgfscope%
+ \pgf@arrows@color@setup%
+ \csname pgf@ar@inst@code@\pgf@arrow@id\endcsname%
+ \endpgfscope%
+ }%
+ \pgf@arrows@bending@hull%
+}
+
+\def\pgf@arrow@drawer@rigid#1#2#3{% (rigid) start, (rigid) end, dummy
+ % Compute the rigid positions:
+ \pgf@x#1% start
+ \pgf@y#2% flexibility*(end-start) + start
+ \advance\pgf@y by-\pgf@x%
+ \pgf@y\pgf@sys@tonumber\pgf@arrows@the@rigidity\pgf@y%
+ \advance\pgf@y by\pgf@x%
+ % Are they equal?
+ \ifdim\pgf@x=\pgf@y%
+ % Yes, do tangent:
+ \pgf@bending@do@tangent%
+ \else%
+ \pgf@bending@do@flex%
+ \fi%
+ \pgf@xc#1%
+ \pgf@xc-\pgf@xc%
+ \pgftransformxshift{+\pgf@xc}%
+ % Do slant:
+ \ifdim\pgfarrows@slant pt=0pt%
+ \else%
+ \pgftransformxslant{\pgfarrows@slant}%
+ \fi%
+ % do swap:
+ \ifpgfarrowswap%
+ \pgftransformyscale{-1}%
+ \fi%
+ \pgfscope%
+ \pgf@arrows@color@setup%
+ \pgflowlevelsynccm\csname pgf@ar@cache@\pgf@arrow@id\endcsname%
+ \endpgfscope%
+ \pgf@arrows@rigid@hull%
+}
+
+\def\pgf@bending@do@tangent{%
+ \pgf@xb\pgf@xa%
+ \advance\pgf@xb by-\pgf@x%
+ \pgfcurvilineardistancetotime{\pgf@xb}%
+ \pgf@xb\pgf@x%
+ % Compute points:
+ \ifdim\pgf@xb=0pt%
+ \pgf@bending@possible@degenerate%
+ \else%
+ \pgf@bending@do@tangent@normal%
+ \fi%
+ \pgf@ya-\pgf@y%
+ \pgfsettransformentries%
+ {\pgf@sys@tonumber\pgf@x}{\pgf@sys@tonumber\pgf@y}%
+ {\pgf@sys@tonumber\pgf@ya}{\pgf@sys@tonumber\pgf@x}{\pgf@xc}{\pgf@yc}%
+}%
+
+\def\pgf@bending@do@tangent@normal{%
+ \pgfpointcurveattime{\pgf@xb}{\pgf@curvilinear@line@a}{\pgf@curvilinear@line@b}{\pgf@curvilinear@line@c}{\pgf@curvilinear@line@d}%
+ \pgf@xc\pgf@x% save
+ \pgf@yc\pgf@y% save
+ % compute normal:
+ \advance\pgf@xb by-\pgf@xa%
+ \advance\pgf@yb by-\pgf@ya%
+ \pgf@process{\pgfpointnormalised{\pgf@x=\pgf@xb\pgf@y=\pgf@yb}}
+}
+
+\def\pgf@bending@possible@degenerate{%
+ \ifx\pgf@curvilinear@line@a\pgf@curvilinear@line@b% degenerate!
+ \ifx\pgf@curvilinear@line@a\pgf@curvilinear@line@c% double degenerate!
+ \let\pgf@ref\pgf@curvilinear@line@d%
+ \else
+ \let\pgf@ref\pgf@curvilinear@line@c%
+ \fi%
+ \pgf@process{\pgf@curvilinear@line@a}%
+ \pgf@xc\pgf@x% save
+ \pgf@yc\pgf@y% save
+ \pgf@process{\pgf@ref}%
+ \advance\pgf@x by-\pgf@xc
+ \advance\pgf@y by-\pgf@yc
+ \pgf@process{\pgfpointnormalised{}}
+ \pgf@x-\pgf@x
+ \pgf@y-\pgf@y
+ \else%
+ \pgf@bending@do@tangent@normal%
+ \fi%
+}
+
+\def\pgf@bending@do@flex{
+ \pgf@xb\pgf@xa%
+ \pgf@xc\pgf@xa%
+ \advance\pgf@xc by-\pgf@x%
+ \advance\pgf@xb by-\pgf@y%
+ \pgfcurvilineardistancetotime{\pgf@xc}%
+ \pgf@xc\pgf@x%
+ \pgfcurvilineardistancetotime{\pgf@xb}%
+ \pgf@xb\pgf@x%
+ % Compute points:
+ \pgf@process{\pgfpointcurveattime{\pgf@xc}{\pgf@curvilinear@line@a}{\pgf@curvilinear@line@b}{\pgf@curvilinear@line@c}{\pgf@curvilinear@line@d}}%
+ \pgf@xc\pgf@x\pgf@yc\pgf@y%
+ \pgf@process{\pgfpointcurveattime{\pgf@xb}{\pgf@curvilinear@line@a}{\pgf@curvilinear@line@b}{\pgf@curvilinear@line@c}{\pgf@curvilinear@line@d}}%
+ \pgf@xb\pgf@x\pgf@yb\pgf@y%
+ \pgftransformarrow{\pgfqpoint{\pgf@xb}{\pgf@yb}}{\pgfqpoint{\pgf@xc}{\pgf@yc}}%
+}
+
+
+
+
+
+
+% Convex hull stuff:
+
+\def\pgf@arrows@bending@hull{%
+ \ifpgf@relevantforpicturesize%
+ % Do bb update:
+ \expandafter\let\expandafter\pgf@temp\csname pgf@ar@hull@\pgf@arrow@id\endcsname%
+ \ifx\pgf@temp\pgfutil@empty\else%
+ \let\pgf@arrow@hull@point\pgf@arrow@bending@hull@point@first%
+ \pgf@temp%
+ \pgf@arrow@bending@update@bb%
+ \fi%
+ \fi%
+}
+
+\def\pgf@arrow@bending@hull@point@first#1#2{%
+ \pgfpointtransformednonlinear{\pgfqpoint{#1}{#2}}%
+ \pgf@xa\pgf@x\pgf@xb\pgf@x%
+ \pgf@ya\pgf@y\pgf@yb\pgf@y%
+ \let\pgf@arrow@hull@point\pgf@arrow@bending@hull@point@other%
+}
+\def\pgf@arrow@bending@hull@point@other#1#2{%
+ \pgfpointtransformednonlinear{\pgfqpoint{#1}{#2}}%
+ \ifdim\pgf@x<\pgf@xa\pgf@xa\pgf@x\else\ifdim\pgf@x>\pgf@xb\pgf@xb\pgf@x\fi\fi%
+ \ifdim\pgf@y<\pgf@ya\pgf@ya\pgf@y\else\ifdim\pgf@y>\pgf@yb\pgf@yb\pgf@y\fi\fi%
+}
+
+\def\pgf@arrow@bending@update@bb{%
+ \ifdim\pgf@picmaxx=-16000pt\relax%
+ \global\pgf@picminx\pgf@xa%
+ \global\pgf@picmaxx\pgf@xb%
+ \global\pgf@picminy\pgf@ya%
+ \global\pgf@picmaxy\pgf@yb%
+ \else%
+ \ifdim\pgf@xa<\pgf@picminx\global\pgf@picminx\pgf@xa\fi%
+ \ifdim\pgf@ya<\pgf@picminy\global\pgf@picminy\pgf@ya\fi%
+ \ifdim\pgf@xb>\pgf@picmaxx\global\pgf@picmaxx\pgf@xb\fi%
+ \ifdim\pgf@yb>\pgf@picmaxy\global\pgf@picmaxy\pgf@yb\fi%
+ \fi%
+}
+
+
+
+
+%
+%
+% Handle the start of a curve
+%
+%
+
+
+% First, the preparation.
+
+\def\pgf@prep@curvedstart{
+ \pgftransformreset%
+ \pgfsetcurvilinearbeziercurve{\pgfpointfirstonpath}{\pgfpointsecondonpath}{\pgfpointthirdonpath}{\pgfpointfourthonpath}%
+}
+
+% Second, the shortening.
+
+\def\pgf@do@shorten@curvedstart{%
+ \expandafter\expandafter\expandafter\pgf@do@shorten@curvedstart@unpack\expandafter\pgfpointthirdonpath\pgfpointfourthonpath%
+}
+\def\pgf@do@shorten@curvedstart@unpack\pgfqpoint#1#2\pgfqpoint#3#4{%
+ \pgf@process{\pgfcurvilineardistancetotime{\pgf@path@shortening@distance}}%
+ % Compute new curve:
+ \pgfpointcurveattime{\pgf@x}{\pgfpointfirstonpath}{\pgfpointsecondonpath}{\pgfpointthirdonpath}{\pgfpointfourthonpath}%
+ % \pgfx/y and \pgf xa/xb already correct. Need to setup remaining vector...
+ \pgf@xb#1%
+ \pgf@yb#2%
+ \pgf@xb\pgf@time@t\pgf@xb%
+ \pgf@yb\pgf@time@t\pgf@yb%
+ \advance\pgf@xb by\pgf@time@s\pgf@xc%
+ \advance\pgf@yb by\pgf@time@s\pgf@yc%
+ \edef\pgfpointfirstonpath{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
+ \edef\pgfpointsecondonpath{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}%
+ \edef\pgfprocessresultpathsuffix{%
+ \noexpand\pgfsyssoftpath@movetotoken{\the\pgf@x}{\the\pgf@y}%
+ \noexpand\pgfsyssoftpath@curvetosupportatoken{\the\pgf@xa}{\the\pgf@ya}%
+ \noexpand\pgfsyssoftpath@curvetosupportbtoken{\the\pgf@xb}{\the\pgf@yb}%
+ \noexpand\pgfsyssoftpath@curvetotoken{#3}{#4}%
+ }
+ \expandafter\expandafter\expandafter\def%
+ \expandafter\expandafter\expandafter\pgfprocessresultpathsuffix%
+ \expandafter\expandafter\expandafter{\expandafter\pgfprocessresultpathsuffix\pgfsubpathend}%
+}
+
+
+% Third, the drawing
+
+\def\pgf@do@draw@curvedstart{%
+ \pgf@do@draw@curved\pgf@start@tip@sequence%
+}
+
+
+
+
+
+\endinput