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+% Copyright 2006 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 $Header: /cvsroot/pgf/pgf/generic/pgf/basiclayer/pgfcorepathconstruct.code.tex,v 1.14 2008/02/13 15:10:06 tantau Exp $
+
+
+\newdimen\pgf@path@lastx
+\newdimen\pgf@path@lasty
+
+
+
+% Replace corners by arcs.
+%
+% #1 = in-size of arc
+% #2 = out-size of arc
+%
+% Description:
+%
+% This command influences path construction command like
+% \pgfpathlineto or \pgfpatharc. It will cause the corners at the end
+% of these commands to be replaced by little arcs. If the
+% corner is a 90 degrees corner and if #1=#2, a quarter-circle of
+% radius #1 is put in place of the corner. If #1 and #2 are different,
+% the quarter circle will instead by a quarter ellipse. If the angle
+% is different from 90 degrees, a deformed quarter circle will
+% result, which may or may not be desirable. For a ``perfect'' arc you
+% must use the \pgfpatharc command.
+%
+%
+% Example: One rounded corner.
+%
+% \pgfpathmoveto{\pgfpointxy{0}{0}}
+% \pgfsetcornersarced{4pt}{4pt}
+% \pgfpathlineto{\pgfpointxy{0}{1}}
+% \pgfpathlineto{\pgfpointxy{1}{1}}
+% \pgfstroke
+%
+% Example: A rounded rectangle
+%
+% \pgfsetcornersarced{4pt}{4pt}
+% \pgfpathrectangle{\pgfpointorigin}{\pgfpoint{1cm}{1cm}}
+% \pgfstroke
+%
+% Example: A rounded triangles
+%
+% \pgfsetcornersarced{4pt}{4pt}
+% \pgfpathmoveto{\pgfpointorigin}
+% \pgfpathlineto{\pgfpoint{1cm}{0cm}}
+% \pgfpathlineto{\pgfpoint{1cm}{1cm}}
+% \pgfpathclose
+% \pgfstroke
+
+\newif\ifpgf@arccorners
+
+\def\pgfsetcornersarced#1{%
+ \pgf@process{#1}%
+ \edef\pgf@corner@arc{{\the\pgf@x}{\the\pgf@y}}%
+ \pgf@arccornerstrue%
+ \ifdim\pgf@x=0pt%
+ \ifdim\pgf@y=0pt\relax%
+ \pgf@arccornersfalse%
+ \fi%
+ \fi%
+}
+
+\def\pgf@roundcornerifneeded{%
+ \ifpgf@arccorners\expandafter\pgfsyssoftpath@specialround\pgf@corner@arc\fi%
+}
+
+
+% Move current point to #1.
+%
+% #1 = new current point
+%
+% Example:
+%
+% \pgfpathmoveto{\pgfxy(0,0)}
+% \pgfpathlineto{\pgfxy(0,1)}
+% \pgfstroke
+
+\def\pgfpathmoveto#1{%
+ \pgfpointtransformed{#1}%
+ \pgf@protocolsizes{\pgf@x}{\pgf@y}%
+ \pgfsyssoftpath@moveto{\the\pgf@x}{\the\pgf@y}%
+ \global\pgf@path@lastx=\pgf@x%
+ \global\pgf@path@lasty=\pgf@y%
+}
+
+\def\pgf@protocolsizes#1#2{%
+ \ifpgf@relevantforpicturesize%
+ \ifdim#1<\pgf@picminx\global\pgf@picminx#1\fi%
+ \ifdim#1>\pgf@picmaxx\global\pgf@picmaxx#1\fi%
+ \ifdim#2<\pgf@picminy\global\pgf@picminy#2\fi%
+ \ifdim#2>\pgf@picmaxy\global\pgf@picmaxy#2\fi%
+ \fi%
+ \ifdim#1<\pgf@pathminx\global\pgf@pathminx#1\fi%
+ \ifdim#1>\pgf@pathmaxx\global\pgf@pathmaxx#1\fi%
+ \ifdim#2<\pgf@pathminy\global\pgf@pathminy#2\fi%
+ \ifdim#2>\pgf@pathmaxy\global\pgf@pathmaxy#2\fi%
+ \ifpgf@size@hooked%
+ \let\pgf@size@hook@x#1\let\pgf@size@hook@y#2\pgf@path@size@hook%
+ \fi%
+}
+\newif\ifpgf@size@hooked
+\let\pgf@path@size@hook=\pgfutil@empty%
+
+\def\pgf@resetpathsizes{%
+ \global\pgf@pathmaxx=-16000pt\relax%
+ \global\pgf@pathminx=16000pt\relax%
+ \global\pgf@pathmaxy=-16000pt\relax%
+ \global\pgf@pathminy=16000pt\relax%
+}
+
+\def\pgf@getpathsizes#1{%
+ \edef#1{{\the\pgf@pathmaxx}{\the\pgf@pathminx}{\the\pgf@pathmaxy}{\the\pgf@pathminy}}%
+}
+\def\pgf@setpathsizes#1{%
+ \expandafter\pgf@@setpathsizes#1%
+}
+\def\pgf@@setpathsizes#1#2#3#4{%
+ \global\pgf@pathmaxx=#1\relax%
+ \global\pgf@pathminx=#2\relax%
+ \global\pgf@pathmaxy=#3\relax%
+ \global\pgf@pathminy=#4\relax%
+}
+
+
+
+
+
+% Append a line from the current point to #1 to the current path.
+%
+% #1 = end of line
+%
+% Example:
+%
+% \pgfpathmoveto{\pgfxy(0,0)}
+% \pgfpathlineto{\pgfxy(0,1)}
+% \pgfstroke
+
+\def\pgfpathlineto#1{%
+ \pgfpointtransformed{#1}%
+ \pgf@protocolsizes{\pgf@x}{\pgf@y}%
+ \pgf@roundcornerifneeded%
+ \pgfsyssoftpath@lineto{\the\pgf@x}{\the\pgf@y}%
+ \global\pgf@path@lastx=\pgf@x%
+ \global\pgf@path@lasty=\pgf@y%
+}
+
+
+
+% Close the current path.
+%
+% Example:
+%
+% % Draws two triangles
+% \pgfpathmoveto{\pgfxy(0,0)}
+% \pgfpathlineto{\pgfxy(0,1)}
+% \pgfpathlineto{\pgfxy(1,0)}
+% \pgfclosepath
+% \pgfpathmoveto{\pgfxy(2,0)}
+% \pgfpathlineto{\pgfxy(2,1)}
+% \pgfpathlineto{\pgfxy(3,0)}
+% \pgfpathclose
+% \pgfstroke
+
+\def\pgfpathclose{%
+ \pgf@roundcornerifneeded%
+ \pgfsyssoftpath@closepath%
+}
+
+
+% Append a bezier spline from the current point to #3 with control
+% points #1 and #2 to the current path.
+%
+% #1 = first control point
+% #2 = second control point
+% #3 = end point
+%
+% Example:
+%
+% \pgfpathmoveto{\pgfxy(0,0)}
+% \pgfpathcurveto{\pgfxy(0,1)}{\pgfxy(1,1)}{\pgfxy(1,2)}
+% \pgfstroke
+
+\def\pgfpathcurveto#1#2#3{%
+ \pgfpointtransformed{#3}%
+ \pgf@protocolsizes{\pgf@x}{\pgf@y}%
+ \pgf@xb=\pgf@x%
+ \pgf@yb=\pgf@y%
+ \pgfpointtransformed{#2}%
+ \pgf@protocolsizes{\pgf@x}{\pgf@y}%
+ \pgf@xa=\pgf@x%
+ \pgf@ya=\pgf@y%
+ \pgfpointtransformed{#1}%
+ \pgf@protocolsizes{\pgf@x}{\pgf@y}%
+ \pgf@roundcornerifneeded%
+ \pgfsyssoftpath@curveto{\the\pgf@x}{\the\pgf@y}{\the\pgf@xa}{\the\pgf@ya}{\the\pgf@xb}{\the\pgf@yb}%
+ \global\pgf@path@lastx=\pgf@xb%
+ \global\pgf@path@lasty=\pgf@yb%
+}
+
+
+% Append an arc to the current point, where the current point is at
+% angle #1 and the end is at angle #2. If #2 > #1, the arc is drawn
+% counter-clockwise, otherwise it is clockwise.
+%
+% #1 = angle of first point
+% #2 = angle of second point
+% #3 = radius or x-radius/y-radius
+%
+% Example:
+%
+% \pgfpathmoveto{\pgfxy(0,0)}
+% \pgfpatharc{0}{90}{2cm}
+% \pgfstroke
+
+\def\pgfpatharc#1#2#3{%
+ {%
+ \pgfmathparse{#1}\let\pgf@temp@a=\pgfmathresult%
+ \pgfmathparse{#2}\let\pgf@temp@b=\pgfmathresult%
+ \pgfutil@in@{and }{#3}%
+ \ifpgfutil@in@%
+ \pgf@arc@get@radii#3\pgf@arc@stop%
+ \else
+ \pgf@arc@get@radii#3and #3\pgf@arc@stop%
+ \fi%
+ \pgf@arc@local@angle@a=\pgf@temp@a pt%
+ \pgf@arc@local@angle@b=\pgf@temp@b pt%
+ \relax%
+ \ifdim\pgf@arc@local@angle@a>360pt\relax%
+ \advance\pgf@arc@local@angle@a by-360pt\relax%
+ \fi%
+ \ifdim\pgf@arc@local@angle@a<-360pt\relax%
+ \advance\pgf@arc@local@angle@a by360pt\relax%
+ \fi%
+ \ifdim\pgf@arc@local@angle@b>360pt\relax%
+ \advance\pgf@arc@local@angle@b by-360pt\relax%
+ \fi%
+ \ifdim\pgf@arc@local@angle@b<-360pt\relax%
+ \advance\pgf@arc@local@angle@b by360pt\relax%
+ \fi%
+ \loop%
+ \pgfutil@tempdima=\pgf@arc@local@angle@a%
+ \advance\pgfutil@tempdima by-\pgf@arc@local@angle@b\relax%
+ \ifdim\pgfutil@tempdima<0pt\relax%
+ \pgfutil@tempdima=-\pgfutil@tempdima\relax%
+ \fi%
+ \ifdim\pgfutil@tempdima>90pt\relax%
+ \ifdim\pgfutil@tempdima>115pt\relax%
+ \pgf@arc@temp=90pt% big skip
+ \else%
+ \pgf@arc@temp=60pt% smaller skip to ensure wide segments
+ % (important shortened end segments because
+ % of arrow tips)
+ \fi%
+ \ifdim\pgf@arc@local@angle@b>\pgf@arc@local@angle@a\relax%
+ {%
+ \pgf@arc@local@angle@b=\pgf@arc@local@angle@a\relax%
+ \advance\pgf@arc@local@angle@b by\pgf@arc@temp\relax%
+ \pgf@arc%
+ }
+ \advance\pgf@arc@local@angle@a by\pgf@arc@temp\relax%
+ \else
+ {%
+ \pgf@arc@local@angle@b=\pgf@arc@local@angle@a\relax%
+ \advance\pgf@arc@local@angle@b by-\pgf@arc@temp\relax%
+ \pgf@arc%
+ }%
+ \advance\pgf@arc@local@angle@a by-\pgf@arc@temp\relax%
+ \fi%
+ \repeat%
+ \pgf@roundcornerifneeded%
+ \pgf@arc%
+ }%
+}
+\dimendef\pgf@arc@local@angle@a=0
+\dimendef\pgf@arc@local@angle@b=1
+\dimendef\pgf@arc@temp=2
+
+\def\pgf@arc@get@radii#1and #2\pgf@arc@stop{%
+ \pgfmathparse{#1}\let\pgf@arc@radius@a=\pgfmathresult%
+ \pgfmathparse{#2}\let\pgf@arc@radius@b=\pgfmathresult%
+}
+
+
+\def\pgf@arc{%
+ {%
+ % \pgfmathsetlength{\pgfutil@tempdima}{#3}%
+ % \pgfmathsetlength{\pgfutil@tempdimb}{#4}%
+ \pgfutil@tempdima=\pgf@arc@radius@a pt%
+ \pgfutil@tempdimb=\pgf@arc@radius@b pt%
+ %
+ \pgf@xa=\pgf@arc@local@angle@a\relax%
+ \pgf@xb=\pgf@arc@local@angle@b\relax%
+ % \pgfutil@tempcnta=#1\relax%
+ % \pgfutil@tempcntb=#2\relax%
+ \advance\pgf@xb by-\pgf@xa\relax%
+ \ifdim\pgf@xb<0pt\relax%
+ \pgf@xb=-\pgf@xb\relax%
+ \fi%
+ \ifdim\pgf@xb>85pt\relax% hackery to correct the control points
+ \pgfutil@tempdima=0.0555\pgfutil@tempdima\relax%
+ \pgfutil@tempdimb=0.0555\pgfutil@tempdimb\relax%
+ \else%
+ \ifdim\pgf@xb>75pt\relax%
+ \pgfutil@tempdima=0.055\pgfutil@tempdima\relax%
+ \pgfutil@tempdimb=0.055\pgfutil@tempdimb\relax%
+ \else%
+ \ifdim\pgf@xb>60pt\relax%
+ \pgfutil@tempdima=0.0545\pgfutil@tempdima\relax%
+ \pgfutil@tempdimb=0.0545\pgfutil@tempdimb\relax%
+ \else%
+ \pgfutil@tempdima=0.054\pgfutil@tempdima\relax%
+ \pgfutil@tempdimb=0.054\pgfutil@tempdimb\relax%
+ \fi%
+ \fi%
+ \fi
+ \pgfutil@tempdima=\pgf@sys@tonumber{\pgf@xb}\pgfutil@tempdima\relax%
+ \divide\pgfutil@tempdima by 9\relax%
+ \pgfutil@tempdimb=\pgf@sys@tonumber{\pgf@xb}\pgfutil@tempdimb\relax%
+ \divide\pgfutil@tempdimb by 9\relax%
+ %.. controls +(\pgf@xa+90:\pgfutil@tempdima) and +(\pgf@xb-90:\pgfutil@tempdima) .. +(-(#1:#3)+(#2:#3))%
+ % store first support vector in xa/ya:
+ \pgf@xa=\pgf@arc@local@angle@a\relax%
+ \ifdim\pgf@arc@local@angle@b>\pgf@arc@local@angle@a\relax%
+ \advance\pgf@xa by 90pt\relax%
+ \else%
+ \advance\pgf@xa by -90pt\relax%
+ \fi%
+ \edef\pgf@arc@angle{\pgf@sys@tonumber{\pgf@xa}}%
+ \pgfpointtransformed{\pgfpointpolar{\pgf@arc@angle}{\pgfutil@tempdima and \pgfutil@tempdimb}}%
+ \advance\pgf@x by-\pgf@pt@x%
+ \advance\pgf@y by-\pgf@pt@y%
+ \pgf@xa=\pgf@path@lastx%
+ \pgf@ya=\pgf@path@lasty%
+ \advance\pgf@xa by \pgf@x%
+ \advance\pgf@ya by \pgf@y%
+ % store target in xb/yb:
+ \pgfpointtransformed{\pgfpointpolar{\pgf@sys@tonumber{\pgf@arc@local@angle@a}}{\pgf@arc@radius@a pt and \pgf@arc@radius@b pt}}%
+ \pgf@xb=\pgf@path@lastx%
+ \pgf@yb=\pgf@path@lasty%
+ \advance\pgf@xb by -\pgf@x%
+ \advance\pgf@yb by -\pgf@y%
+ \pgfpointtransformed{\pgfpointpolar{\pgf@sys@tonumber{\pgf@arc@local@angle@b}}{\pgf@arc@radius@a pt and \pgf@arc@radius@b pt}}%
+ \advance\pgf@xb by \pgf@x%
+ \advance\pgf@yb by \pgf@y%
+ % store second support xc/yc:
+ \ifdim\pgf@arc@local@angle@b>\pgf@arc@local@angle@a\relax%
+ \advance\pgf@arc@local@angle@b by -90pt\relax%
+ \else%
+ \advance\pgf@arc@local@angle@b by 90pt\relax%
+ \fi%
+ \pgfpointtransformed{\pgfpointpolar{\pgf@sys@tonumber{\pgf@arc@local@angle@b}}{\pgfutil@tempdima and \pgfutil@tempdimb}}%
+ \advance\pgf@x by-\pgf@pt@x%
+ \advance\pgf@y by-\pgf@pt@y%
+ \pgf@xc=\pgf@xb\relax%
+ \pgf@yc=\pgf@yb\relax%
+ \advance \pgf@xc by \pgf@x\relax%
+ \advance \pgf@yc by \pgf@y\relax%
+ \pgfsyssoftpath@curveto{\the\pgf@xa}{\the\pgf@ya}{\the\pgf@xc}{\the\pgf@yc}{\the\pgf@xb}{\the\pgf@yb}%
+ \global\pgf@path@lastx=\pgf@xb%
+ \global\pgf@path@lasty=\pgf@yb%
+ \pgf@protocolsizes{\pgf@xa}{\pgf@ya}%
+ \pgf@protocolsizes{\pgf@xb}{\pgf@yb}%
+ \pgf@protocolsizes{\pgf@xc}{\pgf@yc}%
+ }%
+}
+
+% Append an arc to the current point, where the arc is on an ellipse
+% given by two axis vectors.
+%
+% #1 = angle of first point
+% #2 = angle of second point
+% #3 = first axis
+% #4 = second axis
+%
+% Example:
+%
+% \pgfpathmoveto{\pgfxy(0,0)}
+% \pgfpatharcaxes{0}{90}{\pgfpointxy{2}{0}}{\pgfpointxy{0}{2}}
+% \pgfstroke
+
+\def\pgfpatharcaxes#1#2#3#4{%
+ {%
+ \pgftransformtriangle{\pgfpointorigin}{#3}{#4}%
+ \pgfpatharc{#1}{#2}{1pt}%
+ }%
+}
+
+
+
+
+% Append an ellipse to the current path.
+%
+% #1 = center
+% #2 = first axis
+% #3 = second axis
+%
+% Example:
+%
+% % Add a circle of radius 3cm around the origin
+% \pgfpathellipse{\pgforigin}{\pgfxy(2,0)}{\pgfxy(0,1)}
+%
+% % Draw a non-filled circle of radius 1cm around the point (1,1)
+% \pgfpathellipse{\pgfxy(1,1)}{\pgfxy(1,1)}{\pgfxy(-2,2)}
+% \pgfstroke
+
+\def\pgfpathellipse#1#2#3{%
+ \pgfpointtransformed{#1}% store center in xc/yc
+ \pgf@xc=\pgf@x%
+ \pgf@yc=\pgf@y%
+ \pgfpointtransformed{#2}%
+ \pgf@xa=\pgf@x% store first axis in xa/ya
+ \pgf@ya=\pgf@y%
+ \advance\pgf@xa by-\pgf@pt@x%
+ \advance\pgf@ya by-\pgf@pt@y%
+ \pgfpointtransformed{#3}%
+ \pgf@xb=\pgf@x% store second axis in xb/yb
+ \pgf@yb=\pgf@y%
+ \advance\pgf@xb by-\pgf@pt@x%
+ \advance\pgf@yb by-\pgf@pt@y%
+ {%
+ \advance\pgf@xa by\pgf@xc%
+ \advance\pgf@ya by\pgf@yc%
+ \pgfsyssoftpath@moveto{\the\pgf@xa}{\the\pgf@ya}%
+ \pgf@protocolsizes{\pgf@xa}{\pgf@ya}%
+ }%
+ \pgf@x=0.555\pgf@xb% first arc
+ \pgf@y=0.555\pgf@yb%
+ \advance\pgf@x by\pgf@xa%
+ \advance\pgf@y by\pgf@ya%
+ \advance\pgf@x by\pgf@xc%
+ \advance\pgf@y by\pgf@yc%
+ \edef\pgf@temp{{\the\pgf@x}{\the\pgf@y}}%
+ \pgf@protocolsizes{\pgf@x}{\pgf@y}%
+ \pgf@x=0.555\pgf@xa%
+ \pgf@y=0.555\pgf@ya%
+ \advance\pgf@x by\pgf@xb%
+ \advance\pgf@y by\pgf@yb%
+ {%
+ \advance\pgf@x by\pgf@xc%
+ \advance\pgf@y by\pgf@yc%
+ \advance\pgf@xb by\pgf@xc%
+ \advance\pgf@yb by\pgf@yc%
+ \expandafter\pgfsyssoftpath@curveto\pgf@temp{\the\pgf@x}{\the\pgf@y}{\the\pgf@xb}{\the\pgf@yb}%
+ \pgf@protocolsizes{\pgf@x}{\pgf@y}%
+ \pgf@protocolsizes{\pgf@xb}{\pgf@yb}%
+ }%
+ \pgf@xa=-\pgf@xa% flip first axis
+ \pgf@ya=-\pgf@ya%
+ \pgf@x=0.555\pgf@xa% second arc
+ \pgf@y=0.555\pgf@ya%
+ \advance\pgf@x by\pgf@xb%
+ \advance\pgf@y by\pgf@yb%
+ \advance\pgf@x by\pgf@xc%
+ \advance\pgf@y by\pgf@yc%
+ \edef\pgf@temp{{\the\pgf@x}{\the\pgf@y}}%
+ \pgf@protocolsizes{\pgf@x}{\pgf@y}%
+ \pgf@x=0.555\pgf@xb%
+ \pgf@y=0.555\pgf@yb%
+ \advance\pgf@x by\pgf@xa%
+ \advance\pgf@y by\pgf@ya%
+ {%
+ \advance\pgf@x by\pgf@xc%
+ \advance\pgf@y by\pgf@yc%
+ \advance\pgf@xa by\pgf@xc%
+ \advance\pgf@ya by\pgf@yc%
+ \expandafter\pgfsyssoftpath@curveto\pgf@temp{\the\pgf@x}{\the\pgf@y}{\the\pgf@xa}{\the\pgf@ya}%
+ \pgf@protocolsizes{\pgf@x}{\pgf@y}%
+ \pgf@protocolsizes{\pgf@xa}{\pgf@ya}%
+ }%
+ \pgf@xb=-\pgf@xb% flip second axis
+ \pgf@yb=-\pgf@yb%
+ \pgf@x=0.555\pgf@xb% third arc
+ \pgf@y=0.555\pgf@yb%
+ \advance\pgf@x by\pgf@xa%
+ \advance\pgf@y by\pgf@ya%
+ \advance\pgf@x by\pgf@xc%
+ \advance\pgf@y by\pgf@yc%
+ \edef\pgf@temp{{\the\pgf@x}{\the\pgf@y}}%
+ \pgf@protocolsizes{\pgf@x}{\pgf@y}%
+ \pgf@x=0.555\pgf@xa%
+ \pgf@y=0.555\pgf@ya%
+ \advance\pgf@x by\pgf@xb%
+ \advance\pgf@y by\pgf@yb%
+ {%
+ \advance\pgf@x by\pgf@xc%
+ \advance\pgf@y by\pgf@yc%
+ \advance\pgf@xb by\pgf@xc%
+ \advance\pgf@yb by\pgf@yc%
+ \expandafter\pgfsyssoftpath@curveto\pgf@temp{\the\pgf@x}{\the\pgf@y}{\the\pgf@xb}{\the\pgf@yb}%
+ \pgf@protocolsizes{\pgf@x}{\pgf@y}%
+ \pgf@protocolsizes{\pgf@xb}{\pgf@yb}%
+ }%
+ \pgf@xa=-\pgf@xa% flip first axis once more
+ \pgf@ya=-\pgf@ya%
+ \pgf@x=0.555\pgf@xa% fourth arc
+ \pgf@y=0.555\pgf@ya%
+ \advance\pgf@x by\pgf@xb%
+ \advance\pgf@y by\pgf@yb%
+ \advance\pgf@x by\pgf@xc%
+ \advance\pgf@y by\pgf@yc%
+ \edef\pgf@temp{{\the\pgf@x}{\the\pgf@y}}%
+ \pgf@protocolsizes{\pgf@x}{\pgf@y}%
+ \pgf@x=0.555\pgf@xb%
+ \pgf@y=0.555\pgf@yb%
+ \advance\pgf@x by\pgf@xa%
+ \advance\pgf@y by\pgf@ya%
+ {%
+ \advance\pgf@x by\pgf@xc%
+ \advance\pgf@y by\pgf@yc%
+ \advance\pgf@xa by\pgf@xc%
+ \advance\pgf@ya by\pgf@yc%
+ \expandafter\pgfsyssoftpath@curveto\pgf@temp{\the\pgf@x}{\the\pgf@y}{\the\pgf@xa}{\the\pgf@ya}%
+ \pgf@protocolsizes{\pgf@x}{\pgf@y}%
+ \pgf@protocolsizes{\pgf@xa}{\pgf@ya}%
+ }%
+ \pgfsyssoftpath@closepath%
+ \pgfsyssoftpath@moveto{\the\pgf@xc}{\the\pgf@yc}%
+}
+
+
+
+% Append a circle to the current path
+%
+% #1 = center
+% #2 = radius
+%
+% Example:
+%
+% % Append a circle of radius 3cm around the the point (1,1)
+% \pgfpathcircle{\pgxy(1,1)}{3cm}
+
+\def\pgfpathcircle#1#2{\pgfpathellipse{#1}{\pgfpoint{#2}{0pt}}{\pgfpoint{0pt}{#2}}}
+
+
+
+
+% Append a rectangle to the current path
+%
+% #1 = lower left corner point of rectangle
+% #2 = width and height vector
+%
+% Example:
+%
+% % A rectangle with corners (2,2) and (3,3)
+% \pgfpathrectangle{\pgfpointxy{2}{2}}{\pgfpointxy{1}{1}}
+
+\def\pgfpathrectangle{%
+ \let\pgfrect@next=\pgf@specialrect%
+ \ifpgf@pt@identity%
+ \ifpgf@arccorners%
+ \else%
+ \let\pgfrect@next=\pgf@normalrect%
+ \fi%
+ \fi%
+ \pgfrect@next%
+}
+
+\def\pgf@normalrect#1#2{%
+ \pgf@process{#2}%
+ \pgf@xa=\pgf@x%
+ \pgf@ya=\pgf@y%
+ \pgfpointtransformed{#1}%
+ \pgfsyssoftpath@rect{\the\pgf@x}{\the\pgf@y}{\the\pgf@xa}{\the\pgf@ya}%
+ \pgf@protocolsizes{\pgf@x}{\pgf@y}%
+ \advance\pgf@x by\pgf@xa\relax%
+ \advance\pgf@y by\pgf@ya\relax%
+ \pgf@protocolsizes{\pgf@x}{\pgf@y}%
+}
+
+\def\pgf@specialrect#1#2{%
+ \pgf@process{#2}%
+ \pgf@xa=\pgf@x%
+ \pgf@ya=\pgf@y%
+ \pgf@process{#1}%
+ \pgf@xb=\pgf@x%
+ \pgf@yb=\pgf@y%
+ \advance\pgf@xa by\pgf@xb%
+ \advance\pgf@ya by\pgf@yb%
+ \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@ya}}%
+ \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@ya}}%
+ \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@yb}}%
+ \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@yb}}%
+ \pgfpathclose%
+ \pgfpathmoveto{\pgfqpoint{\pgf@xb}{\pgf@yb}}%
+}
+
+% Append a rectangle to the current path
+%
+% #1 = one corner of the rectangle
+% #2 = opposite corner of the rectangle
+%
+% Example:
+%
+% % A rectangle with corners (2,2) and (3,3)
+% \pgfpathrectanglecorners{\pgfpointxy{2}{2}}{\pgfpointxy{3}{3}}
+
+\def\pgfpathrectanglecorners#1#2{%
+ \pgf@process{#2}%
+ \pgf@xc=\pgf@x%
+ \pgf@yc=\pgf@y%
+ \pgf@process{#1}%
+ \advance\pgf@xc by-\pgf@x%
+ \advance\pgf@yc by-\pgf@y%
+ \pgfpathrectangle{#1}{\pgfqpoint{\pgf@xc}{\pgf@yc}}%
+}
+
+
+% Append a grid to the current path.
+%
+% #1 = lower left point of grid
+% #2 = upper right point of grid
+%
+% Options:
+%
+% stepx = x-step dimension (default 1cm)
+% stepy = y-step dimension (default 1cm)
+% step = dimesion vector
+%
+% Example:
+%
+% \pgfsetlinewidth{0.8pt}
+% \pgfgrid{\pgfxy(0,0)}{\pgfxy(3,2)}
+% \pgfsetlinewidth{0.4pt}
+% \pgfgrid[stepx=1cm,stepy=1cm]{\pgfxy(0,0)}{\pgfxy(3,2)}
+
+\pgfkeys{
+ /pgf/stepx/.initial=1cm,
+ /pgf/stepy/.initial=1cm,
+ /pgf/step/.code={\pgf@process{#1}\pgfkeysalso{/pgf/stepx/.expanded=\the\pgf@x,/pgf/stepy/.expanded=\the\pgf@y}},
+ /pgf/step/.value required
+}
+
+\def\pgfpathgrid{\pgfutil@ifnextchar[{\pgf@pathgrid}{\pgf@pathgrid[]}}
+\def\pgf@pathgrid[#1]#2#3{%
+ \pgfset{#1}%
+ \pgfmathsetlength\pgf@xc{\pgfkeysvalueof{/pgf/stepx}}%
+ \pgfmathsetlength\pgf@yc{\pgfkeysvalueof{/pgf/stepy}}%
+ \pgf@process{#3}%
+ \pgf@xb=\pgf@x%
+ \pgf@yb=\pgf@y%
+ \pgf@process{#2}%
+ \pgf@xa=\pgf@x\relax%
+ \pgf@ya=\pgf@y\relax%
+ {%
+ % compute bounding box
+ % first corner
+ \pgf@x=\pgf@xb%
+ \pgf@y=\pgf@yb%
+ \pgf@pos@transform{\pgf@x}{\pgf@y}%
+ \pgf@protocolsizes{\pgf@x}{\pgf@y}%
+ % second corner
+ \pgf@x=\pgf@xb%
+ \pgf@y=\pgf@ya%
+ \pgf@pos@transform{\pgf@x}{\pgf@y}%
+ \pgf@protocolsizes{\pgf@x}{\pgf@y}%
+ % third corner
+ \pgf@x=\pgf@xa%
+ \pgf@y=\pgf@yb%
+ \pgf@pos@transform{\pgf@x}{\pgf@y}%
+ \pgf@protocolsizes{\pgf@x}{\pgf@y}%
+ % fourth corner
+ \pgf@x=\pgf@xa%
+ \pgf@y=\pgf@ya%
+ \pgf@pos@transform{\pgf@x}{\pgf@y}%
+ \pgf@protocolsizes{\pgf@x}{\pgf@y}%
+ }%
+ \c@pgf@counta=\pgf@y\relax%
+ \c@pgf@countb=\pgf@yc\relax%
+ \divide\c@pgf@counta by\c@pgf@countb\relax%
+ \pgf@y=\c@pgf@counta\pgf@yc\relax%
+ \ifdim\pgf@y<\pgf@ya%
+ \advance\pgf@y by\pgf@yc%
+ \fi%
+ \loop% horizontal lines
+ {%
+ \pgf@xa=\pgf@x%
+ \pgf@ya=\pgf@y%
+ \pgf@pos@transform{\pgf@xa}{\pgf@ya}
+ \pgfsyssoftpath@moveto{\the\pgf@xa}{\the\pgf@ya}%
+ \pgf@xa=\pgf@xb%
+ \pgf@ya=\pgf@y%
+ \pgf@pos@transform{\pgf@xa}{\pgf@ya}
+ \pgfsyssoftpath@lineto{\the\pgf@xa}{\the\pgf@ya}%
+ }%
+ \advance\pgf@y by\pgf@yc%
+ \ifdim\pgf@y<\pgf@yb%
+ \repeat%
+ \advance\pgf@y by-0.01pt\relax%
+ \ifdim\pgf@y<\pgf@yb%
+ {%
+ \pgf@xa=\pgf@x%
+ \pgf@ya=\pgf@y%
+ \pgf@pos@transform{\pgf@xa}{\pgf@ya}
+ \pgfsyssoftpath@moveto{\the\pgf@xa}{\the\pgf@ya}%
+ \pgf@xa=\pgf@xb%
+ \pgf@ya=\pgf@y%
+ \pgf@pos@transform{\pgf@xa}{\pgf@ya}
+ \pgfsyssoftpath@lineto{\the\pgf@xa}{\the\pgf@ya}%
+ }%
+ \fi%
+ \c@pgf@counta=\pgf@x\relax%
+ \c@pgf@countb=\pgf@xc\relax%
+ \divide\c@pgf@counta by\c@pgf@countb\relax%
+ \pgf@x=\c@pgf@counta\pgf@xc\relax%
+ \ifdim\pgf@x<\pgf@xa%
+ \advance\pgf@x by\pgf@xc%
+ \fi%
+ \loop% vertical lines
+ {%
+ \pgf@xc=\pgf@x%
+ \pgf@yc=\pgf@ya%
+ \pgf@pos@transform{\pgf@xc}{\pgf@yc}
+ \pgfsyssoftpath@moveto{\the\pgf@xc}{\the\pgf@yc}%
+ \pgf@xc=\pgf@x%
+ \pgf@yc=\pgf@yb%
+ \pgf@pos@transform{\pgf@xc}{\pgf@yc}
+ \pgfsyssoftpath@lineto{\the\pgf@xc}{\the\pgf@yc}%
+ }%
+ \advance\pgf@x by\pgf@xc%
+ \ifdim\pgf@x<\pgf@xb%
+ \repeat%
+ \advance\pgf@x by-0.01pt\relax%
+ \ifdim\pgf@x<\pgf@xb%
+ {%
+ \pgf@xc=\pgf@x%
+ \pgf@yc=\pgf@ya%
+ \pgf@pos@transform{\pgf@xc}{\pgf@yc}
+ \pgfsyssoftpath@moveto{\the\pgf@xc}{\the\pgf@yc}%
+ \pgf@xc=\pgf@x%
+ \pgf@yc=\pgf@yb%
+ \pgf@pos@transform{\pgf@xc}{\pgf@yc}
+ \pgfsyssoftpath@lineto{\the\pgf@xc}{\the\pgf@yc}%
+ }%
+ \fi%
+}
+
+
+
+% Append two half-parabolas to the path
+%
+% #1 = bend (relative to current point)
+% #2 = end point (relative to bend point)
+%
+% Description:
+%
+% This command appends a half-parabola that starts at the current point
+% and has its bend at #1+current point. Then, a second parabola is
+% appended that starts at #1+current point, where it also has its
+% minimum/maximum, and ends at #1+current point+#2, which becomes the
+% new current point.
+%
+% By setting #2 = (0,0) you draw only a half parabola that goes from the
+% current point to the bend; by setting #1 = (0,0)
+% you draw a half parabola that going to current point + #2 and has its
+% bend at the current point.
+%
+% Examples:
+%
+% % Half-parabola going ``up and right''
+% \pgfpathmoveto{\pgfpointorigin}
+% \pgfpathparabola{\pgfpointorigin}{\pgfpoint{2cm}{4cm}}
+%
+% % Half-parabola going ``down and right''
+% \pgfpathmoveto{\pgfpointorigin}
+% \pgfpathparabola{\pgfpoint{-2cm}{4cm}}}{\pgfpointorigin}
+%
+% % Full parabola
+% \pgfpathmoveto{\pgfpointorigin}
+% \pgfpathparabola{\pgfpoint{-2cm}{4cm}}{\pgfpoint{2cm}{4cm}}
+
+\def\pgfpathparabola#1#2{%
+ {%
+ \pgf@process{#2}% untransformed
+ \pgf@xb=\pgf@x%
+ \pgf@yb=\pgf@y%
+ \pgf@process{#1}% untransformed
+ \pgf@xc=\pgf@x%
+ \pgf@yc=\pgf@y%
+ \pgfutil@tempswatrue%
+ \ifdim\pgf@xb=0pt\relax%
+ \ifdim\pgf@yb=0pt\relax%
+ \pgfutil@tempswafalse%
+ \fi%
+ \fi%
+ {%
+ \ifpgfutil@tempswa%
+ \pgf@arccornersfalse
+ \else%
+ \fi%
+ \pgfutil@tempswatrue%
+ \ifdim\pgf@xc=0pt\relax%
+ \ifdim\pgf@yc=0pt\relax%
+ \pgfutil@tempswafalse%
+ \fi%
+ \fi%
+ \ifpgfutil@tempswa
+ {%
+ \pgf@pt@x=\pgf@path@lastx%
+ \pgf@pt@y=\pgf@path@lasty%
+ \pgfpathcurveto%
+ {\pgfqpoint{.1125\pgf@xc}{.225\pgf@yc}}% found by trial and error
+ {\pgfqpoint{.5\pgf@xc}{\pgf@yc}}% found by trial and error
+ {\pgfqpoint{\pgf@xc}{\pgf@yc}}%
+ }%
+ \fi%
+ }%
+ \ifpgfutil@tempswa%
+ \pgf@xc=\pgf@xb%
+ \pgf@yc=\pgf@yb%
+ {%
+ \pgf@pt@x=\pgf@path@lastx%
+ \pgf@pt@y=\pgf@path@lasty%
+ \pgfpathcurveto%
+ {\pgfqpoint{.5\pgf@xc}{0\pgf@yc}}% found by trial and error
+ {\pgfqpoint{.8875\pgf@xc}{.775\pgf@yc}}% found by trial and error
+ {\pgfqpoint{\pgf@xc}{\pgf@yc}}%
+ }%
+ \fi%
+ }%
+}
+
+
+
+
+% Append a sine curve between 0 and \pi/2 to the path.
+%
+% #1 = vector, describing the width and height of the curve
+%
+% Description:
+%
+% This command appends a sine curve in the interval 0 and \pi/2 to the
+% current path. The sine curve ends at currentpoint+#1.
+%
+% Examples:
+%
+% % One complete sine in the interval [0,\pi]
+% \pgfpathmoveto{\pgfpointorigin}
+% \pgfpathsine{\pgfpoint{1.57cm}{1cm}}
+% \pgfpathcosine{\pgfpoint{3.141cm}{0cm}}
+
+\def\pgfpathsine#1{%
+ {%
+ \pgf@process{#1}% untransformed
+ \pgf@xc=\pgf@x%
+ \pgf@yc=\pgf@y%
+ \pgf@pt@x=\pgf@path@lastx% evil trickery to transform to the last point
+ \pgf@pt@y=\pgf@path@lasty%
+ \pgfpathcurveto%
+ {\pgfqpoint{.31831\pgf@xc}{.5\pgf@yc}}% found by trial and error
+ {\pgfqpoint{.63503\pgf@xc}{\pgf@yc}}% found by trial and error
+ {\pgfqpoint{\pgf@xc}{\pgf@yc}}%
+ }%
+}
+
+% Append a cosine curve between 0 and \pi/2 to the path.
+%
+% #1 = vector, describing the width and height of the curve
+%
+% Examples:
+%
+% % One complete sine in the interval [0,\pi]
+% \pgfpathmoveto{\pgfpointorigin}
+% \pgfpathsine{\pgfpoint{1.57cm}{1cm}}
+% \pgfpathcosine{\pgfpoint{3.141cm}{0cm}}
+
+\def\pgfpathcosine#1{%
+ {%
+ \pgf@process{#1}% untransformed
+ \pgf@xc=\pgf@x%
+ \pgf@yc=\pgf@y%
+ \pgf@pt@x=\pgf@path@lastx% evil trickery to transform to the last point
+ \pgf@pt@y=\pgf@path@lasty%
+ \pgfpathcurveto%
+ {\pgfqpoint{.36497\pgf@xc}{0pt}}% found by trial and error
+ {\pgfqpoint{.68169\pgf@xc}{.5\pgf@yc}}% found by trial and error
+ {\pgfqpoint{\pgf@xc}{\pgf@yc}}%
+ }%
+}
+
+
+\endinput