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% Copyright 2019 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{pgfcorepathconstruct.code.tex}
\newdimen\pgf@path@lastx
\newdimen\pgf@path@lasty
\let\pgfgetpath=\pgfsyssoftpath@getcurrentpath
\let\pgfsetpath=\pgfsyssoftpath@setcurrentpath
% 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%
}
% The following protocol the passed sizes and all the corresponding
% softpath commands. The nonlinear transformation (nlt) module
% overwrites these commands.
\def\pgf@lt@moveto#1#2{%
\pgf@protocolsizes{#1}{#2}%
\pgfsyssoftpath@moveto{\the#1}{\the#2}%
}
\def\pgf@lt@lineto#1#2{%
\pgf@protocolsizes{#1}{#2}%
\pgfsyssoftpath@lineto{\the#1}{\the#2}%
}
\def\pgf@lt@curveto#1#2#3#4#5#6{%
\pgf@protocolsizes{#1}{#2}%
\pgf@protocolsizes{#3}{#4}%
\pgf@protocolsizes{#5}{#6}%
\pgfsyssoftpath@curveto{\the#1}{\the#2}{\the#3}{\the#4}{\the#5}{\the#6}%
}
\let\pgf@lt@closepath\pgfsyssoftpath@closepath
\let\pgf@nlt@moveto\pgf@lt@moveto
\let\pgf@nlt@lineto\pgf@lt@lineto
\let\pgf@nlt@curveto\pgf@lt@curveto
\let\pgf@nlt@closepath\pgf@lt@closepath
\let\pgf@nlt@list\pgfutil@empty % If non-empty, the nlt module is active
% 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@nlt@moveto{\pgf@x}{\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%
\ifpgf@size@hooked%
\let\pgf@size@hook@x#1\let\pgf@size@hook@y#2\pgf@path@size@hook%
\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%
}
\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@roundcornerifneeded%
\pgf@nlt@lineto{\pgf@x}{\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%
\pgf@nlt@closepath%
}
% Append a cubic 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{\pgfpointxy{0}{0}}
% \pgfpathcurveto{\pgfpointxy{0}{1}}{\pgfpointxy{1}{1}}{\pgfpointxy{1}{2}}
% \pgfstroke
\def\pgfpathcurveto#1#2#3{%
\pgfpointtransformed{#3}%
\pgf@xb=\pgf@x%
\pgf@yb=\pgf@y%
\pgfpointtransformed{#2}%
\pgf@xa=\pgf@x%
\pgf@ya=\pgf@y%
\pgfpointtransformed{#1}%
\pgf@roundcornerifneeded%
\pgf@nlt@curveto{\pgf@x}{\pgf@y}{\pgf@xa}{\pgf@ya}{\pgf@xb}{\pgf@yb}%
\global\pgf@path@lastx=\pgf@xb%
\global\pgf@path@lasty=\pgf@yb%
}
% Append a quadratic bezier spline from the current point to #2 with
% control point #1 to the current path.
%
% #1 = control point
% #2 = end point
%
% Example:
%
% \pgfpathmoveto{\pgfpointxy{0}{0}}
% \pgfpathquadraticcurveto{\pgfpointxy{1}{1}}{\pgfpointxy{2}{0}}
% \pgfstroke
\def\pgfpathquadraticcurveto#1#2{%
\pgfpointtransformed{#2}%
\pgf@xb=\pgf@x%
\pgf@yb=\pgf@y%
\pgfpointtransformed{#1}%
\pgf@xc=.6666666\pgf@x%
\pgf@yc=.6666666\pgf@y%
% compute second control point:
\pgf@xa=.33333333\pgf@xb%
\pgf@ya=.33333333\pgf@yb%
\advance\pgf@xa by\pgf@xc%
\advance\pgf@ya by\pgf@yc%
% compute first control point
\advance\pgf@xc by.3333333\pgf@path@lastx%
\advance\pgf@yc by.3333333\pgf@path@lasty%
\pgf@roundcornerifneeded%
\pgf@nlt@curveto{\pgf@xc}{\pgf@yc}{\pgf@xa}{\pgf@ya}{\pgf@xb}{\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%
\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{%
{%
\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%
\advance\pgf@xb by-\pgf@xa\relax%
\ifdim\pgf@xb<0pt\relax%
\pgf@xb=-\pgf@xb\relax%
\fi%
\ifdim\pgf@xb=90.0pt%
\def\pgfmathresult{0.55228475}%
\else%
\pgfmathparse{1.333333333*tan(.25*\pgf@sys@tonumber{\pgf@xb})}% many thanks to Ken Starks
\fi%
\pgfutil@tempdima=\pgfmathresult\pgfutil@tempdima%
\pgfutil@tempdimb=\pgfmathresult\pgfutil@tempdimb%
%.. 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%
\pgf@nlt@curveto{\pgf@xa}{\pgf@ya}{\pgf@xc}{\pgf@yc}{\pgf@xb}{\pgf@yb}%
\global\pgf@path@lastx=\pgf@xb%
\global\pgf@path@lasty=\pgf@yb%
}%
}
% 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 arc to the current point that ends at a given position.
%
% #1 = x-radius
% #2 = y-radius
% #3 = x-axis-rotation (in degrees)
% #4 = large-arc-sweep-flag (0 or 1)
% #5 = sweep-flag (0 or 1)
% #6 = target point
%
% Description:
%
% This command implements an arc drawing where a given target
% coordinate (#6) is given and the task is to draw an arc of an
% ellipse with the given radii. The center point of the ellipse is not
% give, but computed automatically.
%
% This kind of "endpoint parameterization" of an arc is exactly the
% same as the one specified by the SVG-specification for the "A" and
% "a" path commands. Please see the SVG-specification for details.
%
% Note that the problem is internally converted to drawing an arc
% using \pgfpatharc. This means that there may be a heavy loss of
% accuracy.
%
% Example:
%
% \pgfpathmoveto{\pgfpoint{1cm}{1cm}}
% \pgfpatharcto{1cm}{1cm}{0}{0}{0}{\pgfpoint{0cm}{2cm}}
\def\pgfpatharcto#1#2#3#4#5#6{%
{%
% The following code is based on the transformation described in svg
% 1.1 specification Section F.6.5
%
% Step 1: store the simple parameters (xa=x1 since TeX does not
% allow numbers in names)
%
\pgfmathsetmacro\pgf@arcto@rx{abs(#1)}%
\pgfmathsetmacro\pgf@arcto@ry{abs(#2)}%
\ifdim\pgf@arcto@rx pt=0pt% special rule: zero radius=straight line
\gdef\pgf@marshal{\pgfpathlineto{#6}}%
\else
\ifdim\pgf@arcto@ry pt=0pt% special rule: zero radius=straight line
\gdef\pgf@marshal{\pgfpathlineto{#6}}%
\else
\pgfmathsetmacro\pgf@arcto@phi{#3}%
\pgfmathsetmacro\pgf@arcto@fA{#4}%
\ifdim\pgf@arcto@fA pt=0pt
\else
\pgfmathsetmacro\pgf@arcto@fA{1.0} % Special rule: every non-zero value is 1.
\fi
\pgfmathsetmacro\pgf@arcto@fS{#5}%
\ifdim\pgf@arcto@fS pt=0pt
\else
\pgfmathsetmacro\pgf@arcto@fS{1.0} % Special rule: every non-zero value is 1.
\fi
\pgf@process{#6}
\edef\pgf@arcto@xb{\the\pgf@x}%
\edef\pgf@arcto@yb{\the\pgf@y}%
%
% Step 2: x1,y1 is more complicated to compute: It is given by lastx
% and lasty, but these are transformed coordinates, we need the
% untransformed ones. So, we inverse the transformation (arghh...)
%
\pgftransforminvert%
\pgf@process{\pgfpointtransformed{\pgfqpoint{\pgf@path@lastx}{\pgf@path@lasty}}}
\edef\pgf@arcto@xa{\the\pgf@x}
\edef\pgf@arcto@ya{\the\pgf@y}
\edef\pgf@temp@a{\pgf@arcto@xa,\pgf@arcto@ya}
\edef\pgf@temp@b{\pgf@arcto@xb,\pgf@arcto@yb}
\ifx\pgf@temp@a\pgf@temp@b% special rule: skip!
\global\let\pgf@marshal\pgfutil@empty
\else
%
% Ok, now we got all the parameters setup. Now comes the
% computation...
%
%
% Step 3: Start with a new coordinate system and rotate everything
% by the negated phi.
%
\pgftransformreset
\pgftransformrotate{-\pgf@arcto@phi}
% Ok, using \pgfpointtransformed we now get transformed points...
%
% Step 4: Compute x1' and y1' (xaprime and yaprime)
%
\pgf@process{
\pgfpointtransformed{\pgfpointscale{.5}{\pgfpointdiff
{\pgfqpoint{\pgf@arcto@xb}{\pgf@arcto@yb}}
{\pgfqpoint{\pgf@arcto@xa}{\pgf@arcto@ya}}
}
}
}
\edef\pgf@arcto@xaprime{\pgf@sys@tonumber\pgf@x}
\edef\pgf@arcto@yaprime{\pgf@sys@tonumber\pgf@y}
%
% Compute Lambda
%
\pgfmathsetmacro\pgf@arcto@frac@x{\pgf@arcto@xaprime/\pgf@arcto@rx}
\pgfmathsetmacro\pgf@arcto@frac@y{\pgf@arcto@yaprime/\pgf@arcto@ry}
\pgfmathsetmacro\pgf@arcto@lambda{
\pgf@arcto@frac@x*\pgf@arcto@frac@x+\pgf@arcto@frac@y*\pgf@arcto@frac@y
}
\ifdim\pgf@arcto@lambda pt>1pt%
\pgfmathsetmacro\pgf@arcto@sqrt@lambda{sqrt(\pgf@arcto@lambda)}
\pgfmathsetmacro\pgf@arcto@rx{\pgf@arcto@sqrt@lambda*\pgf@arcto@rx}
\pgfmathsetmacro\pgf@arcto@ry{\pgf@arcto@sqrt@lambda*\pgf@arcto@ry}
\fi
%
% Do some scaling
%
\pgfmathsetmacro\pgf@arcto@xaprime@abs{abs(\pgf@arcto@xaprime)}
\pgfmathsetmacro\pgf@arcto@yaprime@abs{abs(\pgf@arcto@yaprime)}
\pgfmathmax@{\pgf@arcto@rx,\pgf@arcto@ry,\pgf@arcto@xaprime@abs,\pgf@arcto@yaprime@abs}
\pgfmathsetmacro\pgf@arcto@scaling{20/\pgfmathresult}
\pgfmathsetmacro\pgf@arcto@rx@scaled{\pgf@arcto@scaling*\pgf@arcto@rx}
\pgfmathsetmacro\pgf@arcto@ry@scaled{\pgf@arcto@scaling*\pgf@arcto@ry}
\pgfmathsetmacro\pgf@arcto@xaprime@scaled{\pgf@arcto@scaling*\pgf@arcto@xaprime}
\pgfmathsetmacro\pgf@arcto@yaprime@scaled{\pgf@arcto@scaling*\pgf@arcto@yaprime}
%
% Step 5: Now comes the messy computation of c1' and c2'.
%
\ifdim\pgf@arcto@rx pt>\pgf@arcto@ry pt%
\pgfmathsetmacro\pgf@arcto@rx@over@ry{\pgf@arcto@rx/\pgf@arcto@ry}
\pgfmathsetmacro\pgf@arcto@ry@over@rx{\pgf@arcto@ry/\pgf@arcto@rx}
\pgfmathsetmacro\pgf@arcto@temp{\pgf@arcto@ry@over@rx*\pgf@arcto@xaprime@scaled}
\pgfmathsetmacro\pgf@arcto@numerator{
\pgf@arcto@ry@scaled*\pgf@arcto@ry@scaled-
\pgf@arcto@yaprime@scaled*\pgf@arcto@yaprime@scaled-
\pgf@arcto@temp*\pgf@arcto@temp
}
\pgfmathsetmacro\pgf@arcto@denominator{
\pgf@arcto@yaprime@scaled*\pgf@arcto@yaprime@scaled+
\pgf@arcto@temp*\pgf@arcto@temp
}
\else
\pgfmathsetmacro\pgf@arcto@rx@over@ry{\pgf@arcto@rx/\pgf@arcto@ry}
\pgfmathsetmacro\pgf@arcto@ry@over@rx{\pgf@arcto@ry/\pgf@arcto@rx}
\pgfmathsetmacro\pgf@arcto@temp{\pgf@arcto@rx@over@ry*\pgf@arcto@yaprime@scaled}
\pgfmathsetmacro\pgf@arcto@numerator{
\pgf@arcto@rx@scaled*\pgf@arcto@rx@scaled-
\pgf@arcto@xaprime@scaled*\pgf@arcto@xaprime@scaled-
\pgf@arcto@temp*\pgf@arcto@temp
}
\pgfmathsetmacro\pgf@arcto@denominator{
\pgf@arcto@xaprime@scaled*\pgf@arcto@xaprime@scaled+
\pgf@arcto@temp*\pgf@arcto@temp
}
\fi
\pgfmathsetmacro\pgf@arcto@frac{
\pgf@arcto@numerator/\pgf@arcto@denominator
}
\ifdim\pgf@arcto@frac pt<0pt
\pgfmathsetmacro\pgf@arcto@factor{0}
\else
\pgfmathsetmacro\pgf@arcto@factor{sqrt(\pgf@arcto@frac)}
\fi
\ifx\pgf@arcto@fA\pgf@arcto@fS
\pgfmathsetmacro\pgf@arcto@factor{-\pgf@arcto@factor}
\fi
\pgfmathsetmacro\pgf@arcto@cxprime{
\pgf@arcto@factor*\pgf@arcto@rx@over@ry*\pgf@arcto@yaprime
}
\pgfmathsetmacro\pgf@arcto@cyprime{
-\pgf@arcto@factor*\pgf@arcto@ry@over@rx*\pgf@arcto@xaprime
}
%
% Step 6: Ok, now compute cx,cy
%
\pgftransformreset
\pgftransformrotate{\pgf@arcto@phi}
\pgf@process{
\pgfpointtransformed{\pgfqpoint{\pgf@arcto@cxprime pt}{\pgf@arcto@cyprime pt}}
}
\edef\pgf@arcto@temp{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}
\pgf@process{\pgfpointadd{\pgf@arcto@temp}{
\pgfpointscale{.5}{
\pgfpointadd
{\pgfqpoint{\pgf@arcto@xa}{\pgf@arcto@ya}}
{\pgfqpoint{\pgf@arcto@xb}{\pgf@arcto@yb}} }
}
}
\edef\pgf@arcto@cx{\the\pgf@x}
\edef\pgf@arcto@cy{\the\pgf@y}
%
% Step 7: Compute start angle:
%
\pgfmathsetmacro\pgf@arcto@vec@x{(\pgf@arcto@xaprime-\pgf@arcto@cxprime)/\pgf@arcto@rx}
\pgfmathsetmacro\pgf@arcto@vec@y{(\pgf@arcto@yaprime-\pgf@arcto@cyprime)/\pgf@arcto@ry}
\pgfmathsetmacro\pgf@arcto@denominator{veclen(\pgf@arcto@vec@x,\pgf@arcto@vec@y)}
\pgfmathsetmacro\pgf@arcto@frac{\pgf@arcto@vec@x/\pgf@arcto@denominator}
\pgfmathsetmacro\pgf@arcto@theta@start{acos(\pgf@arcto@frac)}
\ifdim\pgf@arcto@vec@y pt<0pt
\pgfmathsetmacro\pgf@arcto@theta@start{-\pgf@arcto@theta@start}
\fi
%
% Step 8: Compute end angle:
%
\pgfmathsetmacro\pgf@arcto@vec@x{(-\pgf@arcto@xaprime-\pgf@arcto@cxprime)/\pgf@arcto@rx}
\pgfmathsetmacro\pgf@arcto@vec@y{(-\pgf@arcto@yaprime-\pgf@arcto@cyprime)/\pgf@arcto@ry}
\pgfmathsetmacro\pgf@arcto@denominator{veclen(\pgf@arcto@vec@x,\pgf@arcto@vec@y)}
\pgfmathsetmacro\pgf@arcto@frac{\pgf@arcto@vec@x/\pgf@arcto@denominator}
\pgfmathsetmacro\pgf@arcto@theta@end{acos(\pgf@arcto@frac)}
\ifdim\pgf@arcto@vec@y pt<0pt
\pgfmathsetmacro\pgf@arcto@theta@end{-\pgf@arcto@theta@end}
\fi
\pgfmathsetmacro\pgf@arcto@delta@theta{abs(\pgf@arcto@theta@start-\pgf@arcto@theta@end)}
\ifdim\pgf@arcto@fA pt=0pt%
\ifdim\pgf@arcto@delta@theta pt>180pt%
% Ok, we need to adjust the angle!
\ifdim\pgf@arcto@theta@end pt>\pgf@arcto@theta@start pt
\pgfmathsetmacro\pgf@arcto@theta@end{\pgf@arcto@theta@end-360}
\else
\pgfmathsetmacro\pgf@arcto@theta@end{\pgf@arcto@theta@end+360}
\fi
\fi
\else
\ifdim\pgf@arcto@delta@theta pt<180pt%
% Ok, we need to adjust the angle!
\ifdim\pgf@arcto@theta@end pt>\pgf@arcto@theta@start pt
\pgfmathsetmacro\pgf@arcto@theta@end{\pgf@arcto@theta@end-360}
\else
\pgfmathsetmacro\pgf@arcto@theta@end{\pgf@arcto@theta@end+360}
\fi
\fi
\fi
\xdef\pgf@marshal{\noexpand
\pgfpatharcaxes{\pgf@arcto@theta@start}{\pgf@arcto@theta@end}
{\noexpand\pgfpointpolar{\pgf@arcto@phi}{\pgf@arcto@rx}}
{\noexpand\pgfpointpolar{\pgf@arcto@phi+90}{\pgf@arcto@ry}}
}
\fi\fi\fi
}
\pgf@marshal
}
% the quality of arc approximation by means of Bezier splines is
% controlled by a mesh width.
%
% The mesh width is provided in (full!) degrees. The smaller the mesh
% width, the more precise the arc approximation.
%
% Use an empty value to disable spline approximation (uses a single
% cubic polynomial for the complete arc).
%
% The value must be an integer!
\def\pgfpatharctomaxstepsize{45}
% A specialized arc operation for an arc on an (axis--parallel) ellipse.
%
% In contrast to \pgfpatharc, it explicitly interpolates start- and end points.
%
% In contrast to \pgfpatharcto, this routine is numerically stable and
% quite fast since it relies on a lot of precomputed information.
%
% #1 center of ellipse
% #2 angle of last path position inside of the ellipse
% #3 end angle
% #4 end point (a \pgfpoint)
% #5 xradius
% #6 yradius
% #7 the ratio xradius/yradius of the ellipse
% #8 the ratio yradius/xradius of the ellipse
% Example:
% \def\cx{1cm}% center x
% \def\cy{1cm}% center y
% \def\startangle{0}%
% \def\endangle{45}%
% \def\a{5cm}% xradius
% \def\b{10cm}% yradius
% \pgfmathparse{\a/\b}\let\abratio=\pgfmathresult
% \pgfmathparse{\b/\a}\let\baratio=\pgfmathresult
%
% \pgfpathmoveto{\pgfpoint{\cx+\a*cos(\startangle)}{\cy+\b*sin(\startangle)}}%
% \pgfpatharctoprecomputed
% {\pgfpoint{\cx}{\cy}}
% {\startangle}
% {\endangle}
% {\pgfpoint{\cx+\a*cos(\endangle)}{\cy+\b*sin(\endangle)}}%
% {\a}
% {\b}
% {\abratio}
% {\baratio}
%
\def\pgfpatharctoprecomputed#1#2#3#4#5#6#7#8{%
\begingroup
% Implementation idea:
%
% let
% m = center (#1)
% \gamma_0 = start angle
% \gamma_1 = end angle
% a = x radius
% b = y radius
%
% an axis parallel ellipse is parameterized by
% C(\gamma) = m + ( a cos(\gamma), b sin(\gamma) ), \gamma in [0,360].
%
% Now, consider the segment \gamma(t),
% \gamma:[0,1] -> [\gamma_0,\gamma_1],
% t -> \gamma_0 + t(\gamma_1 - \gamma_0)
% and
% C(\gamma(t)) which is defined on [0,1].
%
% I'd like to approximate the arc by one or more cubic bezier
% splines which interpolate through the last and first provided
% points.
%
% In general, a Bezier spline C:[0,1] -> \R of order n fulfills
% C'(0) = n ( P_1 - P_0 ),
% C'(1) = n ( P_n - P_{n-1} ).
% For n=3 and given P_0 and P_3, I can directly compute P_1 and P_2 once I know
% the derivatives at t=0 and t=1.
%
% The derivatives in our case are
% ( C \circ \gamma )'(t) = C'[\gamma(t)] * \gamma'(t)
% = ( -a pi/180 sin(\gamma(t)), b pi/180 cos(\gamma(t)) ) * (\gamma_1 - \gamma_0).
% The pi/180 comes into play since we are working with degrees.
%
% Expression (C\circ\gamma)'(0) using P_0 and (C \circ \gamma)'(1)
% using P_3 yields the expressions
% (C \circ \gamma)'(0) =
% pi/180 * (\gamma_1 - \gamma_0)* [ - a/b(P_0^y - my), b/a (P_0^x - mx) ]
% (C \circ \gamma)'(1) =
% pi/180 * (\gamma_1 - \gamma_0)* [ - a/b(P_3^y - my), b/a (P_3^x - mx) ]
%
% defining
% scaleA = a/b * pi / (3*180) * (\gamma_1 - \gamma_0)
% and
% scaleB = b/a * pi / (3*180) * (\gamma_1 - \gamma_0)
% yields the direct expressions for the intermediate bezier
% control points
%
% P_1 = [
% P_0^x - scaleA* ( P_0^y -my),
% P_0^y + scaleB* ( P_0^x -mx) ]
% and
% P_2 = [
% P_3^x + scaleA* ( P_3^y -my),
% P_3^y - scaleB* ( P_3^x -mx) ].
%
% This works fast, with few operations, if
% - a/b and b/a are known in advance
% - P_0 and P_3 are known in advance
% - \gamma_0 and \gamma_1 are known.
%
% It is also reliable if (\gamma_1 - \gamma_0) is small
%
\pgf@process{#1}%
\edef\pgfpath@center@x{\the\pgf@x}%
\edef\pgfpath@center@y{\the\pgf@y}%
\def\pgfpath@completearcend{#4}%
% compute scale (#3-#2) * pi/(3*180) = (#3 - #2) * pi/27 * 1/20
% splitting pi/(3*180) into two scales has higher TeX accuracy
\pgf@xa=#2pt
\pgf@xb=#3pt
\edef\pgfpath@startangle{#2pt}%
\edef\pgfpath@endangle{\pgf@sys@tonumber\pgf@xb}%
%
\pgf@ya=\pgf@xb
\advance\pgf@ya by-\pgf@xa
%
\ifx\pgfpatharctomaxstepsize\pgfutil@empty
\def\pgfpath@N{1}%
\pgf@xc=\pgf@ya
\else
\pgf@xc=\pgf@ya% compute N = floor((gamma_1 - gamma_0) / max) +1
\ifdim\pgf@xc<0pt
\multiply\pgf@xc by-1
\fi
\divide\pgf@xc by\pgfpatharctomaxstepsize\relax
\afterassignment\pgfutil@gobble@until@relax
\c@pgf@counta=\the\pgf@xc\relax
\advance\c@pgf@counta by1
\edef\pgfpath@N{\the\c@pgf@counta}%
%
\pgf@xc=\pgf@ya
\divide\pgf@xc by\c@pgf@counta
\fi
%
\edef\pgfpath@h{\pgf@sys@tonumber\pgf@xc}%
%
%\message{pgfpathellipse: using N =\pgfpath@N\space spline points y0 = \pgfpath@startangle, y0+i*h, yN=\pgfpath@endangle, i=1,...,(\pgfpath@N-1), with h=\pgfpath@h\space mesh width (total arc angle \pgf@sys@tonumber\pgf@ya).}%
%
%
\pgf@xc=0.116355283466289\pgf@xc % pi/27
\divide\pgf@xc by20
\pgf@xa=#7\pgf@xc
\edef\pgfpath@scale@A{\pgf@sys@tonumber\pgf@xa}%
\pgf@xa=#8\pgf@xc
\edef\pgfpath@scale@B{\pgf@sys@tonumber\pgf@xa}%
%
% compute intermediate spline segments for
% i = 1,...,N-1
% this is a no-op for N=1.
\c@pgf@countd=1
\pgfutil@loop
\ifnum\c@pgf@countd<\pgfpath@N\relax
%
\pgf@xa=\pgfpath@startangle % compute \pgf@xa = y_0 + i*h
\pgf@xb=\pgfpath@h pt
\multiply\pgf@xb by\c@pgf@countd
\advance\pgf@xa by\pgf@xb
\edef\pgfpath@angle@i{\pgf@sys@tonumber\pgf@xa}%
%\message{angle \the\c@pgf@countd: \pgfpath@angle@i...}%
%
\pgfpatharcofellipse@{%
\pgfpoint
{\pgfpath@center@x + #5*cos(\pgfpath@angle@i)}
{\pgfpath@center@y + #6*sin(\pgfpath@angle@i)}%
}%
%
\advance\c@pgf@countd by1
\pgfutil@repeat
%
% compute final spline segment. It only differs insofar as the
% final point is already known explicitly and should be
% interpolated without additional math error.
%\message{angle \pgfpath@N: \pgfpath@endangle...}%
\pgfpatharcofellipse@{\pgfpath@completearcend}%
\endgroup
}%
\def\pgfpatharcofellipse@#1{%
\begingroup
\pgf@process{#1}%
\edef\pgfpath@endpt{\global\pgf@x=\the\pgf@x\space\global\pgf@y=\the\pgf@y\space}%
%
\pgfpathcurveto{
\begingroup
\global\pgf@x=\pgf@path@lastx
\global\pgf@y=\pgf@path@lasty
\pgf@xa=\pgf@x \advance\pgf@xa by-\pgfpath@center@x
\pgf@ya=\pgf@y \advance\pgf@ya by-\pgfpath@center@y
\global\advance\pgf@x by-\pgfpath@scale@A\pgf@ya
\global\advance\pgf@y by \pgfpath@scale@B\pgf@xa
\endgroup
}{%
\begingroup
\pgfpath@endpt
\pgf@xa=\pgf@x \advance\pgf@xa by-\pgfpath@center@x
\pgf@ya=\pgf@y \advance\pgf@ya by-\pgfpath@center@y
\global\advance\pgf@x by \pgfpath@scale@A\pgf@ya
\global\advance\pgf@y by-\pgfpath@scale@B\pgf@xa
\endgroup
}{%
\pgfpath@endpt
}%
\endgroup
}
% 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%
\pgf@nlt@moveto{\pgf@xa}{\pgf@ya}%
}%
\pgf@x=0.55228475\pgf@xb% first arc
\pgf@y=0.55228475\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{\pgf@xc\the\pgf@x\pgf@yc\the\pgf@y}%
\pgf@x=0.55228475\pgf@xa%
\pgf@y=0.55228475\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%
\pgf@temp%
\pgf@nlt@curveto{\pgf@xc}{\pgf@yc}{\pgf@x}{\pgf@y}{\pgf@xb}{\pgf@yb}%
}%
\pgf@xa=-\pgf@xa% flip first axis
\pgf@ya=-\pgf@ya%
\pgf@x=0.55228475\pgf@xa% second arc
\pgf@y=0.55228475\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{\pgf@xc\the\pgf@x\pgf@yc\the\pgf@y}%
\pgf@x=0.55228475\pgf@xb%
\pgf@y=0.55228475\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%
\pgf@temp%
\pgf@nlt@curveto{\pgf@xc}{\pgf@yc}{\pgf@x}{\pgf@y}{\pgf@xa}{\pgf@ya}%
}%
\pgf@xb=-\pgf@xb% flip second axis
\pgf@yb=-\pgf@yb%
\pgf@x=0.55228475\pgf@xb% third arc
\pgf@y=0.55228475\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{\pgf@xc\the\pgf@x\pgf@yc\the\pgf@y}%
\pgf@x=0.55228475\pgf@xa%
\pgf@y=0.55228475\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%
\pgf@temp%
\pgf@nlt@curveto{\pgf@xc}{\pgf@yc}{\pgf@x}{\pgf@y}{\pgf@xb}{\pgf@yb}%
}%
\pgf@xa=-\pgf@xa% flip first axis once more
\pgf@ya=-\pgf@ya%
\pgf@x=0.55228475\pgf@xa% fourth arc
\pgf@y=0.55228475\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{\pgf@xc\the\pgf@x\pgf@yc\the\pgf@y}%
\pgf@x=0.55228475\pgf@xb%
\pgf@y=0.55228475\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%
\pgf@temp%
\pgf@nlt@curveto{\pgf@xc}{\pgf@yc}{\pgf@x}{\pgf@y}{\pgf@xa}{\pgf@ya}%
}%
\pgf@nlt@closepath%
\pgf@nlt@moveto{\pgf@xc}{\pgf@yc}%
}
% Append a circle to the current path
%
% #1 = center
% #2 = radius
%
% Example:
%
% % Append a circle of radius 3cm around 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%
\ifx\pgf@nlt@list\pgfutil@empty%
\let\pgfrect@next=\pgf@normalrect%
\fi%
\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 = first corner point of grid
% #2 = second corner point of grid
%
% Options:
%
% stepx = x-step dimension (default 1cm)
% stepy = y-step dimension (default 1cm)
% step = dimension 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%
\pgf@ya=\pgf@y%
% Swap coordinates if one of them is smaller than the other:
\ifdim\pgf@xa>\pgf@xb%
\pgf@x=\pgf@xb%
\pgf@xb=\pgf@xa%
\pgf@xa=\pgf@x%
\fi%
\ifdim\pgf@ya>\pgf@yb%
\pgf@y=\pgf@yb%
\pgf@yb=\pgf@ya%
\pgf@ya=\pgf@y%
\fi%
\ifdim \pgf@yc > .01pt\relax% if to draw horizontal lines
\c@pgf@counta=\pgf@ya\relax%
\c@pgf@countb=\pgf@yc\relax%
\divide\c@pgf@counta by\c@pgf@countb\relax%
\pgfutil@tempdima=\c@pgf@counta\pgf@yc\relax%
\ifdim\pgfutil@tempdima<\pgf@ya%
\advance\pgfutil@tempdima by\pgf@yc%
\fi%
\pgfutil@tempdimb\pgf@x
\pgfutil@loop% horizontal lines
{%
\pgf@xa=\pgfutil@tempdimb%
\pgf@ya=\pgfutil@tempdima%
\pgf@pos@transform{\pgf@xa}{\pgf@ya}
\pgf@nlt@moveto{\pgf@xa}{\pgf@ya}%
\pgf@xa=\pgf@xb%
\pgf@ya=\pgfutil@tempdima%
\pgf@pos@transform{\pgf@xa}{\pgf@ya}
\pgf@nlt@lineto{\pgf@xa}{\pgf@ya}%
}%
\advance\pgfutil@tempdima by\pgf@yc%
\ifdim\pgfutil@tempdima<\pgf@yb%
\pgfutil@repeat%
\advance\pgfutil@tempdima by-0.01pt\relax%
\ifdim\pgfutil@tempdima<\pgf@yb%
{%
\pgf@xa=\pgfutil@tempdimb%
\pgf@ya=\pgfutil@tempdima%
\pgf@pos@transform{\pgf@xa}{\pgf@ya}
\pgf@nlt@moveto{\pgf@xa}{\pgf@ya}%
\pgf@xa=\pgf@xb%
\pgf@ya=\pgfutil@tempdima%
\pgf@pos@transform{\pgf@xa}{\pgf@ya}
\pgf@nlt@lineto{\pgf@xa}{\pgf@ya}%
}%
\fi%
\fi%
\ifdim \pgf@xc > .01pt\relax% if to draw vertical lines
\c@pgf@counta=\pgf@xa\relax%
\c@pgf@countb=\pgf@xc\relax%
\divide\c@pgf@counta by\c@pgf@countb\relax%
\pgfutil@tempdimb=\c@pgf@counta\pgf@xc\relax%
\ifdim\pgfutil@tempdimb<\pgf@xa%
\advance\pgfutil@tempdimb by\pgf@xc%
\fi%
\pgfutil@loop% vertical lines
{%
\pgf@xc=\pgfutil@tempdimb%
\pgf@yc=\pgf@ya%
\pgf@pos@transform{\pgf@xc}{\pgf@yc}
\pgf@nlt@moveto{\pgf@xc}{\pgf@yc}%
\pgf@xc=\pgfutil@tempdimb%
\pgf@yc=\pgf@yb%
\pgf@pos@transform{\pgf@xc}{\pgf@yc}
\pgf@nlt@lineto{\pgf@xc}{\pgf@yc}%
}%
\advance\pgfutil@tempdimb by\pgf@xc%
\ifdim\pgfutil@tempdimb<\pgf@xb%
\pgfutil@repeat%
\advance\pgfutil@tempdimb by-0.01pt\relax%
\ifdim\pgfutil@tempdimb<\pgf@xb%
{%
\pgf@xc=\pgfutil@tempdimb%
\pgf@yc=\pgf@ya%
\pgf@pos@transform{\pgf@xc}{\pgf@yc}
\pgf@nlt@moveto{\pgf@xc}{\pgf@yc}%
\pgf@xc=\pgfutil@tempdimb%
\pgf@yc=\pgf@yb%
\pgf@pos@transform{\pgf@xc}{\pgf@yc}
\pgf@nlt@lineto{\pgf@xc}{\pgf@yc}%
}%
\fi%
\fi%
\pgf@process{#3}%
\pgf@pos@transform{\pgf@x}{\pgf@y}%
\pgf@nlt@moveto{\pgf@x}{\pgf@y}%
}
% 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{.3260\pgf@xc}{.5120\pgf@yc}}%
{\pgfqpoint{.6380\pgf@xc}{\pgf@yc}}%
{\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{.3620\pgf@xc}{0pt}}%
{\pgfqpoint{.6740\pgf@xc}{.4880\pgf@yc}}%
{\pgfqpoint{\pgf@xc}{\pgf@yc}}%
}%
}
% Draw part of a curve between two specified times s and t.
%
% #1 - a start time s.
% #2 - an end time t.
% #3 - start point of the curve
% #4 - first control
% #5 - second control
% #6 - end point of the curve
%
% There are two versions, \pgfpathcurvebetweentime and
% \pgfpathcurvebetweentimecontinue. The latter does not insert a
% moveto to the first point.
%
\def\pgfpathcurvebetweentime{\pgf@ignoremovetofalse\pgf@@pathcurvebetweentime}
\def\pgfpathcurvebetweentimecontinue{\pgf@ignoremovetotrue\pgf@@pathcurvebetweentime}
\newif\ifpgf@ignoremoveto
\def\pgf@@pathcurvebetweentime#1#2#3#4#5#6{%
\pgfmathparse{#1}%
\let\pgf@time@s=\pgfmathresult%
\pgfmathparse{#2}%
\let\pgf@time@t=\pgfmathresult%
\ifdim\pgf@time@s pt>\pgf@time@t pt\relax%
\pgfmathsetmacro\pgf@time@s{1-#1}%
\pgfmathsetmacro\pgf@time@t{1-#2}%
\pgf@@@pathcurvebetweentime{\pgf@time@t}{#6}{#5}{#4}{#3}%
\else%
\pgf@@@pathcurvebetweentime{\pgf@time@t}{#3}{#4}{#5}{#6}%
\fi%
}
\def\pgf@@@pathcurvebetweentime#1#2#3#4#5{%
% Q1 = P1.
\pgf@process{#2}%
\pgf@xc=\pgf@x%
\pgf@yc=\pgf@y%
% Q2 = P1 + t*(P2-P1).
\pgf@process{%
\pgf@process{#3}%
\pgf@xa=#1\pgf@x%
\pgf@ya=#1\pgf@y%
\pgf@process{#2}%
\pgf@xb=\pgf@x%
\pgf@yb=\pgf@y%
\advance\pgf@x by-#1\pgf@xb%
\advance\pgf@y by-#1\pgf@yb%
\advance\pgf@x by\pgf@xa%
\advance\pgf@y by\pgf@ya%
}%
\pgf@xb=\pgf@x%
\pgf@yb=\pgf@y%
% Q3 = Q2 + t*((P2 + t*(P3-P2)) - Q2).
\pgf@process{%
\pgf@process{#4}%
\pgf@xa=#1\pgf@x%
\pgf@ya=#1\pgf@y%
%
\pgf@process{#3}%
\pgf@xc=\pgf@x%
\pgf@yc=\pgf@y%
\advance\pgf@xc by-#1\pgf@x%
\advance\pgf@yc by-#1\pgf@y%
%
\pgf@x=\pgf@xb%
\pgf@y=\pgf@yb%
\advance\pgf@x by#1\pgf@xa%
\advance\pgf@y by#1\pgf@ya%
\advance\pgf@x by-#1\pgf@xb%
\advance\pgf@y by-#1\pgf@yb%
\advance\pgf@x by#1\pgf@xc%
\advance\pgf@y by#1\pgf@yc%
}%
\pgf@xa=\pgf@x%
\pgf@ya=\pgf@y%
% Q4 = (1-t)^3*P1 + 3*t(1-t)^2*P2 + 3*t^2(1-t)*P3 + t^3*P4.
\pgf@process{\pgfpointcurveattime{#1}{#2}{#3}{#4}{#5}}%
\ifx#1\pgf@time@t%
% First time round...
\pgfmathdivide@{\pgf@time@s}{\pgf@time@t}%
\pgfmathadd@{-\pgfmathresult}{1}%
\let\pgf@time@s=\pgfmathresult%
\edef\pgf@marshal{%
\noexpand\pgf@@@pathcurvebetweentime{\noexpand\pgf@time@s}%
{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}%
{\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}{\noexpand\pgfqpoint{\the\pgf@xc}{\the\pgf@yc}}%
}%
\else%
% ...second time round.
\ifpgf@ignoremoveto%
\edef\pgf@marshal{%
\noexpand\pgfpathcurveto{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}%
{\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}{\noexpand\pgfqpoint{\the\pgf@xc}{\the\pgf@yc}}%
}%
\else%
\edef\pgf@marshal{%
\noexpand\pgfpathmoveto{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
\noexpand\pgfpathcurveto{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}%
{\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}{\noexpand\pgfqpoint{\the\pgf@xc}{\the\pgf@yc}}%
}%
\fi%
\fi%
\pgf@marshal%
}
\endinput