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+\ProvidesFileRCS $Header: /cvsroot/pgf/pgf/generic/pgf/basiclayer/pgfcorepoints.code.tex,v 1.1.1.1 2005/06/29 12:14:04 tantau Exp $
+
+% Copyright 2005 by Till Tantau <tantau@cs.tu-berlin.de>.
+%
+% This program can be redistributed and/or modified under the terms
+% of the GNU Public License, version 2.
+
+\newdimen\pgf@picminx
+\newdimen\pgf@picmaxx
+\newdimen\pgf@picminy
+\newdimen\pgf@picmaxy
+
+\newdimen\pgf@pathminx
+\newdimen\pgf@pathmaxx
+\newdimen\pgf@pathminy
+\newdimen\pgf@pathmaxy
+
+\newif\ifpgf@relevantforpicturesize
+
+\def\pgf@process#1{{#1\global\pgf@x=\pgf@x\global\pgf@y=\pgf@y}}
+
+\newdimen\pgf@tempdim
+\def\pgf@setlength#1#2{% these will be used only when \nullfont is active
+ \begingroup% keep font setting local
+ \pgf@selectfontorig% restore font
+ \pgf@setlengthorig\pgf@tempdim{#2}% calculate dimension (possibly using calc)
+ \global\pgf@tempdim\pgf@tempdim% make dimension global
+ \endgroup%
+ #1=\pgf@tempdim\relax}
+\def\pgf@addtolength#1#2{%
+ \begingroup% keep font setting local
+ \pgf@selectfontorig% restore font
+ \pgf@tempdim#1\relax%
+ \pgf@addtolengthorig\pgf@tempdim{#2}% calculate dimension (possibly using calc)
+ \global\pgf@tempdim\pgf@tempdim% make dimension global
+ \endgroup%
+ #1=\pgf@tempdim\relax}
+\newcounter{pgf@tempcount}
+\def\pgf@setcounter#1#2{%
+ \setcounter{pgf@tempcount}{#2}% makes change global!
+ \csname c@#1\endcsname=\c@pgf@tempcount\relax}
+\def\pgf@selectfont{\pgf@selectfontorig\nullfont}
+
+
+
+% Return a point
+%
+% #1 = x-coordinate of the point
+% #2 = y-coordinate of the point
+%
+% x = #1
+% y = #2
+%
+% Example:
+%
+% \pgfpathmoveto{\pgfpoint{2pt}{3cm}}
+
+\def\pgfpoint#1#2{%
+ \setlength\pgf@x{#1}%
+ \setlength\pgf@y{#2}\ignorespaces}
+
+% Return the origin.
+%
+% x = 0
+% y = 0
+%
+% Example:
+%
+% \pgfpathmoveto{\pgfpointorigin}
+
+\def\pgfpointorigin{\pgfpoint{0pt}{0pt}\ignorespaces}
+
+
+
+% Return a transformed point
+%
+% #1 = a point
+%
+% Description:
+%
+% This command applies pgf's current transformation matrix to the
+% given point. Normally, this is done automatically by commands like
+% lineto or moveto, but sometimes you may wish to access a transformed
+% point yourself. For example, this command is useful for a low level
+% coordinate system shift:
+%
+% Example:
+%
+% \begin{pgflowleveltransformshiftscope}{\pgfpointtransformed{\pgfpointorigin}}
+% \pgfbox[center,center]{Hi!}
+% \end{pgflowleveltransformshiftscope}
+
+\def\pgfpointtransformed#1{%
+ \pgf@process{%
+ #1%
+ \pgf@pos@transform{\pgf@x}{\pgf@y}%
+ }%
+}
+
+
+% Return the difference vector of two points.
+%
+% #1 = start of vector
+% #2 = end of vector
+%
+% x = x-component of difference
+% y = y-component of difference
+%
+% Example:
+%
+% \pgfpathmoveto{\pgfpointdiff{\pgfpointxy{1}{1}}{\pgfpointxy{2}{3}}}
+
+\def\pgfpointdiff#1#2{%
+ \pgf@process{#1}%
+ \pgf@xa=\pgf@x%
+ \pgf@ya=\pgf@y%
+ \pgf@process{#2}%
+ \advance\pgf@x by-\pgf@xa\relax%
+ \advance\pgf@y by-\pgf@ya\relax\ignorespaces}
+
+% Add two vectors.
+%
+% #1 = first vector
+% #2 = second vector
+%
+% x = x-component of addition
+% y = y-component of addition
+%
+% Example:
+%
+% \pgfpathmoveto{\pgfpointadd{\pgfpointxy{0}{1}}{\pgfpointxy{2}{3}}}
+
+\def\pgfpointadd#1#2{%
+ \pgf@process{#1}%
+ \pgf@xa=\pgf@x%
+ \pgf@ya=\pgf@y%
+ \pgf@process{#2}%
+ \advance\pgf@x by\pgf@xa%
+ \advance\pgf@y by\pgf@ya}
+
+
+
+% Multiply a vector by a factor.
+%
+% #1 = factor
+% #2 = vector
+%
+% Example:
+%
+% \pgfpointscale{2}{\pgfpointxy{0}{1}}
+
+\def\pgfpointscale#1#2{%
+ \pgf@process{#2}%
+ \pgf@x=#1\pgf@x%
+ \pgf@y=#1\pgf@y%
+}
+
+
+% The intersection of two lines
+%
+% #1 = point on first line
+% #2 = another point on first line
+% #3 = point on second line
+% #4 = another point on second line
+%
+% Returns the intersection of the two lines. If there is no
+% intersection or if the points #1 and #2 or the points #3 and #4 are
+% identical, the behaviour is not specified.
+%
+% Example:
+%
+% \pgfpointintersectionoflines{\pgfpointxy{0}{1}}{\pgfpointxy{1}{0}}{\pgfpointxy{2}{2}}{\pgfpointxy{3}{4}}
+
+\def\pgfpointintersectionoflines#1#2#3#4{%
+ {
+ %
+ % Compute orthogonal vector to #1--#2
+ %
+ \pgf@process{#2}%
+ \pgf@xa=\pgf@x%
+ \pgf@ya=\pgf@y%
+ \pgf@process{#1}%
+ \advance\pgf@xa by-\pgf@x%
+ \advance\pgf@ya by-\pgf@y%
+ \pgf@ya=-\pgf@ya%
+ % Normalise a bit
+ \c@pgf@counta=\pgf@xa%
+ \ifnum\c@pgf@counta<0\relax%
+ \c@pgf@counta=-\c@pgf@counta\relax%
+ \fi%
+ \c@pgf@countb=\pgf@ya%
+ \ifnum\c@pgf@countb<0\relax%
+ \c@pgf@countb=-\c@pgf@countb\relax%
+ \fi%
+ \advance\c@pgf@counta by\c@pgf@countb\relax%
+ \divide\c@pgf@counta by 65536\relax%
+ \ifnum\c@pgf@counta>0\relax%
+ \divide\pgf@xa by\c@pgf@counta\relax%
+ \divide\pgf@ya by\c@pgf@counta\relax%
+ \fi%
+ %
+ % Compute projection
+ %
+ \pgf@xc=\pgf@sys@tonumber{\pgf@ya}\pgf@x%
+ \advance\pgf@xc by\pgf@sys@tonumber{\pgf@xa}\pgf@y%
+ %
+ % The orthogonal vector is (\pgf@ya,\pgf@xa)
+ %
+ %
+ % Compute orthogonal vector to #3--#4
+ %
+ \pgf@process{#4}%
+ \pgf@xb=\pgf@x%
+ \pgf@yb=\pgf@y%
+ \pgf@process{#3}%
+ \advance\pgf@xb by-\pgf@x%
+ \advance\pgf@yb by-\pgf@y%
+ \pgf@yb=-\pgf@yb%
+ % Normalise a bit
+ \c@pgf@counta=\pgf@xb%
+ \ifnum\c@pgf@counta<0\relax%
+ \c@pgf@counta=-\c@pgf@counta\relax%
+ \fi%
+ \c@pgf@countb=\pgf@yb%
+ \ifnum\c@pgf@countb<0\relax%
+ \c@pgf@countb=-\c@pgf@countb\relax%
+ \fi%
+ \advance\c@pgf@counta by\c@pgf@countb\relax%
+ \divide\c@pgf@counta by 65536\relax%
+ \ifnum\c@pgf@counta>0\relax%
+ \divide\pgf@xb by\c@pgf@counta\relax%
+ \divide\pgf@yb by\c@pgf@counta\relax%
+ \fi%
+ %
+ % Compute projection
+ %
+ \pgf@yc=\pgf@sys@tonumber{\pgf@yb}\pgf@x%
+ \advance\pgf@yc by\pgf@sys@tonumber{\pgf@xb}\pgf@y%
+ %
+ % The orthogonal vector is (\pgf@yb,\pgf@xb)
+ %
+ % Setup transformation matrx (this is just to use the matrix
+ % inversion)
+ %
+ \pgfsettransform{{\pgf@sys@tonumber\pgf@ya}{\pgf@sys@tonumber\pgf@yb}{\pgf@sys@tonumber\pgf@xa}{\pgf@sys@tonumber\pgf@xb}{0pt}{0pt}}%
+ \pgftransforminvert%
+ \pgf@process{\pgfpointtransformed{\pgfpoint{\pgf@xc}{\pgf@yc}}}%
+ }%
+}
+
+
+% Returns point on a line from #2 to #3 at time #1.
+%
+% #1 = a time, where 0 is the start and 1 is the end
+% #2 = start point
+% #3 = end point
+%
+% x = x-component of #1*start + (1-#1)*end
+% y = y-component of #1*start + (1-#1)*end
+%
+% Example:
+%
+% % Middle of (1,1) and (2,3)
+% \pgfpathmoveto{\pgfpointlineattime{0.5}{\pgfpointxy{0}{1}}{\pgfpointxy{2}{3}}}
+
+\def\pgfpointlineattime#1#2#3{%
+ \pgf@process{#3}%
+ \pgf@xa=\pgf@x%
+ \pgf@ya=\pgf@y%
+ \pgf@process{#2}%
+ \advance\pgf@xa by-\pgf@x\relax%
+ \advance\pgf@ya by-\pgf@y\relax%
+ \advance\pgf@x by #1\pgf@xa\relax%
+ \advance\pgf@y by #1\pgf@ya\relax%
+ \ignorespaces}
+
+
+% Move point #2 #1 many units in the direction of #3.
+%
+% #1 = a distance
+% #2 = start point
+% #3 = end point
+%
+% x = x-component of start + #1*(normalise(end-start))
+% y = y-component of start + #1*(normalise(end-start))
+%
+% Example:
+%
+%
+% \pgfpathmoveto{\pgfpointlineatdistance{2pt}{\pgfpointxy{0}{1}}{\pgfpointxy{2}{3}}}
+% \pgfpathlineto{\pgfpointlineatdistance{3pt}{\pgfpointxy{2}{3}}{\pgfpointxy{0}{1}}}
+
+\def\pgfpointlineatdistance#1#2#3{%
+ \pgf@process{#2}%
+ \pgf@xb=\pgf@x\relax% xb/yb = start point
+ \pgf@yb=\pgf@y\relax%
+ \pgf@process{#3}%
+ \advance\pgf@x by-\pgf@xb\relax%
+ \advance\pgf@y by-\pgf@yb\relax%
+ \pgf@process{\pgfpointnormalised{}}% x/y = normalised vector
+ \setlength\pgf@xa{#1}%
+ \pgf@ya=\pgf@xa\relax%
+ \pgf@xa=\pgf@sys@tonumber{\pgf@x}\pgf@xa%
+ \pgf@ya=\pgf@sys@tonumber{\pgf@y}\pgf@ya%
+ \pgf@x=\pgf@xb\relax%
+ \pgf@y=\pgf@yb\relax%
+ \advance\pgf@x by\pgf@xa\relax%
+ \advance\pgf@y by\pgf@ya\relax%
+ \ignorespaces}
+
+
+% Returns point on a curve from #2 to #5 with controls #3 and #4 at time #1.
+%
+% #1 = a time
+% #2 = start point
+% #3 = first control point
+% #4 = second control point
+% #5 = end point
+%
+% x = x-component of place on the curve at time t
+% y = y-component of place on the curve at time t
+%
+% Additionally, (\pgf@xa,\pgf@ya) and (\pgf@xb,\pgf@yb) will be on a
+% tangent to the point on the curve (this can be useful for computing
+% a label rotation).
+%
+% Example:
+%
+% % Middle of (1,1) and (2,3)
+% \pgfpathmoveto{\pgfpointcurveattime{0.5}{\pgfpointxy{0}{1}}{\pgfpointxy{1}{1}}{\pgfpointxy{1}{1}}{\pgfpointxy{2}{3}}}
+
+\def\pgfpointcurveattime#1#2#3#4#5{%
+ \def\pgf@time@s{#1}%
+ \pgf@x=#1pt%
+ \pgf@x=-\pgf@x%
+ \advance\pgf@x by 1pt%
+ \edef\pgf@time@t{\pgf@sys@tonumber{\pgf@x}}%
+ \pgf@process{#5}%
+ \pgf@xc=\pgf@x%
+ \pgf@yc=\pgf@y%
+ \pgf@process{#4}%
+ \pgf@xb=\pgf@x%
+ \pgf@yb=\pgf@y%
+ \pgf@process{#3}%
+ \pgf@xa=\pgf@x%
+ \pgf@ya=\pgf@y%
+ \pgf@process{#2}%
+ % First iteration:
+ \pgf@x=\pgf@time@t\pgf@x\advance\pgf@x by\pgf@time@s\pgf@xa%
+ \pgf@y=\pgf@time@t\pgf@y\advance\pgf@y by\pgf@time@s\pgf@ya%
+ \pgf@xa=\pgf@time@t\pgf@xa\advance\pgf@xa by\pgf@time@s\pgf@xb%
+ \pgf@ya=\pgf@time@t\pgf@ya\advance\pgf@ya by\pgf@time@s\pgf@yb%
+ \pgf@xb=\pgf@time@t\pgf@xb\advance\pgf@xb by\pgf@time@s\pgf@xc%
+ \pgf@yb=\pgf@time@t\pgf@yb\advance\pgf@yb by\pgf@time@s\pgf@yc%
+ % Second iteration:
+ \pgf@x=\pgf@time@t\pgf@x\advance\pgf@x by\pgf@time@s\pgf@xa%
+ \pgf@y=\pgf@time@t\pgf@y\advance\pgf@y by\pgf@time@s\pgf@ya%
+ \pgf@xa=\pgf@time@t\pgf@xa\advance\pgf@xa by\pgf@time@s\pgf@xb%
+ \pgf@ya=\pgf@time@t\pgf@ya\advance\pgf@ya by\pgf@time@s\pgf@yb%
+ % Save x/y
+ \pgf@xb=\pgf@x%
+ \pgf@yb=\pgf@y%
+ % Third iteration:
+ \pgf@x=\pgf@time@t\pgf@x\advance\pgf@x by\pgf@time@s\pgf@xa%
+ \pgf@y=\pgf@time@t\pgf@y\advance\pgf@y by\pgf@time@s\pgf@ya%
+}
+
+
+
+
+
+
+% Internal registers
+\newdimen\pgf@xx
+\newdimen\pgf@xy
+\newdimen\pgf@yx
+\newdimen\pgf@yy
+\newdimen\pgf@zx
+\newdimen\pgf@zy
+
+
+
+% Store a value in polar-coordinates
+%
+% #1 = a degree
+% #2 = a radius
+%
+% x = #2 * cos(#1)
+% y = #2 * sin(#2)
+%
+% Example:
+%
+% % Create a slanted rectangle
+%
+% \pgfpathmoveto{\pgfpointpolar{30}{1cm}}
+
+\def\pgfpointpolar#1#2{%
+ \pgfsincos{#1}%
+ \in@/{#2}%
+ \ifin@%
+ \pgf@polar@#2\@@%
+ \else%
+ \pgf@polar@#2/#2\@@%
+ \fi%
+ \pgf@xa=\pgf@sys@tonumber{\pgf@x}\pgf@xa%
+ \pgf@ya=\pgf@sys@tonumber{\pgf@y}\pgf@ya%
+ \pgf@y=\pgf@xa\relax%
+ \pgf@x=\pgf@ya\ignorespaces}
+
+\def\pgf@polar@#1/#2\@@{%
+ \setlength{\pgf@xa}{#2}%
+ \setlength{\pgf@ya}{#1}%
+}
+
+
+
+% Store the vector #1 * x-vec + #2 * y-vec
+%
+% #1 = a factor for the x-vector
+% #2 = a factor fot the y-vector
+%
+% x = x-component of result vector
+% y = y-component of result vector
+%
+% Description:
+%
+% This command can be used to create a new coordinate system
+% without using the rotate/translate/scale commands. This
+% may be useful, if you do not want arrows and line width to
+% be scaled/transformed together with the coordinate system.
+%
+% Example:
+%
+% % Create a slanted rectangle
+%
+% \pgfsetxvec{\pgfpoint{1cm}{1cm}}
+% \pgfsetyvec{\pgfpoint{0cm}{1cm}}
+%
+% \pgfpathmoveto{\pgfpointxy{0}{0}}
+% \pgfpathlineto{\pgfpointxy{1}{0}}
+% \pgfpathlineto{\pgfpointxy{1}{1}}
+% \pgfpathlineto{\pgfpointxy{0}{1}}
+% \pgfclosestroke
+
+\def\pgfpointxy#1#2{\pgf@x=#1\pgf@xx%
+ \advance\pgf@x by #2\pgf@yx%
+ \pgf@y=#1\pgf@xy%
+ \advance\pgf@y by #2\pgf@yy}
+
+
+% Store the vector #1 * x-vec + #2 * y-vec + #3 * z-vec
+%
+% #1 = a factor for the x-vector
+% #2 = a factor fot the y-vector
+% #3 = a factor fot the z-vector
+%
+% x = x-component of result vector
+% y = y-component of result vector
+%
+%
+% Description:
+%
+% This command allows you to use a 3d coordinate system.
+%
+%
+% Example:
+%
+% % Draw a cubus
+%
+% \pgfline{\pgfpointxyz{0}{0}{0}}{\pgfpointxyz{0}{0}{1}}
+% \pgfline{\pgfpointxyz{0}{1}{0}}{\pgfpointxyz{0}{1}{1}}
+% \pgfline{\pgfpointxyz{1}{0}{0}}{\pgfpointxyz{1}{0}{1}}
+% \pgfline{\pgfpointxyz{1}{1}{0}}{\pgfpointxyz{1}{1}{1}}
+% \pgfline{\pgfpointxyz{0}{0}{0}}{\pgfpointxyz{0}{1}{0}}
+% \pgfline{\pgfpointxyz{0}{0}{1}}{\pgfpointxyz{0}{1}{1}}
+% \pgfline{\pgfpointxyz{1}{0}{0}}{\pgfpointxyz{1}{1}{0}}
+% \pgfline{\pgfpointxyz{1}{0}{1}}{\pgfpointxyz{1}{1}{1}}
+% \pgfline{\pgfpointxyz{0}{0}{0}}{\pgfpointxyz{1}{0}{0}}
+% \pgfline{\pgfpointxyz{0}{0}{1}}{\pgfpointxyz{1}{0}{1}}
+% \pgfline{\pgfpointxyz{0}{1}{0}}{\pgfpointxyz{1}{1}{0}}
+% \pgfline{\pgfpointxyz{0}{1}{1}}{\pgfpointxyz{1}{1}{1}}
+
+\def\pgfpointxyz#1#2#3{%
+ \pgf@x=#1\pgf@xx%
+ \advance\pgf@x by #2\pgf@yx%
+ \advance\pgf@x by #3\pgf@zx%
+ \pgf@y=#1\pgf@xy%
+ \advance\pgf@y by #2\pgf@yy%
+ \advance\pgf@y by #3\pgf@zy}
+
+
+
+
+% Set the x-vector
+%
+% #1 = a point the is the new x-vector
+%
+% Example:
+%
+% \pgfsetxvec{\pgfpoint{1cm}{0cm}}
+
+\def\pgfsetxvec#1{%
+ \pgf@process{#1}%
+ \pgf@xx=\pgf@x%
+ \pgf@xy=\pgf@y%
+ \ignorespaces}
+
+
+% Set the y-vector
+%
+% #1 = a point the is the new y-vector
+%
+% Example:
+%
+% \pgfsetyvec{\pgfpoint{0cm}{1cm}}
+
+\def\pgfsetyvec#1{%
+ \pgf@process{#1}%
+ \pgf@yx=\pgf@x%
+ \pgf@yy=\pgf@y%
+ \ignorespaces}
+
+
+% Set the z-vector
+%
+% #1 = a point the is the new z-vector
+%
+% Example:
+%
+% \pgfsetzvec{\pgfpoint{-0.385cm}{-0.385cm}}
+
+\def\pgfsetzvec#1{%
+ \pgf@process{#1}%
+ \pgf@zx=\pgf@x%
+ \pgf@zy=\pgf@y%
+ \ignorespaces}
+
+
+
+% Default values
+\pgfsetxvec{\pgfpoint{1cm}{0cm}}
+\pgfsetyvec{\pgfpoint{0cm}{1cm}}
+\pgfsetzvec{\pgfpoint{-0.385cm}{-0.385cm}}
+
+
+
+
+% Normalise a point.
+%
+% #1 = point with coordinates (a,b)
+%
+% x = a/\sqrt(a*a+b*b)
+% y = b/\sqrt(a*a+b*b)
+%
+% Example:
+%
+% \pgfpointnormalised{\pgfpointxy{2}{1}}
+
+\def\pgfpointnormalised#1{%
+ \pgf@process{#1}%
+ \pgf@xa=\pgf@x%
+ \pgf@ya=\pgf@y%
+ \ifdim\pgf@x<0pt\relax% move into first quadrant
+ \pgf@x=-\pgf@x%
+ \fi%
+ \ifdim\pgf@y<0pt\relax%
+ \pgf@y=-\pgf@y%
+ \fi%
+ \ifdim\pgf@x>\pgf@y% x > y
+ % make point small
+ \c@pgf@counta=\pgf@x%
+ \divide\c@pgf@counta by 65536\relax%
+ \ifnum\c@pgf@counta=0\relax%
+ \c@pgf@counta=1\relax%
+ \fi%
+ \divide\pgf@x by\c@pgf@counta%
+ \divide\pgf@y by\c@pgf@counta%
+ \divide\pgf@xa by\c@pgf@counta%
+ \divide\pgf@ya by\c@pgf@counta%
+ % ok.
+ \pgf@x=.125\pgf@x%
+ \pgf@y=.125\pgf@y%
+ \c@pgf@counta=\pgf@x%
+ \c@pgf@countb=\pgf@y%
+ \multiply\c@pgf@countb by 100%
+ \ifnum\c@pgf@counta<64\relax%
+ \pgf@x=1pt\relax%
+ \pgf@y=0pt\relax%
+ \else%
+ \divide\c@pgf@countb by \c@pgf@counta%
+ \pgf@setmath{x}{\csname pgf@cosfrac\the\c@pgf@countb\endcsname}%
+ \pgf@xc=8192pt%
+ \divide\pgf@xc by\c@pgf@counta%
+ \pgf@y=\pgf@sys@tonumber{\pgf@xc}\pgf@ya%
+ \pgf@y=\pgf@sys@tonumber{\pgf@x}\pgf@y%
+ \fi%
+ \ifdim\pgf@xa<0pt%
+ \pgf@x=-\pgf@x%
+ \fi%
+ \else% x <= y
+ % make point small
+ \c@pgf@counta=\pgf@y%
+ \divide\c@pgf@counta by 65536\relax%
+ \ifnum\c@pgf@counta=0\relax%
+ \c@pgf@counta=1\relax%
+ \fi%
+ \divide\pgf@x by\c@pgf@counta%
+ \divide\pgf@y by\c@pgf@counta%
+ \divide\pgf@xa by\c@pgf@counta%
+ \divide\pgf@ya by\c@pgf@counta%
+ % ok.
+ \pgf@x=.125\pgf@x%
+ \pgf@y=.125\pgf@y%
+ \c@pgf@counta=\pgf@y%
+ \c@pgf@countb=\pgf@x%
+ \multiply\c@pgf@countb by 100%
+ \ifnum\c@pgf@counta<64\relax%
+ \pgf@y=1pt\relax%
+ \pgf@x=0pt\relax%
+ \else%
+ \divide\c@pgf@countb by \c@pgf@counta%
+ \pgf@setmath{y}{\csname pgf@cosfrac\the\c@pgf@countb\endcsname}%
+ \pgf@xc=8192pt%
+ \divide\pgf@xc by\c@pgf@counta%
+ \pgf@x=\pgf@sys@tonumber{\pgf@xc}\pgf@xa%
+ \pgf@x=\pgf@sys@tonumber{\pgf@y}\pgf@x%
+ \fi%
+ \ifdim\pgf@ya<0pt%
+ \pgf@y=-\pgf@y%
+ \fi%
+ \fi\ignorespaces}
+
+
+
+
+
+% A point on a rectangle in a certain direction.
+%
+% #1 = a point pointing in some direction (length should be about 1pt,
+% but need not be exact)
+% #2 = upper right corner of a rectangle centered at the origin
+%
+% Returns the intersection of a line starting at the origin going in
+% the given direction and the rectangle's border.
+%
+% Example:
+%
+% \pgfpointborderrectangle{\pgfpointnormalised{\pgfpointxy{2}{1}}
+% {\pgfpoint{1cm}{2cm}}
+
+\def\pgfpointborderrectangle#1#2{%
+ \pgf@process{#2}%
+ \pgf@xb=\pgf@x%
+ \pgf@yb=\pgf@y%
+ \pgf@process{#1}%
+ % Ok, let's find out about the direction:
+ \pgf@xa=\pgf@x%
+ \pgf@ya=\pgf@y%
+ \ifnum\pgf@xa<0\relax% move into first quadrant
+ \pgf@x=-\pgf@x%
+ \fi%
+ \ifnum\pgf@ya<0\relax%
+ \pgf@y=-\pgf@y%
+ \fi%
+ \pgf@xc=.125\pgf@x%
+ \pgf@yc=.125\pgf@y%
+ \c@pgf@counta=\pgf@xc%
+ \c@pgf@countb=\pgf@yc%
+ \ifnum\c@pgf@countb<\c@pgf@counta%
+ \ifnum\c@pgf@counta<255\relax%
+ \pgf@y=\pgf@yb\relax%
+ \pgf@x=0pt\relax%
+ \else%
+ \pgf@xc=8192pt%
+ \divide\pgf@xc by\c@pgf@counta% \pgf@xc = 1/\pgf@x
+ \pgf@y=\pgf@sys@tonumber{\pgf@xc}\pgf@y%
+ \pgf@y=\pgf@sys@tonumber{\pgf@xb}\pgf@y%
+ \ifnum\pgf@y<\pgf@yb%
+ \pgf@x=\pgf@xb%
+ \else% rats, calculate intersection on upper side
+ \ifnum\c@pgf@countb<255\relax%
+ \pgf@x=\pgf@xb\relax%
+ \pgf@y=0pt\relax%
+ \else%
+ \pgf@yc=8192pt%
+ \divide\pgf@yc by\c@pgf@countb% \pgf@xc = 1/\pgf@x
+ \pgf@x=\pgf@sys@tonumber{\pgf@yc}\pgf@x%
+ \pgf@x=\pgf@sys@tonumber{\pgf@yb}\pgf@x%
+ \pgf@y=\pgf@yb%
+ \fi%
+ \fi%
+ \fi%
+ \else%
+ \ifnum\c@pgf@countb<255\relax%
+ \pgf@x=\pgf@xb\relax%
+ \pgf@y=0pt\relax%
+ \else%
+ \pgf@yc=8192pt%
+ \divide\pgf@yc by\c@pgf@countb% \pgf@xc = 1/\pgf@x
+ \pgf@x=\pgf@sys@tonumber{\pgf@yc}\pgf@x%
+ \pgf@x=\pgf@sys@tonumber{\pgf@yb}\pgf@x%
+ \ifnum\pgf@x<\pgf@xb%
+ \pgf@y=\pgf@yb%
+ \else%
+ \ifnum\c@pgf@counta<255\relax%
+ \pgf@y=\pgf@yb\relax%
+ \pgf@x=0pt\relax%
+ \else%
+ \pgf@xc=8192pt%
+ \divide\pgf@xc by\c@pgf@counta% \pgf@xc = 1/\pgf@x
+ \pgf@y=\pgf@sys@tonumber{\pgf@xc}\pgf@y%
+ \pgf@y=\pgf@sys@tonumber{\pgf@xb}\pgf@y%
+ \pgf@x=\pgf@xb%
+ \fi%
+ \fi%
+ \fi%
+ \fi%
+ \ifnum\pgf@xa<0\relax\pgf@x=-\pgf@x\fi%
+ \ifnum\pgf@ya<0\relax\pgf@y=-\pgf@y\fi%
+}
+
+
+
+
+% An approximation to a point on an ellipse in a certain
+% direction. Will be exact only if the ellipse is a circle.
+%
+% #1 = a point pointing in some direction
+% #2 = upper right corner of a bounding box for the ellipse
+%
+% Returns the intersection of a line starting at the origin going in
+% the given direction and the ellipses border.
+%
+% Example:
+%
+% \pgfpointborderellipse{\pgfpointnormalised{\pgfpointxy{2}{1}}
+% {\pgfpoint{1cm}{2cm}}
+
+\def\pgfpointborderellipse#1#2{%
+ \pgf@process{#2}%
+ \pgf@xa=\pgf@x%
+ \pgf@ya=\pgf@y%
+ \ifdim\pgf@xa=\pgf@ya% circle. that's easy!
+ \pgf@process{\pgfpointnormalised{#1}}%
+ \pgf@x=\pgf@sys@tonumber{\pgf@xa}\pgf@x%
+ \pgf@y=\pgf@sys@tonumber{\pgf@xa}\pgf@y%
+ \else%
+ \ifdim\pgf@xa<\pgf@ya%
+ % Ok, first, let's compute x/y:
+ \c@pgf@countb=\pgf@ya%
+ \divide\c@pgf@countb by65536\relax%
+ \divide\pgf@x by\c@pgf@countb%
+ \divide\pgf@y by\c@pgf@countb%
+ \pgf@xc=\pgf@x%
+ \pgf@yc=8192pt%
+ \pgf@y=.125\pgf@y%
+ \c@pgf@countb=\pgf@y%
+ \divide\pgf@yc by\c@pgf@countb%
+ \pgf@process{#1}%
+ \pgf@y=\pgf@sys@tonumber{\pgf@yc}\pgf@y%
+ \pgf@y=\pgf@sys@tonumber{\pgf@xc}\pgf@y%
+ \pgf@process{\pgfpointnormalised{}}%
+ \pgf@x=\pgf@sys@tonumber{\pgf@xa}\pgf@x%
+ \pgf@y=\pgf@sys@tonumber{\pgf@ya}\pgf@y%
+ \else%
+ % Ok, now let's compute y/x:
+ \c@pgf@countb=\pgf@xa%
+ \divide\c@pgf@countb by65536\relax%
+ \divide\pgf@x by\c@pgf@countb%
+ \divide\pgf@y by\c@pgf@countb%
+ \pgf@yc=\pgf@y%
+ \pgf@xc=8192pt%
+ \pgf@x=.125\pgf@x%
+ \c@pgf@countb=\pgf@x%
+ \divide\pgf@xc by\c@pgf@countb%
+ \pgf@process{#1}%
+ \pgf@x=\pgf@sys@tonumber{\pgf@yc}\pgf@x%
+ \pgf@x=\pgf@sys@tonumber{\pgf@xc}\pgf@x%
+ \pgf@process{\pgfpointnormalised{}}%
+ \pgf@x=\pgf@sys@tonumber{\pgf@xa}\pgf@x%
+ \pgf@y=\pgf@sys@tonumber{\pgf@ya}\pgf@y%
+ \fi%
+ \fi%
+}
+
+
+
+
+
+% Extract the x-coordinate of a point to a dimensions
+%
+% #1 = a TeX dimension
+% #2 = a point
+%
+% Example:
+%
+% \newdimen\mydim
+% \pgfextractx{\mydim}{\pgfpoint{2cm}{4pt}}
+% % \mydim is now 2cm
+
+\def\pgfextractx#1#2{%
+ \pgf@process{#2}%
+ #1=1.00374\pgf@x\relax}
+
+
+% Extract the y-coordinate of a point to a dimensions
+%
+% #1 = a TeX dimension
+% #2 = a point
+%
+% Example:
+%
+% \newdimen\mydim
+% \pgfextracty{\mydim}{\pgfpoint{2cm}{4pt}}
+% % \mydim is now 4pt
+
+\def\pgfextracty#1#2{%
+ \pgf@process{#2}%
+ #1=1.00374\pgf@y\relax}
+
+
+\endinput