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diff --git a/Master/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepoints.code.tex b/Master/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepoints.code.tex deleted file mode 100644 index 0edcd6d7b2c..00000000000 --- a/Master/texmf-dist/tex/generic/pgf/basiclayer/pgfcorepoints.code.tex +++ /dev/null @@ -1,999 +0,0 @@ -% 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/pgfcorepoints.code.tex,v 1.9 2007/04/19 11:57:08 tantau Exp $ - -\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}} - - - - -% Return a point -% -% #1 = x-coordinate of the point -% #2 = y-coordinate of the point -% -% x = #1 -% y = #2 -% -% Example: -% -% \pgfpathmoveto{\pgfpoint{2pt+3cm}{3cm}} - -\def\pgfpoint#1#2{% - \pgfmathsetlength\pgf@x{#1}% - \pgfmathsetlength\pgf@y{#2}\ignorespaces} - - -% Quickly a point -% -% #1 = x-coordinate of the point (no calculations done) -% #2 = y-coordinate of the point (no calculations done) -% -% x = #1 -% y = #2 -% -% Example: -% -% \pgfpathmoveto{\pgfqpoint{2pt}{3cm}} - -\def\pgfqpoint#1#2{\pgf@x=#1\pgf@y=#2} - - - -% Return the origin. -% -% x = 0 -% y = 0 -% -% Example: -% -% \pgfpathmoveto{\pgfpointorigin} - -\def\pgfpointorigin{\pgf@x=0pt\pgf@y=\pgf@x\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)) -% xa = #1*(normalise(end-start)) -% ya = #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 - \pgfmathsetlength\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{% - \pgfmathparse{#1}% - \let\pgf@time@s=\pgfmathresult% - \pgf@x=\pgfmathresult pt% - \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 - - - -% A polar coordinate -% -% #1 = a degree -% #2 = a radius -- either a dimension or two dimensions separated by -% " and ". -% -% x = (first dimension in #2) * cos(#1) -% y = (second dimension in #2) * sin(#2) -% -% Example: -% -% \pgfpathmoveto{\pgfpointpolar{30}{1cm}} -% \pgfpathlineto{\pgfpointpolar{30}{1cm and 2cm}} - -\def\pgfpointpolar#1#2{% - \pgfutil@in@{and }{#2}% - \ifpgfutil@in@% - \pgf@polar@#2\@@% - \else% - \pgf@polar@#2 and #2\@@% - \fi% - \pgfmathparse{#1}% - \let\pgfpoint@angle=\pgfmathresult% - \pgfmathcos@{\pgfpoint@angle}% - \pgf@x=\pgfmathresult\pgf@x% - \pgfmathsin@{\pgfpoint@angle}% - \pgf@y=\pgfmathresult\pgf@y% -} - -\def\pgf@polar@#1and #2\@@{% - \pgfmathsetlength{\pgf@y}{#2}% - \pgfmathsetlength{\pgf@x}{#1}% -} - -% Quick version of the polar coordinate method - -\def\pgfqpointpolar#1#2{% - \pgf@x=#2% - \pgf@y=\pgf@x% - \pgfmathcos@{#1}% - \pgf@x=\pgfmathresult\pgf@x% - \pgfmathsin@{#1}% - \pgf@y=\pgfmathresult\pgf@y\relax% -} - - - - -% A polar coordinate in the xy plane. -% -% #1 = a degree -% #2 = a radius given as a number or two radi -% -% result = (first dim in #2) * x-vector * cos(#1) + -% (second dim in #2) * y-vector * sin(#1) -% -% Example: -% -% \pgfpathmoveto{\pgfpointpolarxy{30}{2}} - -\def\pgfpointpolarxy#1#2{% - \pgfutil@in@{and }{#2}% - \ifpgfutil@in@% - \pgf@polarxy@#2\@@% - \else% - \pgf@polarxy@#2and #2\@@% - \fi% - \pgfmathparse{#1}% - \let\pgfpoint@angle=\pgfmathresult% - \pgfmathcos@{\pgfpoint@angle}% - \pgf@xa=\pgfmathresult\pgf@xa% - \pgfmathsin@{\pgfpoint@angle}% - \pgf@ya=\pgfmathresult\pgf@ya% - \pgf@x=\pgf@sys@tonumber{\pgf@xa}\pgf@xx% - \advance\pgf@x by \pgf@sys@tonumber{\pgf@ya}\pgf@yx% - \pgf@y=\pgf@sys@tonumber{\pgf@xa}\pgf@xy% - \advance\pgf@y by \pgf@sys@tonumber{\pgf@ya}\pgf@yy} - -\def\pgf@polarxy@#1and #2\@@{% - \pgfmathsetlength{\pgf@xa}{#1}% - \pgfmathsetlength{\pgf@ya}{#2}% -} - - - -% A cylindrical coordinate. -% -% #1 = a degree -% #2 = a radius given as a number -% #3 = a height given as a number -% -% result = #2*(x-vector * cos(#1) + y-vector * sin(#1)) + #3*z-vector -% -% Example: -% -% \pgfpathmoveto{\pgfpointcylindrical{30}{2}{1}} - -\def\pgfpointcylindrical#1#2#3{% - \pgfpointpolarxy{#1}{#2}% - \pgfmathparse{#3}% - \advance\pgf@x by \pgfmathresult\pgf@zx% - \advance\pgf@y by \pgfmathresult\pgf@zy} - - -% A spherical coordinate. -% -% #1 = a longitude -% #2 = a latitude -% #3 = a radius -% -% result = #3*(cos(#2)*(x-vector * cos(#1) + y-vector * sin(#1)) + sin(#2)*z-vector) -% -% Example: -% -% \pgfpathmoveto{\pgfpointspherical{30}{30}{2}} - -\def\pgfpointspherical#1#2#3{% - \pgfmathparse{#1}% - \let\pgfpoint@angle=\pgfmathresult% - \pgfmathsin@{\pgfpoint@angle}% - \pgf@xb=\pgfmathresult\pgf@xx% - \pgf@yb=\pgfmathresult\pgf@xy% - \pgfmathcos@{\pgfpoint@angle}% - \advance\pgf@xb by \pgfmathresult\pgf@yx% - \advance\pgf@yb by \pgfmathresult\pgf@yy% - % - \pgfmathparse{#2}% - \let\pgfpoint@angle=\pgfmathresult% - \pgfmathcos@{\pgfpoint@angle}% - \pgf@xc=\pgfmathresult\pgf@xb% - \pgf@yc=\pgfmathresult\pgf@yb% - \pgfmathsin@{\pgfpoint@angle}% - \advance\pgf@xc by \pgfmathresult\pgf@zx% - \advance\pgf@yc by \pgfmathresult\pgf@zy% - \pgfmathparse{#3}% - \pgf@x=\pgfmathresult\pgf@xc% - \pgf@y=\pgfmathresult\pgf@yc\relax% -} - - -% 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{% - \pgfmathparse{#1}% - \let\pgftemp@x=\pgfmathresult% - \pgfmathparse{#2}% - \let\pgftemp@y=\pgfmathresult% - \pgf@x=\pgftemp@x\pgf@xx% - \advance\pgf@x by \pgftemp@y\pgf@yx% - \pgf@y=\pgftemp@x\pgf@xy% - \advance\pgf@y by \pgftemp@y\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{% - \pgfmathparse{#1}% - \let\pgftemp@x=\pgfmathresult% - \pgfmathparse{#2}% - \let\pgftemp@y=\pgfmathresult% - \pgfmathparse{#3}% - \let\pgftemp@z=\pgfmathresult% - \pgf@x=\pgftemp@x\pgf@xx% - \advance\pgf@x by \pgftemp@y\pgf@yx% - \advance\pgf@x by \pgftemp@z\pgf@zx% - \pgf@y=\pgftemp@x\pgf@xy% - \advance\pgf@y by \pgftemp@y\pgf@yy% - \advance\pgf@y by \pgftemp@z\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@x=\csname pgf@cosfrac\the\c@pgf@countb\endcsname pt% - \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@y=\csname pgf@cosfrac\the\c@pgf@countb\endcsname pt% - \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=\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=\pgf@y\relax} - - - -\def\pgf@def#1#2#3{\expandafter\def\csname pgf@#1#2\endcsname{#3}} -\pgf@def{cosfrac}{0}{1} -\pgf@def{cosfrac}{1}{0.99995} \pgf@def{cosfrac}{2}{0.9998} -\pgf@def{cosfrac}{3}{0.99955} \pgf@def{cosfrac}{4}{0.999201} -\pgf@def{cosfrac}{5}{0.998752} \pgf@def{cosfrac}{6}{0.998205} -\pgf@def{cosfrac}{7}{0.997559} \pgf@def{cosfrac}{8}{0.996815} -\pgf@def{cosfrac}{9}{0.995974} \pgf@def{cosfrac}{10}{0.995037} -\pgf@def{cosfrac}{11}{0.994004} \pgf@def{cosfrac}{12}{0.992877} -\pgf@def{cosfrac}{13}{0.991656} \pgf@def{cosfrac}{14}{0.990342} -\pgf@def{cosfrac}{15}{0.988936} \pgf@def{cosfrac}{16}{0.987441} -\pgf@def{cosfrac}{17}{0.985856} \pgf@def{cosfrac}{18}{0.984183} -\pgf@def{cosfrac}{19}{0.982424} \pgf@def{cosfrac}{20}{0.980581} -\pgf@def{cosfrac}{21}{0.978653} \pgf@def{cosfrac}{22}{0.976644} -\pgf@def{cosfrac}{23}{0.974555} \pgf@def{cosfrac}{24}{0.972387} -\pgf@def{cosfrac}{25}{0.970143} \pgf@def{cosfrac}{26}{0.967823} -\pgf@def{cosfrac}{27}{0.965429} \pgf@def{cosfrac}{28}{0.962964} -\pgf@def{cosfrac}{29}{0.960429} \pgf@def{cosfrac}{30}{0.957826} -\pgf@def{cosfrac}{31}{0.955157} \pgf@def{cosfrac}{32}{0.952424} -\pgf@def{cosfrac}{33}{0.949629} \pgf@def{cosfrac}{34}{0.946773} -\pgf@def{cosfrac}{35}{0.943858} \pgf@def{cosfrac}{36}{0.940887} -\pgf@def{cosfrac}{37}{0.937862} \pgf@def{cosfrac}{38}{0.934784} -\pgf@def{cosfrac}{39}{0.931655} \pgf@def{cosfrac}{40}{0.928477} -\pgf@def{cosfrac}{41}{0.925252} \pgf@def{cosfrac}{42}{0.921982} -\pgf@def{cosfrac}{43}{0.918669} \pgf@def{cosfrac}{44}{0.915315} -\pgf@def{cosfrac}{45}{0.911922} \pgf@def{cosfrac}{46}{0.90849} -\pgf@def{cosfrac}{47}{0.905024} \pgf@def{cosfrac}{48}{0.901523} -\pgf@def{cosfrac}{49}{0.89799} \pgf@def{cosfrac}{50}{0.894427} -\pgf@def{cosfrac}{51}{0.890835} \pgf@def{cosfrac}{52}{0.887217} -\pgf@def{cosfrac}{53}{0.883573} \pgf@def{cosfrac}{54}{0.879905} -\pgf@def{cosfrac}{55}{0.876216} \pgf@def{cosfrac}{56}{0.872506} -\pgf@def{cosfrac}{57}{0.868777} \pgf@def{cosfrac}{58}{0.865031} -\pgf@def{cosfrac}{59}{0.861269} \pgf@def{cosfrac}{60}{0.857493} -\pgf@def{cosfrac}{61}{0.853704} \pgf@def{cosfrac}{62}{0.849903} -\pgf@def{cosfrac}{63}{0.846092} \pgf@def{cosfrac}{64}{0.842271} -\pgf@def{cosfrac}{65}{0.838444} \pgf@def{cosfrac}{66}{0.834609} -\pgf@def{cosfrac}{67}{0.83077} \pgf@def{cosfrac}{68}{0.826927} -\pgf@def{cosfrac}{69}{0.82308} \pgf@def{cosfrac}{70}{0.819232} -\pgf@def{cosfrac}{71}{0.815383} \pgf@def{cosfrac}{72}{0.811534} -\pgf@def{cosfrac}{73}{0.807687} \pgf@def{cosfrac}{74}{0.803842} -\pgf@def{cosfrac}{75}{0.8} \pgf@def{cosfrac}{76}{0.796162} -\pgf@def{cosfrac}{77}{0.792329} \pgf@def{cosfrac}{78}{0.788502} -\pgf@def{cosfrac}{79}{0.784682} \pgf@def{cosfrac}{80}{0.780869} -\pgf@def{cosfrac}{81}{0.777064} \pgf@def{cosfrac}{82}{0.773268} -\pgf@def{cosfrac}{83}{0.769481} \pgf@def{cosfrac}{84}{0.765705} -\pgf@def{cosfrac}{85}{0.761939} \pgf@def{cosfrac}{86}{0.758185} -\pgf@def{cosfrac}{87}{0.754443} \pgf@def{cosfrac}{88}{0.750714} -\pgf@def{cosfrac}{89}{0.746997} \pgf@def{cosfrac}{90}{0.743294} -\pgf@def{cosfrac}{91}{0.739605} \pgf@def{cosfrac}{92}{0.735931} -\pgf@def{cosfrac}{93}{0.732272} \pgf@def{cosfrac}{94}{0.728628} -\pgf@def{cosfrac}{95}{0.724999} \pgf@def{cosfrac}{96}{0.721387} -\pgf@def{cosfrac}{97}{0.717792} \pgf@def{cosfrac}{98}{0.714213} -\pgf@def{cosfrac}{99}{0.710651} \pgf@def{cosfrac}{100}{0.707107} - - - -\endinput |