| Current File : //usr/share/texlive/texmf-dist/tex/generic/pgf/math/pgfmathcalc.code.tex |
% Copyright 2019 by Mark Wibrow
%
% 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.
% This file loads all the parsing, functions and operator stuff
%
% Version 1.414213 29/9/2007
\input pgfmathutil.code.tex
\input pgfmathparser.code.tex
\input pgfmathfunctions.code.tex
%\input pgfmathbase.code.tex
% \pgfmathsetlength, \pgfmathaddtolength
%
% #1 = dimension register
% #2 = expression
%
% Description:
%
% These functions work similar to \setlength and \addtolength. Only,
% they allow #2 to contain an expression, which is evaluated before
% assignment. Furthermore, the font is setup before the assignment is
% done, so that dimensions like 1em are evaluated correctly.
%
% If #2 starts with "+", then a simple assignment is done (but the
% font is still setup). This is orders of magnitude faster than a
% parsed assignment.
\def\pgfmathsetlength#1#2{%
\expandafter\pgfmath@onquick#2\pgfmath@%
{%
% Ok, quick version:
\begingroup%
\pgfmath@selectfont%
#1#2\unskip%
\expandafter\endgroup%
\expandafter#1\the#1\relax%
}%
{%
\pgfmathparse{#2}%
\ifpgfmathmathunitsdeclared%
#1\pgfmathresult mu\relax%
\else%
#1\pgfmathresult pt\relax%
\fi%
}%
\ignorespaces%
}
% \pgfmathaddtolength
%
% Add to #1 the result of evaluating #2.
%
% #1 - a dimension register
% #2 - an expression
%
\def\pgfmathaddtolength#1#2{%
\expandafter\pgfmath@onquick#2\pgfmath@%
{%
\begingroup%
\pgfmath@selectfont%
\advance#1#2\unskip%
\expandafter%
\endgroup%
\expandafter#1\the#1\relax%
}%
{%
\pgfmathparse{#2}%
\ifpgfmathmathunitsdeclared%
\advance#1\pgfmathresult mu\relax%
\else%
\advance#1\pgfmathresult pt\relax%
\fi%
}%
\ignorespaces%
}
% \pgfmathsetcount
%
% Assign #1 the truncated evaluation of #2.
%
% #1 - a count register
% #2 - an expression
%
\def\pgfmathsetcount#1#2{%
\expandafter\pgfmath@onquick#2\pgfmath@%
{%
\afterassignment\pgfmath@gobbletilpgfmath@%
#1#2\relax\pgfmath@%
}%
{%
\pgfmathparse{#2}%
\afterassignment\pgfmath@gobbletilpgfmath@%
#1\pgfmathresult\relax\pgfmath@%
}%
\ignorespaces%
}
% \pgfmathaddtocount
%
% Add to #1 the truncated evaluation of #2.
%
% #1 - a count register
% #2 - an expression
%
\def\pgfmathaddtocount#1#2{%
\expandafter\pgfmath@onquick#2\pgfmath@%
{%
\edef\pgfmath@addtocounttemp{\the#1}%
\afterassignment\pgfmath@gobbletilpgfmath@%
#1#2\relax\pgfmath@%
\advance#1\pgfmath@addtocounttemp\relax%
}%
{%
\edef\pgfmath@addtocounttemp{\the#1}%
\pgfmathparse{#2}%
\afterassignment\pgfmath@gobbletilpgfmath@%
#1\pgfmathresult\relax\pgfmath@%
\advance#1\pgfmath@addtocounttemp\relax%
}%
\ignorespaces%
}
% \pgfmathnewcounter
%
% LaTeX style counter which also works in plain TeX. Defines
% \c@<name> as a count register and also defines \the<name>.
%
% #1 the name of the counter.
%
% Example:
%
% \pgfmathnewcounter{counter}
% \pgfmathsetcounter{counter}{12}
% \thecounter (same as \the\c@counter)
%
\def\pgfmathnewcounter#1{%
\expandafter\ifx\csname c@#1\endcsname\relax%
\def\pgfmath@marshal{\csname newcount\endcsname}% Ha! Who cares about \outer?
\expandafter\pgfmath@marshal\csname c@#1\endcsname%
\expandafter\def\csname the#1\endcsname{\expandafter\the\csname c@#1\endcsname}%
\fi%
}
% \pgfmathsetcounter
%
% Set the counter #1 to the evaluation of #2.
%
% #1 - a counter name
% #2 - an expression
%
\def\pgfmathsetcounter#1#2{%
\expandafter\pgfmathsetcount\csname c@#1\endcsname{#2}%
}
% \pgfmathaddtocounter
%
% Add the counter #1 to the evaluation of #2.
%
% #1 - a counter name
% #2 - an expression
%
\def\pgfmathaddtocounter#1#2{%
\expandafter\pgfmathaddtocount\csname c@#1\endcsname{#2}%
}
% \pgfmathmakecounterglobal
%
% Make the current value of a counter globally defined.
%
% #1 - a (valid) counter name.
%
\def\pgfmath@pgftext{pgf}
\def\pgfmath@tikztext{tikz}
\def\pgfmathmakecounterglobal#1{%
\pgfmath@ifundefined{c@#1}{}{%
\expandafter\pgfmath@in@\expandafter{\pgfmath@pgftext}{#1}%
\ifpgfmath@in@%
\else%
\expandafter\pgfmath@in@\expandafter{\pgfmath@tikztext}{#1}%
\ifpgfmath@in@%
\else%
\expandafter\global\csname c@#1\endcsname\csname c@#1\endcsname\relax%
\fi%
\fi%
}%
}
% \pgfmathsetmacro
%
% \edef#1 as the result of evaluating #2.
%
% #1 - a macro
% #2 - an expression
%
\def\pgfmathsetmacro#1#2{%
\begingroup%
\pgfmathparse{#2}%
\let#1=\pgfmathresult
\pgfmath@smuggleone{#1}%
\endgroup%
}
% \pgfmathsetlengthmacro
%
% \edef#1 as the result of evaluating #2 with pt.
%
% #1 - a macro
% #2 - an expression
%
\def\pgfmathsetlengthmacro#1#2{%
\begingroup%
\pgfmathsetlength\pgfmath@x{#2}%
\edef#1{\the\pgfmath@x}%
\pgfmath@smuggleone{#1}%
\endgroup%
}
% \pgfmathtruncatemacro
%
% \edef#1 as the truncated result of evaluating #2.
%
% #1 - a macro
% #2 - an expression
%
\def\pgfmathtruncatemacro#1#2{%
\begingroup%
\pgfmathsetcount\c@pgfmath@counta{#2}%
\edef#1{\the\c@pgfmath@counta}%
\pgfmath@smuggleone{#1}%
\endgroup%
}
% Check whether a given parameter starts with quick.
%
% The command should be followed by nonempty text, ending with
% \pgfmath@ as a stop-token. Then should follow
%
% #1 - code to execute if text starts with +
% #2 - code to execute if text does not
%
% Example:
%
% \pgfmath@onquick+0pt\pgfmath@{is quick}{is slow}
\def\pgfmath@onquick{%
\futurelet\pgfmath@next%
\pgfmath@@onquick}
\def\pgfmath@@onquick#1\pgfmath@{%
\ifx\pgfmath@next+%
\let\pgfmath@next=\pgfmath@firstoftwo%
\else%
\let\pgfmath@next=\pgfmath@secondoftwo%
\fi%
\pgfmath@next%
}
% *** The following commands DO NOT WORK without the rest of PGF ***
%
% (a dumping ground for stuff that doesn't really belong anywhere else)
% \pgfmathanglebetweenpoints
%
% Define \pgfmathresult as the angle between points #1 and #2
% Should get the quadrants right as well.
%
\def\pgfmathanglebetweenpoints#1#2{%
\begingroup%
\pgf@process{\pgfpointdiff{#1}{#2}}%
\edef\pgf@marshall{\expandafter\noexpand\csname pgfmathatan2@\endcsname{\expandafter\Pgf@geT\the\pgf@y}{\expandafter\Pgf@geT\the\pgf@x}}%
\pgf@marshall%
\ifdim\pgfmathresult pt<0pt%
\pgfmathparse{\pgfmathresult+360}%
\fi%
\expandafter%
\endgroup\expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult}%
}
%
% \pgfmathrotatepointaround
%
% Rotate point #1 about point #2 by #3 degrees.
%
\def\pgfmathrotatepointaround#1#2#3{%
\pgf@process{%
\pgf@process{#1}%
\pgf@xc=\pgf@x%
\pgf@yc=\pgf@y%
\pgf@process{#2}%
\pgf@xa\pgf@x%
\pgf@ya\pgf@y%
\pgf@xb\pgf@x%
\pgf@yb\pgf@y%
\pgf@x=\pgf@xc%
\pgf@y=\pgf@yc%
\advance\pgf@x-\pgf@xa%
\advance\pgf@y-\pgf@ya%
\pgfmathsetmacro\angle{#3}%
\pgfmathsin@{\angle}%
\let\sineangle\pgfmathresult%
\pgfmathcos@{\angle}%
\let\cosineangle\pgfmathresult%
\pgf@xa\cosineangle\pgf@x%
\advance\pgf@xa-\sineangle\pgf@y%
\pgf@ya\sineangle\pgf@x%
\advance\pgf@ya\cosineangle\pgf@y%
\pgf@x\pgf@xb%
\pgf@y\pgf@yb%
\advance\pgf@x\pgf@xa%
\advance\pgf@y\pgf@ya%
}%
}
% \pgfmathanglebetweenlines
%
% Calculate the clockwise angle between a line from point #1
% to point #2 and a line from #3 to point #4.
%
\def\pgfmathanglebetweenlines#1#2#3#4{%
\begingroup%
\pgfmathanglebetweenpoints{#1}{#2}%
\let\firstangle\pgfmathresult%
\pgfmathanglebetweenpoints{#3}{#4}%
\let\secondangle\pgfmathresult%
\ifdim\firstangle pt>\secondangle pt\relax%
\pgfmathadd@{\secondangle}{360}%
\let\secondangle\pgfmathresult%
\fi%
\pgfmathsubtract@{\secondangle}{\firstangle}%
\pgfmath@smuggleone\pgfmathresult%
\endgroup%
}
% \pgfmathpointreflectalongaxis
%
% Reflects point #1 around an axis centered on #2 at an angle #3.
%
\def\pgfmathreflectpointalongaxis#1#2#3{%
\pgf@process{%
\pgfmathanglebetweenpoints{#2}{#1}%
\pgfmath@tempdima\pgfmathresult pt\relax%
\pgfmathparse{#3}%
\advance\pgfmath@tempdima-\pgfmathresult pt\relax%
\pgfmath@tempdima-2.0\pgfmath@tempdima%
\pgfmathrotatepointaround{#1}{#2}{\pgfmath@tonumber{\pgfmath@tempdima}}%
}%
}
% \pgfmathpointintersectionoflineandarc
%
% A bit experimental at the moment:
%
% Locates the point where a line crosses an eliptical arc. If the line
% does not cross the arc, a meaningless point will result.
%
% #1 the point of the line on the "convex" side of the arc.
% #2 the point of the line on the "concave" side of the arc.
% #3 the center of the eliptical arc.
% #4 start angle of the arc.
% #5 end angle of the arc.
% #6 radii of the arc.
%
\def\pgfmathpointintersectionoflineandarc#1#2#3#4#5#6{%
\pgf@process{%
%
% Get the required angle.
%
\pgfmathanglebetweenpoints{#2}{#1}%
\let\x\pgfmathresult%
%
% Get the radii of the arc.
%
\pgfmath@in@{and }{#6}%
\ifpgfmath@in@%
\pgf@polar@#6\@@%
\else%
\pgf@polar@#6 and #6\@@%
\fi%
\edef\xarcradius{\the\pgf@x}%
\edef\yarcradius{\the\pgf@y}%
%
% Get the start and end angles of the arc...
%
\pgfmathsetmacro\s{#4}%
\pgfmathsetmacro\e{#5}%
%
% ...and also with rounding.
%
\pgfmathmod@{\s}{360}%
\ifdim\pgfmathresult pt<0pt\relax%
\pgfmathadd@{\pgfmathresult}{360}%
\fi%
\let\ss\pgfmathresult%
\pgfmathmod@{\e}{360}%
\ifdim\pgfmathresult pt<0pt\relax%
\pgfmathadd@{\pgfmathresult}{360}%
\fi%
\let\ee\pgfmathresult%
%
% Hackery for when arc straddles zero.
%
\ifdim\ee pt<\ss pt\relax%
\pgfmathadd@{\x}{180}%
\pgfmathmod@{\pgfmathresult}{360}%
\let\x\pgfmathresult%
\fi%
\def\m{360}% Measure of nearness.
\pgfmathadd@{\s}{\e}%
\pgfmathdivide@{\pgfmathresult}{2}%
\let\n\pgfmathresult% The best estimate (default to middle of arc).
\pgfmathloop%
\pgfmathadd@{\s}{\e}%
\pgfmathdivide@{\pgfmathresult}{2}%
\let\p\pgfmathresult%
\ifdim\p pt=\s pt\relax%
\else%
\pgfmathanglebetweenpoints{#2}{%
\pgfpointadd{#3}{%
\pgf@x\xarcradius\relax%
\pgfmathcos@{\p}%
\pgf@x\pgfmathresult\pgf@x%
\pgf@y\yarcradius\relax%
\pgfmathsin@{\p}%
\pgf@y\pgfmathresult\pgf@y%
}%
}%
%
% Hackery for when arc straddles zero.
%
\ifdim\ee pt<\ss pt\relax%
\pgfmathadd@{\pgfmathresult}{180}%
\pgfmathmod@{\pgfmathresult}{360}%
\fi%
\let\q\pgfmathresult%
%
% More hackery...
%
\ifdim\x pt>335pt\relax%
\ifdim\q pt<45pt\relax%
\pgfmathadd@{\q}{360}%
\let\q\pgfmathresult%
\fi%
\fi%
\ifdim\x pt=\q pt% Found it!
\pgfmathbreakloop% Breaks after current iteration is complete.
\else
\ifdim\x pt<\q pt\relax%
\let\e\p%
\else%
\let\s\p%
\fi%
\fi%
\pgfmathsubtract@{\x}{\q}%
\pgfmathabs@{\pgfmathresult}%
%
% Save the estimate if it is better than any previous estimate.
%
\ifdim\pgfmathresult pt<\m pt\relax%
\let\m\pgfmathresult%
\let\n\p%
\fi%
\repeatpgfmathloop%
\pgfpointadd{#3}{\pgfpointpolar{\n}{\xarcradius and \yarcradius}}%
}%
}
% \pgfmathangleonellipse
%
% Find the angle corresponding to a point on the border of an ellispe.
%
% #1 - the point on the border.
% #2 - the radii of the ellipse.
%
\def\pgfmathangleonellipse#1#2{%
\begingroup%
\pgfmath@in@{and }{#2}%
\ifpgfmath@in@%
\pgf@polar@#2\@@%
\else%
\pgf@polar@#2 and #2\@@%
\fi%
\pgf@xa\pgf@x%
\pgf@ya\pgf@y%
\pgf@process{#1}%
\ifdim\pgf@x=0pt\relax%
\pgfutil@tempdima1pt\relax%
\else%
\pgfutil@tempdima\pgf@x%
\pgfmathdivide@{\pgfmath@tonumber{\pgf@xa}}{\pgfmath@tonumber{\pgfutil@tempdima}}%
\pgfutil@tempdima\pgfmathresult pt\relax%
\fi%
\ifdim\pgf@y=0pt\relax%
\pgfutil@tempdima1pt\relax%
\else%
\pgfmathdivide@{\pgfmath@tonumber{\pgf@y}}{\pgfmath@tonumber{\pgf@ya}}%
\pgfutil@tempdima\pgfmathresult\pgfutil@tempdima%
\pgfmathatan@{\pgfmath@tonumber{\pgfutil@tempdima}}%
\fi%
%
\pgfutil@tempdima\pgfmathresult pt\relax%
\ifdim\pgfutil@tempdima<0pt\relax%
\advance\pgfutil@tempdima360pt\relax%
\fi%
\ifdim\pgf@x<0pt\relax%
\ifdim\pgf@y=0pt\relax%
\pgfutil@tempdima180pt\relax%
\else%
\ifdim\pgf@y<0pt\relax%
\advance\pgfutil@tempdima180pt\relax%
\else%
\advance\pgfutil@tempdima-180pt\relax%
\fi%
\fi%
\else%
\ifdim\pgf@x=0pt\relax%
\ifdim\pgf@y<0pt\relax%
\pgfutil@tempdima270pt\relax%
\else%
\pgfutil@tempdima90pt\relax%
\fi%
\else%
\ifdim\pgf@y=0pt\relax%
\pgfutil@tempdima0pt\relax%
\fi%
\fi%
\fi%
\pgfmath@returnone\pgfutil@tempdima%
\endgroup%
}
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