% 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{tikzlibrarycalc.code.tex}

%
%
% Part I: The let path command
%
%


%
% Syntax: let \p{name1} = (coord), \p{name2} = (coord), ... in ...
%
% Currently (this may get more fancy in the future), the (coord)s are
% evaluated one by one. If the first evaluates to, say, (10pt,20pt),
% the macro \p{name1} is set to "10pt,20pt" (without parentheses), the
% macro \x{name1} is set to "10pt" and the macro \y{name1} is set to
% "20pt".
%
% If you use a number for {name}, you need no parentheses, so you
% could write:
%
% \draw let
%         \p1 = (1,1),
%         \p2 = ($ 2.5*(3,2) $)
%       in
%         (\x1,\x2) -- (\y1,\y2);

\def\tikz@let@command et{%
  \let\p=\tikz@cc@dop%
  \let\x=\tikz@cc@dox%
  \let\y=\tikz@cc@doy%
  \let\n=\tikz@cc@don%
  \pgfutil@ifnextchar i{\tikz@cc@stop@let}{\tikz@cc@handle@line}%
}%
\def\tikz@cc@handle@line{%
  \pgfutil@ifnextchar\p{%
    \tikz@cc@handle@coor%
  }{%
    \pgfutil@ifnextchar\n{%
      \tikz@cc@handle@num%
    }{%
      \pgfutil@ifnextchar i{%
        \tikz@cc@stop@let
      }{%
        \tikzerror{``\string\p'' or ``\string\n'' expected}%
      }%
    }%
  }%
}%
\def\tikz@cc@handle@num\n#1#2=#3{%
  \pgfmathparse{#3}%
  \expandafter\edef\csname tikz@cc@n@#1\endcsname{\pgfmathresult\ifpgfmathunitsdeclared pt\fi}
  \pgfutil@ifnextchar,{\tikz@cc@handle@nextline}{\tikz@cc@stop@let}%
}%
\def\tikz@cc@handle@coor\p#1#2={%
  \def\tikz@cc@coord@name{#1}%
  \tikz@scan@one@point\tikz@cc@dolet%
}%
\def\tikz@cc@dolet#1{%
  \pgf@process{#1}%
  \expandafter\edef\csname tikz@cc@p@\tikz@cc@coord@name\endcsname{\the\pgf@x,\the\pgf@y}%
  \expandafter\edef\csname tikz@cc@x@\tikz@cc@coord@name\endcsname{\the\pgf@x}%
  \expandafter\edef\csname tikz@cc@y@\tikz@cc@coord@name\endcsname{\the\pgf@y}%
  \pgfutil@ifnextchar,{\tikz@cc@handle@nextline}{\tikz@cc@stop@let}%
}%
\def\tikz@cc@handle@nextline,{%
  \tikz@cc@handle@line%
}%
\def\tikz@cc@stop@let in{%
  \tikz@scan@next@command%
}%

\def\tikz@cc@dop#1{\csname tikz@cc@p@#1\endcsname}%
\def\tikz@cc@dox#1{\csname tikz@cc@x@#1\endcsname}%
\def\tikz@cc@doy#1{\csname tikz@cc@y@#1\endcsname}%
\def\tikz@cc@don#1{\csname tikz@cc@n@#1\endcsname}%



%
%
% Part II: The ($...$) parser
%
%

\def\tikz@parse@calculator#1(${%$
  \def\tikz@cc@command{#1}%
  \begingroup%
    %
    % Parse main computation. It's a series of optional factors in front
    % of coordinates.
    %
    \pgf@xa=0pt% We accumulate the result in here.
    \pgf@ya=0pt%
    \tikz@cc@parse+%
}%

\def\tikz@cc@parse{%
  \pgfutil@ifnextchar${%$
    % Ok, we found the end...
    \tikz@cc@end%
  }
  {\pgfutil@ifnextchar+{%
      % Ok, we found a coordinate...
      \tikz@cc@add%
    }{%
      \pgfutil@ifnextchar-{%
        \tikz@cc@sub%
      }{%
        \tikzerror{+ or - expected}%
        \tikz@cc@end$%$
      }%
    }%
  }%
}%

%
% The end is reached with $
%
\def\tikz@cc@end$#1){%$
    \xdef\tikz@marshal{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}%
  \endgroup%
  \expandafter\tikz@cc@command\expandafter{\tikz@marshal}%
}%


%
% Another coordinate with +/-, possibly with a factor
%
\def\tikz@cc@add+{%
  \def\tikz@cc@factor{1}%
  \tikz@cc@factororcoordinate%
}%
\def\tikz@cc@sub-{%
  \def\tikz@cc@factor{-1}%
  \tikz@cc@factororcoordinate%
}%

%
% Check for a factor: If we see a (, its a coordinate...
%
\def\tikz@cc@factororcoordinate{%
  \pgfutil@ifnextchar({%)
    % Ok, found coordinate
    \tikz@cc@coordinate%
  }{%
    \tikz@cc@parse@factor%
  }%
}%

%
% ... otherwise it's a factor. It ends at ...*(
%
\def\tikz@cc@parse@factor#1*({%
  \pgfmathparse{#1*\tikz@cc@factor}%
  \let\tikz@cc@factor=\pgfmathresult%
  \tikz@cc@coordinate(%)
}%

\def\tikz@cc@coordinate{%
  \tikz@scan@absolute\tikz@cc@after@coordinate%
}%
\def\tikz@cc@after@coordinate#1{%
  \pgf@process{#1}%
  \pgf@xb=\pgf@x%
  \pgf@yb=\pgf@y%
  \tikz@cc@mid@checks%
}%


%
% A coordinate can be followed by !...!(...)
%

\def\tikz@cc@mid@checks{%
  \ifnum\the\catcode`\!=\active\relax
    \expandafter\tikz@cc@mid@checks@active
  \else
    \expandafter\tikz@cc@mid@checks@nonactive
  \fi
}%

\def\tikz@cc@mid@checks@nonactive{%
  \pgfutil@ifnextchar!{%
    \tikz@cc@mid@nonactive%
  }{%
    \advance\pgf@xa by\tikz@cc@factor\pgf@xb
    \advance\pgf@ya by\tikz@cc@factor\pgf@yb
    \tikz@cc@parse%
  }%
}%

\def\tikz@cc@mid@nonactive!{%
  \pgfutil@ifnextchar({%
    \tikz@scan@one@point\tikz@cc@project%
  }{%
    \tikz@cc@mid@num@nonactive%
  }%
}%

\begingroup
  \catcode`\!=\active
  \gdef\tikz@cc@mid@checks@active{%
    \pgfutil@ifnextchar!{%
      \tikz@cc@mid@active%
    }{%
      \advance\pgf@xa by\tikz@cc@factor\pgf@xb
      \advance\pgf@ya by\tikz@cc@factor\pgf@yb
      \tikz@cc@parse%
    }%
  }%

  \gdef\tikz@cc@mid@active!{%
    \pgfutil@ifnextchar({%
      \tikz@scan@one@point\tikz@cc@project%
    }{%
      \tikz@cc@mid@num@active%
    }%
  }%
\endgroup

%
% Partway case: (coord a)!number!(coord b)
%
% Returns the position that is at <number> fraction on the way from a
% to b. This, (a)!0!(b) is (a), (a)!.5!(b) is the middle and (a)!1!(b)
% is (b)
%

\def\tikz@cc@mid@num@nonactive#1!{\tikz@cc@mid@num{#1}}%

\begingroup
  \catcode`\!=\active
  \gdef\tikz@cc@mid@num@active#1!{\tikz@cc@mid@num{#1}}%
\endgroup

\def\tikz@cc@mid@num#1{%
  \pgfmathparse{#1}%
  \ifpgfmathunitsdeclared%
    \let\tikz@cc@mid@unit=\pgfmathresult%
    \expandafter\tikz@cc@scan@rot\expandafter\tikz@cc@after@unit%
  \else%
    \let\tikz@cc@mid@factor=\pgfmathresult%
    \pgfmathparse{1-\tikz@cc@mid@factor}%
    \let\tikz@cc@mid@factor@one=\pgfmathresult%
    \expandafter\tikz@cc@scan@rot\expandafter\tikz@cc@after@num%
  \fi%
}%

\def\tikz@cc@after@num#1{%
  \pgf@process{#1}%
  \pgf@xb=\tikz@cc@mid@factor@one\pgf@xb%
  \pgf@yb=\tikz@cc@mid@factor@one\pgf@yb%
  \advance\pgf@xb by\tikz@cc@mid@factor\pgf@x%
  \advance\pgf@yb by\tikz@cc@mid@factor\pgf@y%
  \tikz@cc@mid@checks%
}%



%
% Distance case: (coord a)!dimension!(coord b)
%
% Returns the position that is at <dimension> removed from (coord a)
% in the direction of (coord b).
%

\def\tikz@cc@after@unit#1{%
  \pgf@process{#1}%
  \advance\pgf@x by-\pgf@xb%
  \advance\pgf@y by-\pgf@yb%
  \pgf@process{\pgfpointnormalised{}}%
  \advance\pgf@xb by\tikz@cc@mid@unit\pgf@x%
  \advance\pgf@yb by\tikz@cc@mid@unit\pgf@y%
  \tikz@cc@mid@checks%
}%

%
% Projection case: (a)!(p)!(b)
%
% Projection of p on line from a to b
%
\def\tikz@cc@project#1{%
  \pgf@process{#1}%
  % Save in c
  \pgf@xc=\pgf@x%
  \pgf@yc=\pgf@y%
  \begingroup
    \ifnum\the\catcode`\!=\active
      \def\tikz@next{%
        \endgroup
        \expandafter\tikz@cc@scan@rot\expandafter\tikz@cc@after@project
        \tikz@cc@scan@ex@active}%
    \else
      \def\tikz@next{%
        \endgroup
        \expandafter\tikz@cc@scan@rot\expandafter\tikz@cc@after@project
        \tikz@cc@scan@ex@nonactive}%
    \fi
    \tikz@next%
}%

\def\tikz@cc@scan@ex@nonactive!{}%

\begingroup
  \catcode`\!=\active
  \gdef\tikz@cc@scan@ex@active!{}%
\endgroup

\def\tikz@cc@after@project#1{%
  \pgf@process{#1}%
  % Ok, now we need to project (xc,yc) on the line (xb,xc) to (x,y)
  \advance\pgf@x by-\pgf@xb%
  \advance\pgf@y by-\pgf@yb%
  \advance\pgf@xc by-\pgf@xb%
  \advance\pgf@yc by-\pgf@yb%
  \pgf@process{\pgfpointnormalised{}}%
  % Scalar product
  \pgf@xc=\pgf@sys@tonumber{\pgf@xc}\pgf@x%
  \advance\pgf@xc by\pgf@sys@tonumber{\pgf@yc}\pgf@y%
  % and add
  \advance\pgf@xb by\pgf@sys@tonumber{\pgf@xc}\pgf@x%
  \advance\pgf@yb by\pgf@sys@tonumber{\pgf@xc}\pgf@y%
  \tikz@cc@mid@checks%
}%

%
% Rotational scanner: radius:(x)
%

\def\tikz@cc@scan@rot#1{%
  \pgfutil@ifnextchar({%)
    \tikz@scan@one@point#1% normal
  }%
  {%
    \def\tikz@cc@scan@rot@cmd{#1}%
    \ifnum\the\catcode`\:=\active\relax
      \expandafter\tikz@cc@scan@one@rot@active%
    \else
      \expandafter\tikz@cc@scan@one@rot@nonactive%
    \fi
  }%
}%

\def\tikz@cc@scan@one@rot@nonactive#1:{%
  \def\tikz@cc@scan@rot@angle{#1}%
  \tikz@scan@one@point\tikz@cc@handle@rot%
}%

\begingroup
  \catcode`\:=\active
  \gdef\tikz@cc@scan@one@rot@active#1:{%
    \def\tikz@cc@scan@rot@angle{#1}%
    \tikz@scan@one@point\tikz@cc@handle@rot%
  }%
\endgroup

\def\tikz@cc@handle@rot#1{%
  \pgf@process{#1}%
  % Ok, now we need to rotate x/y around xb/xb by ...rot@angle
  {%
    \pgftransformreset%
    % Save them...
    \pgf@xc=\pgf@x%
    \pgf@yc=\pgf@y%
    \pgftransformshift{\pgfqpoint{\pgf@xb}{\pgf@yb}}%
    \pgftransformrotate{\tikz@cc@scan@rot@angle}%
    \pgftransformshift{\pgfqpoint{-\pgf@xb}{-\pgf@yb}}%
    \pgfpointtransformed{\pgfqpoint{\pgf@xc}{\pgf@yc}}%
    \expandafter
  }%
  \edef\tikz@marshal{\noexpand\tikz@cc@scan@rot@cmd{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}}%
  \tikz@marshal%
}%




%
%
% Part III: Calculation coordinate systems
%
%

% Tangent cs: Keys are a node and a point. Depending on the type of
% node, the appropriate tangent computation should be done.

\tikzdeclarecoordinatesystem{tangent}
{%
  \tikzset{cs/.cd,#1}%
  \expandafter\ifx\csname tikz@tangent@\tikz@cs@type\endcsname\relax%
    \tikzerror{I do not know how to compute the tangent to
    a \tikz@cs@type}%
    \pgfpointorigin%
  \else%
    \expandafter\tikz@scan@one@point\expandafter\tikz@lib@do@tangent\tikz@cs@point%
  \fi%
}%

\tikzset{cs/node/.code=\tikz@cs@unpack{\tikz@cs@node}{\tikz@cs@type}{#1}}%
\tikzset{cs/point/.store in=\tikz@cs@point}%

\def\tikz@lib@do@tangent{\csname tikz@tangent@\tikz@cs@type\endcsname}%

\def\tikz@tangent@coordinate#1{%
  \pgfpointanchor{\tikz@cs@node}{center}%
}%

\def\tikz@tangent@circle#1{%
  {%
    % Step 1: Compute the transformed position of the input:
    \pgf@process{\pgfpointtransformed{#1}}%
    \pgf@xa=\pgf@x%
    \pgf@ya=\pgf@y%
    %
    % Step 2: Compute vector from center of circle to transformed #1
    %
    \pgf@process{\pgfpointtransformed{\pgfpointanchor{\tikz@cs@node}{center}}}%
    \advance\pgf@xa by-\pgf@x%
    \advance\pgf@ya by-\pgf@y%
    %
    % Step 2: Reset transformations, they distract...
    %
    \pgftransformreset%
    %
    % Step 3: Transform to the center of the circle.
    %
    \pgftransformshift{\pgfpointanchor{\tikz@cs@node}{center}}%
    %
    % Step 4: Compute the radius
    %
    \pgf@process{\pgfpointanchor{\tikz@cs@node}{east}}%
    \pgf@xc=\pgf@x%
    %
    % Now, (xa,ya) is a point. Compute the tangent from this point to
    % a circle around the origin of radius xc.
    %
    % acos(radius/veclen(xa,ya)) is the angle of the tangent.
    \pgfmathparse{veclen(\the\pgf@xa,\the\pgf@ya)}
    \pgfmathparse{acos(\the\pgf@xc/\pgfmathresult)}
    \ifnum\pgfkeysvalueof{/tikz/cs/solution}>1\relax%
      \pgfmathparse{0-\pgfmathresult}%
    \fi%
    \let\tikz@lib@temp=\pgfmathresult%
    %
    % Now \pgfmathparse contains the desired angle. Use this to
    % compute the correct position on the circle...
    %
    % But, first, rotate to the point.
    \pgf@process{\pgfpointnormalised{\pgfqpoint{\pgf@xa}{\pgf@ya}}}%
    \pgf@ya=-\pgf@y%
    \pgftransformcm{\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@y}}{\pgf@sys@tonumber{\pgf@ya}}{\pgf@sys@tonumber{\pgf@x}}{\pgfpointorigin}%
    % Finally, rotate...
    \pgf@process{\pgfpointtransformed{\pgfpointpolar{\tikz@lib@temp}{\the\pgf@xc}}}%
    %
    % Ok, undo transformations...
  }%
  % \pgf@x, \pgf@y have been smuggled outside by \pgf@process
  {%
    \pgftransforminvert%
    \pgf@process{\pgfpointtransformed{}}%
  }%
}%


% Implementation of intersections


\def\tikz@intersect@circle@and@circle{%
  {%
    \pgftransformreset% transformations only confuse us, here...
    %
    % Compute origin and radius of first circle
    %
    \pgf@process{\pgfpointanchor{\tikz@cs@node@a}{center}}%
    \pgf@xa=\pgf@x%
    \pgf@ya=\pgf@y%
    \pgf@process{\pgfpointanchor{\tikz@cs@node@a}{east}}%
    \advance\pgf@x by-\pgf@xa%
    \pgf@xc=\pgf@x% ok, pgf@xc is first radius, (xa,ya) is center
    %
    % Compute origin and radius of second circle
    %
    \pgf@process{\pgfpointanchor{\tikz@cs@node@b}{center}}%
    \pgf@xb=\pgf@x%
    \pgf@yb=\pgf@y%
    \pgf@process{\pgfpointanchor{\tikz@cs@node@b}{east}}%
    \advance\pgf@x by-\pgf@xb%
    \pgf@yc=\pgf@x% \pgf@yc is second radius, (xb,yb) is center
    %
    \pgf@process{%
      \pgfpointintersectionofcircles{\pgfqpoint{\pgf@xa}{\pgf@ya}}{\pgfqpoint{\pgf@xb}{\pgf@yb}}{\pgf@xc}{\pgf@yc}{\pgfkeysvalueof{/tikz/cs/solution}}%
    }%
  }%
  % \pgf@x, \pgf@y have been smuggled outside by \pgf@process,
  % reinstall transformations...
  {%
    \pgftransforminvert%
    \pgf@process{\pgfpointtransformed{}}%
  }%
}%


\def\tikz@intersect@line@and@circle{%
  {%
    %
    % Step 1: Get line
    %
    \expandafter\tikz@scan@one@point\expandafter\tikz@parse@line\tikz@cs@line@a%
    \pgf@process{\pgfpointtransformed{}}%
    \pgf@xb=\pgf@x%
    \pgf@yb=\pgf@y%
    \pgf@process{\pgfpointtransformed{\pgfqpoint{\pgf@xc}{\pgf@yc}}}%
    \pgf@xa=\pgf@x%
    \pgf@ya=\pgf@y%
    %
    % Step 2: Subtract center of circle
    %
    \pgf@process{\pgfpointtransformed{\pgfpointanchor{\tikz@cs@node@b}{center}}}%
    \advance\pgf@xa by-\pgf@x%
    \advance\pgf@ya by-\pgf@y%
    \advance\pgf@xb by-\pgf@x%
    \advance\pgf@yb by-\pgf@y%
    %
    % Step 3: Reset transformations, they distract...
    %
    \pgftransformreset%
    %
    % Step 4: Transform to the center of the circle.
    %
    \pgftransformshift{\pgfpointanchor{\tikz@cs@node@b}{center}}%
    %
    % Step 5: Compute the radius
    %
    \pgf@process{\pgfpointanchor{\tikz@cs@node@b}{east}}%
    \edef\tikz@lib@saved@radius{\pgf@sys@tonumber{\pgf@x}}%
    %
    % Step 6: Compute projection of origin on line (xa,ya) -- (xb,yb),
    % store in (xa,ya)
    \pgf@x=\pgf@xb%
    \pgf@y=\pgf@yb%
    \advance\pgf@x by-\pgf@xa%
    \advance\pgf@y by-\pgf@ya%
    \pgf@process{\pgfpointnormalised{}}%
    % Scalar product
    \pgf@xc=\pgf@sys@tonumber{\pgf@xa}\pgf@x%
    \advance\pgf@xc by\pgf@sys@tonumber{\pgf@ya}\pgf@y%
    \pgf@xc=-\pgf@xc%
    % and add
    \advance\pgf@xa by\pgf@sys@tonumber{\pgf@xc}\pgf@x%
    \advance\pgf@ya by\pgf@sys@tonumber{\pgf@xc}\pgf@y%
    %
    % Now, we have a triangle with a right angle at (xa,ya). The
    % second point of the triangle is the origin. The third point is
    % sought.
    % Save x/y
    \pgf@xc=\pgf@x%
    \pgf@yc=\pgf@y%
    % Square radius
    \pgf@xb=\tikz@lib@saved@radius pt%
    %
    % First, make numbers smaller, in case they are too large
    %
    \c@pgf@counta=1\relax%
    \loop%
    \ifdim\pgf@xb>50pt%
      \multiply\c@pgf@counta by2\relax%
      \divide\pgf@xa by2\relax%
      \divide\pgf@ya by2\relax%
      \divide\pgf@xb by2\relax%
    \repeat%
    \pgf@xb=\pgf@sys@tonumber{\pgf@xb}\pgf@xb%
    % Subtract xa^2 + ya^2
    \pgf@yb=\pgf@sys@tonumber{\pgf@xa}\pgf@xa%
    \advance\pgf@xb by-\pgf@yb%
    \pgf@yb=\pgf@sys@tonumber{\pgf@ya}\pgf@ya%
    \advance\pgf@xb by-\pgf@yb%
    % Square root
    \ifdim\pgf@xb<0pt%
      \pgf@xb=0pt%
    \fi%
    \pgfmathsqrt@{\pgf@sys@tonumber{\pgf@xb}}%
    \pgfmathmultiply@{\pgfmathresult}{\the\c@pgf@counta}%
    \multiply\pgf@xa by\c@pgf@counta\relax%
    \multiply\pgf@ya by\c@pgf@counta\relax%
    \ifnum\pgfkeysvalueof{/tikz/cs/solution}>1\relax%
      \pgfmathsubtract{0}{\pgfmathresult}%
    \fi%
    % Ok, now add things...
    \advance\pgf@xa by \pgfmathresult\pgf@xc%
    \advance\pgf@ya by \pgfmathresult\pgf@yc%
    \pgf@process{\pgfpointtransformed{\pgfqpoint{\pgf@xa}{\pgf@ya}}}%
    % Ok, undo transformations...
  }%
  % \pgf@x, \pgf@y have been smuggled outside by \pgf@process
  {%
    \pgftransforminvert%
    \pgf@process{\pgfpointtransformed{}}%
  }%
}%

\def\tikz@intersect@circle@and@line{%
  % Swap
  {%
    \let\tikz@cs@node@b=\tikz@cs@node@a%
    \let\tikz@cs@line@a=\tikz@cs@line@b%
    \tikz@intersect@line@and@circle%
  }%
}%
