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diff --git a/Master/texmf-dist/tex/generic/pgf/libraries/pgflibraryintersections.code.tex b/Master/texmf-dist/tex/generic/pgf/libraries/pgflibraryintersections.code.tex new file mode 100644 index 00000000000..698ec524ba8 --- /dev/null +++ b/Master/texmf-dist/tex/generic/pgf/libraries/pgflibraryintersections.code.tex @@ -0,0 +1,767 @@ +% Copyright 2008 by Mark Wibrow +% +% This file may be distributed and/or modified +% +% 1. under the LaTeX Project Public License and/or +% 2. under the GNU Free Documentation License. +% +% See the file doc/generic/pgf/licenses/LICENSE for more details. + + +\newcount\pgf@intersect@solutions + +\newif\ifpgf@intersect@sort +\newif\ifpgf@intersect@sort@by@second@path + +\def\pgfintersectionsortbyfirstpath{% + \pgf@intersect@sorttrue% + \pgf@intersect@sort@by@second@pathfalse% +} + +\def\pgfintersectionsortbysecondpath{% + \pgf@intersect@sorttrue% + \pgf@intersect@sort@by@second@pathtrue% +} + +\def\pgfpointintersectionsolution#1{% + \ifnum#1<1\relax% + \pgfpoint@intersect@solution@orgin% + \else% + \ifnum#1>\pgfintersectionsolutions\relax% + \pgfpoint@intersect@solution@orgin% + \else% + \csname pgfpoint@intersect@solution@#1\endcsname% + \fi% + \fi% +} + +\def\pgfpoint@intersect@solution@orgin{% + \begingroup% + \pgftransforminvert% + \pgfpointorigin% + \pgf@pos@transform{\pgf@x}{\pgf@y}% + \global\pgf@x=\pgf@x% + \global\pgf@y=\pgf@y% + \endgroup% +} + +\long\def\pgfintersectionofpaths#1#2{% + \begingroup% + \pgfinterruptpath% + #1% + \pgfgetpath\pgf@intersect@path@a% + \global\let\pgf@intersect@path@temp=\pgf@intersect@path@a% + \endpgfinterruptpath% + \endgroup% + \let\pgf@intersect@path@a=\pgf@intersect@path@temp% + % + \begingroup% + \pgfinterruptpath% + #2% + \pgfgetpath\pgf@intersect@path@b% + \global\let\pgf@intersect@path@temp=\pgf@intersect@path@b% + \endpgfinterruptpath% + \endgroup% + \let\pgf@intersect@path@b=\pgf@intersect@path@temp% + % + \pgf@intersect@solutions=0\relax% + \def\pgf@intersect@time@offset{0}% + % + \ifpgf@intersect@sort@by@second@path% + \let\pgf@intersect@temp=\pgf@intersect@path@a% + \let\pgf@intersect@path@a=\pgf@intersect@path@b% + \let\pgf@intersect@path@b=\pgf@intersect@temp% + \fi% + \let\pgf@intersect@token@after=\pgf@intersect@path@process@a% + \expandafter\pgf@intersectionofpaths\pgf@intersect@path@a\pgf@stop% + \edef\pgfintersectionsolutions{\the\pgf@intersect@solutions}% + \pgfmathloop% + \ifnum\pgfmathcounter>\pgfintersectionsolutions\relax% + \else% + \pgfutil@namelet{pgfpoint@intersect@solution@\pgfmathcounter}% + {pgfpoint@g@intersect@solution@\pgfmathcounter}% + \ifpgf@intersect@sort% + \pgfutil@namelet{pgf@intersect@solution@\pgfmathcounter @time@a}% + {pgf@g@intersect@solution@\pgfmathcounter @time@a}% + \fi% + \repeatpgfmathloop% + \ifpgf@intersect@sort% + \pgfintersectionsolutionsortbytime% + \fi% +} + +\def\pgf@intersectionofpaths#1{% + \ifx#1\pgf@stop% + \let\pgf@intersect@next=\relax% + \else% + \ifx#1\pgfsyssoftpath@movetotoken% + \let\pgf@intersect@next=\pgf@intersect@token@moveto% + \else% + \ifx#1\pgfsyssoftpath@linetotoken% + \let\pgf@intersect@next=\pgf@intersect@token@lineto% + \else% + \ifx#1\pgfsyssoftpath@closepathtoken% + \let\pgf@intersect@next=\pgf@intersect@token@lineto% + \else% + \ifx#1\pgfsyssoftpath@curvetosupportatoken% + \let\pgf@intersect@next=\pgf@intersect@token@curveto% + \else% + \ifx#1\pgfsyssoftpath@rectcornertoken% + \let\pgf@intersect@next=\pgf@intersect@token@rect% + \fi% + \fi% + \fi% + \fi% + \fi% + \fi% + \pgf@intersect@next} + +\def\pgf@intersect@token@moveto#1#2{% + \def\pgfpoint@intersect@start{\pgfqpoint{#1}{#2}}% + \pgf@intersectionofpaths% +} + +\def\pgf@intersect@token@lineto#1#2{% + \def\pgfpoint@intersect@end{\pgfqpoint{#1}{#2}}% + \def\pgf@intersect@type{line}% + \pgf@intersect@token@after% +} +\def\pgf@intersect@token@curveto#1#2\pgfsyssoftpath@curvetosupportbtoken#3#4\pgfsyssoftpath@curvetotoken#5#6{% + \def\pgfpoint@intersect@firstsupport{\pgfqpoint{#1}{#2}}% + \def\pgfpoint@intersect@secondsupport{\pgfqpoint{#3}{#4}}% + \def\pgfpoint@intersect@end{\pgfqpoint{#5}{#6}}% + \def\pgf@intersect@type{curve}% + \pgf@intersect@token@after% +} + +\def\pgf@intersect@token@rect#1#2\pgfsyssoftpath@rectsizetoken#3#4{% + \pgf@xa=#1\relax% + \advance\pgf@xa by#3\relax% + \pgf@ya=#2\relax% + \advance\pgf@ya by#4\relax% + \edef\pgf@marshal{% + \noexpand\pgfsyssoftpath@movetotoken{#1}{#2}% + \noexpand\pgfsyssoftpath@linetotoken{#1}{\the\pgf@ya}% + \noexpand\pgfsyssoftpath@linetotoken{\the\pgf@xa}{\the\pgf@ya}% + \noexpand\pgfsyssoftpath@linetotoken{\the\pgf@xa}{#2}% + \noexpand\pgfsyssoftpath@closepathtoken{#1}{#2}% + }% + \expandafter\pgf@intersectionofpaths\pgf@marshal% +} + +\def\pgf@intersect@path@process@a{% + \pgf@intersect@path@getpoints@a% + \let\pgf@intersect@token@after=\pgf@intersect@path@process@b% + \expandafter\pgf@intersectionofpaths\pgf@intersect@path@b\pgf@stop% + \let\pgfpoint@intersect@start=\pgfpoint@intersect@end@a% + \let\pgf@intersect@token@after=\pgf@intersect@path@process@a% + \c@pgf@counta=\pgf@intersect@time@offset\relax% + \advance\c@pgf@counta by1\relax% + \edef\pgf@intersect@time@offset{\the\c@pgf@counta}% + \pgf@intersectionofpaths% +} + +\def\pgf@intersect@path@getpoints@a{% + \let\pgfpoint@intersect@start@a=\pgfpoint@intersect@start% + \let\pgfpoint@intersect@end@a=\pgfpoint@intersect@end% + \let\pgfpoint@intersect@firstsupport@a=\pgfpoint@intersect@firstsupport% + \let\pgfpoint@intersect@secondsupport@a=\pgfpoint@intersect@secondsupport% + \let\pgf@intersect@type@a=\pgf@intersect@type% +} + +\def\pgf@intersect@path@process@b{% + \pgf@intersect@path@getpoints@b% + \csname pgf@intersect@\pgf@intersect@type@a @and@\pgf@intersect@type@b\endcsname% + \let\pgfpoint@intersect@start=\pgfpoint@intersect@end@b% + \pgf@intersectionofpaths} + +\def\pgf@intersect@path@getpoints@b{% + \let\pgfpoint@intersect@start@b=\pgfpoint@intersect@start% + \let\pgfpoint@intersect@end@b=\pgfpoint@intersect@end% + \let\pgfpoint@intersect@firstsupport@b=\pgfpoint@intersect@firstsupport% + \let\pgfpoint@intersect@secondsupport@b=\pgfpoint@intersect@secondsupport% + \let\pgf@intersect@type@b=\pgf@intersect@type% +} + +\def\pgf@intersect@line@and@line{% + \pgf@intersectionoflines{\pgfpoint@intersect@start@a}{\pgfpoint@intersect@end@a}% + {\pgfpoint@intersect@start@b}{\pgfpoint@intersect@end@b}% +}% + +\def\pgf@intersect@line@and@curve{% + \pgf@intersectionoflineandcurve% + {\pgf@process{\pgfpoint@intersect@start@a}}{\pgf@process{\pgfpoint@intersect@end@a}}% + {\pgf@process{\pgfpoint@intersect@start@b}}{\pgf@process{\pgfpoint@intersect@firstsupport@b}}% + {\pgf@process{\pgfpoint@intersect@secondsupport@b}}{\pgf@process{\pgfpoint@intersect@end@b}}% +} + +\def\pgf@intersect@curve@and@line{% + \pgf@intersectionofcurveandline% + {\pgf@process{\pgfpoint@intersect@start@a}}{\pgf@process{\pgfpoint@intersect@firstsupport@a}}% + {\pgf@process{\pgfpoint@intersect@secondsupport@a}}{\pgf@process{\pgfpoint@intersect@end@a}}% + {\pgf@process{\pgfpoint@intersect@start@b}}{\pgf@process{\pgfpoint@intersect@end@b}}% +} + +\def\pgf@intersect@curve@and@curve{% + \pgf@intersectionofcurves% + {\pgf@process{\pgfpoint@intersect@start@a}}{\pgf@process{\pgfpoint@intersect@firstsupport@a}}% + {\pgf@process{\pgfpoint@intersect@secondsupport@a}}{\pgf@process{\pgfpoint@intersect@end@a}}% + {\pgf@process{\pgfpoint@intersect@start@b}}{\pgf@process{\pgfpoint@intersect@firstsupport@b}}% + {\pgf@process{\pgfpoint@intersect@secondsupport@b}}{\pgf@process{\pgfpoint@intersect@end@b}}% +} + + +\def\pgfintersectionoflines#1#2#3#4{% + \pgf@intersect@solutions=0\relax% + \pgf@intersectionoflines{#1}{#2}{#3}{#4}% +} + +\def\pgf@intersectionoflines#1#2#3#4{% + \pgf@iflinesintersect{#1}{#2}{#3}{#4}% + {% + \global\advance\pgf@intersect@solutions by1\relax% + \expandafter\pgfextract@process\csname pgfpoint@g@intersect@solution@\the\pgf@intersect@solutions\endcsname{% + \pgfpointintersectionoflines{\pgfpoint@intersect@start@a}{\pgfpoint@intersect@end@a}% + {\pgfpoint@intersect@start@b}{\pgfpoint@intersect@end@b}% + }% + \ifpgf@intersect@sort% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgf@process{\pgfpointdiff{\pgfpoint@intersect@start@a}{\pgfpoint@intersect@end@a}}% + \edef\pgf@marshal{% + \noexpand\pgfmathveclen@{\pgfmath@tonumber{\pgf@xa}}{\pgfmath@tonumber{\pgf@ya}}% + }% + \pgf@marshal% + \let\pgf@intersect@length@a=\pgfmathresult% + \pgf@process{\pgfpointdiff{\pgfpoint@intersect@start@a}{\pgfqpoint{\pgf@xc}{\pgf@yc}}}% + \edef\pgf@marshal{% + \noexpand\pgfmathveclen@{\pgfmath@tonumber{\pgf@x}}{\pgfmath@tonumber{\pgf@y}}% + }% + \pgf@marshal% + \pgfmathdivide@{\pgfmathresult}{\pgf@intersect@length@a}% + \pgf@x=\pgfmathresult pt\relax% + \advance\pgf@x by\pgf@intersect@time@offset pt\relax% + \expandafter\xdef\csname pgf@g@intersect@solution@\the\pgf@intersect@solutions @time@a\endcsname% + {\pgfmath@tonumber{\pgf@x}}% + \fi% + }{}% +} + +% Test if two lines L1 and L2 intersect. +% +% #1 - first point P1 on L1. +% #2 - second point P2 on L1. +% #3 - first point P3 on L2. +% #2 - second point P4 on L2. +% #5 - code executed if intersection occurs. +% #6 - code executed if intersection does no occur. +% +% Let L1 be represented by P1+(P2-P1)s where 0<=s<=1 +% Let L2 be represented by P3+(P4-P3)t where 0<=t<=1 +% +% Then L1 and L2 intersect at +% +% s = |x2-x1 x3-x1| / |x4-x3 x2-x1| +% |y2-y1 y3-y1| |y4-y3 y2-y1| +% +% t = |x4-x3 x3-x1| / |x4-x3 x2-x1| +% |y4-y3 y3-y1| |y4-y3 y2-y1| +% +% with 0<=s,t<=1 +% +% s and t do not need to be calculated: +% +% Let s = A / C and t = B / C +% +% Then 0<=s<=1 if !(C=0) && ((A=0) || ((A>0) && !(C<A)) || ((A<0) && !(C>A))) +% 0<=t<=1 if !(C=0) && ((B=0) || ((B>0) && !(C<B)) || ((B<0) && !(C>B))) +% +\newif\ifpgf@s +\newif\ifpgf@t +\def\pgfiflinesintersect#1#2#3#4{% + \begingroup% + \pgf@iflinesintersect{\pgf@process{#1}}{\pgf@process{#2}}{\pgf@process{#3}}{\pgf@process{#4}}% + {\aftergroup\pgfutil@firstoftwo}{\aftergroup\pgfutil@secondoftwo}% + \endgroup% +} + +\def\pgf@iflinesintersect#1#2#3#4{% + #4\relax% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + #3\relax% + \advance\pgf@xc by-\pgf@x% + \advance\pgf@yc by-\pgf@y% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + #2\relax% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + #1\relax% + \advance\pgf@xa by-\pgf@x% + \advance\pgf@ya by-\pgf@y% + \advance\pgf@xb by-\pgf@x% + \advance\pgf@yb by-\pgf@y% + % + % xc = x4-x3; yc=y4-y3; + % xb = x3-x1; yb=y3-y1; + % xa = x2-x1; ya=y2-y1; + % + % + % Normalise a little. 16384 may not be a robust choice. + % + \c@pgf@counta=\pgf@xa\divide\c@pgf@counta by16384\relax% + \c@pgf@countb=\pgf@xb\divide\c@pgf@countb by16384\relax% + \c@pgf@countc=\pgf@ya\divide\c@pgf@countc by16384\relax% + \c@pgf@countd=\pgf@yb\divide\c@pgf@countd by16384\relax% + \multiply\c@pgf@counta by\c@pgf@countd% + \multiply\c@pgf@countc by\c@pgf@countb% + \advance\c@pgf@counta by-\c@pgf@countc% + \pgfutil@tempcnta=\c@pgf@counta% + % + \c@pgf@counta=\pgf@xc\divide\c@pgf@counta by16384\relax% + \c@pgf@countc=\pgf@yc\divide\c@pgf@countc by16384\relax% + \multiply\c@pgf@countd by\c@pgf@counta% + \multiply\c@pgf@countb by\c@pgf@countc% + \advance\c@pgf@countd by-\c@pgf@countb% + \pgfutil@tempcntb=\c@pgf@countd% + % + \c@pgf@countb=\pgf@xa\divide\c@pgf@countb by16384\relax% + \c@pgf@countd=\pgf@ya\divide\c@pgf@countd by16384\relax% + \multiply\c@pgf@counta by\c@pgf@countd% + \multiply\c@pgf@countc by\c@pgf@countb% + \advance\c@pgf@counta by-\c@pgf@countc% + % + \pgf@sfalse% + \pgf@tfalse% + \ifnum\c@pgf@counta=0\relax% + \else% + \ifnum\pgfutil@tempcnta=0\relax% + \pgf@strue% + \else% + \ifnum\pgfutil@tempcnta>0\relax% + \ifnum\c@pgf@counta<\pgfutil@tempcnta% + \else% + \pgf@strue% + \fi% + \else% + \ifnum\c@pgf@counta>\pgfutil@tempcnta% + \else% + \pgf@strue% + \fi% + \fi% + \fi% + \ifnum\pgfutil@tempcntb=0\relax% + \pgf@ttrue% + \else% + \ifnum\pgfutil@tempcntb>0\relax% + \ifnum\c@pgf@counta<\pgfutil@tempcntb% + \else% + \pgf@ttrue% + \fi% + \else% + \ifnum\c@pgf@counta>\pgfutil@tempcntb% + \else% + \pgf@ttrue% + \fi% + \fi% + \fi% + \fi% + \let\pgf@intersect@next=\pgfutil@secondoftwo% + \ifpgf@s% + \ifpgf@t% + \let\pgf@intersect@next=\pgfutil@firstoftwo% + \fi% + \fi% + \pgf@intersect@next% +} + + + + +\def\pgfintersectionoflineandcurve#1#2#3#4#5#6{% + \pgf@intersect@solutions=0\relax% + \pgf@intersectionoflineandcurve{#1}{#2}{#3}{#4}{#5}{#6}% +} + +\def\pgf@intersectionoflineandcurve#1#2#3#4#5#6{% + \pgf@intersectionofcurves% + {\pgf@process{#1}}% + {% + \pgf@process{% + \pgfpointadd{#1\relax\pgf@x=0.666666\pgf@x\pgf@y=0.666666\pgf@y}% + {#2\relax\pgf@x=0.333333\pgf@x\pgf@y=0.333333\pgf@y}% + }% + }% + {% + \pgf@process{% + \pgfpointadd{#1\relax\pgf@x=0.333333\pgf@x\pgf@y=0.333333\pgf@y}% + {#2\relax\pgf@x=0.666666\pgf@x\pgf@y=0.666666\pgf@y}% + }% + }% + {\pgf@process{#2}}% + {\pgf@process{#3}}% + {\pgf@process{#4}}% + {\pgf@process{#5}}% + {\pgf@process{#6}}% +}% + +\def\pgf@intersectionofcurveandline#1#2#3#4#5#6{% + \pgf@intersectionofcurves% + {\pgf@process{#1}}% + {\pgf@process{#2}}% + {\pgf@process{#3}}% + {\pgf@process{#4}}% + {\pgf@process{#5}}% + {% + \pgf@process{% + \pgfpointadd{#5\relax\pgf@x=0.666666\pgf@x\pgf@y=0.666666\pgf@y}% + {#6\relax\pgf@x=0.333333\pgf@x\pgf@y=0.333333\pgf@y}% + }% + }% + {% + \pgf@process{% + \pgfpointadd{#5\relax\pgf@x=0.333333\pgf@x\pgf@y=0.333333\pgf@y}% + {#6\relax\pgf@x=0.666666\pgf@x\pgf@y=0.666666\pgf@y}% + }% + }% + {\pgf@process{#6}}% +}% + + + + +\def\pgfintersectiontolerance{0.1pt} +\def\pgfintersectiontolerancefactor{0.1} + + + +% Find the intersections of two bezier curves. +% +% #1 - #4 = curve 1. +% #5 - #8 = curve 2. +% #9 = the solution number. +% +% There is no guarantee of ordering of solutions. If there are +% no solutions, the origin is returned. +% +\def\pgfpointintersectionofcurves#1#2#3#4#5#6#7#8#9{% + \pgf@intersect@solutions=0\relax% + \pgf@intersectionofcurves% + {\pgf@process{#1}}{\pgf@process{#2}}{\pgf@process{#3}}{\pgf@process{#4}}% + {\pgf@process{#5}}{\pgf@process{#6}}{\pgf@process{#7}}{\pgf@process{#8}}% + \pgfpointintersectionsolution{#9}% +} + +% Return any intersection points of two curves C1 and C2. +% No order can be guaranteed for the solutions. +% +% #1, #2, #3, #4 - the points on C1 +% #5, #6, #7, #8 - the points on C2 +% +% Returns: +% +% \pgf@intersect@solutions - the number of solutions. +% \pgfpointintersectionsolution{<S>} - the point for soultion S. +% +% (Sort of) use: +% +% intersection(C1,C2) +% S = {}; +% intersection'(C1,C2); +% return S; +% +% intersection'(C1,C2) +% B1 = boundingbox(C1); +% B2 = boundingbox(C2); +% if intersect(B1,B2) +% if (B1.width < q) and (B1.height < q) and +% (B2.width < q) and (B2.height < q) +% S = S + {average_of_all_points(B1,B2)}; \\ is there a better choice? +% else +% Q = subdivideLeft(C1); +% R = subdivideRight(C1); +% intersection'(C2,Q); +% intersection'(C2,R); +% +% where q is a small value (tolerance). +% +\def\pgfintersectionofcurves#1#2#3#4#5#6#7#8{% + \pgf@intersect@solutions=0\relax% + \pgf@intersectionofcurves% + {\pgf@process{#1}}{\pgf@process{#2}}{\pgf@process{#3}}{\pgf@process{#4}}% + {\pgf@process{#5}}{\pgf@process{#6}}{\pgf@process{#7}}{\pgf@process{#8}}% +}% +\def\pgf@intersectionofcurves#1#2#3#4#5#6#7#8{% + \begingroup% + \dimendef\pgf@time@a=2\relax% + \dimendef\pgf@time@aa=4\relax% + \dimendef\pgf@time@b=6\relax% + \dimendef\pgf@time@bb=8\relax% + \pgf@time@a=0pt\relax% + \pgf@time@aa=1pt\relax% + \pgf@time@b=0pt\relax% + \pgf@time@bb=1pt\relax% + \let\pgf@intersect@subdivide@curve=\pgf@intersect@subdivide@curve@b% + \let\pgf@curve@subdivde@after=\pgf@@intersectionofcurves% + \pgf@@intersectionofcurves{#1}{#2}{#3}{#4}{#5}{#6}{#7}{#8}% + \endgroup% +} + +\def\pgf@@intersectionofcurves#1#2#3#4#5#6#7#8{% + \pgf@intersect@boundingbox@reset% + \pgf@intersect@boundingbox@update{#1}% + \pgf@intersect@boundingbox@update{#2}% + \pgf@intersect@boundingbox@update{#3}% + \pgf@intersect@boundingbox@update{#4}% + \edef\pgf@intersect@boundingbox@b{% + \noexpand\pgf@x=\the\pgf@xa% + \noexpand\pgf@y=\the\pgf@ya% + \noexpand\pgf@xa=\the\pgf@xb% + \noexpand\pgf@ya=\the\pgf@yb% + }% + \pgf@intersect@boundingbox@reset% + \pgf@intersect@boundingbox@update{#5}% + \pgf@intersect@boundingbox@update{#6}% + \pgf@intersect@boundingbox@update{#7}% + \pgf@intersect@boundingbox@update{#8}% + \edef\pgf@intersect@boundingbox@a{% + \noexpand\pgf@xb=\the\pgf@xa% + \noexpand\pgf@yb=\the\pgf@ya% + \noexpand\pgf@xc=\the\pgf@xb% + \noexpand\pgf@yc=\the\pgf@yb% + }% + \pgf@intersect@boundingbox@a% + \pgf@intersect@boundingbox@b% + \ifdim\pgf@xa<\pgf@xb% + \else% + \ifdim\pgf@x>\pgf@xc% + \else% + \ifdim\pgf@ya<\pgf@yb% + \else% + \ifdim\pgf@y>\pgf@yc% + \else% + \advance\pgf@xc by-\pgf@xb% + \advance\pgf@yc by-\pgf@yb% + \advance\pgf@xa by-\pgf@x% + \advance\pgf@ya by-\pgf@y% + \let\pgf@intersect@subdivde=\relax% + \ifdim\pgf@xc<\pgfintersectiontolerance\relax% + \ifdim\pgf@xa<\pgfintersectiontolerance\relax% + \ifdim\pgf@yc<\pgfintersectiontolerance\relax% + \ifdim\pgf@ya<\pgfintersectiontolerance\relax% + \pgfextract@process\pgf@intersect@solution@candidate{% + \pgf@intersect@boundingbox@a% + \pgf@intersect@boundingbox@b% + \pgf@x=0.25\pgf@x% + \advance\pgf@x by0.25\pgf@xa% + \advance\pgf@x by0.25\pgf@xb% + \advance\pgf@x by0.25\pgf@xc% + \pgf@y=0.25\pgf@y% + \advance\pgf@y by0.25\pgf@ya% + \advance\pgf@y by0.25\pgf@yb% + \advance\pgf@y by0.25\pgf@yc% + }% + % We must avoid duplicate solutions. + \let\pgf@intersect@subdivde=\pgf@stop% + \pgf@ifsolution@duplicate\pgf@intersect@solution@candidate{}% + {% + \global\advance\pgf@intersect@solutions by1\relax% + \expandafter\global\expandafter\let% + \csname pgfpoint@g@intersect@solution@\the\pgf@intersect@solutions\endcsname=% + \pgf@intersect@solution@candidate% + {% + \ifpgf@intersect@sort% + \advance\pgf@time@a by\pgf@time@aa% + \divide\pgf@time@a by2\relax% + \advance\pgf@time@a by\pgf@intersect@time@offset pt\relax% + \expandafter\xdef% + \csname pgf@g@intersect@solution@\the\pgf@intersect@solutions @time@a\endcsname% + {\pgfmath@tonumber{\pgf@time@a}}% + \fi% + }% + }% + \fi% + \fi% + \fi% + \fi% + \ifx\pgf@intersect@subdivde\pgf@stop% + \else% + \pgf@intersect@subdivide@curve{#1}{#2}{#3}{#4}{#5}{#6}{#7}{#8}% + \fi% + \fi% + \fi% + \fi% + \fi% +} + +\def\pgf@intersect@subdivide@curve@b#1#2#3#4#5#6#7#8{% + \begingroup% + \advance\pgf@time@bb by\pgf@time@b\relax% + \divide\pgf@time@bb by2\relax% + \let\pgf@intersect@subdivide@curve=\pgf@intersect@subdivide@curve@a% + \pgf@curve@subdivide@left{#5}{#6}{#7}{#8}{#1}{#2}{#3}{#4}% + \endgroup% + \begingroup% + \advance\pgf@time@b by\pgf@time@bb\relax% + \divide\pgf@time@b by2\relax% + \let\pgf@intersect@subdivide@curve=\pgf@intersect@subdivide@curve@a% + \pgf@curve@subdivide@right{#5}{#6}{#7}{#8}{#1}{#2}{#3}{#4}% + \endgroup% +} + +\def\pgf@intersect@subdivide@curve@a#1#2#3#4#5#6#7#8{% + \begingroup% + \advance\pgf@time@aa by\pgf@time@a\relax% + \divide\pgf@time@aa by2\relax% + \let\pgf@intersect@subdivide@curve=\pgf@intersect@subdivide@curve@b% + \pgf@curve@subdivide@left{#5}{#6}{#7}{#8}{#1}{#2}{#3}{#4}% + \endgroup% + \begingroup% + \advance\pgf@time@a by\pgf@time@aa\relax% + \divide\pgf@time@a by2\relax% + \let\pgf@intersect@subdivide@curve=\pgf@intersect@subdivide@curve@b% + \pgf@curve@subdivide@right{#5}{#6}{#7}{#8}{#1}{#2}{#3}{#4}% + \endgroup% +} + +\def\pgf@intersect@boundingbox@reset{% + \pgf@xa=16000pt\relax% + \pgf@ya=16000pt\relax% + \pgf@xb=-16000pt\relax% + \pgf@yb=-16000pt\relax% +} + +\def\pgf@intersect@boundingbox@update#1{% + #1\relax% + \ifdim\pgf@x<\pgf@xa\pgf@xa=\pgf@x\fi% + \ifdim\pgf@y<\pgf@ya\pgf@ya=\pgf@y\fi% + \ifdim\pgf@x>\pgf@xb\pgf@xb=\pgf@x\fi% + \ifdim\pgf@y>\pgf@yb\pgf@yb=\pgf@y\fi% +} + + +\def\pgf@curve@subdivide@left#1#2#3#4{% + % + % The left curve (from t=0 to t=.5) + % + #1\relax% + \pgfutil@tempdima=\pgf@x% + \pgfutil@tempdimb=\pgf@y% + \pgf@xa=.5\pgf@x\pgf@ya=.5\pgf@y% + \pgf@xb=.25\pgf@x\pgf@yb=.25\pgf@y% + \pgf@xc=.125\pgf@x\pgf@yc=.125\pgf@y% + #2\relax% + \advance\pgf@xa by.5\pgf@x\advance\pgf@ya by.5\pgf@y% + \advance\pgf@xb by.5\pgf@x\advance\pgf@yb by.5\pgf@y% + \advance\pgf@xc by.375\pgf@x\advance\pgf@yc by.375\pgf@y% + #3\relax% + \advance\pgf@xb by.25\pgf@x\advance\pgf@yb by.25\pgf@y% + \advance\pgf@xc by.375\pgf@x\advance\pgf@yc by.375\pgf@y% + #4\relax% + \advance\pgf@xc by.125\pgf@x\advance\pgf@yc by.125\pgf@y% + \edef\pgf@marshal{% + \noexpand\pgf@curve@subdivde@after% + {\noexpand\pgf@x=\the\pgfutil@tempdima\noexpand\pgf@y=\the\pgfutil@tempdimb}% + {\noexpand\pgf@x=\the\pgf@xa\noexpand\pgf@y\the\pgf@ya}% + {\noexpand\pgf@x=\the\pgf@xb\noexpand\pgf@y=\the\pgf@yb} + {\noexpand\pgf@x=\the\pgf@xc\noexpand\pgf@y=\the\pgf@yc}% + }% + \pgf@marshal% +} + +\def\pgf@curve@subdivide@right#1#2#3#4{% + % + % The right curve (from t=0.5 to t=1) + % + #1\relax% + \pgfutil@tempdima=.125\pgf@x\pgfutil@tempdimb=.125\pgf@y% + #2\relax% + \advance\pgfutil@tempdima by.375\pgf@x\advance\pgfutil@tempdimb by.375\pgf@y% + \pgf@xa=.25\pgf@x\pgf@ya=.25\pgf@y% + #3\relax% + \advance\pgfutil@tempdima by.375\pgf@x\advance\pgfutil@tempdimb by.375\pgf@y% + \advance\pgf@xa by.5\pgf@x\advance\pgf@ya by.5\pgf@y% + \pgf@xb=.5\pgf@x\pgf@yb=.5\pgf@y% + #4\relax% + \advance\pgfutil@tempdima by.125\pgf@x\advance\pgfutil@tempdimb by.125\pgf@y% + \advance\pgf@xa by.25\pgf@x\advance\pgf@ya by.25\pgf@y% + \advance\pgf@xb by.5\pgf@x\advance\pgf@yb by.5\pgf@y% + \pgf@xc=\pgf@x\pgf@yc=\pgf@y% + \edef\pgf@marshal{% + \noexpand\pgf@curve@subdivde@after% + {\pgf@x\the\pgfutil@tempdima\pgf@y\the\pgfutil@tempdimb}% + {\pgf@x\the\pgf@xa\pgf@y\the\pgf@ya}{\pgf@x\the\pgf@xb\pgf@y\the\pgf@yb} + {\pgf@x\the\pgf@xc\pgf@y\the\pgf@yc}% + }% + \pgf@marshal% +} + + +% A solution S1 is considered a duplicate of S2, if +% +% |x1 - x2|f < q and |y1 - y2|f < q +% +% where q is a small value (tolerance). +% +% #1 - the solution. +% +\def\pgf@ifsolution@duplicate#1{% + #1% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \let\pgf@intersect@next=\pgfutil@secondoftwo% + \pgfmathloop% + \ifnum\pgfmathcounter>\pgf@intersect@solutions\relax% + \else% + \pgf@process{\csname pgfpoint@g@intersect@solution@\pgfmathcounter\endcsname}% + \advance\pgf@x by-\pgf@xa% + \advance\pgf@y by-\pgf@ya% + \ifdim\pgf@x<0pt\relax\pgf@x=-\pgf@x\fi% + \ifdim\pgf@y<0pt\relax\pgf@y=-\pgf@y\fi% + % + \pgf@x=\pgfintersectiontolerancefactor\pgf@x% + \pgf@y=\pgfintersectiontolerancefactor\pgf@y% + \ifdim\pgf@x<\pgfintersectiontolerance\relax% + \ifdim\pgf@y<\pgfintersectiontolerance\relax% + \let\pgf@intersect@next=\pgfutil@firstoftwo% + \fi% + \fi% + \repeatpgfmathloop% + \pgf@intersect@next% +} + + +\newif\ifpgf@intersect@solutions@sortfinish + +% Sort solutions according to their time index. +% +\def\pgfintersectionsolutionsortbytime{% + \pgf@intersect@solutions@sortfinishtrue% + \pgfmathloop% + \ifnum\pgfmathcounter=\pgfintersectionsolutions\relax% + \else% + \pgfutil@tempcnta=\pgfmathcounter% + \advance\pgfutil@tempcnta by1\relax% + \ifdim\csname pgf@intersect@solution@\pgfmathcounter @time@a\endcsname pt>% + \csname pgf@intersect@solution@\the\pgfutil@tempcnta @time@a\endcsname pt\relax% + \pgf@intersect@solutions@sortfinishfalse% + % + \pgfutil@namelet{pgf@intersect@temp}{pgfpoint@intersect@solution@\pgfmathcounter}% + \pgfutil@namelet{pgfpoint@intersect@solution@\pgfmathcounter}% + {pgfpoint@intersect@solution@\the\pgfutil@tempcnta}% + \pgfutil@namelet{pgfpoint@intersect@solution@\the\pgfutil@tempcnta}{pgf@intersect@temp}% + % + \pgfutil@namelet{pgf@intersect@temp}{pgf@intersect@solution@\pgfmathcounter @time@a}% + \pgfutil@namelet{pgf@intersect@solution@\pgfmathcounter @time@a}% + {pgf@intersect@solution@\the\pgfutil@tempcnta @time@a}% + \pgfutil@namelet{pgf@intersect@solution@\the\pgfutil@tempcnta @time@a}{pgf@intersect@temp}% + \fi% + \repeatpgfmathloop% + \ifpgf@intersect@solutions@sortfinish% + \else% + \expandafter\pgfintersectionsolutionsortbytime% + \fi% +} + +\endinput |