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Diffstat (limited to 'Master/texmf-dist/tex/latex/tkz-base/tkz-tools-math.tex')
| -rw-r--r-- | Master/texmf-dist/tex/latex/tkz-base/tkz-tools-math.tex | 695 |
1 files changed, 62 insertions, 633 deletions
diff --git a/Master/texmf-dist/tex/latex/tkz-base/tkz-tools-math.tex b/Master/texmf-dist/tex/latex/tkz-base/tkz-tools-math.tex index a4f46d22378..c6579e09029 100644 --- a/Master/texmf-dist/tex/latex/tkz-base/tkz-tools-math.tex +++ b/Master/texmf-dist/tex/latex/tkz-base/tkz-tools-math.tex @@ -1,223 +1,15 @@ +% tkz-tools-math.tex % Copyright 2011 by Alain Matthes -% % This file may be distributed and/or modified -% % 1. under the LaTeX Project Public License and/or % 2. under the GNU Public License. - - -\def\fileversion{1.16 d} -\def\filedate{2018/09/19} - - - -% Objet : outils mathématiques pour la géométrie euclideienne avec pgf/tikz -% utilisable de préférence avec un repère orthonormé et le cm comme unité -% utile pour la compatibilité avec pgf 2 -%<--------------------------------------------------------------------------–> -%<--------------------------------------------------------------------------–> -% Duplicate Length à revoir pas de pt pas de global -% ||v(CN)||= ||v(AB)|| et v(CN) colineaire à v(CD) -% A-->#1 B-->#2 C-->#3 D-->#4 N-->#5 ????? -%<--------------------------------------------------------------------------–> -\def\tkzDuplicateLen(#1,#2)(#3,#4){% -\begingroup - \tkzCalcLength(#1,#2)\tkzGetLength{tkz@firstlen}% - \tkzCalcLength(#3,#4)\tkzGetLength{tkz@secondlen}% - \FPdiv\tkz@ratio{\tkz@firstlen}{\tkz@secondlen}% - \tkz@VecKCoLinear[\tkz@ratio](#3,#4,#3){tkzPointResult}% -\endgroup -} -\let\tkzDuplicateSegment\tkzDuplicateLen %<--------------------------------------------------------------------------–> -% Coordonnées d'un vecteur (couple de points) -% Deux points A et B donc un vecteur on récupère les coordonnées de v(AB) -% en cm -% tkzGetVecCoord en cm ou en pt ??? -%<--------------------------------------------------------------------------–> -%result in #3x et #3y #1 et #2 sont les points -% passage en cm avec fp ? -\def\tkzGetVectxy(#1,#2)#3{% -\begingroup -\pgfpointdiff{\pgfpointanchor{#1}{center}}% - {\pgfpointanchor{#2}{center}}% -\pgfmathparse{\pgf@sys@tonumber{\pgf@x}/28.45274}% -\global\let\tkzresultx\pgfmathresult -\pgfmathparse{\pgf@sys@tonumber{\pgf@y}/28.45274}% -\global\let\tkzresulty\pgfmathresult -\global\expandafter\edef\csname #3x\endcsname{\tkzresultx}% -\global\expandafter\edef\csname #3y\endcsname{\tkzresulty}% -\endgroup -} -\let\tkzGetVecCoord\tkzGetVectxy -%<--------------------------------------------------------------------------–> -%<--------------------------------------------------------------------------–> -\def\tkz@numv{0} -\pgfkeys{/tkzdefv/.cd, -K/.code = {\pgfmathparse{#1}\global\def\tkz@ratio{\pgfmathresult}}, -colinear/.code args = {at #1}{\global\def\tkz@numv{0}% - \global\def\tkz@frompoint{#1}}, -orthogonal/.code = {\global\def\tkz@numv{1}}, -linear/.code = {\global\def\tkz@numv{2}}\pgfmathparse{#1}, -normed orthogonal/.code = {\global\def\tkz@numv{3}}, -normed linear/.code = {\global\def\tkz@numv{4}}, -} -\def\tkzDefVector[#1](#2,#3)#4{% -\begingroup -\pgfkeys{/tkzdefv/.cd,K=1} -\pgfqkeys{/tkzdefv}{#1} -\ifcase\tkz@numv% - % first case 0 - \tkzDefVectorfrom[\tkz@ratio](#2,#3){#4} - \or% 1 - \tkz@VecKOrth[\tkz@ratio](#2,#3){#4} - \or% 2 - \tkz@VecK[\tkz@ratio](#2,#3){#4} - \or% 3 - \tkz@VecKOrthNorm[\tkz@ratio](#2,#3){#4} - \or% 4 - \tkz@VecKCoLinear[#1](#2,#3)#4 - \fi -\endgroup -} - -\def\tkzDefVectorfrom[#1](#2,#3)#4{% -\begingroup - \pgfpointdiff{\pgfpointanchor{#2}{center}}% - {\pgfpointanchor{#3}{center}}% - \pgf@xa=\pgf@x% - \pgf@ya=\pgf@y% - \path[coordinate](\tkz@frompoint)--+(\tkz@ratio\pgf@xa,% - \tkz@ratio\pgf@ya) coordinate (#4); -\endgroup -} -%<--------------------------------------------------------------------------–> -% VecKCoLinear CN = K x AB #1 pt #2 pt #3 pt #4 nb #5 pt result -% il faut modifier cette macro : on supprime #3 pour la colinéarité -% Il suffit d'utiliser Replicate ou Duplicate coeff dans #1 -% v(CD)=#1 x v(AB) #1 le coeff; #2-->A #3-->B #4-->C #5-->N -%<--------------------------------------------------------------------------–> -\def\tkzVecKCoLinear{\pgfutil@ifnextchar[{\tkz@VecKCoLinear}{\tkz@VecKCoLinear[1]}} -\def\tkz@VecKCoLinear[#1](#2,#3,#4)#5{% -\begingroup - \pgfpointdiff{\pgfpointanchor{#2}{center}}% - {\pgfpointanchor{#3}{center}}% - \pgf@xa=\pgf@x% - \pgf@ya=\pgf@y% - \pgfmathparse{#1}\edef\tkz@coeff{\pgfmathresult} - \path[coordinate](#4)--+(\tkz@coeff\pgf@xa,\tkz@coeff\pgf@ya)% - coordinate (#5);% -\endgroup -}% -%<--------------------------------------------------------------------------–> -% v(AN)=#1 x v(AB) -% #1 le coeff; #2--> A #3--> B #4-->N tq #4-#2 = #1*(#3-#2) -%<--------------------------------------------------------------------------–> -\pgfkeys{ - /tkzscalev/.cd, - ratio/.code = {\pgfmathparse{#1}\global\edef\tkz@ratio{\pgfmathresult}} - } -\def\tkzScaleVector{\pgfutil@ifnextchar[{\tkz@ScaleVector}{% - \tkz@ScaleVector[]}} -\def\tkz@ScaleVector[#1](#2,#3)#4{% -\begingroup -\pgfkeys{/tkzscalev/.cd,ratio=-1} -\pgfqkeys{/tkzscalev}{#1} - \pgfpointdiff{\pgfpointanchor{#2}{center}}% - {\pgfpointanchor{#3}{center}}% - \pgf@xa=\pgf@x% - \pgf@ya=\pgf@y% - \path[coordinate](#2)--++(\pgf@xa *\tkz@ratio,\pgf@ya *\tkz@ratio)% - coordinate (#4);% -\endgroup -}% -%<--------------------------------------------------------------------------–> -% Outils pour les vecteurs -%<--------------------------------------------------------------------------–> -% ce sont des outils élémentaires qui à partir de deux points en définissent -% un troisième -% #1 si c'est une option alors c'est un nombre réel -% #2 et #3 sont deux points -% #4 est le nom du point qui résulte de la transformation -% exemple : \tkzVecKNorm (A,B){C} définit un point C tel que AC = 1 et C est % % un point de la droite (AC). #1 peut être négatif - -%<--------------------------------------------------------------------------–> -% VectorNormalised ou K*VectorNormalised -% A-->#2 B-->#3 N-->#4 v(AB) devient v(AN) tq ||v(AN)||=1 si #1=1 -% sinon ||v(AN)||=#1 -%<--------------------------------------------------------------------------–> -\def\tkzVecKNorm{\pgfutil@ifnextchar[{\tkz@VecKNorm}{\tkz@VecKNorm[1]}} -\def\tkz@VecKNorm[#1](#2,#3)#4{% -\begingroup - \tkzpointnormalised{% - \pgfpointdiff{\pgfpointanchor{#2}{center}} - {\pgfpointanchor{#3}{center}}} - \pgf@xa=\pgf@x\relax% - \pgf@ya=\pgf@y\relax% - \pgfmathparse{#1}\edef\tkz@coeff{\pgfmathresult} - \FPmul\tkz@coeff{28.45274}{\tkz@coeff} - \FPmul\tkz@x{\tkz@coeff}{\pgf@sys@tonumber{\pgf@xa}} - \FPmul\tkz@y{\tkz@coeff}{\pgf@sys@tonumber{\pgf@ya}} - \path[coordinate](#2)--++(\tkz@x pt,\tkz@y pt)% - coordinate (#4);% -\endgroup -}% -%<--------------------------------------------------------------------------–> -% v(AN)=#1 x v(AB) -% #1 le coeff; #2--> A #3--> B #4-->N tq #4-#2 = #1*(#3-#2) -%<--------------------------------------------------------------------------–> -\def\tkzVecK{\pgfutil@ifnextchar[{\tkz@VecK}{\tkz@VecK[1]}} -\def\tkz@VecK[#1](#2,#3)#4{% -\begingroup - \pgfpointdiff{\pgfpointanchor{#2}{center}}% - {\pgfpointanchor{#3}{center}}% - \pgf@xa=\pgf@x% - \pgf@ya=\pgf@y% - \pgfmathparse{#1}\edef\tkz@coeff{\pgfmathresult} - \path[coordinate](#2)--++(\pgf@xa *\tkz@coeff,% - \pgf@ya *\tkz@coeff)% - coordinate (#4);% -\endgroup -}% -%<--------------------------------------------------------------------------–> -% tkzVector K Orth coeff dans #1 -% v(AN) perp v(AB) v(AB) v(AN) sens direct cercle trigo -% ||v(AN)||=||v(AB)|| -%<--------------------------------------------------------------------------–> -\def\tkzVecKOrth{\pgfutil@ifnextchar[{\tkz@VecKOrth}{\tkz@VecKOrth[1]}} -\def\tkz@VecKOrth[#1](#2,#3)#4{% -\begingroup - \pgfpointdiff{\pgfpointanchor{#2}{center}}% - {\pgfpointanchor{#3}{center}}% - \pgf@xa=-\pgf@y% - \pgf@ya=\pgf@x% - \pgfmathparse{#1}\edef\tkz@coeff{\pgfmathresult} - \path[coordinate](#2)--++(\tkz@coeff\pgf@xa,\tkz@coeff\pgf@ya)% - coordinate (#4);% -\endgroup -}% -%<--------------------------------------------------------------------------–> -% tkzVecKOrthNorm coeff dans #1 -% v(AN) perp v(AB) v(AB) v(AN) sens direct cercle trigo -% ||v(AN||=1 si #1 est vide ou =1 sinon ||v(AN||=K -%<--------------------------------------------------------------------------–> -\def\tkzVecKOrthNorm{\pgfutil@ifnextchar[{\tkz@VecKOrthNorm}% - {\tkz@VecKOrthNorm[1]}} -\def\tkz@VecKOrthNorm[#1](#2,#3)#4{% -\begingroup - \tkzpointnormalised{\pgfpointdiff{\pgfpointanchor{#2}{center}}% - {\pgfpointanchor{#3}{center}}} - \pgf@xa=-\pgf@y% - \pgf@ya=\pgf@x% - \FPmul\tkz@coeff{28.45274}{#1} - \FPmul\tkz@x{\tkz@coeff}{\pgf@sys@tonumber{\pgf@xa}} - \FPmul\tkz@y{\tkz@coeff}{\pgf@sys@tonumber{\pgf@ya}} - \path[coordinate](#2)--++(\tkz@x pt,\tkz@y pt)% - coordinate (#4);% -\endgroup -}% -%<--------------------------------------------------------------------------–> +\def\fileversion{3.01c} +\def\filedate{2020/01/23} +\typeout{2020/01/23 3.01c tkz-tools-math.tex} +\makeatletter +%<--------------------------------------------------------------------------> % \tkzpointnormalised normalise un point A-->A' tq ||v(OA')=1|| -% équivalent de \pgfpointnormalised avec fp +% équivalent de \pgfpointnormalised avec fp % example % \tkzpointnormalised{% % \pgfpointdiff{\pgfpointanchor{A}{center}} @@ -226,463 +18,100 @@ normed linear/.code = {\global\def\tkz@numv{4}}, % or % \pgf@x=1 cm % \pgf@y=12 cm -% \tkzpointnormalised{} %<--------------------------------------------------------------------------–> +% \tkzpointnormalised{} +%<-------------------------------------------------------------------------- \def\tkzpointnormalised#1{% \pgf@process{#1}% -\FPmul{\tkz@sx}{\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@x}} -\FPmul{\tkz@sy}{\pgf@sys@tonumber{\pgf@y}}{\pgf@sys@tonumber{\pgf@y}} -\FPadd{\tkz@sxy}{\tkz@sx}{\tkz@sy} -\FProot{\tkz@den}{\tkz@sxy}{2} -\FPdiv{\tkz@coordx}{\pgf@sys@tonumber{\pgf@x}}{\tkz@den} -\FPround{\tkz@coordx}{\tkz@coordx}{5} -\FPdiv{\tkz@coordy}{\pgf@sys@tonumber{\pgf@y}}{\tkz@den} -\FPround{\tkz@coordy}{\tkz@coordy}{5} +\edef\tkz@den{\fpeval{sqrt((\pgf@x)^2+(\pgf@y)^2)}} +\edef\tkz@coordx{\fpeval{\pgf@x/\tkz@den}} +\edef\tkz@coordx{\fpeval{round(\tkz@coordx,5)}} +\edef\tkz@coordy{\fpeval{\pgf@y/\tkz@den}} +\edef\tkz@coordy{\fpeval{round(\tkz@coordy,5)}} \pgf@x = \tkz@coordx pt \pgf@y = \tkz@coordy pt } -%<--------------------------------------------------------------------------–> +%<--------------------------------------------------------------------------> % restaure and save length \def\tkz@save@length{% \global\let\tkz@temp@length\tkzLengthResult}% \def\tkz@restore@length{% \global\let\tkzLengthResult\tkz@temp@length }% -%<--------------------------------------------------------------------------–> -%<--------------------------------------------------------------------------–> -% \tkzCalcLength Distance entre deux points en pt ou en cm avec FP +%<--------------------------------------------------------------------------> +% \tkzCalcLength Distance entre deux points en pt ou en cm avec xfp % \veclen mais avec fp -% option cm le résultat est en cm sinon en pt -%<--------------------------------------------------------------------------–> - -\newif\iftkzLengthIncm -\pgfkeys{ -DefVecLen/.cd, +% option cm le résultat est en cm sinon en pt +%<--------------------------------------------------------------------------> +\pgfkeys{@CalcLength/.cd, cm/.is if = tkzLengthIncm, cm/.default = true} \def\tkzCalcLength{\pgfutil@ifnextchar[{\tkz@CalcLength}{\tkz@CalcLength[]}} \def\tkz@CalcLength[#1](#2,#3){% -\pgfkeys{DefVecLen/.cd, cm = false} -\pgfqkeys{/DefVecLen}{#1}% +\pgfkeys{@CalcLength/.cd, cm = false} +\pgfqkeys{/@CalcLength}{#1}% \begingroup \tkz@@CalcLength(#2,#3){tkzLengthResult} -\iftkzLengthIncm - \FPdiv\tkzFPMathLen{\tkzFPMathLen}{28.45274} - \FPround\tkzFPMathLen\tkzFPMathLen5\relax% - \global\let\tkzLengthResult\tkzFPMathLen +\iftkzLengthIncm + \pgfmathparse{\tkz@xfpMathLen pt/1cm} + \edef\tkz@xfpMathLen{\fpeval{round(\pgfmathresult,5)}} + \global\let\tkzLengthResult\tkz@xfpMathLen \fi \endgroup }% \def\tkz@@CalcLength(#1,#2)#3{% \pgfpointdiff{\pgfpointanchor{#1}{center}}% {\pgfpointanchor{#2}{center}}% -\pgf@xa=\pgf@x% -\pgf@ya=\pgf@y% -\FPeval\tkz@temp@a{\pgfmath@tonumber{\pgf@xa}}% -\FPeval\tkz@temp@b{\pgfmath@tonumber{\pgf@ya}}% -\FPeval\tkz@temp@sum{(\tkz@temp@a*\tkz@temp@a+\tkz@temp@b*\tkz@temp@b)}% -\FProot{\tkzFPMathLen}{\tkz@temp@sum}{2}% -\FPround\tkzFPMathLen\tkzFPMathLen5\relax -\global\expandafter\edef\csname #3\endcsname{\tkzFPMathLen} +\edef\tkz@xfpMathLen{\fpeval{sqrt((\pgf@x)^2+(\pgf@y)^2)}} +\edef\tkz@xfpMathLen{\fpeval{round(\tkz@xfpMathLen,5)}} +\global\expandafter\edef\csname #3\endcsname{\tkz@xfpMathLen} } -%<--------------------------------------------------------------------------–> +%<--------------------------------------------------------------------------> \def\tkzGetLength#1{% \global\expandafter\edef\csname #1\endcsname{\tkzLengthResult}} -%<--------------------------------------------------------------------------–> -% \tkzpttocm passage de pt à cm div par 28.45274 -%<--------------------------------------------------------------------------–> +%<--------------------------------------------------------------------------> +% \tkzpttocm passage de pt cm div par 28.45274 +%<--------------------------------------------------------------------------> \def\tkzpttocm(#1)#2{% \begingroup - \FPdiv\tkz@mathresult{#1}{28.45274} - \FPround\tkz@mathresult\tkz@mathresult5\relax% - \global\let\tkz@mathresult\tkz@mathresult - \global\expandafter\edef\csname #2\endcsname{\tkz@mathresult}% + \pgfmathparse{#1/1cm} + \edef\tkz@mathresult{\fpeval{round(\pgfmathresult,5)}} + \global\let\tkz@mathresult\tkz@mathresult + \global\expandafter\edef\csname #2\endcsname{\tkz@mathresult}% \endgroup }% -%<--------------------------------------------------------------------------–> -% \tkzcmtopt passage de cm à pt mul par 28.45274 %<--------------------------------------------------------------------------– +%<--------------------------------------------------------------------------> +% \tkzcmtopt passage de cm pt mul par 28.45274 +%<-------------------------------------------------------------------------- \def\tkzcmtopt(#1)#2{% \begingroup - \FPmul\tkz@mathresult{#1}{28.45274} - \FPround\tkz@mathresult\tkz@mathresult5\relax% - \global\let\tkz@mathresult\tkz@mathresult -\global\expandafter\edef\csname #2\endcsname{\tkz@mathresult}% + \pgfmathparse{#1/1pt} + \edef\tkz@mathresult{\fpeval{round(\pgfmathresult,5)}} + \global\let\tkz@mathresult\tkz@mathresult + \global\expandafter\edef\csname #2\endcsname{\tkz@mathresult}% \endgroup }% -%<--------------------------------------------------------------------------–> +%<--------------------------------------------------------------------------> % Slope -%<--------------------------------------------------------------------------–> +%<--------------------------------------------------------------------------> \def\tkzFindSlope{\tkz@FindSlope} \def\tkz@FindSlope(#1,#2)#3{% - \begingroup - \tkzpointnormalised{\pgfpointdiff{\pgfpointanchor{#1}{center}}% - {\pgfpointanchor{#2}{center}}} - \tkz@ax=\pgf@x\relax% - \tkz@ay=\pgf@y\relax% - \FPdiv{\tkz@Slope}{\pgfmath@tonumber{\tkz@ay}}{\pgfmath@tonumber{\tkz@ax}} - \FPround{\tkz@Slope}{\tkz@Slope}{5} +\begingroup + \tkzpointnormalised{\pgfpointdiff{\pgfpointanchor{#1}{center}}% + {\pgfpointanchor{#2}{center}}} + \edef\tkz@Slope{\fpeval{\pgfmath@tonumber{\pgf@y}/\pgfmath@tonumber{\pgf@x}}} + \edef\tkz@Slope{\fpeval{round(\tkz@Slope,5)}} \global\expandafter\edef\csname #3\endcsname{\tkz@Slope}% \endgroup } -%<--------------------------------------------------------------------------–> -%<----------------– for compatibility --------------------------------------–> -%<--------------------------------------------------------------------------–> -\def\tkzmathanglebetweenpoints#1#2{% -\begingroup - \pgf@process{\pgfpointdiff{#1}{#2}}% - % - % First approximate the angle of the external point... - % - \pgf@xa\pgf@x% - \pgf@ya\pgf@y% - \pgf@xb\pgf@x% - \pgf@yb\pgf@y% - \ifdim\pgf@xa<0pt\relax% - \pgf@xa-\pgf@xa% - \fi - \ifdim\pgf@ya<0pt\relax% - \pgf@ya-\pgf@ya% - \fi - \ifdim\pgf@ya>\pgf@xa% - \pgf@x\pgf@xa% - \pgf@y\pgf@ya% - \else - \pgf@x\pgf@ya% - \pgf@y\pgf@xa% - \fi - \ifdim\pgf@y=0pt\relax% - \pgf@x0pt% - \else - \FPdiv\pgfmathresult{1}{\pgfmath@tonumber{\pgf@y}} - \FPround\pgfmathresult\pgfmathresult5\relax% - \pgf@x\pgfmathresult\pgf@x% - \fi - \multiply\pgf@x1000\relax% - \afterassignment\pgfmath@gobbletilpgfmath@% - \expandafter\c@pgf@counta\the\pgf@x\relax\pgfmath@% -\expandafter\pgf@x\csname pgfmath@atan@\the\c@pgf@counta\endcsname pt\relax% - \ifdim\pgfmath@ya>\pgfmath@xa\relax% - \pgf@x-\pgf@x% - \advance\pgf@x90pt% - \fi - \ifdim\pgf@xb<0pt% - \ifdim\pgf@yb>0pt% - \pgf@x-\pgf@x% - \fi - \advance\pgf@x180pt\relax% - \else - \ifdim\pgf@yb<0pt% - \pgf@x-\pgf@x% - \advance\pgf@x360pt\relax% - \fi - \fi - \ifdim\pgf@x>180pt% - \advance\pgf@x-360pt\relax% - \fi - \pgfmath@returnone\pgf@x% - \endgroup -} - -% \tkzmathrotatepointaround -% -% Rotate point #1 about point #2 by #3 degrees. -% -\def\tkzmathrotatepointaround#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\tkz@angle{#3}% - \pgfmathsin@{\tkz@angle}% - \let\sineangle\pgfmathresult% - \pgfmathcos@{\tkz@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% - }% -} - - -% \tkzmathanglebetweenlines -% -% Calculate the clockwise angle between a line from point #1 -% to point #2 and a line from #3 to point #4. -% -\def\tkzmathanglebetweenlines#1#2#3#4{% - \begingroup - \tkzmathanglebetweenpoints{#1}{#2}% - \let\firstangle\pgfmathresult% - \tkzmathanglebetweenpoints{#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 #2 around an axis centered on #2 at an angle #3. -% -\def\tkzmathreflectpointalongaxis#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\tkzmathpointintersectionoflineandarc#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 - \tkzmathanglebetweenpoints{#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}}% - }% -} - -% \tkzmathangleonellipse -% -% 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\tkzmathangleonellipse#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}}% -\FPdiv\pgfmathresult{\pgfmath@tonumber{\pgf@xa}}{\pgfmath@tonumber{\pgfutil@tempdima}} -\FPround\pgfmathresult\pgfmathresult5\relax% - \pgfutil@tempdima\pgfmathresult pt\relax% - \fi - \ifdim\pgf@y=0pt\relax% - \pgfutil@tempdima1pt\relax% - \else - % \pgfmathdivide@{\pgfmath@tonumber{\pgf@y}}{\pgfmath@tonumber{\pgf@ya}}% - \FPdiv\pgfmathresult{\pgfmath@tonumber{\pgf@y}}{% - \pgfmath@tonumber{\pgf@ya}}% - \FPround\pgfmathresult\pgfmathresult5\relax% - \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 -} - -\def\tkzpointborderellipse#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 -} +% Schrodinger's cat idea 03/01/20 +\tikzset{xfp/.code={% +\pgfmathdeclarefunction*{veclen}{2}{% +\begingroup% + \pgfmath@x##1pt\relax% + \pgfmath@y##2pt\relax% + \edef\tkz@xfpMathLen{\fpeval{sqrt((\pgf@x)^2+(\pgf@y)^2)}} + \pgfmath@returnone\tkz@xfpMathLen pt% +\endgroup% +}}} + \makeatother \endinput
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