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diff --git a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-lua-points-with.tex b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-lua-points-with.tex new file mode 100644 index 00000000000..73a3d9799ff --- /dev/null +++ b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-lua-points-with.tex @@ -0,0 +1,269 @@ +% tkz-obj-lua-points-with.tex +% Copyright 2023 Alain Matthes +% This work may be distributed and/or modified under the +% conditions of the LaTeX Project Public License, either version 1.3 +% of this license or (at your option) any later version. +% The latest version of this license is in +% http://www.latex-project.org/lppl.txt +% and version 1.3 or later is part of all distributions of LaTeX +% version 2005/12/01 or later. +% This work has the LPPL maintenance status “maintained”. +% The Current Maintainer of this work is Alain Matthes. + +\def\fileversion{5.00c} +\def\filedate{2023/01/23} +\typeout{2023/01/23 5.00c tkz-obj-lua-points-with.tex} +\makeatletter +%<--------------------------------------------------------------------------–> +% Vectors +%<--------------------------------------------------------------------------–> +% 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 ????? +%<--------------------------------------------------------------------------–> +%<--------------------------------------------------------------------------–> +% 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 + +\def\tkzDuplicateSegment(#1,#2)(#3,#4){% +\begingroup + \tkz@@CalcLength(#1,#2){tkz@firstlen}% + \tkz@@CalcLength(#3,#4){tkz@secondlen}% + \edef\tkz@ratio{\tkz@Dec{\tkz@firstlen/\tkz@secondlen}} + \tkz@VecKCoLinear[\tkz@ratio](#3,#4,#3)% +\endgroup +} +\let\tkzDuplicateLength\tkzDuplicateSegment +%<--------------------------------------------------------------------------–> +% 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 ? +% 28.45274 =1 cm +\def\tkzGetVectxy(#1,#2)#3{% +\begingroup +\pgfpointdiff{\pgfpointanchor{#1}{center}}% + {\pgfpointanchor{#2}{center}}% +\pgfmathparse{\pgf@sys@tonumber{\pgf@x}/1cm}% +\let\tkzresultx\pgfmathresult +\pgfmathparse{\pgf@sys@tonumber{\pgf@y}/1cm}% +\let\tkzresulty\pgfmathresult +\global\expandafter\edef\csname #3x\endcsname{\tkzresultx}% +\global\expandafter\edef\csname #3y\endcsname{\tkzresulty}% +\endgroup +} +%<--------------------------------------------------------------------------–> +% options #1 two points #2,#3 result in #4 +% +%<--------------------------------------------------------------------------–> +%<--------------------------------------------------------------------------–> +% tkzDefPointWith +%<--------------------------------------------------------------------------–> +\def\tkz@numv{0} +\pgfkeys{/@pointwith/.cd, + colinear/.code args = {at #1}{\def\tkz@numv{0}\def\tkz@frompoint{#1}}, + orthogonal/.code = {\def\tkz@numv{1}}, + linear/.code = {\def\tkz@numv{2}}, + orthogonal normed/.code = {\def\tkz@numv{3}}, + linear normed/.code = {\def\tkz@numv{4}}, + colinear normed/.code args = {at #1}{\def\tkz@numv{5}\def\tkz@frompoint{#1}}, + K/.code = {\edef\tkz@coeff{\fpeval{#1}}}, + K = 1, + normed/.is if = tkz@line@normed, + normed/.default = true, + normed = false, + orthogonal +} +\def\tkzDefPointWith{\pgfutil@ifnextchar[{\tkz@DefPointWith}{\tkz@DefPointWith[]}} + +\def\tkz@DefPointWith[#1](#2,#3){% +\begingroup +\pgfkeys{/@pointwith/.cd,K=1} +\pgfqkeys{/@pointwith}{#1} +\ifcase\tkz@numv% + % first case 0 + \tkz@DefVectorColinearat[\tkz@coeff](#2,#3) + \or% 1 + \tkz@VecKOrth[\tkz@coeff](#2,#3) + \or% 2 + \tkz@VecK[\tkz@coeff](#2,#3) + \or% 3 + \tkz@VecKOrthNorm[\tkz@coeff](#2,#3) + \or% 4 + \tkz@VecKNorm[\tkz@coeff](#2,#3) + \or% 5 + \tkz@VecKColinearNorm[\tkz@coeff](#2,#3) + \fi +\endgroup +} +%<--------------------------------------------------------------------------–> +% tkzDefVectorfrom +%<--------------------------------------------------------------------------–> +% tkz@numv 0 +\def\tkz@DefVectorColinearat[#1](#2,#3){% +\iftkz@line@normed + \tkz@VecKColinearNorm[#1](#2,#3) +\else +\begingroup + \pgfpointdiff{\pgfpointanchor{#2}{center}}{\pgfpointanchor{#3}{center}}% + \pgf@xa=\pgf@x\relax% + \pgf@ya=\pgf@y\relax% + \pgfinterruptboundingbox + \path (\tkz@frompoint)--++(\tkz@coeff\pgf@xa,\tkz@coeff\pgf@ya) coordinate (tkzPointResult); + \endpgfinterruptboundingbox +\endgroup +\fi +} +%<--------------------------------------------------------------------------–> +% tkzVector K Orth coeff dans #1 +% v(AN) perp v(AB) (v(AB) , v(AN) ) sens direct cercle trigo +% ||v(AN)||=||v(AB)|| +%<--------------------------------------------------------------------------–> +% tkz@numv 1 +\def\tkzVecKOrth{\pgfutil@ifnextchar[{\tkz@VecKOrth}{\tkz@VecKOrth[1]}} +\def\tkz@VecKOrth[#1](#2,#3){% +\iftkz@line@normed + \tkz@VecKOrthNorm[#1](#2,#3) +\else +\begingroup + \pgfpointdiff{\pgfpointanchor{#2}{center}}{\pgfpointanchor{#3}{center}}% + \pgf@xa=-\pgf@y% + \pgf@ya=\pgf@x% + \pgfinterruptboundingbox + \path (#2)--++(\tkz@coeff\pgf@xa,\tkz@coeff\pgf@ya) coordinate (tkzPointResult); + \endpgfinterruptboundingbox +\endgroup +\fi +}% + +%<--------------------------------------------------------------------------–> +% v(AN)=#1 x v(AB) +% #1 le coeff; #2--> A #3--> B #4-->N tq #4-#2 = #1*(#3-#2) +%<--------------------------------------------------------------------------–> +% tkz@numv 2 +\def\tkzVecK{\pgfutil@ifnextchar[{\tkz@VecK}{\tkz@VecK[1]}} +\def\tkz@VecK[#1](#2,#3){% +\iftkz@line@normed + \tkz@VecKNorm[#1](#2,#3) +\else +\begingroup + \pgfpointdiff{\pgfpointanchor{#2}{center}}% + {\pgfpointanchor{#3}{center}}% + \pgf@xa=\pgf@x\relax% + \pgf@ya=\pgf@y\relax% + \pgfmathparse{#1} + \let\tkz@coeff\pgfmathresult + \pgfinterruptboundingbox + \path (#2)--++(\tkz@coeff\pgf@xa,\tkz@coeff\pgf@ya) coordinate (tkzPointResult); + \endpgfinterruptboundingbox +\endgroup +\fi +}% +%<--------------------------------------------------------------------------–> +% 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 +%<--------------------------------------------------------------------------–> +% tkz@numv 3 +\def\tkzVecKOrthNorm{\pgfutil@ifnextchar[{\tkz@VecKOrthNorm}% + {\tkz@VecKOrthNorm[1]}} +\def\tkz@VecKOrthNorm[#1](#2,#3){% +\begingroup + \tkzpointnormalised{\pgfpointdiff{\pgfpointanchor{#2}{center}}% + {\pgfpointanchor{#3}{center}}} + \pgf@xa=-\pgf@y\relax% + \pgf@ya=\pgf@x\relax% + \pgfmathparse{#1} + \let\tkz@tmp\pgfmathresult + \edef\tkz@x{\tkz@Dec{28.45274*\tkz@tmp*\strip@pt\pgf@xa}} + \edef\tkz@y{\tkz@Dec{28.45274*\tkz@tmp*\strip@pt\pgf@ya}} + \pgfinterruptboundingbox + \path (#2)--++(\tkz@x pt,\tkz@y pt) coordinate (tkzPointResult); + \endpgfinterruptboundingbox +\endgroup +}% +%<--------------------------------------------------------------------------–> +% 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 +%<--------------------------------------------------------------------------–> +% tkz@numv 4 +\def\tkzVecKNorm{\pgfutil@ifnextchar[{\tkz@VecKNorm}{\tkz@VecKNorm[1]}} +\def\tkz@VecKNorm[#1](#2,#3){% +\begingroup + \tkzpointnormalised{% + \pgfpointdiff{\pgfpointanchor{#2}{center}} + {\pgfpointanchor{#3}{center}}} + \pgf@xa=\pgf@x\relax% + \pgf@ya=\pgf@y\relax% + \pgfmathparse{#1} + \let\tkz@tmp\pgfmathresult + \edef\tkz@x{\tkz@Dec{28.45274*\tkz@tmp*\strip@pt\pgf@xa}} + \edef\tkz@y{\tkz@Dec{28.45274*\tkz@tmp*\strip@pt\pgf@ya}} + \pgfinterruptboundingbox + \path (#2)--++(\tkz@x pt,\tkz@y pt) coordinate (tkzPointResult); + \endpgfinterruptboundingbox +\endgroup +}% +%<--------------------------------------------------------------------------–> +% \tkz@VecKColinearNorm +%<--------------------------------------------------------------------------–> +%% tkz@numv 5 +\def\tkz@VecKColinearNorm[#1](#2,#3){% +\begingroup + \tkzpointnormalised{% + \pgfpointdiff{\pgfpointanchor{#2}{center}} + {\pgfpointanchor{#3}{center}}} + \pgf@xa=\pgf@x\relax% + \pgf@ya=\pgf@y\relax% + \edef\tkz@x{\tkz@Dec{28.45274*(\tkz@coeff)*\strip@pt\pgf@xa}} + \edef\tkz@y{\tkz@Dec{28.45274*(\tkz@coeff)*\strip@pt\pgf@ya}} + \pgfinterruptboundingbox + \path (\tkz@frompoint)--++(\tkz@x pt,\tkz@y pt) coordinate (tkzPointResult); + \endpgfinterruptboundingbox +\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 +%<--------------------------------------------------------------------------–> +\def\tkz@VecKCoLinear[#1](#2,#3,#4){% +\begingroup + \pgfpointdiff{\pgfpointanchor{#2}{center}}% + {\pgfpointanchor{#3}{center}}% + \pgf@xa=\pgf@x\relax% + \pgf@ya=\pgf@y\relax% + \edef\tkz@coeff{\fpeval{#1}} + \pgfinterruptboundingbox + \path (#4)--+(\tkz@coeff\pgf@xa,\tkz@coeff\pgf@ya) coordinate (tkzPointResult); + \endpgfinterruptboundingbox +\endgroup +}% +\def\tkz@VecCoLinear(#1,#2,#3){% +\begingroup + \pgfpointdiff{\pgfpointanchor{#1}{center}}% + {\pgfpointanchor{#2}{center}}% + \pgf@xa=\pgf@x\relax% + \pgf@ya=\pgf@y\relax% + \pgfinterruptboundingbox + \path (#3)--+(\pgf@xa,\pgf@ya) coordinate (tkzPointResult); + \endpgfinterruptboundingbox +\endgroup +}% +\makeatother +\endinput
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