% tkz-obj-el-points-with.tex % Copyright 2022 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{4.24c} \def\filedate{2022/09/21} \typeout{2022/09/21 4.24c tkz-obj-eu-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{\fpeval{\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% \edef\tkz@x{\fpeval{28.45274*(#1)*\pgf@xa}} \edef\tkz@y{\fpeval{28.45274*(#1)*\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% \edef\tkz@x{\fpeval{28.45274*(#1)*\pgf@xa}} \edef\tkz@y{\fpeval{28.45274*(#1)*\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{\fpeval{28.45274*(#1)*\pgf@xa}} \edef\tkz@y{\fpeval{28.45274*(#1)*\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