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% 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
|
