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diff --git a/Master/texmf-dist/doc/latex/visualtikz/Source/tkzcoord.tex b/Master/texmf-dist/doc/latex/visualtikz/Source/tkzcoord.tex new file mode 100644 index 00000000000..328a3a92747 --- /dev/null +++ b/Master/texmf-dist/doc/latex/visualtikz/Source/tkzcoord.tex @@ -0,0 +1,880 @@ + +\subsection{Coordonnées} +\RRR{13-2-1} + +\subsubsection{Système de coordonnées \og canvas \fg} + +\tikzset{every picture/.style=blue,very thick,inner sep=0pt} + +\begin{tabular}{|c|c|} \hline +Explicite & Implicite +\\ \hline +\begin{tikzpicture} +\draw[help lines] (0,0) grid (3,2); +\fill (canvas cs:x=2cm,y=1.5cm) circle (2pt); +\end{tikzpicture} +& +\begin{tikzpicture} +\draw[help lines] (0,0) grid (3,2); +\fill (2,1.5) circle (2pt); +\end{tikzpicture} + +\\ \hline + \BS{fill} (\RDD{canvas cs}:x=2cm,y=1.5cm) circle (2pt); +& \BS{fill} {\color{blue}(2cm,1.5cm)} circle (2pt); +\\ \hline +\end{tabular} + + +\subsubsection{Système de coordonnées xyz} + +\begin{tabular}{|c|c|c|} \hline +\begin{tikzpicture}[->] +\draw (0,0) -- (xyz cs:x=1); +\draw (0,0) -- (xyz cs:y=1); +\draw (0,0) -- (xyz cs:z=1); +\end{tikzpicture} +& +\begin{tikzpicture}[->] +\draw (0,0) -- (1,0,0); +\draw (0,0) -- (0,1,0); +\draw (0,0) -- (0,0,1); +\end{tikzpicture} +\\ \hline +\BS{draw} (0,0) - - (\RDD{xyz cs}:x=1); & \BS{draw} (0,0) - - (1,0,0); \\ +\BS{draw} (0,0) - - (\RDD{xyz cs}:y=1); & \BS{draw} (0,0) - - (0,1,0); \\ +\BS{draw} (0,0) - - (\RDD{xyz cs}:z=1); & \BS{draw} (0,0) - - (0,0,1); +\\ \hline + +\end{tabular} + +\subsubsection{Système de coordonnées polaire \og canvas \fg} + +\begin{tabular}{|c|c|c|} \hline +Explicite & Implicite +\\ \hline +\begin{tikzpicture} +\draw[help lines] (0,0) grid (3,2); +\draw [dotted](0,2) arc (90 :0 :2); +\draw [dotted](0,0) --(2,2); +\fill (canvas polar cs:angle=45,radius=2cm) circle (2pt); +\end{tikzpicture} +& +\begin{tikzpicture} +\draw[help lines] (0,0) grid (3,2); +\draw [dotted](0,2) arc (90 :0 :2); +\draw [dotted](0,0) --(2,2); +\fill (45:2cm) circle (2pt); +\end{tikzpicture} +\\ \hline +\BS{fill} (\RDD{canvas polar cs}:\RDD{angle}=45,\RDD{radius}=2cm) circle (2pt); +& +\BS{fill} {\color{blue}(45:2cm)} circle (2pt); +\\ \hline +\end{tabular} + +\bigskip +\begin{tabular}{|c|} \hline +\begin{tikzpicture} +\draw[help lines] (0,0) grid (3,2); +\draw [dotted](0,2) arc (90 :0 :3 and 2); +\draw [dotted](0,0) --(3,2); +\fill (canvas polar cs:angle=45,x radius=3cm,y radius=2cm) circle (2pt); +\end{tikzpicture} +\\ \hline +\BS{fill} (canvas polar cs:angle=45,\RDD{x radius}=3cm,\RDD{y radius}=2cm) circle (2pt); +\\ \hline +\end{tabular} + + + +\newpage +\subsubsection{Coordinate system xyz polar} % A VOIR + + +\begin{tabular}{|c|c|c|} \hline +Explicite & Implicite +\\ \hline +\begin{tikzpicture} +\draw[help lines] (0,0) grid (3,2); +\draw [dotted](0,2) arc (90 :0 :2); +\draw [dotted](0,0) --(2,2); +\fill (xyz polar cs:angle=45,radius=2) circle (2pt); +\end{tikzpicture} +& +\begin{tikzpicture} +\draw[help lines] (0,0) grid (3,2); +\draw [dotted](0,2) arc (90 :0 :2); +\draw [dotted](0,0) --(2,2); +\fill (45:2) circle (2pt); +\end{tikzpicture} +\\ \hline +\BS{fill} (\RDD{xyz polar cs}:\RDD{angle}=45,\RDD{radius}=2) circle (2pt); +& +\BS{fill} {\color{blue}(45:2cm)} circle (2pt); +\\ \hline +\end{tabular} + +\bigskip +\begin{tabular}{|c|} \hline +\begin{tikzpicture} +\draw[help lines] (0,0) grid (3,2); +\draw [dotted](0,2) arc (90 :0 :3 and 2); +\draw [dotted](0,0) --(3,2); +\fill (xyz polar cs:angle=45,x radius=3,y radius=2) circle (2pt); +\end{tikzpicture} +\\ \hline +\BS{fill} (xyz polar cs:angle=45,\RDD{x radius}=3,\RDD{y radius}=2) circle (2pt); +\\ \hline +\end{tabular} + +\bigskip + +\begin{tabular}{|c|c|c|} \hline +\multicolumn{2}{|c|}{\BS{begin}\AC{tikzpicture}{\color{red}[x=1.5cm,y=1cm]} } +\\ \hline +\begin{tikzpicture}[x=1.5cm,y=1cm] +\draw[help lines] (0,0) grid (3,2); +\draw [dotted](0,2) arc (90 :0 :2); +\draw [dotted](0,0) --(2,2); +\fill (xyz polar cs:angle=45,radius=2) circle (2pt); +\end{tikzpicture} +& +\begin{tikzpicture}[x=1.5cm,y=1cm] +\draw[help lines] (0,0) grid (3,2); +\draw [dotted](0,2) arc (90 :0 :2); +\draw [dotted](0,0) --(2,2); +\fill (45:2) circle (2pt); +\end{tikzpicture} +\\ \hline +\BS{fill} (\RDD{xyz polar cs}:\RDD{angle}=45,\RDD{radius}=2) circle (2pt); +& +\BS{fill} {\color{blue}(45:2cm)} circle (2pt); +\\ \hline +\end{tabular} +\bigskip + +\begin{tabular}{|c|c|c|} \hline +\multicolumn{2}{|c|}{\BS{begin}\AC{tikzpicture}{\color{red}[x=\AC{(0cm,1cm)},y=\AC{(-1cm,0cm)}]} } +\\ \hline +\begin{tikzpicture}[x={(0cm,1cm)},y={(-1cm,0cm)}] +\draw[help lines] (0,0) grid (3,2); +\draw [dotted](0,2) arc (90 :0 :2); +\draw [dotted](0,0) --(2,2); +\fill (xyz polar cs:angle=45,radius=2) circle (2pt); +\end{tikzpicture} +& +\begin{tikzpicture}[x={(0cm,1cm)},y={(-1cm,0cm)}] +\draw[help lines] (0,0) grid (3,2); +\draw [dotted](0,2) arc (90 :0 :2); +\draw [dotted](0,0) --(2,2); +\fill (45:2) circle (2pt); +\end{tikzpicture} +\\ \hline +\BS{fill} (\RDD{xyz polar cs}:\RDD{angle}=45,\RDD{radius}=2) circle (2pt); +& +\BS{fill} {\color{blue}(45:2cm)} circle (2pt); +\\ \hline +\end{tabular} + + + +%-------------------------------------------------------- +\subsubsection{Coordonnées barycentriques} +\RRR{13-2-2} + +\begin{tabular}{|c|c|c|} \hline +\multicolumn{3}{|c|}{ \BS{node} [circle,fill=red!20] at (\RDD{barycentric cs}:A=0.6,B=0.3 ) \AC{X}; }\\ +\hline +\begin{tikzpicture}[scale=.6] +\draw[help lines] (0,0) grid (4,4); +\node[circle,fill=green!20,] (A) at (0,0) {A}; +\node[circle,fill=green!20,] (B) at (4,0) {B}; +\node[circle,fill=red!20] at (barycentric cs:A=0.3,B=0.3 ) {X}; +\end{tikzpicture} +& +\begin{tikzpicture}[scale=.6] +\draw[help lines] (0,0) grid (4,4); +\node[circle,fill=green!20,] (A) at (0,0) {A}; +\node[circle,fill=green!20,] (B) at (4,0) {B}; +\node[circle,fill=green!20,] (C) at (4,4) {C}; +\node[circle,fill=red!20] at (barycentric cs:A=0.4,B=0.4 ,C=.4) {X}; +\end{tikzpicture} +& +\begin{tikzpicture}[scale=.6] +\draw[help lines] (0,0) grid (4,4); +\node[circle,fill=green!20,] (A) at (0,0) {A}; +\node[circle,fill=green!20,] (B) at (4,0) {B}; +\node[circle,fill=green!20,] (C) at (1,4) {C}; +\node[circle,fill=green!20,] (D) at (4,4) {D}; +\node[circle,fill=red!20] at (barycentric cs:A=0.5,B=0.5,C=.5,D=.5 ) {X}; +\end{tikzpicture} +\\ \hline +A=0.3,B=0.3 & A=0.4,B=0.4 ,C=.4 & A=0.5,B=0.5,C=.5,D=.5 +\\ \hline +\begin{tikzpicture}[scale=.6] +\draw[help lines] (0,0) grid (4,4); +\node[circle,fill=green!20,] (A) at (0,0) {A}; +\node[circle,fill=green!20,] (B) at (4,0) {B}; +\node[circle,fill=red!20] at (barycentric cs:A=0.6,B=0.3 ) {X}; +\end{tikzpicture} +& +\begin{tikzpicture}[scale=.6] +\draw[help lines] (0,0) grid (4,4); +\node[circle,fill=green!20,] (A) at (0,0) {A}; +\node[circle,fill=green!20,] (B) at (4,0) {B}; +\node[circle,fill=green!20,] (C) at (4,4) {C}; +\node[circle,fill=red!20] at (barycentric cs:A=0.2,B=0.4 ,C=.6) {X}; +\end{tikzpicture} +& +\begin{tikzpicture}[scale=.6] +\draw[help lines] (0,0) grid (4,4); +\node[circle,fill=green!20,] (A) at (0,0) {A}; +\node[circle,fill=green!20,] (B) at (4,0) {B}; +\node[circle,fill=green!20,] (C) at (1,4) {C}; +\node[circle,fill=green!20,] (D) at (4,4) {D}; +\node[circle,fill=red!20] at (barycentric cs:A=0.2,B=0.4,C=.6,D=.8 ) {X}; +\end{tikzpicture} +\\ \hline +A=0.6,B=0.3 & A=0.2,B=0.4 ,C=.6 & A=0.2,B=0.4,C=.6,D=.8 +\\ \hline +\end{tabular} + + +\subsection{Coordonnées nominatives : n\oe ud} +\RRR{13-2-3} + +\begin{tabular}{|c|c|} \hline +\begin{tikzpicture}[blue,very thick,baseline=1cm] +\draw[help lines] (0,0) grid (3,3); +\coordinate (centre) at (1.5,1.5) ; +\coordinate (A) at (.5,.5) ; +\coordinate (B) at (2.5,2.5) ; +\fill (centre) circle (3pt); +\draw[red] (A) rectangle (B) ; +\end{tikzpicture} +& +\parbox[c]{8cm}{ +\BSS{coordinate} {\color{blue}(centre)} at(1.5,1.5) ; \\ +\BSS{coordinate} {\color{blue}(A)} at (.5,.5) ;\\ +\BSS{coordinate} {\color{blue}(B)} at (2.5,2.5) ;\\ +\\ +\BS{fill} {\color{blue}(centre)} circle (3pt);\\ +\BS{draw}[red] {\color{blue}(A)} rectangle {\color{blue}(B)} ;\\ +} +\\ \hline +\end{tabular} + +voir aussi page \pageref{nomnoeud} + +%--------------------------------------------------------- +\subsubsection{Coordonnées relatives à un noeud} + + +\begin{tabular}{|c|c|c|c|} \hline +\multicolumn{4}{|l|}{ \BS{node} [draw,fill=green!20,] (A) at (1,1) \AC{\BS{huge} noeud}; }\\ +\multicolumn{4}{|l|}{ \BS{fill}[red] (\RDD{node cs}:\RDD{name}=A,\RDD{anchor}=south) circle (3pt); }\\ +\hline + +\begin{tikzpicture} +\draw[help lines] (0,0) grid (2,2); +\node[draw,fill=green!20,] (A) at (1,1) {\huge noeud}; +\fill[red] (node cs:name=A,anchor=south) circle (3pt); +\end{tikzpicture} +& +\begin{tikzpicture} +\draw[help lines] (0,0) grid (2,2); +\node[draw,fill=green!20,] (A) at (1,1) {\huge noeud}; +\fill[red] (node cs:name=A,anchor=west) circle (3pt); +\end{tikzpicture} +& +\begin{tikzpicture} +\draw[help lines] (0,0) grid (2,2); +\node[draw,fill=green!20,] (A) at (1,1) {\huge noeud}; +\fill[red] (node cs:name=A,anchor=north) circle (3pt); +\end{tikzpicture} +& +\begin{tikzpicture} +\draw[help lines] (0,0) grid (2,2); +\node[draw,fill=green!20,] (A) at (1,1) {\huge noeud}; +\fill[red] (node cs:name=A,anchor=east) circle (3pt); +\end{tikzpicture} +\\ \hline +name=A,anchor=south & name=A,anchor=west & name=A,anchor=north & name=A,anchor=east +\\ \hline +\end{tabular} + +\bigskip +\begin{tabular}{|c|c|c|c|} \hline +\multicolumn{4}{|c|}{ \BS{fill}[red] (node cs:\RDD{name}=A,\RDD{angle}=0) circle (3pt); }\\ +\hline + +\begin{tikzpicture} +\draw[help lines] (0,0) grid (2,2); +\node[draw,fill=green!20,] (A) at (1,1) {\huge noeud}; +\fill[red] (node cs:name=A,angle=0) circle (3pt); +\end{tikzpicture} +& +\begin{tikzpicture} +\draw[help lines] (0,0) grid (2,2); +\node[draw,fill=green!20,] (A) at (1,1) {\huge noeud}; +\fill[red] (node cs:name=A,angle=-30) circle (3pt); +\end{tikzpicture} +& +\begin{tikzpicture} +\draw[help lines] (0,0) grid (2,2); +\node[draw,fill=green!20,] (A) at (1,1) {\huge noeud}; +\fill[red] (node cs:name=A,angle=-90) circle (3pt); +\end{tikzpicture} +& +\begin{tikzpicture} +\draw[help lines] (0,0) grid (2,2); +\node[draw,fill=green!20,] (A) at (1,1) {\huge noeud}; +\fill[red] (node cs:name=A,angle=-150) circle (3pt); +\end{tikzpicture} +\\ \hline +name=A,angle=0 & name=A,angle=-30 & nname=A,angle=-90 & name=A,angle=-150 +\\ \hline +\end{tabular} + + +% % % % % % % % % % % % % % % % A voir % % % % % % % % % % % % % % % % % + + +%\subsubsection{Coordonnée à un intersection} +% +%\begin{tikzpicture} +%\draw[help lines] (0,0) grid (3,3); +%%\draw (intersection cs: first line={(A)- -(B)},second line={(1,2)- -(3,0)})coordinate (C); +%%\fill[red](C) circle (2pt); +%%\draw (C) circle (1cm); +%%\node [above]at(C){C}; +%\end{tikzpicture} + +\subsubsection{ Coordonnée relative à 2 points} + +\RRR{13-3-1} + +\begin{tabular}{|c|c|} \hline +\multicolumn{2}{|c|}{ \BS{node} [circle,fill=red!20] at (1,1 {\color{red}|-} 3,3) \AC{X} }\\ +\hline +\begin{tikzpicture} +\draw[help lines] (0,0) grid (4,4); +\node[circle,fill=green!20,] (A) at (1,1) {A}; +\node[circle,fill=green!20,] (B) at (3,3) {B}; +\node[circle,fill=red!20] at (1,1 |- 3,3) {X}; +\end{tikzpicture} +& +\begin{tikzpicture} +\draw[help lines] (0,0) grid (4,4); +\node[circle,fill=green!20,] (A) at (1,1) {A}; +\node[circle,fill=green!20,] (B) at (3,3) {B}; +\node[circle,fill=red!20] at (1,1 -| 3,3) {X}; +\end{tikzpicture} +\\ \hline +at (1,1 {\color{red}|-} 3,3) +& +at (1,1 {\color{red}-|} 3,3) +\\ \hline +\end{tabular} + + +\newpage +\subsubsection{ Coordonnée relative à une intersection} + +\RRR{13-3-2} + + \maboite{\BS{usetikzlibrary}\AC{intersections}} +\label{lib-intersections} + + +\begin{tabular}{|c|c|c|c|} \hline +\multicolumn{4}{|l|}{ \BS{draw} [\RDD{name path}=cercle] (2,1) circle (1cm); }\\ +\multicolumn{4}{|l|}{ \BS{draw} [\RDD{name path}=rectangle] (0.5,0.5) rectangle +(3,1); }\\ +\multicolumn{4}{|l|}{ \BS{fill} [red,\RDD{ name intersections}=\AC{of=cercle and rectangle}] +(\RDD{intersection}-1) circle (2pt) }\\ +\hline +\begin{tikzpicture}[scale=.8] +\draw [help lines] grid (4,2); +\draw [name path=cercle] (2,1) circle (1cm); +\draw [name path=rectangle] (0.5,0.5) rectangle +(3,1); +\fill [red, name intersections={of=cercle and rectangle}] +(intersection-1) circle (2pt) ; +\end{tikzpicture} +& +\begin{tikzpicture}[scale=.8] +\draw [help lines] grid (4,2); +\draw [name path=cercle] (2,1) circle (1cm); +\draw [name path=rectangle] (0.5,0.5) rectangle +(3,1); +\fill [red, name intersections={of=cercle and rectangle}] (intersection-2) circle (2pt) ; +\end{tikzpicture} +& +\begin{tikzpicture}[scale=.8] +\draw [help lines] grid (4,2); +\draw [name path=cercle] (2,1) circle (1cm); +\draw [name path=rectangle] (0.5,0.5) rectangle +(3,1); +\fill [red, name intersections={of=cercle and rectangle}] (intersection-3) circle (2pt) ; +\end{tikzpicture} +& +\begin{tikzpicture}[scale=.8] +\draw [help lines] grid (4,2); +\draw [name path=cercle] (2,1) circle (1cm); +\draw [name path=rectangle] (0.5,0.5) rectangle +(3,1); +\fill [red, name intersections={of=cercle and rectangle}] (intersection-4) circle (2pt) ; +\end{tikzpicture} +\\ +\hline intersection-1 & intersection-2 &intersection-3 & intersection-4 \\ +\hline +\end{tabular} + +\bigskip + +\begin{tabular}{|c|} \hline +\BS{fill} [red, name intersections=\AC{of=cercle and rectangle}] \\ +(intersection-1) circle (2pt) {\color{red} node[black,above right] \AC{point a}} ; +\\ \hline +\begin{tikzpicture} +\draw [help lines] grid (4,2); +\draw [name path=cercle] (2,1) circle (1cm); +\draw [name path=rectangle] (0.5,0.5) rectangle +(3,1); +\fill [red, name intersections={of=cercle and rectangle}] +(intersection-1) circle (2pt) node[black,above right] {point a} ; +\end{tikzpicture} +\\ \hline +\end{tabular} + + + + +\bigskip + +\begin{tabular}{|c|} \hline +\BS{fill} [red, name intersections=\AC{of=cercle and rectangle, \RDD{name}=point}]; \\ +\BS{draw} [red] (point-1) -- (point-3); \BS{draw} [green] (point-2) -- (point-4); +\\ \hline +\begin{tikzpicture} +\draw [help lines] grid (4,2); +\draw [name path=cercle] (2,1) circle (1cm); +\draw [name path=rectangle] (0.5,0.5) rectangle +(3,1); +\fill [red, name intersections={of=cercle and rectangle, name=point}]; +\draw [red] (point-1) -- (point-3); +\draw [green] (point-2) -- (point-4); +\end{tikzpicture} +\\ \hline +\end{tabular} + +\bigskip +\begin{tabular}{|c|} \hline +\BS{fill} [red, name intersections=\AC{of=cercle and rectangle, \RDD{by}=\AC{a,b,c,d}}]; \\ +\BS{draw} [red] (a) -- (c); \hspace{1cm} \BS{draw} [green] (b) -- (d); +\\ \hline +\begin{tikzpicture} +\draw [help lines] grid (4,2); +\draw [name path=cercle] (2,1) circle (1cm); +\draw [name path=rectangle] (0.5,0.5) rectangle +(3,1); +\fill [red, name intersections={of=cercle and rectangle, by={a,b,c,d}}]; +\draw [red] (a) -- (c); +\draw [green] (b) -- (d); +\end{tikzpicture} +\\ \hline +\end{tabular} + +\bigskip + +\begin{tabular}{|c|} \hline +\BS{fill} [name intersections=\AC{of=cercle and rectangle, name=i, \RDD{total}=\BS{t}}] [red] \\ +\BS{foreach} \BS{s} in \AC{1,...,\BS{t}} \AC{(i-\BS{s}) circle (2pt) node[black,above right] \AC{\BS{s}}} +\\ \hline +\begin{tikzpicture} +\draw [help lines] grid (4,2); +\draw [name path=cercle] (2,1) circle (1cm); +\draw [name path=rectangle] (0.5,0.5) rectangle +(3,1); +\fill [name intersections={of=cercle and rectangle, name=i, total=\t}] +[red] +\foreach \s in {1,...,\t}{(i-\s) circle (2pt) node[black,above right] {\s}}; +\end{tikzpicture} +\\ \hline +\end{tabular} + + + +%\begin{tikzpicture} +%\clip (-0.5,-0.75) rectangle (3.25,2.25); +%\foreach \pathname/\shift in {line/0cm, curve/2cm}{ +%\tikzset{xshift=\shift} +%\draw [->, name path=curve] (1,1.5) .. controls (-1,1) and (2,0.5) .. (0,0); +% +%\draw [->, name path=line] (0,-.5) -- (1,2) ; +% +%\fill [name intersections={of=line and curve,sort by=\pathname, name=i}] +%[red, opacity=0.5, every node/.style={left=.25cm, black, opacity=1}] +%\foreach \s in {1,2,3}{(i-\s) circle (2pt) node {\footnotesize\s}}; +%} +%\end{tikzpicture} +%--------------------------------------------------------------------------- +\newpage + +\subsection{Position calculée} + + +\subsubsection{Position calculée avec le module \og pgfmath \fg} + +\RRR{13-2-1} + +Ce module est chargé automatiquement avec le module Tikz + +\begin{tabular}{|c|} \hline +\begin{tikzpicture} +\draw[help lines] (0,0) grid (4,2); +\fill [red] (canvas cs:x=2cm+1.5cm,y=1.5cm-1cm) circle (3pt); +\fill [blue] (2cm,1.5cm) circle (3pt); +\draw[dashed] (2,1.5) -| (3.5,.5); +\end{tikzpicture} +\\ \hline +\emph{Explicite} : \BS{fill} [red] (\RDD{canvas cs}:x=2cm+1.5cm,y=1.5cm-1cm) circle (3pt); + \\ \hline +\emph{Implicite} : \BS{fill} [red] {\color{red}(2cm+1.5cm,1.5cm-1cm)} circle (3pt); +\\ \hline +\end{tabular} + +\bigskip +\begin{tabular}{|c|c|c|} \hline +\begin{tikzpicture}[baseline=0pt] +\draw[help lines] (0,0) grid (4,4); + \draw[dashed] (2,2) circle (2); +\fill[red](2+ 2*cos 30,2+2*sin 30) circle (3pt); +\fill[magenta](2+ 2*cos{(120)},2+2*sin{(120)}) circle (3pt); +\end{tikzpicture} +& +\parbox[c]{8cm}{ + \BS{draw}[dashed] (2,2) circle (2);\\ + \smallskip + \BS{fill} [red]{\color{red}(2+ 2*cos 30 , 2+2*sin 30)} circle (3pt);\\ + \smallskip + \BS{fill}[magenta] {\color{red}(2+2*cos\AC{(120)} , 2+2*sin\AC{(120)})} circle (3pt); + } +\\ \hline +\end{tabular} +% +\subsubsection{Position calculée avec \og librairy calc \fg} + +\RRR{13-5} +\label{lib-calc} +Insérer dans le préambule : + + \maboite{\BS{usetikzlibrary}\AC{calc}} + +\begin{tabular}{|c|c|} \hline +\begin{tikzpicture}[baseline=0pt] +\draw [help lines] (0,0) grid (3,2); +\node (a) at (1,1) {A}; +\fill [red] ($(a) + 2/3*(1cm,0)$) circle (2pt); +\fill [red] ($(a) + 4/3*(1cm,0)$) circle (2pt); +\end{tikzpicture} +& +\parbox{8cm}{ +\BS{node} (a) at (1,1) \AC{A}; \\ +\BS{fill} [red] {\color{red} (\$(a) + 2/3*(1cm,0)\$)} circle (2pt); \\ +\BS{fill} [red] {\color{red}(\$(a) + 4/3*(1cm,0)\$)} circle (2pt); \\ +} +\\ +\hline +\end{tabular} + + +\subsubsection{Tangentes avec \og librairy calc \fg} + +\RRR{13-2-4} + +\begin{tabular}{|c|c|} \hline +\multicolumn{2}{|l|}{\BS{node}[fill=green!20] (a) at (3,1.5) \AC{A}; } \\ +\multicolumn{2}{|l|}{\BS{fill}[red] (\RDD{tangent cs}:\RDD{node}=c,\RDD{point}=\AC{(A)},\RDD{solution}=1); }\\ +%\multicolumn{2}{|l|}{\BS{draw}[red] (1,1) - -(\RDD{tangent} cs:\RDD{node}=c,\RDD{point}=\AC{(3,1.5)} ,\RDD{solution}=1); }\\ +\hline +\begin{tikzpicture} +\draw[help lines] (0,0) grid (4,2); +\node[fill=green!20] (A) at (3,1.5) {A}; +\node [circle,draw] (c) at (1,1) [minimum size=1.5cm] {$c$}; +\draw[red,dashed] (A) - -(tangent cs:node=c,point={(A)},solution=1) ; +\draw[red,dashed] (1,1) - -(tangent cs:node=c,point={(3,1.5)},solution=1) ; +\fill[red] (tangent cs:node=c,point={(A)},solution=1) circle (3pt); +\end{tikzpicture} +& +\begin{tikzpicture} +\draw[help lines] (0,0) grid (4,2); +\node[fill=green!20] (A) at (3,1.5) {A}; +\node [circle,draw] (c) at (1,1) [minimum size=1.5cm] {$c$}; +\draw[red,dashed] (A) - -(tangent cs:node=c,point={(A)},solution=2) ; +\draw[red,dashed] (1,1) - -(tangent cs:node=c,point={(A)},solution=2) ; +\fill[red] (tangent cs:node=c,point={(A)},solution=2) circle (3pt); +\end{tikzpicture} +\\ \hline +\RDD{solution}=1 & \RDD{solution}=2 +\\ \hline +\end{tabular} + +\newpage + +\subsubsection{Point à pourcentage donné } + +\RRR{13-5-3} + + +\begin{tabular}{|c|c|} \hline +\multicolumn{2}{|c|}{\BS{fill}[red] ({\color{red}\$(0,1)!.25!(4,1)\$}) circle (4pt); } \\ \hline + +\begin{tikzpicture} +\draw [help lines] (0,0) grid (4,2); +\draw [line width= 3pt] (0,1) -- (4,1); +\fill[red] ($(0,1)!.25!(4,1)$) circle (4pt); +\end{tikzpicture} +& +\begin{tikzpicture} +\draw [help lines] (0,0) grid (4,2); +\draw [line width= 3pt] (0,1) -- (4,1); +\fill[red] ($(0,1)!.75!(4,1)$) circle (4pt); +\end{tikzpicture} +\\ \hline (0,1)!{\color{red}0.25}!(4,1) & (0,1)!{\color{red}0.75}!(4,1) \\ +\hline +\end{tabular} + +\bigskip + +\begin{tabular}{|c|} \hline +\begin{tikzpicture} +\draw [help lines] (0,0) grid (4,3); +\draw [line width=2pt ](0,2) -- (4,2); +\draw[red] ($(0,2)!.75!(4,2)$) -- (0,0); +\fill[red] ($(0,2)!.75!(4,2)!.66!(0,0)$) circle (4pt); +\end{tikzpicture} +\\ \hline +\BS{fill}[red] (\${\color{blue}(0,2)!0.75!(4,2)}!{\color{red}0.66!(0,0)}\$) circle (2pt); +\\ \hline +\end{tabular} + + + +\subsubsection{Point à distance donnée} + +\RRR{13-5-4} + +\begin{tabular}{|c|c|} \hline +\multicolumn{2}{|c|}{\BS{fill}[red] ({\color{red}\$(0,1)!1.5cm!(4,1)\$}) circle (4pt); } \\ \hline + +\begin{tikzpicture} +\draw [help lines] (0,0) grid (4,2); +\draw [line width= 2pt] (0,1) -- (4,1); +\fill[red] ($(0,1)!1.5cm!(4,1)$) circle (4pt); +\end{tikzpicture} +& +\begin{tikzpicture} +\draw [help lines] (0,0) grid (4,2); +\draw [line width= 2pt] (0,1) -- (4,1); +\fill[red] ($(0,1)!3cm!(4,1)$) circle (4pt); +\end{tikzpicture} +\\ \hline (0,1)!{\color{red}1.5cm}!(4,1) & (0,1)!{\color{red}3cm}!(4,1) \\ +\hline +\end{tabular} + +\bigskip + +\begin{tabular}{|c|} \hline +\begin{tikzpicture} +\draw [help lines] (0,0) grid (4,4); +\coordinate (a) at (1,0); +\coordinate (b) at (4,1); +\draw [line width= 3pt] (0,0) -- (4,1); +\draw [line width= 2pt,red](2,.5) -- ($ (2,.5)!2cm!90:(4,1) $); +\end{tikzpicture} +\\ \hline +\BS{draw} (2,.05) - - ($ (2,0.5)!{\color{red}2cm!90:(4,1)} $); +\\ \hline +\end{tabular} + +\subsection{Coordonnées relatives} + +%Dimension par défaut : 1cm +\subsubsection{Cartésienne} + +\RRR{13-4-1} + +\begin{tabular}{|c|c|c|} \hline +relative à l'origine & relative à une position & relative à la dernière position +\\ \hline + +\begin{tikzpicture} %[scale=.8] +\draw[help lines] (0,-1) grid (3,1); + \draw[blue,very thick] (0,0) -- (1,0) - - (2,1) - - (2,-1); + \fill[red] (0,0) circle (4pt); +\end{tikzpicture} +& +\begin{tikzpicture} %[scale=.8] +\draw[help lines] (0,-1) grid (4,1); + \draw[blue,very thick] (0,0) - - (1,0) -- +(2,1) -- +(2,-1) ; %–- +(2,-1) ; + \fill[red] (1,0) circle (4pt); +\end{tikzpicture} +& +\begin{tikzpicture} %[scale=.8] +\draw[help lines] (0,-1) grid (5,1); + \draw[blue,very thick] (0,0) -- (1,0) - - ++(2,1) - - ++(2,-1); + \fill[red] (1,0) circle (4pt); + \fill[red] (3,1) circle (4pt); +\end{tikzpicture} +\\ \hline +\tikz \fill node[fill=green!20,inner sep=0pt]{(0,0)}; - - (1,0) & + (0,0) - - \tikz \fill node[fill=green!20,inner sep=0pt]{(1,0)}; & (0,0) - - \tikz \fill node[fill=green!20,inner sep=0pt]{(1,0)}; \\ + - - (2,1) - - (2,-1) & + - - +(2,1) - - +(2,-1) & - - ++\tikz \fill node[fill=green!20,inner sep=0pt]{(2,1)}; - - ++(2,-1) +\\ \hline +\end{tabular} + +\bigskip + +\begin{tabular}{|c|c|c|} \hline +\begin{tikzpicture} [scale=.5] +\draw[help lines] (0,-1) grid (6,6); + \draw[red,dotted,line width=2pt] (0,0) rectangle (2,2) ; + \draw[green,dotted,line width=2pt] (0,0) rectangle (3,3) ; + \draw[blue,line width=2pt] (0,0) rectangle (1,1) rectangle (2,2) rectangle (3,3); + +\end{tikzpicture} + +& +\begin{tikzpicture} [scale=.5] +\draw[help lines] (0,-1) grid (6,6); + \draw[green,dotted,line width=2pt] (1,1) rectangle (4,4) ; + \draw[blue,line width=2pt] (0,0) rectangle (1,1) rectangle +(2,2) rectangle +(3,3); + \fill[red] (1,1) circle (4pt); +\end{tikzpicture} +& +\begin{tikzpicture} [scale=.5] +\draw[help lines] (0,-1) grid (6,6); + \draw[blue,line width=2pt] (0,0) rectangle (1,1) rectangle ++(2,2) rectangle ++(3,3); + \fill[red] (1,1) circle (4pt); + \fill[green] (3,3) circle (4pt); +\end{tikzpicture} +\\ +\hline +\BS{draw} (0,0) rectangle (1,1) & +\BS{draw} (0,0) rectangle (1,1) & +\BS{draw} (0,0) rectangle (1,1) \\ +rectangle (2,2) rectangle (3,3); & +rectangle +(2,2) rectangle +(3,3); & +rectangle ++(2,2) rectangle ++(3,3); \\ +\hline +\end{tabular} + + + +\subsubsection{Polaire } + +\begin{tabular}{|c|c|c|c|} \hline +relative à l'origine & relative à une position & relative à la dernière position +\\ \hline +\begin{tikzpicture} %[scale=.8] +\draw[help lines] (0,-1) grid (3,1); + \fill[red] (0:0) circle (4pt); + \draw[blue,very thick] (0:0)-- (0:1) -- (30:2) -- (-30:2); +\end{tikzpicture} +& +\begin{tikzpicture} %[scale=.8] +\draw[help lines] (0,-1) grid (4,1); + + \draw[blue,very thick] (0:0) -- (0:1) -- +(30:2) -- +(-30:2); +\end{tikzpicture} +& +\begin{tikzpicture} %[scale=.8] +\draw[help lines] (0,-1) grid (5,1); + + \draw[blue,very thick] (0:0)-- (0:1) -- ++(30:2) -- ++(-30:2); +\end{tikzpicture} +\\ \hline +\tikz \fill node[fill=green!20,inner sep=0pt] {(0:0)}; - - (0:1)& + (0:0) - - \tikz \fill node[fill=green!20,inner sep=0pt] {(0:1)}; & (0:0)- - \tikz \fill node[fill=green!20,inner sep=0pt] {(0:1)}; \\ + - - (30:2) - - (-30:2) & - - +(30:2) - - +(-30:2) & - - ++\tikz \fill node[fill=green!20,inner sep=0pt] {(30:2)}; - - ++(-30:2) +\\ \hline +\end{tabular} + +\subsubsection{coordonnée relative en polaire} + +\RRR{13-4-2} +\bigskip + +\begin{tabular}{|c|c|} \hline +\begin{tikzpicture} %[scale=.8] +\draw[help lines] (0,0) grid (4,2); + \draw[dotted] (0,0) -- (4,2); + \draw[blue,very thick] (0,0) -- (2,1) -- ([turn]-45:1cm); +\end{tikzpicture} +& +\begin{tikzpicture} %[scale=.8] +\draw[help lines] (0,0) grid (4,2); + \draw[dotted] (0,0) -- (4,2); + \draw[blue,very thick] (0,0) -- (2,1) -- ([turn]45:1cm); +\end{tikzpicture} +\\ \hline ([\RDD{turn}]-45:1cm) & ([\RDD{turn}]45:1cm) \\ +\hline +\end{tabular} + +\bigskip + +\begin{tabular}{|c|c|} \hline +\begin{tikzpicture} +\draw[help lines] (-1,0) grid (4,3); +\draw [line width=2pt] (4,0) arc (0 :120 :2) -- ([turn]90:2cm) ; + +\end{tikzpicture} +& +\begin{tikzpicture} %[scale=.8] +\draw[help lines] (0,0) grid (4,3); +\draw [line width=2pt] (0,0) to [bend left] (2,2) -- ([turn]0:2cm); +\fill [red](2,2) circle (4pt); +\end{tikzpicture} +\\ \hline +\BS{draw} (4,0) arc (0 :120 :2) - - ([\RDD{turn}]90:2cm) ; +& \BS{draw} (0,0) to [bend left] (2,2) - - ([\RDD{turn}]0:2cm); \\ + +\hline +\end{tabular} + + +%\bigskip +% +% +%\tikz [delta angle=30, radius=1cm] +%\draw (0,0) arc [start angle=0] -- ([turn]0:1cm) +%arc [start angle=30] -- ([turn]0:1cm) +%arc [start angle=60] -- ([turn]30:1cm); + + + +\bigskip + +\begin{tabular}{|c|c|c|} \hline +\multicolumn{3}{|c|}{ \BS{draw}(1,2) +.. controls ([turn]0:2cm) .. ([turn]-90:2cm); } +\\ \hline +\begin{tikzpicture} %[scale=.8] +\draw[help lines] (0,0) grid (4,4); + \draw [line width=2pt] (1,2) +.. controls ([turn]0:2cm) .. ([turn]-90:2cm); +\end{tikzpicture} +& +\begin{tikzpicture} %[scale=.8] +\draw[help lines] (0,0) grid (4,4); + \draw [line width=2pt] (1,2) +.. controls ([turn]30:2cm) .. ([turn]-90:2cm); +\end{tikzpicture} +& +\begin{tikzpicture} %[scale=.8] +\draw[help lines] (-2,0) grid (2,4); + \draw [line width=2pt] (1,2) +.. controls ([turn]0:2cm) .. ([turn]90:2cm); + +\end{tikzpicture} +\\ \hline ([turn]0:2cm) .. ([turn]-90:2cm) & ([turn]30:2cm) .. ([turn]-90:2cm) & ([turn]0:2cm) .. ([turn]90:2cm) \\ +\hline +\end{tabular} + + +\tikzset{every picture/.style=blue,very thick,inner sep=.3333em} |