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-rw-r--r--Master/texmf-dist/doc/latex/tkz-euclide/latex/TKZdoc-euclide-pointby.tex171
1 files changed, 81 insertions, 90 deletions
diff --git a/Master/texmf-dist/doc/latex/tkz-euclide/latex/TKZdoc-euclide-pointby.tex b/Master/texmf-dist/doc/latex/tkz-euclide/latex/TKZdoc-euclide-pointby.tex
index 35046719d0c..fdc4f91fb99 100644
--- a/Master/texmf-dist/doc/latex/tkz-euclide/latex/TKZdoc-euclide-pointby.tex
+++ b/Master/texmf-dist/doc/latex/tkz-euclide/latex/TKZdoc-euclide-pointby.tex
@@ -1,26 +1,26 @@
\section{Definition of points by transformation; \tkzcname{tkzDefPointBy} }
These transformations are:
-\begin{enumerate}
- \item the translation;
- \item l'homothety;
+\begin{itemize}
+ \item translation;
+ \item homothety;
\item orthogonal reflection or symmetry;
\item central symmetry;
\item orthogonal projection;
\item rotation (degrees or radians);
- \item inversion with respect to a circle
-\end{enumerate}
+ \item inversion with respect to a circle.
+\end{itemize}
-The choice of transformations is made through the options. There are two macros, one for the transformation of a single point \tkzcname{tkzDefPointBy} and the other for the transformation of a list of points \tkzcname{tkzDefPointsBy}. By default the image of $A$ is $A'$. For example, we'll write~:
+The choice of transformations is made through the options. There are two macros, one for the transformation of a single point \tkzcname{tkzDefPointBy} and the other for the transformation of a list of points \tkzcname{tkzDefPointsBy}. By default the image of $A$ is $A'$. For example, we'll write:
\begin{tkzltxexample}[]
-\tkzDefPointBy[translation= from A to A'](B) the result is in \tkzname{tkzPointResult}}
+\tkzDefPointBy[translation= from A to A'](B)
\end{tkzltxexample}
-
+The result is in \tkzname{tkzPointResult}
\medskip
-\begin{NewMacroBox}{tkzDefPointBy}{\oarg{local options}\parg{pt}}
+\begin{NewMacroBox}{tkzDefPointBy}{\oarg{local options}\parg{pt}}%
The argument is a simple existing point and its image is stored in \tkzname{tkzPointResult}. If you want to keep this point then the macro \tkzcname{tkzGetPoint\{M\}} allows you to assign the name \tkzname{M} to the point.
-\begin{tabular}{lll}
+\begin{tabular}{lll}%
\toprule
arguments & definition & examples \\
\midrule
@@ -28,7 +28,7 @@ arguments & definition & examples \\
\bottomrule
\end{tabular}
-\begin{tabular}{lll}
+\begin{tabular}{lll}%
options & & examples \\
\midrule
\TOline{translation}{= from \#1 to \#2}{[translation=from A to B](E)}
@@ -37,7 +37,7 @@ options & & examples \\
\TOline{symmetry } {= center \#1}{[symmetry=center A](E)}
\TOline{projection }{= onto \#1--\#2}{[projection=onto A--B](E)}
\TOline{rotation } {= center \#1 angle \#2}{[rotation=center O angle 30](E)}
-\TOline{rotation in rad}{= center \#1 angle \#2}{rotation=center O angle pi/3}
+\TOline{rotation in rad}{= center \#1 angle \#2}{[rotation in rad=center O angle pi/3](E)}
\TOline{inversion}{= center \#1 through \#2}{[inversion =center O through A](E)}
\bottomrule
\end{tabular}
@@ -45,14 +45,26 @@ options & & examples \\
The image is only defined and not drawn.
\end{NewMacroBox}
-\subsection{Orthogonal reflection or symmetry }
+\subsection{Examples of transformations}
+\subsubsection{Example of translation}
-\subsubsection{Example of reflection}
+\subsection{Example of translation}
+\begin{tkzexample}[latex=7cm,small]
+\begin{tikzpicture}[>=latex]
+ \tkzDefPoint(0,0){A} \tkzDefPoint(3,1){B}
+ \tkzDefPoint(3,0){C}
+ \tkzDefPointBy[translation= from B to A](C)
+ \tkzGetPoint{D}
+ \tkzDrawPoints[teal](A,B,C,D)
+ \tkzLabelPoints[color=teal](A,B,C,D)
+ \tkzDrawSegments[orange,->](A,B D,C)
+\end{tikzpicture}
+\end{tkzexample}
+
+\subsubsection{Example of reflection (orthogonal symmetry)}
\begin{tkzexample}[vbox,small]
\begin{tikzpicture}[scale=1]
- \tkzInit[ymin=-4,ymax=6,xmin=-7,xmax=3]
- \tkzClip
\tkzDefPoints{1.5/-1.5/C,-4.5/2/D}
\tkzDefPoint(-4,-2){O}
\tkzDefPoint(-2,-2){A}
@@ -69,56 +81,50 @@ The image is only defined and not drawn.
\end{tikzpicture}
\end{tkzexample}
-
-\subsection{Homothety}
-\subsubsection{Example of homothety and projection}
+
+\subsubsection{Example of \tkzname{homothety} and \tkzname{projection}}
\begin{tkzexample}[vbox,small]
-\begin{tikzpicture}[scale=1.25]
- \tkzInit \tkzClip
- \tkzDefPoint(0,1){A} \tkzDefPoint(6,3){B} \tkzDefPoint(3,6){C}
- \tkzDrawLines[add= 0 and .3](A,B A,C)
+\begin{tikzpicture}[scale=1.2]
+ \tkzDefPoint(0,1){A} \tkzDefPoint(5,3){B} \tkzDefPoint(3,4){C}
\tkzDefLine[bisector](B,A,C) \tkzGetPoint{a}
\tkzDrawLine[add=0 and 0,color=magenta!50 ](A,a)
\tkzDefPointBy[homothety=center A ratio .5](a) \tkzGetPoint{a'}
- \tkzDefPointBy[projection = onto A--B](a') \tkzGetPoint{k}
- \tkzDrawSegment[blue](a',k)
- \tkzDrawPoints(a,a',k,A)
- \tkzDrawCircle(a',k)
+ \tkzDefPointBy[projection = onto A--B](a') \tkzGetPoint{k'}
+ \tkzDefPointBy[projection = onto A--B](a) \tkzGetPoint{k}
+ \tkzDrawLines[add= 0 and .3](A,k A,C)
+ \tkzDrawSegments[blue](a',k' a,k)
+ \tkzDrawPoints(a,a',k,k',A)
+ \tkzDrawCircles(a',k' a,k)
\tkzLabelPoints(a,a',k,A)
\end{tikzpicture}
\end{tkzexample}
-\subsection{The projection }
\subsubsection{Example of projection}
-
\begin{tkzexample}[vbox,small]
\begin{tikzpicture}[scale=1.5]
- \tkzInit[xmin=-3,xmax=5,ymax=4] \tkzClip[space=.5]
\tkzDefPoint(0,0){A}
\tkzDefPoint(0,4){B}
- \tkzDrawTriangle[pythagore](B,A) \tkzGetPoint{C}
+ \tkzDefTriangle[pythagore](B,A) \tkzGetPoint{C}
\tkzDefLine[bisector](B,C,A) \tkzGetPoint{c}
\tkzInterLL(C,c)(A,B) \tkzGetPoint{D}
- \tkzDrawSegment(C,D)
- \tkzDrawCircle(D,A)
\tkzDefPointBy[projection=onto B--C](D) \tkzGetPoint{G}
\tkzInterLC(C,D)(D,A) \tkzGetPoints{E}{F}
+ \tkzDrawPolygon[teal](A,B,C)
+ \tkzDrawSegment(C,D)
+ \tkzDrawCircle(D,A)
+ \tkzDrawSegment[orange](D,G)
+ \tkzMarkRightAngle[fill=orange!20](D,G,B)
\tkzDrawPoints(A,C,F) \tkzLabelPoints(A,C,F)
\tkzDrawPoints(B,D,E,G)
\tkzLabelPoints[above right](B,D,E,G)
\end{tikzpicture}
\end{tkzexample}
-
-
-\newpage
-\subsection{Symmetry }
\subsubsection{Example of symmetry}
-
\begin{tkzexample}[vbox,small]
-\begin{tikzpicture}[scale=1.5]
+\begin{tikzpicture}[scale=1]
\tkzDefPoint(0,0){O}
\tkzDefPoint(2,-1){A}
\tkzDefPoint(2,2){B}
@@ -134,84 +140,65 @@ The image is only defined and not drawn.
\end{tikzpicture}
\end{tkzexample}
-
-\newpage
-\subsection{Rotation }
\subsubsection{Example of rotation}
-
-
-\begin{tkzexample}[latex=8cm,small]
- \begin{tikzpicture}[scale=1]
- \tkzInit
+\begin{tkzexample}[latex=7cm,small]
+\begin{tikzpicture}[scale=0.5]
\tkzDefPoint(0,0){A}
\tkzDefPoint(5,0){B}
\tkzDrawSegment(A,B)
- \tkzDefPointBy[rotation=%
- center A angle 60](B)
+ \tkzDefPointBy[rotation=center A angle 60](B)
\tkzGetPoint{C}
- \tkzDefPointBy[symmetry=%
- center C](A)
+ \tkzDefPointBy[symmetry=center C](A)
\tkzGetPoint{D}
\tkzDrawSegment(A,tkzPointResult)
\tkzDrawLine(B,D)
- \tkzDrawArc[delta=10](A,B)(C)
- \tkzDrawArc[delta=10](B,C)(A)
- \tkzDrawArc[delta=10](C,D)(D)
+ \tkzDrawArc[orange,delta=10](A,B)(C)
+ \tkzDrawArc[orange,delta=10](B,C)(A)
+ \tkzDrawArc[orange,delta=10](C,D)(D)
\tkzMarkRightAngle(D,B,A)
\end{tikzpicture}
\end{tkzexample}
-
-\subsection{Rotation in radian }
\subsubsection{Example of rotation in radian}
-
-\begin{tkzexample}[latex=8cm,small]
+\begin{tkzexample}[latex=6cm,small]
\begin{tikzpicture}
\tkzDefPoint["$A$" left](1,5){A}
\tkzDefPoint["$B$" right](5,2){B}
\tkzDefPointBy[rotation in rad= center A angle pi/3](B)
- \tkzGetPoint{C}
-
+ \tkzGetPoint{C}
\tkzDrawSegment(A,B)
\tkzDrawPoints(A,B,C)
\tkzCompass[color=red](A,C)
- \tkzCompass[color=red](B,C)
-
+ \tkzCompass[color=red](B,C)
\tkzLabelPoints(C)
\end{tikzpicture}
\end{tkzexample}
-
-\newpage
-\subsection{Inversion with respect to a circle }
\subsubsection{Inversion of points}
-
-
\begin{tkzexample}[latex=8cm,small]
\begin{tikzpicture}[scale=1.5]
\tkzDefPoint(0,0){O}
\tkzDefPoint(1,0){A}
- \tkzDrawCircle(O,A)
\tkzDefPoint(-1.5,-1.5){z1}
\tkzDefPoint(0.35,0){z2}
- \tkzDrawPoints[color=black,
- fill=red,size=4](O,z1,z2)
\tkzDefPointBy[inversion =%
center O through A](z1)
\tkzGetPoint{Z1}
\tkzDefPointBy[inversion =%
center O through A](z2)
- \tkzGetPoint{Z2}
+ \tkzGetPoint{Z2}
+ \tkzDrawCircle(O,A)
\tkzDrawPoints[color=black,
fill=red,size=4](Z1,Z2)
\tkzDrawSegments(z1,Z1 z2,Z2)
+ \tkzDrawPoints[color=black,
+ fill=red,size=4](O,z1,z2)
\tkzLabelPoints(O,A,z1,z2,Z1,Z2)
\end{tikzpicture}
\end{tkzexample}
\subsubsection{Point Inversion: Orthogonal Circles}
-
\begin{tkzexample}[latex=8cm,small]
\begin{tikzpicture}[scale=1.5]
\tkzDefPoint(0,0){O}
@@ -230,24 +217,29 @@ The image is only defined and not drawn.
\end{tikzpicture}
\end{tkzexample}
-\newpage
-\section{Transformation of multiple points; \tkzcname{tkzDefPointsBy} }
-
+\subsection{Transformation of multiple points; \tkzcname{tkzDefPointsBy} }
Variant of the previous macro for defining multiple images.
You must give the names of the images as arguments, or indicate that the names of the images are formed from the names of the antecedents, leaving the argument empty.
\begin{tkzltxexample}[]
-\tkzDefPointsBy[translation= from A to A'](B,C){} the images are B' and C'.
-\tkzDefPointsBy[translation= from A to A'](B,C){D,E} the images are D and E
-\tkzDefPointsBy[translation= from A to A'](B) the image is B'.
+\tkzDefPointsBy[translation= from A to A'](B,C){}
\end{tkzltxexample}
+The images are $B'$ and $C'$.
-\begin{NewMacroBox}{tkzDefPointsBy}{\oarg{local options}\parg{list of points}\marg{list of points}}
-\begin{tabular}{lll}
-\toprule
-arguments & exemples & \\
+\begin{tkzltxexample}[]
+\tkzDefPointsBy[translation= from A to A'](B,C){D,E}
+\end{tkzltxexample}
+The images are $D$ and $E$.
+
+\begin{tkzltxexample}[]
+\tkzDefPointsBy[translation= from A to A'](B)
+\end{tkzltxexample}
+The image is $B'$.
+\begin{NewMacroBox}{tkzDefPointsBy}{\oarg{local options}\parg{list of points}\marg{list of points}}%
+\begin{tabular}{lll}%
+arguments & examples & \\
\midrule
-\TAline{\parg{liste de pts}\marg{list of pts}}{(A,B)\{E,F\}}{E is the image of A and F is the image of B.} \\
+\TAline{\parg{list of points}\marg{list of pts}}{(A,B)\{E,F\}}{$E$ is the image of $A$ and $F$ is the image of $B$.} \\
\bottomrule
\end{tabular}
@@ -255,9 +247,9 @@ arguments & exemples & \\
If the list of images is empty then the name of the image is the name of the antecedent to which " ' " is added.
\medskip
-\begin{tabular}{lll}
+\begin{tabular}{lll}%
\toprule
-options & & exemples \\
+options & & examples \\
\midrule
\TOline{translation = from \#1 to \#2}{}{[translation=from A to B](E)\{\}}
\TOline{homothety = center \#1 ratio \#2}{}{[homothety=center A ratio .5](E)\{F\}}
@@ -265,7 +257,7 @@ options & & exemples \\
\TOline{symmetry = center \#1}{}{[symmetry=center A](E)\{F\}}
\TOline{projection = onto \#1--\#2}{}{[projection=onto A--B](E)\{F\}}
\TOline{rotation = center \#1 angle \#2}{}{[rotation=center angle 30](E)\{F\}}
-\TOline{rotation in rad = center \#1 angle \#2}{}{par exemple angle pi/3}
+\TOline{rotation in rad = center \#1 angle \#2}{}{for instance angle pi/3}
\bottomrule
\end{tabular}
@@ -273,11 +265,10 @@ options & & exemples \\
The points are only defined and not drawn.
\end{NewMacroBox}
-\subsection{Example de translation}
-
+\subsubsection{Example of translation}
\begin{tkzexample}[latex=7cm,small]
-\begin{tikzpicture}
- \tkzDefPoint(0,0){A} \tkzDefPoint(4,2){A'}
+\begin{tikzpicture}[>=latex]
+ \tkzDefPoint(0,0){A} \tkzDefPoint(3,1){A'}
\tkzDefPoint(3,0){B} \tkzDefPoint(1,2){C}
\tkzDefPointsBy[translation= from A to A'](B,C){}
\tkzDrawPolygon[color=blue](A,B,C)