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-rw-r--r--macros/latex/contrib/tkz/tkz-euclide/doc/latex/TKZdoc-euclide-pointby.tex103
1 files changed, 62 insertions, 41 deletions
diff --git a/macros/latex/contrib/tkz/tkz-euclide/doc/latex/TKZdoc-euclide-pointby.tex b/macros/latex/contrib/tkz/tkz-euclide/doc/latex/TKZdoc-euclide-pointby.tex
index 9c3f682563..a2f5584670 100644
--- a/macros/latex/contrib/tkz/tkz-euclide/doc/latex/TKZdoc-euclide-pointby.tex
+++ b/macros/latex/contrib/tkz/tkz-euclide/doc/latex/TKZdoc-euclide-pointby.tex
@@ -38,6 +38,7 @@ options & & examples \\
\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 in rad=center O angle pi/3](E)}
+\TOline{rotation with nodes}{= center \#1 from \#2 to \#3}{[center O from A to B](E)}
\TOline{inversion}{= center \#1 through \#2}{[inversion =center O through A](E)}
\TOline{inversion negative}{= center \#1 through \#2}{...}
\bottomrule
@@ -116,7 +117,8 @@ The image is only defined and not drawn.
\tkzMarkRightAngle[fill=orange!10,opacity=.4](D,G,B)
\tkzDrawPoints(A,C,F) \tkzLabelPoints(A,C,F)
\tkzDrawPoints(B,D,E,G)
- \tkzLabelPoints[above right](B,D,E,G)
+ \tkzLabelPoints[above right](B,D,E)
+ \tkzLabelPoints[above](G)
\end{tikzpicture}
\end{tkzexample}
@@ -148,13 +150,13 @@ The image is only defined and not drawn.
\tkzGetPoint{D}
\tkzDrawSegment(A,tkzPointResult)
\tkzDrawLine(B,D)
- \tkzDrawArc(A,B)(C)
- \tkzDrawArc(B,C)(A)
+ \tkzDrawArc(A,B)(C) \tkzDrawArc(B,C)(A)
\tkzDrawArc(C,D)(D)
\tkzMarkRightAngle(D,B,A)
\tkzDrawPoints(A,B)
\tkzLabelPoints(A,B)
- \tkzLabelPoints[above](C,D)
+ \tkzLabelPoints[above](C)
+ \tkzLabelPoints[right](D)
\end{tikzpicture}
\end{tkzexample}
@@ -173,6 +175,24 @@ The image is only defined and not drawn.
\end{tikzpicture}
\end{tkzexample}
+\subsubsection{\tkzname{rotation with nodes}}
+\begin{tkzexample}[latex=6cm,small]
+\begin{tikzpicture}
+ \tkzDefPoint(0,0){O}
+ \tkzDefPoint(0:2){A}
+ \tkzDefPoint(40:2){B}
+ \tkzDefPoint(20:4){C}
+ \tkzDrawLine(O,A)
+ \tkzDefPointBy[rotation with nodes%
+ =center O from A to B](C)
+ \tkzGetPoint{D}
+\tkzDrawPoints(A,B,C,D)
+\tkzDrawCircle(O,A)
+\tkzLabelPoints(A,C,D)
+\tkzLabelPoints[above](B)
+\end{tikzpicture}
+\end{tkzexample}
+
\subsubsection{\tkzname{inversion }}
Inversion is the process of transforming points to a corresponding set of points known as their inverse points. Two points $P$ and $P'$ are said to be inverses with respect to an inversion circle having inversion center $O$ and inversion radius $k$ if $P'$ is the perpendicular foot of the altitude of $OQP$, where $Q$ is a point on the circle such that $OQ$ is perpendicular to $PQ$.\\
@@ -189,14 +209,31 @@ Some propositions :
\item Angles are preserved in inversion.
\end{itemize}
-Explanation
+Explanation:
+
+Directly
+(Center O power=$k^2={OA}^2=OP \times OP'$)
+
+\begin{tkzexample}[latex=6cm,small]
+\begin{tikzpicture}[scale=.5]
+ \tkzDefPoints{4/0/A,6/0/P,0/0/O}
+ \tkzDefCircle(O,A)
+ \tkzDefPointBy[inversion = center O through A](P)
+ \tkzGetPoint{P'}
+ \tkzDrawSegments(O,P)
+ \tkzDrawCircle(O,A)
+ \tkzLabelPoints[above right,font=\scriptsize](O,A,P,P')
+ \tkzDrawPoints(O,A,P,P')
+\end{tikzpicture}
+\end{tkzexample}
+
\begin{tkzexample}[latex=6cm,small]
\begin{tikzpicture}[scale=.5]
\tkzDefPoints{4/0/A,6/0/P,0/0/O}
\tkzDefCircle(O,A)
\tkzDefLine[orthogonal=through P](O,P)
\tkzGetPoint{L}
- \tkzDefTangent[from = P](O,A) \tkzGetPoints{Q}{R}
+ \tkzDefTangent[from = P](O,A) \tkzGetPoints{R}{Q}
\tkzDefPointBy[projection=onto O--A](Q) \tkzGetPoint{P'}
\tkzDrawSegments(O,P O,A)
\tkzDrawSegments[new](O,P O,Q P,Q Q,P')
@@ -214,22 +251,6 @@ Explanation
\end{tikzpicture}
\end{tkzexample}
-Directly
-(Center O power=$k^2={OA}^2=OP \times OP'$)
-
-\begin{tkzexample}[latex=6cm,small]
-\begin{tikzpicture}[scale=.5]
- \tkzDefPoints{4/0/A,6/0/P,0/0/O}
- \tkzDefCircle(O,A)
- \tkzDefPointBy[inversion = center O through A](P)
- \tkzGetPoint{P'}
- \tkzDrawSegments(O,P)
- \tkzDrawCircle(O,A)
- \tkzLabelPoints[above right,font=\scriptsize](O,A,P,P')
- \tkzDrawPoints(O,A,P,P')
-\end{tikzpicture}
-\end{tkzexample}
-
\subsubsection{Inversion of lines}
\begin{tkzexample}[latex=6cm,small]
@@ -293,7 +314,7 @@ Directly
\tkzInterCC(A,P)(A',P') \tkzGetPoints{C}{D}
\tkzCalcLength(A,P)
\tkzGetLength{rAP}
-\tkzDefPointOnCircle[angle=190,center=A,radius=\rAP]
+\tkzDefPointOnCircle[R= angle 190 center A radius \rAP]
\tkzGetPoint{M}
\tkzDefPointBy[inversion = center O through C](M)
\tkzGetPoint{M'}
@@ -368,7 +389,7 @@ The inversion circle itself, circles orthogonal to it, and lines through the inv
\tkzInterCC(A,P)(A',P') \tkzGetPoints{C}{D}
\tkzCalcLength(A,P)
\tkzGetLength{rAP}
-\tkzDefPointOnCircle[angle=190,center=A,radius=\rAP]
+\tkzDefPointOnCircle[R= angle 190 center A radius \rAP]
\tkzGetPoint{M}
\tkzDefPointBy[inversion = center O through C](M)
\tkzGetPoint{M'}
@@ -404,7 +425,7 @@ It's an inversion followed by a symmetry of center $O$
\end{tkzexample}
-
+\newpage
\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.
@@ -446,6 +467,9 @@ options & & examples \\
\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}{}{for instance angle pi/3}
+\TOline{rotation with nodes = center \#1 from \#2 to \#3}{}{[center O from A to B](E)\{F\}}
+\TOline{inversion = center \#1 through \#2}{}{[inversion = center O through A](E)\{F\}}
+\TOline{inversion negative = center \#1 through \#2}{}{...}
\bottomrule
\end{tabular}
@@ -469,32 +493,29 @@ The points are only defined and not drawn.
\end{tikzpicture}
\end{tkzexample}
-\subsubsection{Example of symmetry}
+\subsubsection{Example of symmetry: an oval}
\begin{tkzexample}[latex=7cm,small]
-\begin{tikzpicture}[scale=.4]
+\begin{tikzpicture}[scale=0.4]
\tkzDefPoint(-4,0){I}
\tkzDefPoint(4,0){J}
\tkzDefPoint(0,0){O}
\tkzInterCC(J,O)(O,J) \tkzGetPoints{L}{H}
\tkzInterCC(I,O)(O,I) \tkzGetPoints{K}{G}
- \tkzDrawLines[add=1.5 and 1.5](I,K I,G J,H J,L)
- \tkzDrawLines[add=.5 and .5](I,J)
\tkzInterLL(I,K)(J,H) \tkzGetPoint{M}
\tkzInterLL(I,G)(J,L) \tkzGetPoint{N}
\tkzDefPointsBy[symmetry=center J](L,H){D,E}
\tkzDefPointsBy[symmetry=center I](G,K){C,F}
- \tkzDrawPoints(H,L,K,G,I,J,D,E,C,F,M,N)
- \tkzDrawCircle[R](O,4)
- \tkzDrawCircle[R](I,4)
- \tkzDrawCircle[R](J,4)
- \tkzDrawArc(N,D)(C)
- \tkzDrawArc(M,F)(E)
- \tkzDrawArc(J,E)(D)
- \tkzDrawArc(I,C)(F)
- \tkzLabelPoints[font=\scriptsize](H,L,K,G,I,J,%
- D,E,C,F,M,N)
-\end{tikzpicture}
-\end{tkzexample}
+ \begin{scope}[line style/.style = {very thin,teal}]
+ \tkzDrawLines[add=1.5 and 1.5](I,K I,G J,H J,L)
+ \tkzDrawLines[add=.5 and .5](I,J)
+ \tkzDrawCircles(O,I I,O J,O)
+ \tkzDrawArc[delta=0,orange](N,D)(C)
+ \tkzDrawArc[delta=0,orange](M,F)(E)
+ \tkzDrawArc[delta=0,orange](J,E)(D)
+ \tkzDrawArc[delta=0,orange](I,C)(F)
+ \end{scope}
+\end{tikzpicture}
+\end{tkzexample}
\endinput \ No newline at end of file