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authorNorbert Preining <norbert@preining.info>2023-12-16 03:01:40 +0000
committerNorbert Preining <norbert@preining.info>2023-12-16 03:01:40 +0000
commitcf11d08f6fe4d61a3da648d820601e3fca67d8d4 (patch)
tree2eea226ec62bd73e49dce85df85c093393d58af3 /macros/latex/contrib/tkz/tkz-elements/doc
parent9dd4909414ccbc438a2c6276bf642904d6036891 (diff)
CTAN sync 202312160301
Diffstat (limited to 'macros/latex/contrib/tkz/tkz-elements/doc')
-rw-r--r--macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-circle.tex320
-rw-r--r--macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-line.tex2
-rw-r--r--macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-point.tex111
-rw-r--r--macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-triangle.tex6
-rw-r--r--[-rwxr-xr-x]macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-examples.tex60
-rw-r--r--macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-main.pdfbin537824 -> 0 bytes
-rw-r--r--macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-main.tex11
-rw-r--r--macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-presentation.tex22
-rw-r--r--macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-transferts.tex4
-rw-r--r--macros/latex/contrib/tkz/tkz-elements/doc/tkz-elements.pdfbin537824 -> 551541 bytes
10 files changed, 420 insertions, 116 deletions
diff --git a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-circle.tex b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-circle.tex
index 6eb97c239b..1ed09078a3 100644
--- a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-circle.tex
+++ b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-circle.tex
@@ -115,8 +115,8 @@ Three attributes are used (south, west, radius).
\midrule
\Imeth{circle}{orthogonal\_from (pt)} & |C = C.OA: orthogonal_from (z.P)| & \\
\Imeth{circle}{orthogonal\_through (pta,ptb)} & |C = C.OA: orthogonal_through (z.z1,z.z2)|\\
-\Imeth{circle}{inversion (circle)} & |L or C = C.AC: inversion (C.EF)|&\\
-
+\Imeth{circle}{inversion (...)} & | C.AC: inversion (pt, pts, L or C )|& see \ref{ssub:inversion}, \ref{ssub:inversion_point}, \ref{ssub:inversion_line}, \ref{ssub:inversion_circle}\\
+\Imeth{circle}{midcircle (C)} & |C.inv = C.OA: midcircle (C.EF)| & see \ref{ssub:midcircle} \\
\midrule
\textbf{Miscellaneous} &&\\
\midrule
@@ -265,7 +265,7 @@ The "inversion" method can be used on a point, a line or a circle. Depending on
\subsubsection{Inversion: point} % (fold)
\label{ssub:inversion_point}
-The "inversion" method can be used on a point, a line or a circle. Depending on the type of object, the function determines the correct algorithm to use.
+The "inversion" method can be used on a point, a group of points, a line or a circle. Depending on the type of object, the function determines the correct algorithm to use.
\begin{minipage}{.5\textwidth}
\begin{verbatim}
@@ -424,9 +424,321 @@ color = "orange"
\tkzLabelPoints(a,...,f,o,p,q)
\end{tikzpicture}
\end{minipage}
+% subsubsection inversion (end)
+\subsubsection{midcircle} % (fold)
+\label{ssub:midcircle}
-% subsubsection inversion (end)
+\begin{minipage}{0.95\linewidth }
+\emph{From Eric Danneels and Floor van Lamoen: A midcircle of two given circles is a circle that swaps the two given circles by inversion. Midcircles are in the same pencil of circles as the given circles. The center of the midcircle(s) is one or both of the centers of similitude. We can distinguish four cases:
+\begin{enumerate}[label=(\roman*)]
+ \item The two given circles intersect: there are two midcircles with centers at the centers of similitude of the given circles;
+ \item One given circle is in the interior of the other given circle. Then there is one midcircle with center of similitude at the internal center of similitude of the given circles;
+ \item One given circle is in the exterior of the other given circle. Then there is one midcircle with center at the external center of similitude of the given circles.
+Clearly the tangency cases can be seen as limit cases of the above;
+\item If the circles intersect in a single point, the unique midcircle has center at the external similitude center or at internal similitude center.
+\end{enumerate} }
+\end{minipage}
+
+
+Let's look at each of these cases:
+\begin{enumerate}[label=(\roman*)]
+\item If the two given circles intersect, then there are two circles of inversion through their common points, with centers at the centers of similitudes. The two midcircles bisect their angles and are orthogonal to each other. The centers of the midcircles are the internal center of similitude and the external center of similitude $I$ and $J$.
+
+Consider two intersecting circles $(\mathcal{A})$ and $(\mathcal{B})$.
+We can obtain the centers of similarity of these two circles by constructing $EH$ and $FG$ two diameters parallel of the circles $(\mathcal{A})$ and $(\mathcal{B})$. The line $(GE)$ intercepts the line $(AB)$ in $J$ and the line $(EF)$ intercepts the line $(AB)$ in $I$. The circles $(\mathcal{I})$ and $(\mathcal{J})$ are orthogonal and are the midcircles of $(\mathcal{A})$ and $(\mathcal{B})$. The division $(A,B;I,J)$ is harmonic.
+
+\begin{minipage}{.4\textwidth}
+\begin{verbatim}
+\begin{tkzelements}
+scale = .8
+z.A = point : new ( 1 , 0 )
+z.B = point : new ( 3 , 0 )
+z.O = point : new ( 2.1, 0 )
+z.P = point : new ( 1 ,0 )
+C.AO = circle : new (z.A,z.O)
+C.BP = circle : new (z.B,z.P)
+z.E = C.AO.south
+z.H = C.AO.north
+z.F = C.BP.north
+z.G = C.BP.south
+C.IT,C.JV = midcircle_ (C.AO,C.BP)
+z.I,z.T = get_points ( C.IT )
+z.J,z.V = get_points ( C.JV )
+z.X,z.Y = intersection (C.AO,C.BP)
+\end{tkzelements}
+\end{verbatim}
+\end{minipage}
+\begin{minipage}{.6\textwidth}
+ \begin{tkzelements}
+ scale = .8
+ z.A = point : new ( 1 , 0 )
+ z.B = point : new ( 3 , 0 )
+ z.O = point : new ( 2.1, 0 )
+ z.P = point : new ( 1 ,0 )
+ C.AO = circle : new (z.A,z.O)
+ C.BP = circle : new (z.B,z.P)
+ z.E = C.AO.south
+ z.H = C.AO.north
+ z.F = C.BP.north
+ z.G = C.BP.south
+ C.IT,C.JV = midcircle_ (C.AO,C.BP)
+ z.I,z.T = get_points ( C.IT )
+ z.J,z.V = get_points ( C.JV )
+ z.X,z.Y = intersection (C.AO,C.BP)
+ \end{tkzelements}
+ \begin{tikzpicture}
+ \tkzGetNodes
+ \tkzDrawCircles[teal,thick](A,O B,P)
+ \tkzDrawSegments[dashed,red](E,F I,B I,G I,F)
+ \tkzDrawLines[gray](I,T J,V)
+ \tkzDrawCircles[teal,thick](A,O B,P)
+ \tkzDrawCircles[red,thick](I,X J,X)
+ \tkzDrawPoints(A,B,I,J,E,F,G,H,X,Y)
+ \tkzDrawPoints[red](I,J)
+ \begin{scope}[font = \scriptsize]
+ \tkzLabelPoints(A,I,J,G)
+ \tkzLabelPoints[below left](E)
+ \tkzLabelPoints[right](B)
+ \tkzLabelPoints[above](F,H,X)
+ \tkzLabelPoints[above right](Y)
+ \end{scope}
+ \end{tikzpicture}
+\end{minipage}
+
+
+\vfill
+
+\item One given circle is in the interior of the other given circle.
+
+\begin{minipage}{.6\textwidth}
+\begin{verbatim}
+ \begin{tkzelements}
+ scale =.75
+ z.A = point : new ( 3 , 0 )
+ z.B = point : new ( 5 , 0 )
+ z.O = point : new ( 2 , 0 )
+ z.P = point : new ( 1 , 0 )
+ L.AB = line : new (z.A,z.B)
+ C.AO = circle : new (z.A,z.O)
+ C.BP = circle : new (z.B,z.P)
+ z.R,z.S = intersection (L.AB,C.BP)
+ z.U,z.V = intersection (L.AB,C.AO)
+ C.SV = circle : diameter (z.S,z.V)
+ C.UR = circle : diameter (z.U,z.R)
+ z.x = C.SV.center
+ z.y = C.UR.center
+ C.IT = midcircle_ (C.AO,C.BP)
+ z.I,z.T = get_points ( C.IT )
+\end{tkzelements}
+\end{verbatim}
+\end{minipage}
+\begin{minipage}{.6\textwidth}
+ \begin{tkzelements}
+ scale =.75
+ z.A = point : new ( 3 , 0 )
+ z.B = point : new ( 5 , 0 )
+ z.O = point : new ( 2 , 0 )
+ z.P = point : new ( 1 , 0 )
+ L.AB = line : new (z.A,z.B)
+ C.AO = circle : new (z.A,z.O)
+ C.BP = circle : new (z.B,z.P)
+ z.R,z.S = intersection (L.AB,C.BP)
+ z.U,z.V = intersection (L.AB,C.AO)
+ C.SV = circle : diameter (z.S,z.V)
+ C.UR = circle : diameter (z.U,z.R)
+ z.x = C.SV.center
+ z.y = C.UR.center
+ C.IT = midcircle_ (C.AO,C.BP)
+ z.I,z.T = get_points ( C.IT )
+ \end{tkzelements}
+ \begin{tikzpicture}
+ \tkzGetNodes
+ \tkzDrawCircles[teal,thick](A,O B,P)
+ \tkzDrawCircles[green!20!black](x,S y,R)
+ \tkzDrawPoints(A,B)
+ \tkzDrawPoints[red](I)
+ \tkzLabelPoints(A,B,I)
+ \tkzDrawCircles[red,thick](I,T)
+ \tkzLabelCircle[below](x,V)(270){$(\alpha)$}
+ \tkzLabelCircle[below](y,R)(270){$(\beta)$}
+ \tkzLabelCircle[below](I,T)(250){$\textcolor{red}{(\gamma)}$}
+ \end{tikzpicture}
+ \end{minipage}
+
+
+This case is a little more complicated. We'll construct the two circles $(\alpha)$ and $(\beta)$ tangent to the two given circles. Then we construct the radical circle orthogonal to the circles $(\alpha)$ and $(\beta)$. Its center is the radical center as well as the center of internal similtude of circles of center $A$ and $B$.
+
+\item When the two given circles are external to each other, we construct the external center of similitude of the two given circles.
+$I$ is the center of external similarity of the two given circles. To obtain the inversion circle, simply note that $H$ is such that $IH^2= IE\times IF$
+
+\begin{minipage}{.4\textwidth}
+\begin{verbatim}
+\begin{tkzelements}
+scale=.75
+local a,b,c,d
+z.A = point : new ( 0 , 0 )
+z.B = point : new ( 4 , 0 )
+z.a = point : new ( .5 , 0)
+z.b = point : new ( 1 , 0)
+C.Aa = circle : new (z.A,z.a)
+C.Bb = circle : new (z.B,z.b)
+L.AB = line : new (z.A,z.B)
+z.E = C.Aa.north
+z.F = C.Bb.north
+L.EF = line : new (z.E,z.F)
+C.IT = midcircle_ (C.Aa,C.Bb)
+z.I,z.T = get_points ( C.IT )
+L.TF = C.Bb : tangent_from (z.I)
+z.H = intersection (L.TF,C.IT)
+z.E = intersection (L.TF,C.Aa)
+z.F=L.TF.pb
+\end{tkzelements}
+\end{verbatim}
+\end{minipage}
+\begin{minipage}{.6\textwidth}
+\begin{tkzelements}
+scale=.75
+local a,b,c,d
+z.A = point : new ( 0 , 0 )
+z.B = point : new ( 4 , 0 )
+z.a = point : new ( .5 , 0)
+z.b = point : new ( 1 , 0)
+C.Aa = circle : new (z.A,z.a)
+C.Bb = circle : new (z.B,z.b)
+L.AB = line : new (z.A,z.B)
+z.E = C.Aa.north
+z.F = C.Bb.north
+L.EF = line : new (z.E,z.F)
+C.IT = midcircle_ (C.Aa,C.Bb)
+z.I,z.T = get_points ( C.IT )
+L.TF = C.Bb : tangent_from (z.I)
+z.H = intersection (L.TF,C.IT)
+z.E = intersection (L.TF,C.Aa)
+z.F=L.TF.pb
+\end{tkzelements}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircles[teal,thick](A,a B,b)
+\tkzDrawCircles[red,thick](I,T)
+\tkzDrawSegments[gray](I,F)
+\tkzDrawPoints(A,B,E,F)
+\tkzDrawPoints[red](I,H)
+\tkzDrawLine(I,B)
+\tkzLabelPoints(A,B)
+\tkzLabelPoints[above](E,F)
+\tkzLabelPoints[above left,red](I,H)
+\end{tikzpicture}
+\end{minipage}
+
+
+\item Consider two tangent circles $(\mathcal{A})$ and $(\mathcal{B})$,
+\begin{itemize}
+
+\item $(\mathcal{B})$ being external and angent to $(\mathcal{A})$. The construction is identical to the previous one.
+
+\begin{minipage}{.4\textwidth}
+\begin{verbatim}
+\begin{tkzelements}
+scale=.75
+local a,b,c,d
+z.A = point : new ( 0 , 0 )
+z.B = point : new ( 4 , 0 )
+z.a = point : new ( 1 , 0)
+z.b = point : new ( 1 , 0)
+C.Aa = circle : new (z.A,z.a)
+C.Bb = circle : new (z.B,z.b)
+L.AB = line : new (z.A,z.B)
+z.E = C.Aa.north
+z.F = C.Bb.north
+L.EF = line : new (z.E,z.F)
+C.IT = midcircle_ (C.Aa,C.Bb)
+z.I,z.T = get_points ( C.IT )
+L.TF = C.Bb : tangent_from (z.I)
+z.H = intersection (L.TF,C.IT)
+z.E = intersection (L.TF,C.Aa)
+z.F=L.TF.pb
+\end{tkzelements}
+\end{verbatim}
+\end{minipage}
+\begin{minipage}{.6\textwidth}
+\begin{tkzelements}
+scale=.75
+local a,b,c,d
+z.A = point : new ( 0 , 0 )
+z.B = point : new ( 4 , 0 )
+z.a = point : new ( 1 , 0)
+z.b = point : new ( 1 , 0)
+C.Aa = circle : new (z.A,z.a)
+C.Bb = circle : new (z.B,z.b)
+L.AB = line : new (z.A,z.B)
+z.E = C.Aa.north
+z.F = C.Bb.north
+L.EF = line : new (z.E,z.F)
+C.IT = midcircle_ (C.Aa,C.Bb)
+z.I,z.T = get_points ( C.IT )
+L.TF = C.Bb : tangent_from (z.I)
+z.H = intersection (L.TF,C.IT)
+z.E = intersection (L.TF,C.Aa)
+z.F=L.TF.pb
+\end{tkzelements}
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircles[teal,thick](A,a B,b)
+\tkzDrawCircles[red,thick](I,T)
+\tkzDrawSegments[gray](I,F)
+\tkzDrawPoints(A,B,E,F)
+\tkzDrawPoints[red](I,H)
+\tkzDrawLine(I,B)
+\tkzLabelPoints(A,B)
+\tkzLabelPoints[above](E,F)
+\tkzLabelPoints[above left,red](I,H)
+\end{tikzpicture}
+\end{minipage}
+
+
+\item When one of the given circles is inside and tangent to the other, the construction is easy.
+
+\begin{minipage}{.4\textwidth}
+\begin{verbatim}
+\begin{tkzelements}
+z.A = point : new ( 2 , 0 )
+z.B = point : new ( 4 , 0 )
+z.a = point : new ( 1 , 0)
+z.b = point : new ( 1 , 0)
+C.Aa = circle : new (z.A,z.a)
+C.Bb = circle : new (z.B,z.b)
+C.IT = midcircle_ (C.Aa,C.Bb)
+z.I,z.T = get_points ( C.IT )
+\end{tkzelements}
+\end{verbatim}
+\end{minipage}
+\begin{minipage}{.6\textwidth}
+\begin{tkzelements}
+z.A = point : new ( 2 , 0 )
+z.B = point : new ( 4 , 0 )
+z.a = point : new ( 1 , 0)
+z.b = point : new ( 1 , 0)
+C.Aa = circle : new (z.A,z.a)
+C.Bb = circle : new (z.B,z.b)
+C.IT = midcircle_ (C.Aa,C.Bb)
+z.I,z.T = get_points ( C.IT )
+\end{tkzelements}
+
+\begin{tikzpicture}
+\tkzGetNodes
+\tkzDrawCircles[teal,thick](A,a B,b)
+\tkzDrawCircles[red,thick](I,T)
+\tkzDrawPoints(A,B)
+\tkzDrawPoints[red](I)
+\tkzLabelPoints(A,B)
+\tkzLabelPoints[above left,red](I)
+\end{tikzpicture}
+\end{minipage}
+\end{itemize}
+\end{enumerate}
+
+% subsubsection midcircle (end)
% subsection methods_of_the_class_circle (end)
diff --git a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-line.tex b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-line.tex
index 1bd4b831e4..337a36f2eb 100644
--- a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-line.tex
+++ b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-line.tex
@@ -397,7 +397,7 @@ z.a,z.b = L.ab.pa,L.ab.pb
\tkzGetNodes
\tkzDrawPoints(A,...,F)
\tkzLabelPoints(A,...,F)
-\tkzDrawSegments[->,red,> =latex](C,E D,F A,B) )
+\tkzDrawSegments[->,red,> =latex](C,E D,F A,B)
\end{tikzpicture}
\end{tkzexample}
\end{minipage}
diff --git a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-point.tex b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-point.tex
index c9b5928ff0..ef9ddbfc76 100644
--- a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-point.tex
+++ b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-point.tex
@@ -8,73 +8,70 @@ The class on which the whole edifice rests, it's the class \Iclass{point}. This
The creation of a point is done using the following method, but there are other possibilities. If a scaling factor has been given, the method takes it into account.
-\setbox\strutbox=\hbox{\vrule height6.8pt depth3.2pt width0pt}
\def\size{42mm}
\begin{tikzpicture}[remember picture]
- \node[ draw, fill=red!10] (tbl) {%
+\node[ draw, fill=red!10] (tbl) {%
\centering
- \begin{minipage}{\size}
- \hspace{\fill} \texttt{Arguments}\hspace{\fill}
-
- \tikz\node[minimum width=\size,font=\small,
- draw, fill=cyan!10,
- rectangle split, rectangle split parts=5
- ] {
- \texttt{re (real)\strutbox}
- \nodepart{two}\texttt{im (real)\strutbox}
- \nodepart{three}\texttt{type = 'point'\strutbox}
- \nodepart{four}\texttt{argument (rad)\strutbox}
- \nodepart{five}\texttt{modulus (cm)\strutbox}
- };
-
- \hspace{\fill} \texttt{Methods}\hspace{\fill}
-
- \tikz\node[minimum width=\size,font=\small,
- draw, fill=orange!20,sharp corners,
- rectangle split, rectangle split parts=4
- ] {
- \texttt{homothety(coeff,obj)\strutbox}
- \nodepart{two}\texttt{rotation (angle,object)\strutbox}
- \nodepart{three}\texttt{symmetry (object)\strutbox}
- \nodepart{four}\texttt{\ldots}
- };
-
- \end{minipage}
- };
+\begin{minipage}{\size}
+
+ \hspace{\fill} \texttt{Arguments}\hspace{\fill}
+
+ \tikz\node[minimum width=\size,font=\small,
+ draw, fill=cyan!10,
+ rectangle split, rectangle split parts=5
+ ] {
+ \texttt{re (real)}
+ \nodepart{two}\texttt{im (real)}
+ \nodepart{three}\texttt{type = 'point'}
+ \nodepart{four}\texttt{argument (rad)}
+ \nodepart{five}\texttt{modulus (cm)}
+ };
+
+ \hspace{\fill} \texttt{Methods}\hspace{\fill}
+
+ \tikz\node[minimum width=\size,font=\small,
+ draw, fill=orange!20,sharp corners,
+ rectangle split, rectangle split parts=4
+ ] {
+ \texttt{homothety(coeff,obj)}
+ \nodepart{two}\texttt{rotation (angle,object)}
+ \nodepart{three}\texttt{symmetry (object)}
+ \nodepart{four}\texttt{\ldots}
+ };
+\end{minipage}};
\node[ draw, fill=red!10,,minimum height = 2em,
rounded corners,anchor=south] (tc) at (tbl.north){Class |Point|};
\end{tikzpicture}
\hspace{5cm}\begin{tikzpicture}[remember picture]
\node[ draw, fill=red!10] (tbl) {%
\centering
- \begin{minipage}{\size}
- \hspace{\fill} \texttt{Arguments}\hspace{\fill}
-
- \tikz\node[minimum width=\size,font=\small,
- draw, fill=cyan!10,
- rectangle split, rectangle split parts=5
- ] {
- \texttt{re = 1\strutbox}
- \nodepart{two}\texttt{im = 2\strutbox}
- \nodepart{three}\texttt{type = 'point'\strutbox}
- \nodepart{four}\texttt{argument = atan(2)\strutbox}
- \nodepart{five}\texttt{modulus = $\sqrt{5}$\strutbox}
- };
-
- \hspace{\fill} \texttt{Methods}\hspace{\fill}
-
- \tikz\node[minimum width=\size,font=\small,
- draw, fill=orange!20,sharp corners,
- rectangle split, rectangle split parts=4
- ] {
- \texttt{homothety(coeff,obj)\strutbox}
- \nodepart{two}\texttt{rotation (angle,object)\strutbox}
- \nodepart{three}\texttt{symmetry (object)\strutbox}
- \nodepart{four}\texttt{\ldots\strutbox}
- };
-
- \end{minipage}
+\begin{minipage}{\size}
+ \hspace{\fill} \texttt{Arguments}\hspace{\fill}
+
+ \tikz\node[minimum width=\size,font=\small,
+ draw, fill=cyan!10,
+ rectangle split, rectangle split parts=5
+ ] {
+ \texttt{re = 1}
+ \nodepart{two}\texttt{im = 2}
+ \nodepart{three}\texttt{type = 'point'}
+ \nodepart{four}\texttt{argument = atan(2)}
+ \nodepart{five}\texttt{modulus = $\sqrt{5}$}
+ };
+
+ \hspace{\fill} \texttt{Methods}\hspace{\fill}
+
+ \tikz\node[minimum width=\size,font=\small,
+ draw, fill=orange!20,sharp corners,
+ rectangle split, rectangle split parts=4
+ ] {
+ \texttt{homothety(coeff,obj)}
+ \nodepart{two}\texttt{rotation (angle,object)}
+ \nodepart{three}\texttt{symmetry (object)}
+ \nodepart{four}\texttt{\ldots}
+ };
+\end{minipage}
};
\node[ draw, fill=red!10,remember picture,minimum height = 2em,
rounded corners,anchor=south] (to) at (tbl.north){object |z.A|};
diff --git a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-triangle.tex b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-triangle.tex
index 7b051cd723..9c6e822704 100644
--- a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-triangle.tex
+++ b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-classes-triangle.tex
@@ -34,8 +34,8 @@ The triangle object is created using the \Imeth{triangle}{new} method, for examp
\Iattr{triangle}{beta}& Vertex angle of the second vertex\\
\Iattr{triangle}{gamma}& Vertex angle of the third vertex\\
\Iattr{triangle}{ab}& Line defined by the first two points of the triangle\\
-\Iattr{triangle}{ac}& Line defined by the first point and the last point\\
-\Iattr{triangle}{bc}& Line defined by the last two points of the triangle\\
+\Iattr{triangle}{bc}& Line defined by the last two points \\
+\Iattr{triangle}{ca}& Line defined by the last and the first points of the triangle\\
\bottomrule %
\end{tabular}
\egroup
@@ -87,7 +87,7 @@ The triangle object is created using the \Imeth{triangle}{new} method, for examp
b = T.abc.b
c = T.abc.c
alpha = T.abc.alpha
- beta = T.abc.beta
+ beta = T.abc.beta
gamma = T.abc.gamma
\end{tkzelements}
\hspace*{\fill}
diff --git a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-examples.tex b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-examples.tex
index 7a00735fd4..91923e2232 100755..100644
--- a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-examples.tex
+++ b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-examples.tex
@@ -2467,7 +2467,7 @@ z.t = intersection (L.ox,L.MaS) -- through
\tkzLabelPoints(C_1,C_2)
\tkzLabelPoints[above](T)
\tkzLabelSegment[left](C_1,T){r}
- \tkzLabelSegments[right](C_2,T){\gamma}
+ \tkzLabelSegments[right](C_2,T){$\gamma$}
\tkzLabelSegment[below](C_1,C_2){d}
\tkzLabelCircle[left=10pt](C_1,T)(180){Circle 1}
\tkzLabelCircle[right=10pt](C_2,T)(180){Circle 2}
@@ -2494,7 +2494,7 @@ z.S,z.T = get_points (C: orthogonal_from (z.C_2))
\tkzLabelPoints(C_1,C_2)
\tkzLabelPoints[above](T)
\tkzLabelSegment[left](C_1,T){r}
-\tkzLabelSegments[right](C_2,T){\gamma}
+\tkzLabelSegments[right](C_2,T){$\gamma$}
\tkzLabelSegment[below](C_1,C_2){d}
\tkzLabelCircle[left=10pt](C_1,T)(180){Circle 1}
\tkzLabelCircle[right=10pt](C_2,T)(180){Circle 2}
@@ -2507,21 +2507,20 @@ z.S,z.T = get_points (C: orthogonal_from (z.C_2))
\begin{tkzexample}[latex=0cm,small,code only]
\begin{tkzelements}
- scale = .75
- z.O = point: new (2,2)
- z.Op = point: new (-4,1)
- z.P = point: polar (4,0)
- C.OP = circle: new (z.O,z.P)
- C.Oz1,C.Oz2 = C.OP : orthogonal_from (z.Op)
- z.z1 = C.Oz1.through
- z.z2 = C.Oz2.through
- L.OP = line : new (z.O,z.P)
- C.Opz1 = circle: new (z.Op,z.z1)
- L.T,L.Tp = C.Opz1 : tangent_from (z.O)
- z.T = L.T.pb
- z.Tp = L.Tp.pb
- L.OOp = line : new (z.O,z.Op)
- z.M = L.OOp.mid
+scale = .75
+z.O = point: new (2,2)
+z.Op = point: new (-4,1)
+z.P = point: polar (4,0)
+C.OP = circle: new (z.O,z.P)
+C.Oz1 = C.OP : orthogonal_from (z.Op)
+z.z1 = C.Oz1.through
+L.OP = line : new (z.O,z.P)
+C.Opz1 = circle: new (z.Op,z.z1)
+L.T,L.Tp = C.Opz1 : tangent_from (z.O)
+z.T = L.T.pb
+z.Tp = L.Tp.pb
+L.OOp = line : new (z.O,z.Op)
+z.M = L.OOp.mid
\end{tkzelements}
\begin{tikzpicture}
\tkzGetNodes
@@ -2543,20 +2542,19 @@ z.S,z.T = get_points (C: orthogonal_from (z.C_2))
\begin{tkzelements}
scale = .75
-z.O = point: new (2,2)
-z.Op = point: new (-4,1)
-z.P = point: polar (4,0)
-C.OP = circle: new (z.O,z.P)
-C.Oz1,C.Oz2 = C.OP : orthogonal_from (z.Op)
-z.z1 = C.Oz1.through
-z.z2 = C.Oz2.through
-L.OP = line : new (z.O,z.P)
-C.Opz1 = circle: new (z.Op,z.z1)
-L.T,L.Tp = C.Opz1 : tangent_from (z.O)
-z.T = L.T.pb
-z.Tp = L.Tp.pb
-L.OOp = line : new (z.O,z.Op)
-z.M = L.OOp.mid
+z.O = point: new (2,2)
+z.Op = point: new (-4,1)
+z.P = point: polar (4,0)
+C.OP = circle: new (z.O,z.P)
+C.Oz1 = C.OP : orthogonal_from (z.Op)
+z.z1 = C.Oz1.through
+L.OP = line : new (z.O,z.P)
+C.Opz1 = circle: new (z.Op,z.z1)
+L.T,L.Tp = C.Opz1 : tangent_from (z.O)
+z.T = L.T.pb
+z.Tp = L.Tp.pb
+L.OOp = line : new (z.O,z.Op)
+z.M = L.OOp.mid
\end{tkzelements}
\hspace*{\fill}
diff --git a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-main.pdf b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-main.pdf
deleted file mode 100644
index d05eb7fbb9..0000000000
--- a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-main.pdf
+++ /dev/null
Binary files differ
diff --git a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-main.tex b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-main.tex
index 101a65ed15..e36bac1aa7 100644
--- a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-main.tex
+++ b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-main.tex
@@ -21,10 +21,10 @@
headings = small
]{tkz-doc}
\gdef\tkznameofpack{tkz-elements}
-\gdef\tkzversionofpack{1.50c}
+\gdef\tkzversionofpack{1.60c}
\gdef\tkzdateofpack{\today}
\gdef\tkznameofdoc{tkz-elements.pdf}
-\gdef\tkzversionofdoc{1.50c}
+\gdef\tkzversionofdoc{1.60c}
\gdef\tkzdateofdoc{\today}
\gdef\tkzauthorofpack{Alain Matthes}
\gdef\tkzadressofauthor{}
@@ -97,7 +97,7 @@
\usepackage[english]{babel}
\usepackage[normalem]{ulem}
\usepackage{multirow,multido,booktabs,cellspace}
-\usepackage{shortvrb,bookmark,caption}
+\usepackage{shortvrb,bookmark,caption,enumitem}
\usepackage{makeidx}
\usepackage[most]{tcolorbox}
@@ -175,7 +175,7 @@ sharp corners
\defoffile{\lefthand\
This document brings together some notes about \tkzname{\tkznameofpack}, the first version of a library written in lua, allowing to make all the necessary calculations to define the objects of a Euclidean geometry figure. You need to compile with Lua\LaTeX.\\ With \pkg{tkz-elements}, the definitions and calculations are only done with \pkg{lua}. \\ The main possibility of programmation proposed is oriented "object programming" with object classes like point, line, triangle, circle and ellipse. For the moment, once the calculations are done, it is \pkg{tkz-euclide} or \pkg{TikZ} which allows the drawings.\\
- I discovered Lua and object-oriented programming when I created this package, so it's highly probable that I've made a few mistakes. If you'd like to participate in the development of this package or give me advice on how to proceed, please contact me via my email. \\ This version \tkzversionofpack\ is a beta version.\\
+ I discovered Lua and object-oriented programming when I created this package, so it's highly probable that I've made a few mistakes. If you'd like to participate in the development of this package or give me advice on how to proceed, please contact me via my email. \\
English is not my native language so there might be some errors.
}
@@ -183,7 +183,8 @@ English is not my native language so there might be some errors.
\vspace*{1cm}
-\lefthand\ Acknowledgements : I received much valuable advice, remarks, corrections from \\ \tkzimp{Nicolas Kisselhoff}, \tkzimp{David Carlisle}, \tkzimp{Roberto Giacomelli} and \tkzimp{Qrrbrbirlbel}.
+\lefthand\ Acknowledgements : I received much valuable advice, remarks, corrections from \\ \tkzimp{Nicolas Kisselhoff}, \tkzimp{David Carlisle}, \tkzimp{Roberto Giacomelli} and \tkzimp{Qrrbrbirlbel}.\\
+ Thanks to Wolfgang Büchel, for correcting the examples.
\vspace*{12pt}
\lefthand\ I would also like to thank \tkzimp{Eric Weisstein}, creator of
diff --git a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-presentation.tex b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-presentation.tex
index 900bdef5e6..b02c8cc0ba 100644
--- a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-presentation.tex
+++ b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-presentation.tex
@@ -130,25 +130,25 @@ When all the points necessary for the drawing are obtained, they must be transfo
\begin{tkzelements}
z.A = point: new (0 , 0)
-z.B = point: new (10 , 0) creation of two fixed points $A$ and $B$
+z.B = point: new (10 , 0) -- creation of two fixed points $A$ and $B$
L.AB = line: new ( z.A, z.B)
-z.C = L.AB: gold_ratio () use of a method linked to "line"
-z.O_0 = line: new ( z.A, z.B).mid midpoint of segment with an attribute of "line"
-z.O_1 = line: new ( z.A, z.C).mid objects are not stored and cannot be reused.
+z.C = L.AB: gold_ratio () -- use of a method linked to "line"
+z.O_0 = line: new ( z.A, z.B).mid -- midpoint of segment with an attribute of "line"
+z.O_1 = line: new ( z.A, z.C).mid -- objects are not stored and cannot be reused.
z.O_2 = line: new ( z.C, z.B).mid
-C.AB = circle: new ( z.O_0, z.B) new object "circle" stored and reused
+C.AB = circle: new ( z.O_0, z.B) -- new object "circle" stored and reused
C.AC = circle: new ( z.O_1, z.C)
C.CB = circle: new ( z.O_2, z.B)
-z.P = C.CB.north "north" atrributes of a circle
+z.P = C.CB.north -- "north" atrributes of a circle
z.Q = C.AC.north
z.O = C.AB.south
-z.c = z.C : north (2) "north" method of a point (needs a parameter)
+z.c = z.C : north (2) -- "north" method of a point (needs a parameter)
C.PC = circle: new ( z.P, z.C)
C.QA = circle: new ( z.Q, z.A)
-z.P_0 = intersection (C.PC,C.AB) search for intersections of two circles.
-z.P_1 = intersection (C.PC,C.AC) idem
-_,z.P_2 = intersection (C.QA,C.CB) idem
-z.O_3 = triangle: new ( z.P_0, z.P_1, z.P_2).circumcenter attribute of "triangle"
+z.P_0 = intersection (C.PC,C.AB) -- search for intersections of two circles.
+z.P_1 = intersection (C.PC,C.AC) -- idem
+_,z.P_2 = intersection (C.QA,C.CB) -- idem
+z.O_3 = triangle: new ( z.P_0, z.P_1, z.P_2) -- circumcenter attribute of "triangle"
\end{tkzelements}
\begin{tikzpicture}
diff --git a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-transferts.tex b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-transferts.tex
index 8106fbd2e8..dc177d09be 100644
--- a/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-transferts.tex
+++ b/macros/latex/contrib/tkz/tkz-elements/doc/latex/TKZdoc-elements-transferts.tex
@@ -134,12 +134,8 @@ The intersection of the two lines lies at
\tkzLabelPoints(a,...,d)
\end{tikzpicture}
\hspace{\fill}
-
-
-
% subsubsection other_transfers (end)
% subsubsection points_transfer (end)
-
% section transferts (end)
\endinput \ No newline at end of file
diff --git a/macros/latex/contrib/tkz/tkz-elements/doc/tkz-elements.pdf b/macros/latex/contrib/tkz/tkz-elements/doc/tkz-elements.pdf
index d05eb7fbb9..25c613e374 100644
--- a/macros/latex/contrib/tkz/tkz-elements/doc/tkz-elements.pdf
+++ b/macros/latex/contrib/tkz/tkz-elements/doc/tkz-elements.pdf
Binary files differ