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-rw-r--r--Master/texmf-dist/doc/latex/tkz-euclide/latex/TKZdoc-euclide-intersec.tex81
1 files changed, 24 insertions, 57 deletions
diff --git a/Master/texmf-dist/doc/latex/tkz-euclide/latex/TKZdoc-euclide-intersec.tex b/Master/texmf-dist/doc/latex/tkz-euclide/latex/TKZdoc-euclide-intersec.tex
index 70492509f7f..3f7619188db 100644
--- a/Master/texmf-dist/doc/latex/tkz-euclide/latex/TKZdoc-euclide-intersec.tex
+++ b/Master/texmf-dist/doc/latex/tkz-euclide/latex/TKZdoc-euclide-intersec.tex
@@ -4,14 +4,11 @@ It is possible to determine the coordinates of the points of intersection betwee
The associated commands have no optional arguments and the user must determine the existence of the intersection points himself.
-\subsection{Intersection de deux droites}
-
- \begin{NewMacroBox}{tkzInterLL}{\parg{$A,B$}\parg{$C,D$}}
+\subsection{Intersection of two straight lines}
+\begin{NewMacroBox}{tkzInterLL}{\parg{$A,B$}\parg{$C,D$}}%
Defines the intersection point \tkzname{tkzPointResult} of the two lines $(AB)$ and $(CD)$. The known points are given in pairs (two per line) in brackets, and the resulting point can be retrieved with the macro \tkzcname{tkzDefPoint}.
-
\end{NewMacroBox}
-\medskip
\subsubsection{Example of intersection between two straight lines}
\begin{tkzexample}[latex=7cm,small]
@@ -28,37 +25,36 @@ Defines the intersection point \tkzname{tkzPointResult} of the two lines $(AB)$
\end{tikzpicture}
\end{tkzexample}
-\subsection{Intersection of a straight line and a circle} % (fold)
-\label{sub:intersection_d_une_droite_et_d_un_cercle}
+\subsection{Intersection of a straight line and a circle}
As before, the line is defined by a couple of points. The circle
is also defined by a couple:
\begin{itemize}
\item $(O,C)$ which is a pair of points, the first is the centre and the second is any point on the circle.
-\item $(O,r)$ The $r$ measure is the shelf measure. It is expressed soint en \emph{cm}, that is to say in \emph{pt}.
+\item $(O,r)$ The $r$ measure is the radius measure. The unit can be the \emph{cm} or \emph{pt}.
\end{itemize}
-\begin{NewMacroBox}{tkzInterLC}{\oarg{options}\parg{$A,B$}\parg{$O,C$} or \parg{$O,r$} or \parg{$O,C,D$}}
+\begin{NewMacroBox}{tkzInterLC}{\oarg{options}\parg{$A,B$}\parg{$O,C$} or \parg{$O,r$} or \parg{$O,C,D$}}%
So the arguments are two couples.
\medskip
-\begin{tabular}{lll}
+\begin{tabular}{lll}%
\toprule
options & default & definition \\
\midrule
\TOline{N} {N} { (O,C) determines the circle}
-\TOline{R} {N} { (O, 1 cm) ou (O, 120 pt)}
+\TOline{R} {N} { (O, 1 cm) or (O, 120 pt)}
\TOline{with nodes}{N} { (O,C,D) CD is a radius}
\bottomrule
\end{tabular}
\medskip
-The macro defines the intersection points $I$ and $J$ of the line $(AB)$ and the center circle $O$ with radius $r$ if they exist; otherwise, an error will be reported in the .log file.
+The macro defines the intersection points $I$ and $J$ of the line $(AB)$ and the center circle $O$ with radius $r$ if they exist; otherwise, an error will be reported in the |.log| file.
\end{NewMacroBox}
\subsubsection{Simple example of a line-circle intersection}
-In the following example, the drawing of the circle uses two points and the intersection of the straight line and the circle uses two pairs of points
+In the following example, the drawing of the circle uses two points and the intersection of the straight line and the circle uses two pairs of points:
\begin{tkzexample}[latex=7cm,small]
\begin{tikzpicture}[scale=.75]
@@ -77,7 +73,7 @@ In the following example, the drawing of the circle uses two points and the inte
\end{tkzexample}
\subsubsection{More complex example of a line-circle intersection}
-\url{http://gogeometry.com/problem/p190_tangent_circle}
+Figure from \url{http://gogeometry.com/problem/p190_tangent_circle}
\begin{tkzexample}[latex=7cm,small]
\begin{tikzpicture}[scale=.75]
@@ -104,8 +100,6 @@ In the following example, the drawing of the circle uses two points and the inte
\end{tikzpicture}
\end{tkzexample}
-
-\newpage
\subsubsection{Circle defined by a center and a measure, and special cases}
Let's look at some special cases like straight lines tangent to the circle.
@@ -128,7 +122,7 @@ Let's look at some special cases like straight lines tangent to the circle.
\end{tkzexample}
\subsubsection{More complex example}
-\tkzHandBomb\ Be careful with the syntax. First of all, calculations for the points can be done during the passage of the arguments, but the syntax of \tkzname{xfp} must be respected. You can see that I use the term \tkzname{pi} because \NamePack{xfp} works in radians!. Furthermore, when calculations require the use of parentheses, they must be inserted in a group... \TEX \{ \dots \}.
+\tkzHandBomb\ Be careful with the syntax. First of all, calculations for the points can be done during the passage of the arguments, but the syntax of \tkzname{xfp} must be respected. You can see that I use the term \tkzname{pi} because \NamePack{xfp} can work with radians. You can also work with degrees but in this case, you need to use specific commands like |sind| or |cosd|. Furthermore, when calculations require the use of parentheses, they must be inserted in a group... \TEX \{ \dots \}.
\begin{tkzexample}[latex=7cm,small]
\begin{tikzpicture}[scale=1.25]
@@ -152,15 +146,15 @@ Let's look at some special cases like straight lines tangent to the circle.
\end{tikzpicture}
\end{tkzexample}
-\subsubsection{Calculation of radius dimension}
+\subsubsection{Calculation of radius example 1}
With \tkzname{pgfmath} and \tkzcname{pgfmathsetmacro}
The radius measurement may be the result of a calculation that is not done within the intersection macro, but before.
A length can be calculated in several ways. It is possible of course,
to use the module \tkzname{pgfmath} and the macro \tkzcname{pgfmathsetmacro}. In some cases, the results obtained are not precise enough, so the following calculation $0.0002 \div 0.0001$ gives $1.98$ with pgfmath while xfp will give $2$.
-\subsubsection{Calculation of radius dimension 1}
-With \tkzname{xfp} and \tkzcname{fpeval}
+\subsubsection{Calculation of radius example 2}
+With \tkzname{xfp} and \tkzcname{fpeval}:
\begin{tkzexample}[latex=7cm,small]
\begin{tikzpicture}
@@ -177,10 +171,10 @@ With \tkzname{xfp} and \tkzcname{fpeval}
\end{tikzpicture}
\end{tkzexample}
-\subsubsection{Calculation of radius dimension 2}
+\subsubsection{Calculation of radius example 3}
With \TEX\ and \tkzcname{tkzLength}.
- This dimension was created with \tkzcname{newdimen}. 2 cm has been transformed into points. It is of course possible to use \TEX to calculate.
+ This dimension was created with \tkzcname{newdimen}. 2 cm has been transformed into points. It is of course possible to use \TEX\ to calculate.
\begin{tkzexample}[latex=7cm,small]
\begin{tikzpicture}
@@ -231,32 +225,26 @@ A Sangaku look! It is a question of proving that one can inscribe in a half-disc
\end{tikzpicture}
\end{tkzexample}
-\clearpage \newpage
\subsection{Intersection of two circles}
The most frequent case is that of two circles defined by their center and a point, but as before the option \tkzname{R} allows to use the radius measurements.
-\begin{NewMacroBox}{tkzInterCC}{\oarg{options}\parg{$O,A/r$}\parg{$O',A'/r'$}\marg{$I$}\marg{$J$}}
-
-\medskip
-\begin{tabular}{lll}
-\toprule
-options & defect & definition \\
+\begin{NewMacroBox}{tkzInterCC}{\oarg{options}\parg{$O,A$}\parg{$O',A'$} or \parg{$O,r$}\parg{$O',r'$} or \parg{$O,A,B$} \parg{$O',C,D$}}%
+\begin{tabular}{lll}%
+options & default & definition \\
\midrule
-\TOline{N} {N} {OA and O'A' are radii, O and O' are the centres}
-\TOline{R} {N} {$r$ et $r'$ shave dimensions and measure the radii}
-\TOline{with nodes} {N} {$r$ et $r'$ are dimensions and measure the radii}
+\TOline{N} {N} {$OA$ and $O'A'$ are radii, $O$ and $O'$ are the centres}
+\TOline{R} {N} {$r$ and $r'$ are dimensions and measure the radii}
+\TOline{with nodes} {N} { in (A,A,C)(C,B,F) AC and BF give the radii. }
+\bottomrule
\end{tabular}
\medskip
-
This macro defines the intersection point(s) $I$ and $J$ of the two center circles $O$ and $O'$. If the two circles do not have a common point then the macro ends with an error that is not handled. \\
It is also possible to use directly \tkzcname{tkzInterCCN} and \tkzcname{tkzInterCCR}.
\end{NewMacroBox}
-
\subsubsection{Construction of an equilateral triangle}
-
\begin{tkzexample}[latex=7cm,small]
\begin{tikzpicture}[trim left=-1cm,scale=.5]
\tkzDefPoint(1,1){A}
@@ -275,7 +263,6 @@ It is also possible to use directly \tkzcname{tkzInterCCN} and \tkzcname{tkzInte
\end{tkzexample}
\subsubsection{Example a mediator}
-
\begin{tkzexample}[latex=7cm,small]
\begin{tikzpicture}[scale=.5]
\tkzDefPoint(0,0){A}
@@ -290,7 +277,6 @@ It is also possible to use directly \tkzcname{tkzInterCCN} and \tkzcname{tkzInte
\end{tkzexample}
\subsubsection{An isosceles triangle.}
-
\begin{tkzexample}[latex=7cm,small]
\begin{tikzpicture}[rotate=120,scale=.75]
\tkzDefPoint(1,2){A}
@@ -345,26 +331,7 @@ It is also possible to use directly \tkzcname{tkzInterCCN} and \tkzcname{tkzInte
\end{tikzpicture}
\end{tkzexample}
-\subsubsection{Angle trisection}
-
-\begin{tkzexample}[latex=7cm,small]
-\begin{tikzpicture}
- \tikzset{arc/.style={color=gray,style=dashed}}
- \tkzDefPoints{0/0/a,0/5/I,5/0/J}
- \tkzDrawArc[angles](O,I)(0,90)
- \tkzDrawArc[angles,/tikz/arc](I,O)(90,180)
- \tkzDrawArc[angles,/tikz/arc](J,O)(-90,0)
- \tkzInterCC(O,I)(I,O)\tkzGetPoints{B}{C}
- \tkzInterCC(O,I)(J,O)\tkzGetPoints{D}{A}
- \tkzInterCC(I,O)(J,O)\tkzGetPoints{L}{K}
- \tkzDrawPoints(A,B,K)
- \foreach \point in {I,A,B,J,K}{%
- \tkzDrawSegment(O,\point)}
-\end{tikzpicture}
-\end{tkzexample}
-
-
-\subsubsection{with the option \tkzimp{with nodes}}
+\subsubsection{With the option \tkzimp{with nodes}}
\begin{tkzexample}[latex=6cm,small]
\begin{tikzpicture}[scale=.5]
\tkzDefPoints{0/0/a,0/5/B,5/0/C}