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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} |