%==================================================================== \section{TeX Interface Macros (\texttt{tkz-elements.sty})} \label{sec:sty_interface} \subsection{Purpose} The file \texttt{tkz-elements.sty} provides a small set of macros that act as a bridge between \TeX{} and the Lua engine used by \tkzNamePack{tkz-elements}. Their main goals are: \begin{itemize} \item printing Lua values safely in \TeX{}; \item transferring geometric objects (points, paths, circles) from Lua to TikZ; \item simplifying the drawing stage when computations are done in Lua. \end{itemize} \medskip Unless stated otherwise, these macros assume that \tkzNamePack{tkz-elements} has been initialized in Lua (typically via |\directlua{init_elements()}|. %-------------------------------------------------------------------- \subsection{Summary of provided macros} \begin{tabular}{ll} \toprule \texttt{Macro} & \texttt{Reference} \\ \midrule \tkzMacro{tkz-elements}{tkzUseLua\{...\}} & \\ \tkzMacro{tkz-elements}{tkzPrintNumber\{...\}} & \\ \tkzMacro{tkz-elements}{tkzEraseLuaObj\{name\}} & \\ \tkzMacro{tkz-elements}{tkzDrawCoordinates(\dots)} & \\ \tkzMacro{tkz-elements}{tkzGetPointsFromPath\{P\}\{A\}} & \\ \tkzMacro{tkz-elements}{tkzDrawPointsFromPath(\dots)} & \\ \tkzMacro{tkz-elements}{tkzDrawSegmentsFromPaths(\dots)}& \\ \tkzMacro{tkz-elements}{tkzDrawCirclesFromPaths(\dots)} & \\ \bottomrule \end{tabular} \medskip \texttt{Note:} The exact internal Lua object layout may evolve; these macros are designed to remain stable at the user level. %==================================================================== \subsection{Macro \tkzMacro{tkz-elements}{tkzUseLua}} \label{subsec:tkzUseLua} \medskip \texttt{Syntax: } \verb|tkzUseLua{\}| \medskip \texttt{Description: } Evaluates the Lua expression and prints its result in the \TeX{} stream. \medskip \texttt{Argument: } \begin{itemize} \item \tkzname{}: a Lua expression returning a value. \end{itemize} \medskip \texttt{Notes: } \begin{itemize} \item This macro is meant for \emph{values} (numbers, booleans, strings). \item For Lua objects (point, line, circle, path, \dots), prefer dedicated transfer/draw macros or call an explicit Lua method that returns a value. \end{itemize} \texttt{Example: } \begin{minipage}{.52\textwidth} \begin{verbatim} \directlua{init_elements() z.A = point(0,0) z.B = point(4,2) } The slope is \tkzUseLua{(z.B.im-z.A.im)/(z.B.re-z.A.re)}. \end{verbatim} \end{minipage} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% This macro evaluates a Lua expression and inserts its result in the document. \texttt{Syntax: }\verb|\tkzUseLua{}| \texttt{Example usage: } \begin{mybox} \begin{verbatim} \tkzUseLua{utils_checknumber(math.pi)} \end{verbatim} \end{mybox} %==================================================================== \subsection{Macro \tkzMacro{tkz-elements}{tkzPrintNumber}} This macro formats and prints a number using PGF’s fixed-point output, with a default precision of 2 decimal places. \medskip %\texttt{Syntax: }\verb|\tkzPrintNumber[]{}| \texttt{Syntax: } \begin{quote} \tkzMacro{tkz-elements}{tkzPrintNumber\{\}} \qquad \tkzMacro{tkz-elements}{tkzPN\{\}} \end{quote} \texttt{Example: } \begin{mybox} \begin{verbatim} \tkzPrintNumber{pi} % outputs 3.14 \tkzPrintNumber[4]{sqrt(2)} % outputs 1.4142 \end{verbatim} \end{mybox} \texttt{Alias: } The macro \tkzMacro{tkz-elements}{tkzPN} is a shorthand for \tkzMacro{tkz-elements}{tkzPrintNumber}. \texttt{Example: } \begin{minipage}{.52\textwidth} \begin{verbatim} \directlua{init_elements() x = math.pi/7 } $\alpha = \tkzPN{x}$. \end{verbatim} \end{minipage} %==================================================================== \subsection{Macro \tkzMacro{tkz-elements}{tkzEraseLuaObj}} \label{sub:macro_tkzEraseLuaObj} \texttt{Syntax: } \begin{quote} \tkzMacro{tkz-elements}{tkzEraseLuaObj\{\}} \end{quote} \texttt{Description: } Removes a stored Lua object from the global storage table (typically \code{z}, \code{L}, \code{C}, \code{CO}, etc., depending on your conventions). \texttt{Syntax: } \verb|\tkzEraseLuaObj{}| \texttt{Example usage: } \begin{mybox} \begin{verbatim} \tkzEraseLuaObj{z.A} \tkzEraseLuaObj{T.ABC} \end{verbatim} \end{mybox} \texttt{Notes: } Use this macro to avoid name collisions when compiling large documents or when reusing the same object names across figures. %==================================================================== \subsection{Macro \tkzMacro{tkz-elements}{tkzPathCount}} This macro retrieves the number of vertices in a Lua path and stores the result in a TeX macro. \texttt{Syntax: }\verb|\tkzPathCount(){}| \texttt{Arguments: } \verb||: identifier of a Lua \verb|path| object. \verb||: name of a TeX macro (without the backslash) that will store the count. \texttt{Example usage: } \begin{tkzexample}[latex=.5\textwidth] \directlua{ z.A = point(0, 0) z.B = point(5, 4) L.AB = line(z.A, z.B) PA.AB = L.AB:path(3) z.O = point(2, 0) } \tkzPathCount(PA.AB){N} \begin{center} \begin{tikzpicture} \tkzGetNodes \tkzDrawCoordinates[blue](PA.AB) \tkzDrawPointsFromPath[red,size=2](PA.AB) \foreach \i in {1,...,\N}{ \tkzGetPointFromPath(PA.AB,\i){P\i} \tkzDrawSegment[orange](O,P\i) } \end{tikzpicture} \end{center} \end{tkzexample} %==================================================================== \subsection{Macro \tkzMacro{tkz-elements}{tkzDrawCoordinates}} This macro draws a curve using the TikZ \code{plot coordinates} syntax, with coordinates generated by Lua. \medskip \texttt{Conceptual perspective:} A Lua \code{path} is a computational object: it stores geometric data produced during the Lua phase (coordinates, sampling, transformations, concatenations, etc.). The TikZ command \code{plot coordinates} is a graphical instruction: it simply draws what it receives as explicit coordinates. \medskip \emph{Lua computes — TikZ draws.} \medskip The macro \tkzMacro{tkz-elements}{tkzDrawCoordinates} establishes the bridge between these two worlds: \begin{itemize} \item Lua constructs and manipulates the geometric object; \item TikZ renders the explicit list of coordinates; \item No additional geometric interpretation is performed during drawing. \end{itemize} This strict separation guarantees consistency between the computed geometry and the final graphical output. \texttt{Syntax: } |\tkzDrawCoordinates[](lua-path)| \texttt{Example usage: } \begin{tkzexample}[latex=.5\textwidth] \directlua{ z.A = point(0, 0) z.B = point(6, 0) z.C = point(1, 4) T.ABC = triangle(z.A, z.B, z.C) z.M = T.ABC.bc.mid z.N = T.ABC.ca.mid PA.path = T.ABC:path(z.M,z.N,4) } \begin{tikzpicture}[gridded] \tkzGetNodes \tkzDrawPolygon(A,B,C) \tkzDrawCoordinates[orange,thick](PA.path) \tkzDrawPoints(A,B,C,M,N) \tkzLabelPoints(A,B) \tkzLabelPoints[above](C) \end{tikzpicture} \end{tkzexample} \medskip \texttt{Description: } Draws a Lua \code{path} object as a TikZ path. This macro is typically used after the computational phase in Lua. Draws the polyline defined by the sequence of points in a Lua path, using explicit \code{(x,y)} coordinates. \medskip \texttt{Alias: } % \let\tkzDrawPath\tkzDrawCoordinates \label{subsec:tkzDrawPath} \begin{quote} \tkzMacro{tkz-elements}{tkzDrawPath[](lua-path)} \end{quote} %==================================================================== \subsection{Macro \tkzMacro{tkz-elements}{tkzDrawPointsFromPath}} \label{sub:macro_tkzDrawPointsFromPath} This macro draws all points of a path using \tkzname{tkzDrawPoint}, without exporting point names. \medskip \texttt{Syntax: } \verb|\tkzDrawPointsFromPath[](lua-path)| \medskip \texttt{Example usage: } \begin{tkzexample}[latex=.5\textwidth] \directlua{ init_elements() LP.test = list_point() LP.test:add(point(0, 0)) LP.test:add(point(1, 0)) LP.test:add(point(1, 1)) PA.curve = LP.test:as_path() } \begin{tikzpicture} \tkzDrawCoordinates[blue](PA.curve) \tkzDrawPointsFromPath[red,size=2](PA.curve) \end{tikzpicture} \end{tkzexample} %==================================================================== %==================================================================== \subsection{Macro \tkzMacro{tkz-elements}{tkzGetPointsFromPath}} This macro defines TikZ points from a Lua path. Each point is named with a base name followed by an index. \texttt{Syntax: }\verb|\tkzGetPointsFromPath[](,)| \medskip \texttt{Description: } Exports the points of a Lua path as named \TeX/TikZ points. The naming scheme is \code{1}, \code{2}, \dots \medskip \texttt{Example: } \begin{tkzexample}[latex=.5\textwidth] \directlua{ init_elements() PA.g = path({ "(0, 0)", "(1, 0)","(1, 1)" }) } \begin{tikzpicture} \tkzGetPointsFromPath(PA.g,A) \tkzDrawPolygon(A_1,A_2,A_3) \tkzDrawPoints(A_1,A_2,A_3) \end{tikzpicture} \end{tkzexample} %==================================================================== \subsection{Macro \tkzMacro{tkz-elements}{tkzGetPointFromPath}} This macro extracts the i-th vertex of a Lua path and defines it as a TikZ point with a given name. \texttt{Syntax: }\verb|\tkzGetPointFromPath(,){}| \texttt{Arguments: } \verb||: identifier of a Lua \verb|path| object. \verb||: index of the vertex to retrieve (TeX number or numeric macro). \verb||: name of the TikZ point to create. \medskip \texttt{Example usage:} \begin{mybox} \begin{verbatim} % Get the 3rd vertex of PA.A and name it P3 \tkzGetPointFromPath(PA.A,3){P3} % With counting and a loop \tkzPathCount(PA.A){N} \foreach \i in {1,...,\N}{ \expandafter\tkzGetPointFromPath\expandafter(PA.A,\i){P\i} } \end{verbatim} \end{mybox} %==================================================================== \subsection{Macro \tkzMacro{tkz-elements}{tkzDrawSegmentsFromPaths}} \label{sub:macro_tkzDrawSegmentsFromPaths} \texttt{Description: } Draws segments encoded in one or more Lua paths (pairs of points or consecutive points, depending on the chosen convention). \texttt{Syntax: }\verb|\tkzDrawSegmentsFromPaths[](,)| \texttt{Example: } \begin{tkzexample}[vbox] \directlua{ init_elements() z.A = point(0, 0) z.B = point(3, 0) C.AB = circle(z.A, z.B) PA.c = path() PA.u = path() PA.v = path() for i = 0, 18, 2 do local angle = i * 2 * math.pi / 18 local p = point(polar(8, angle)) local Lu, Lv = C.AB:tangent_from(p) local u , v = Lu.pb, Lv.pb PA.c:add_point(p) PA.u:add_point(u) PA.v:add_point(v) end} \begin{center} \begin{tikzpicture}[scale =.6] \tkzGetNodes \tkzDrawSegmentsFromPaths[draw,red](PA.c,PA.u) \tkzDrawSegmentsFromPaths[draw,red](PA.c,PA.v) \tkzDrawCircle[blue](A,B) \end{tikzpicture} \end{center} \end{tkzexample} %==================================================================== \subsection{Macro \tkzMacro{tkz-elements}{tkzDrawCirclesFromPaths}} \label{sub:macro_tkzDrawCirclesFromPaths} This macro draws circles defined by two paths: one for the centers and one for the points through which each circle passes. \medskip \texttt{Syntax: }\verb|\tkzDrawCirclesFromPaths[](,)| \medskip \texttt{Example usage: } \begin{mybox} \begin{verbatim} \tkzDrawCirclesFromPaths[blue](PA.O, PA.A) \end{verbatim} \end{mybox} See the document \tkzname{Euclidean Geometry} presented in \href{http://altermundus.fr}{altermundus.fr}for other examples. \medskip \begin{tkzexample}[vbox] \directlua{ init_elements() z.A = point(-4, -4) z.B = point(4, -4) L.AB = line(z.A, z.B) C.AB = circle(z.A, z.B) S.AB = L.AB:square() _, _, z.C, z.D = S.AB:get() z.O = S.AB.ac.mid z.a = S.AB.ab.mid z.c = S.AB.cd.mid z.o1 = tkz.midpoint(z.a, z.O) z.o = tkz.midpoint(z.c, z.O) z.b = S.AB.bc.mid z.g = (z.o1 - z.O) + (z.b - z.O) z.o2 = intersection(line(z.c, z.g), line(z.O,z.b)) z.o3 = (z.o - z.O) + (z.o2 - z.O) z.j = intersection(line(z.c, z.b), line(z.o2,z.o3)) local C2 = circle(z.O, z.a) local C1 = circle(z.o, z.c) local C3 = circle(z.o3, z.j) PA.pc, PA.pt, n = C1:CCC(C2, C3) } \begin{center} \begin{tikzpicture}[scale=1] \tkzGetNodes \tkzDrawPolygon[cyan](A,B,C,D) \tkzDrawCircles(O,a o,c o1,a o2,b o3,j) \tkzDrawCirclesFromPaths[draw,red](PA.pc,PA.pt) \end{tikzpicture} \end{center} \end{tkzexample} %=============================================================== \subsection{Macro \tkzMacro{tkz-elements}{tkzDrawFromPointToPath}} This macro draws a set of line segments from a given TikZ point to every point of a Lua \emph{path} object. \medskip \texttt{Syntax: }\verb|\tkzDrawFromPointToPath[](,)| \medskip \texttt{Arguments: } \verb|| (optional): pgf/tikz drawing options (color, thickness, etc.). \verb||: the name of a TikZ point (already defined). \verb||: identifier of a Lua \verb|path| object. \medskip \texttt{Example usage: } \medskip \begin{tkzexample}[vbox] \directlua{ init_elements() z.O = point(0, 0) z.A = point(5, 1) z.Ta = point(8, 2) C.A = circle(z.A, z.Ta) L.OA = line(z.O,z.A) z.x, z.y = intersection(C.A, L.OA,{near=z.O}) C.A.through = z.y z.m = tkz.midpoint(z.O, z.x) z.n = tkz.midpoint(z.O, z.y) z.w = tkz.midpoint(z.m, z.n) PA.A = path() PA.c = path() for t = 0, 1 - 1e-12, 0.1 do PA.A:add_point(C.A:point(t)) local m = tkz.midpoint(z.O, C.A:point(t)) PA.c:add_point(m) end } \begin{center} \begin{tikzpicture}[scale=.8] \tkzGetNodes \tkzDrawCircle(A,Ta) \tkzDrawLine(O,A) \tkzDrawPoints(O,A,m,n,w,x,y) \tkzLabelPoints(O,A,m,n,w) \tkzDrawCircle[red](w,n) \tkzDrawPointsFromPath[red](PA.c) \tkzDrawPointsFromPath[blue](PA.A) \tkzDrawSegmentsFromPaths[draw,teal](PA.c,PA.A) \tkzDrawFromPointToPath[orange](O,PA.A) \end{tikzpicture} \end{center} \end{tkzexample} \subsection{Archimedes spiral, a complete example} This example is built with the help of some of the macros presented in this section. It is inspired by an example created with tkz-euclide by Jean-Marc Desbonnez. \vspace{1em} \begin{tkzexample}[vbox] \directlua{ z.O = point(0, 0) z.A = point(5, 0) L.OA = line(z.O, z.A) PA.spiral = path() PA.center = path() PA.through = path() PA.ray = path() for i = 1, 48 do local k = i / 48 z["P"..i] = L.OA:point(k) local angle = i * tkz.tau / 48 z["r"..i] = point(polar(5, angle)) ray = line(z.O, z["r"..i]) circ = circle(z.O, z["P"..i]) z["X"..i], _ = intersection(ray, circ, { near = z["r"..i] }) PA.spiral:add_point(z["X"..i]) PA.center:add_point(z.O) PA.through:add_point(z["P"..i]) PA.ray:add_point(z["r"..i]) end} \begin{center} \begin{tikzpicture}[scale = .8] \tkzGetNodes \tkzDrawCircle(O,A) \tkzDrawCirclesFromPaths[draw, orange!50](PA.center,PA.through) \tkzDrawSegmentsFromPaths[draw,teal](PA.center,PA.ray) \tkzDrawPath[red,thick,smooth](PA.spiral) \tkzDrawPointsFromPath[blue, size=2](PA.spiral) \end{tikzpicture} \end{center} \end{tkzexample} \endinput