\newpage \section{Presentation} \subsection{With Lua} % (fold) \label{sub:with_lua} The primary function of tkz-elements is to calculate dimensions and define points, which is achieved using Lua. You can view tkz-elements as a kernel that is utilized either by tkz-euclide or by TikZ, Definitions and calculations take place within the environment \tkzNameEnv{tkzelements}, which is based on \tkzNameEnv{luacode}. \begin{minipage}[t]{.52\textwidth}\vspace{0pt}% The key points are: \begin{itemize} \item The source file must be \tkzEHand\ {\color{red}\uline{ \color{black}UTF8}} encoded. \item Compilation is done with \tkzEHand\ {\color{red}\uline{ \color{black}Lua\LATEX{}}}. \item You need to load \tkzimp{\TIKZ}{} or \tkzimp{tkz-euclide} and \tkzimp{tkz-elements}. \item Definitions and calculations are performed in an (orthonormal) Cartesian coordinate system, using Luawithin the \tkzimp{tkzelements} environment. \end{itemize} On the right, you can see the minimum template. The code is divided into two parts, represented by two environments \tkzNameEnv{tkzelements} and \tkzNameEnv{tikzpicture}. In the first environment, you place your Lua code, while in the second, you use tkz-euclide commands. \vspace*{4.1 cm}% \end{minipage}\hspace*{\fill} \begin{minipage}[t]{.45\textwidth}\vspace{0pt}% \begin{mybox} \begin{Verbatim} % !TEX TS-program = lualatex % Created by Alain Matthes \documentclass{standalone} \usepackage{tkz-euclide} % or simply TikZ \usepackage{tkz-elements} begin{document} \begin{tkzelements} scale = 1 % definition of some points z.A = point : new ( , ) z.B = point : new ( , ) ...code... \end{tkzelements} \begin{tikzpicture} % point transfer to Nodes \tkzGetNodes \end{tikzpicture} \end{document} \end{Verbatim} \end{mybox} \end{minipage} % subsection with_lua (end) \subsection{The main process} % (fold) \label{sub:the_main_process} \tikzset{concept/.append style={fill={none}}} \tikzset{root concept/.style= {minimum size=3cm,text width=2.8cm}}% \tikzset{level 1 concept/.append style={minimum size=4cm, font=\large, text width=3cm}}% \begin{tikzpicture} \path[mindmap,concept color=orange,text=black] node[concept] {Transfers\\\textcolor{orange}{ \textbackslash{tkzGetNodes}}} child[concept color=red,grow=right] { node[concept] {Drawings\\\textcolor{red}{tkz-euclide}\\\textcolor{red}{\TIKZ}} } child[concept color=purple,grow=left] { node[concept] {Definitions\\Calculations\\\textcolor{purple}{tkz-elements}} }; \end{tikzpicture} After obtaining all the necessary points for the drawing, they must be transformed into \tkzname{nodes} so that \pkg{TikZ} or \pkg{tkz-euclide} can render the figure. This is accomplished using the macro \tkzcname{tkzGetNodes}. This macro iterates through all the elements of the table |z| using the key (which is essentially the name of the point) and retrieves the associated values, namely the coordinates of the point (node). % subsection the_main_process (end) \newpage \subsection{Complete example: Pappus circle} % (fold) \label{sub:the_figure_pappus_circle} \subsubsection{The figure} \begin{tkzelements} scale = 1.2 z.A = point: new (0 , 0) z.B = point: new (10 , 0) L.AB = line: new ( z.A, z.B) z.C = L.AB: gold_ratio () L.AC = line: new ( z.A, z.C) L.CB = line: new ( z.C, z.B) L.AB = line: new ( z.A, z.B) z.O_0 = L.AB.mid z.O_1 = L.AC.mid z.O_2 = L.CB.mid C.AB = circle: new ( z.O_0, z.B) C.AC = circle: new ( z.O_1, z.C) C.CB = circle: new ( z.O_2, z.B) z.P = C.CB.north z.Q = C.AC.north z.O = C.AB.south z.c = z.C : north (2) C.PC = circle: new ( z.P, z.C) C.QA = circle: new ( z.Q, z.A) z.P_0 = intersection (C.PC,C.AB) z.P_1 = intersection (C.PC,C.AC) _,z.P_2 = intersection (C.QA,C.CB) z.O_3 = triangle: new ( z.P_0, z.P_1, z.P_2).circumcenter \end{tkzelements} \hspace*{\fill} \begin{tikzpicture} \tkzGetNodes \tkzDrawCircle[black,fill=yellow!20,opacity=.4](O_0,B) \tkzDrawCircles[teal,fill=teal!40,opacity=.6](O_1,C O_2,B) \tkzDrawCircle[purple,fill=purple!20,opacity=.4](O_3,P_0) \tkzDrawArc[cyan,delta=10](Q,A)(P_0) \tkzDrawArc[cyan,delta=10](P,P_0)(B) \tkzDrawArc[cyan,delta=10](O,B)(A) \tkzDrawPoints(A,B,C,O_0,O_1,O_2,P,Q,P_0,P_0,P_1,P_2,O) \tkzLabelPoints(A,B,C,O_0,O_1,O_2,P,Q,P_0,P_0,P_1,P_2,O) \end{tikzpicture} \hspace*{\fill} % subsection the_figure_pappus_circle (end) \subsubsection{The code} % (fold) \label{ssub:the_code} \begin{Verbatim} % !TEX TS-program = lualatex \documentclass{article} \usepackage{tkz-euclide} \usepackage{tkz-elements} \begin{document} \begin{tkzelements} z.A = point: new (0 , 0) 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.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.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.Q = C.AC.north z.O = C.AB.south 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 -- circumcenter attribute of “triangle” \end{tkzelements} \end{Verbatim} \begin{Verbatim} \begin{tikzpicture} \tkzGetNodes \tkzDrawCircle[black,fill=yellow!20,opacity=.4](O_0,B) \tkzDrawCircles[teal,fill=teal!40,opacity=.6](O_1,C O_2,B) \tkzDrawCircle[purple,fill=purple!20,opacity=.4](O_3,P_0) \tkzDrawArc[cyan,delta=10](Q,A)(P_0) \tkzDrawArc[cyan,delta=10](P,P_0)(B) \tkzDrawArc[cyan,delta=10](O,B)(A) \tkzDrawPoints(A,B,C,O_0,O_1,O_2,P,Q,P_0,P_0,P_1,P_2,O) \tkzLabelPoints(A,B,C,O_0,O_1,O_2,P,Q,P_0,P_0,P_1,P_2,O) \end{tikzpicture} \end{document} \end{Verbatim} % subsubsection the_code (end) \subsection{Another example with comments: South Pole} % (fold) \label{sub:south_pole} Here's another example with comments \begin{Verbatim} % !TEX TS-program = lualatex \documentclass{standalone} \usepackage{tkz-euclide,tkz-elements} \begin{document} \begin{tkzelements} z.A = point: new (2 , 4) -- we create environment tkzelements z.B = point: new (0 , 0) -- three fixed points are used z.C = point: new (8 , 0) T.ABC = triangle: new (z.A,z.B,z.C) -- we create a new triangle object C.ins = T.ABC: in_circle () -- we get the incircle of this triangle z.I = C.ins.center -- center is an attribute of the circle z.T = C.ins.through -- through is also an attribute -- z.I,z.T = get_points (C.ins) -- get_points is a shortcut C.cir = T.ABC : circum_circle () -- we get the circumscribed circle z.W = C.cir.center -- we get the center of this circle z.O = C.cir.south -- now we get the south pole of this circle L.AO = line: new (z.A,z.O) -- we create an object "line" L.BC = T.ABC.bc -- we get the line (BC) z.I_A = intersection (L.AO,L.BC) -- we search the intersection of the last lines \end{tkzelements} \end{Verbatim} \begin{tkzelements} scale = 1.2 z.A = point: new (2 , 4) z.B = point: new (0 , 0) z.C = point: new (8 , 0) T.ABC = triangle: new (z.A,z.B,z.C) C.ins = T.ABC: in_circle () z.I = C.ins.center z.T = C.ins.through -- z.I,z.T = get_points (C.ins) C.cir = T.ABC : circum_circle () z.W = C.cir.center z.O = C.cir.south L.AO = line: new (z.A,z.O) L.BC = T.ABC.bc z.I_A = intersection (L.AO,L.BC) \end{tkzelements} \hspace*{\fill} \begin{tikzpicture} \tkzGetNodes \tkzDrawCircles(W,A I,T) \tkzDrawArc(O,C)(B) \tkzDrawPolygon(A,B,C) \tkzDrawSegments[new](A,O B,O C,O) \tkzDrawLine(B,I) \tkzDrawPoints(A,B,C,I,I_A,W,O) \tkzFillAngles[green!20,opacity=.3](A,O,B A,C,B) \tkzFillAngles[teal!20,opacity=.3](O,B,C B,C,O B,A,O O,A,C) \tkzLabelPoints(I,I_A,W,B,C,O) \tkzLabelPoints[above](A) \end{tikzpicture} \hspace*{\fill} Here's the tikzpicture environment to obtain the drawing: \begin{Verbatim} \begin{tikzpicture} \tkzGetNodes \tkzDrawCircles(W,A I,T) \tkzDrawArc(O,C)(B) \tkzDrawPolygon(A,B,C) \tkzDrawSegments[new](A,O B,O C,O) \tkzDrawLine(B,I) \tkzDrawPoints(A,B,C,I,I_A,W,O) \tkzFillAngles[green!20,opacity=.3](A,O,B A,C,B) \tkzFillAngles[teal!20,opacity=.3](O,B,C B,C,O B,A,O O,A,C) \tkzLabelPoints(I,I_A,W,B,C,O) \tkzLabelPoints[above](A) \end{tikzpicture} \end{Verbatim} % subsection south_pole (end) \endinput