\newpage \section{Class \tkzClass{square}} The variable \tkzVar{square}{S} holds a table used to store squares. It is optional, and you are free to choose the variable name. However, using \code{S} is a recommended convention for clarity and consistency. If you use a custom variable (e.g., Squares), you must initialize it manually. The \code{init\_elements()} function reinitializes the \code{S} table if used. \subsection{Creating a square} \label{sub:creating_a_square} The \tkzClass{square} class constructs a square from two adjacent vertices. The order of the points defines the orientation. \medskip The result is stored in \tkzVar{square}{S}. \begin{mybox} \begin{verbatim} S.ABCD = square:new(z.A, z.B) \end{verbatim} \end{mybox} \textbf{Short form.} The short form \code{square(z.A, z.B)} is equivalent: \begin{mybox} \begin{verbatim} S.ABCD = square(z.A, z.B) \end{verbatim} \end{mybox} \subsection{Square attributes} \label{sub:square_attributes} Points are created in the direct direction. A test is performed to check whether the points form a square. Otherwise, compilation is blocked." \begin{mybox} Creation | S.AB = square(z.A,z.B,z.C,z.D)| \end{mybox} \bgroup \catcode`_=12 \small \captionof{table}{Square attributes.}\label{square:attributes} \begin{tabular}{lll} \toprule \textbf{Attributes} & \textbf{Application} & \\ \midrule \tkzAttr{square}{pa} & |z.A = S.AB.pa| & \\ \tkzAttr{square}{pb} & |z.B = S.AB.pb| & \\ \tkzAttr{square}{pc} & |z.C = S.AB.pc| & \\ \tkzAttr{square}{pd} & |z.D = S.AB.pd| & \\ \tkzAttr{square}{type} & |S.AB.type= 'square'| & \\ \tkzAttr{square}{side} & |s = S.AB.center| & s = length of side \\ \tkzAttr{square}{center} & |z.I = S.AB.center| & center of the square \\ \tkzAttr{square}{circumradius} & |S.AB.circumradius| & radius of the circumscribed circle \\ \tkzAttr{square}{inradius} & |S.AB.inxradius| & radius of the inscribed circle (apothem) \\ \tkzAttr{square}{apothem\_foot} & |S.AB.proj| & projection of the center on one side \\ \tkzAttr{square}{ab} & |S.AB.ab| & line passing through two vertices \\ \tkzAttr{square}{ac} & |S.AB.ca| & idem. \\ \tkzAttr{square}{ad} & |S.AB.ad| & idem. \\ \tkzAttr{square}{bc} & |S.AB.bc| & idem. \\ \tkzAttr{square}{bd} & |S.AB.bd| & idem. \\ \tkzAttr{square}{cd} & |S.AB.cd| & idem. \\ \bottomrule % \end{tabular} \egroup \subsubsection{Example: square attributes } \label{ssub:example_square_attributes} \begin{minipage}{.5\textwidth} \begin{verbatim} \directlua{ init_elements() z.A = point(0, 0) z.B = point(4, 0) z.C = point(4, 4) z.D = point(0, 4) S.new = square(z.A, z.B, z.C, z.D) z.I = S.new.center z.H = S.new.proj} \begin{tikzpicture} \tkzGetNodes \tkzDrawCircles[orange](I,A I,H) \tkzDrawPolygon(A,B,C,D) \tkzDrawPoints(A,B,C,D,H,I) \tkzLabelPoints(A,B,H,I) \tkzLabelPoints[above](C,D) \tkzDrawSegments(I,B I,H) \tkzLabelSegment[sloped](I,B){% \pmpn{\tkzUseLua{S.new.circumradius}}} \tkzLabelSegment[sloped](I,H){% \pmpn{\tkzUseLua{S.new.inradius}}} \tkzLabelSegment[sloped](D,C){% \pmpn{\tkzUseLua{S.new.side}}} \end{tikzpicture} \end{verbatim} \end{minipage} \begin{minipage}{.5\textwidth} \directlua{ init_elements() z.A = point(0, 0) z.B = point(4, 0) z.C = point(4, 4) z.D = point(0, 4) S.new = square(z.A, z.B, z.C, z.D) z.I = S.new.center z.H = S.new.proj} \begin{center} \begin{tikzpicture} \tkzGetNodes \tkzDrawCircles[orange](I,A I,H) \tkzDrawPolygon(A,B,C,D) \tkzDrawPoints(A,B,C,D,H,I) \tkzLabelPoints(A,B,H,I) \tkzLabelPoints[above](C,D) \tkzDrawSegments(I,B I,H) \tkzLabelSegment[sloped](I,B){\pmpn{\tkzUseLua{S.new.circumradius}}} \tkzLabelSegment[sloped](I,H){\pmpn{\tkzUseLua{S.new.inradius}}} \tkzLabelSegment[sloped](D,C){\pmpn{\tkzUseLua{S.new.side}}} \end{tikzpicture} \end{center} \end{minipage} \newpage \subsection{Square Methods and Functions} \label{sub:square_methods} \bgroup \catcode`_=12 \small \captionof{table}{Square methods}\label{square:methods} \begin{tabular}{lll} \toprule \textbf{Methods} & \texttt{Reference}& \\ \midrule \tkzMeth{square}{new(za,zb,zc,zd)} &[\ref{ssub:method_square_rotation}]\\ \tkzFct{square}{square.by\_rotation (zi,za)} &[\ref{ssub:method_square_rotation}]\\ \tkzFct{square}{square.from\_side(za,zb,"swap")} & \ref{ssub:square_with_side_method} \\ \bottomrule % \end{tabular} \egroup \subsubsection{Function \tkzFct{square}{square.by\_rotation(pt,pt)}} \label{ssub:method_square_rotation} $I$ square center; $A$ first vertex \vspace{1em} \begin{tkzexample}[latex=.5\textwidth] \directlua{ z.A = point(0, 0) z.I = point(2, -1) S = square.by_rotation(z.I, z.A) z.B = S.pb z.C = S.pc z.D = S.pd z.I = S.center} \begin{tikzpicture} \tkzGetNodes \tkzDrawPolygon(A,B,C,D) \tkzDrawPoints(A,B,C,D) \tkzLabelPoints(B) \tkzLabelPoints[above](A) \tkzLabelPoints[right](C,D) \tkzDrawPoints[red](I) \end{tikzpicture} \end{tkzexample} \subsubsection{Method \tkzFct{square}{square.from\_side(za,zb)}} \label{ssub:square_with_side_method} With the option \code{"swap"} then the square is defined in counterclockwise. The result can also be obtained from a line [\ref{ssub:method_line_square}]. \begin{minipage}{.5\textwidth} \begin{verbatim} \directlua{ init_elements() z.A = point(0, 0) z.B = point(2, 1) S.side = square.from_side(z.A, z.B) z.B = S.side.pb z.C = S.side.pc z.D = S.side.pd z.I = S.side.center} \begin{tikzpicture}[scale = 2] \tkzGetNodes \tkzDrawPolygon(A,B,C,D) \tkzDrawPoints(A,B,C,D) \tkzLabelPoints(A,B) \tkzLabelPoints[above](C,D) \tkzDrawPoints[red](I) \end{tikzpicture} \end{verbatim} \end{minipage} \begin{minipage}{.5\textwidth} \directlua{ init_elements() z.A = point(0, 0) z.B = point(2, 1) S.side = square.from_side(z.A, z.B) z.B = S.side.pb z.C = S.side.pc z.D = S.side.pd z.I = S.side.center} \begin{center} \begin{tikzpicture}[scale = 2] \tkzGetNodes \tkzDrawPolygon(A,B,C,D) \tkzDrawPoints(A,B,C,D) \tkzLabelPoints(A,B) \tkzLabelPoints[above](C,D) \tkzDrawPoints[red](I) \end{tikzpicture} \end{center} \end{minipage} \endinput