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diff --git a/Master/texmf-dist/doc/latex/tzplot/tzplot-doc-C-v1.0.1.tex b/Master/texmf-dist/doc/latex/tzplot/tzplot-doc-C-v1.0.1.tex new file mode 100644 index 00000000000..6b2dd29562e --- /dev/null +++ b/Master/texmf-dist/doc/latex/tzplot/tzplot-doc-C-v1.0.1.tex @@ -0,0 +1,4132 @@ +%!TEX root = tzplot-doc.tex +%\begin{document} + +%%%========================== +\part{Points, Lines, and Curves} +%%%========================== +\label{p:linesandcurves} + + +%%================================== +\chapter{Getting Ready} +\label{c:gettingready} + +%%------------------------------------------------------------ +\section{Styles: \texttt{tzdotted}, \texttt{tzdashed}, \texttt{tzhelplines}} +\label{s:styles:tzhelplines} + +The styles \ixttw{tzdotted}, \ixttw{tzdashed}, and \ixttw{tzhelplines} are defined as follows: + +\begin{tzsty}{} +% styles: tzdotted, tzdashed, tzhelplines +\tikzset{% + tzdotted/.style={line cap=round,dash pattern=on 0pt off 1cm/(#1)}, + tzdotted/.default=10 +} +\tikzset{% + tzdashed/.style={dashed=none,dash pattern=on 5mm/(#1) off 5mm/(#1)}, + tzdashed/.default=10 +} +\tikzset{% + tzhelplines/.style={help lines,-,tzdotted} +} +\end{tzsty} + +The styles |tzdotted| and |tzdashed| print 10 dots and 10 dashes per 1cm, respectively, by default. +The style |tzhelplines| uses |tzdotted| by default. + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzhelplines}, \protect\cmd{\tzhelplines*}} +\label{s:tzhelplines} + +\icmd{\tzhelplines} draws |grid| from the first coordinate to the second coordinate. +If only one coordinate is specified, then the first coordinate is regarded as |(0,0)|. + +The starred version \icmd{\tzhelplines*} uses the grid as a \iisw{bounding box}. + +\begin{tzdef}{} +% syntax: minimum +\tzhelplines(<coor>) +% syntax: full +\tzhelplines[<opt>](<coor1>)(<coor2>) +% defaults + [help lines,tzdotted=10](<m>)() +% (<m>): mandatory argument +\end{tzdef} + +Here, |(|\ixxw{<m>}|)| stands for a \xem{mandatory} argument. + +\begin{tztikz}{} +\tzhelplines(4,3) % works similarly to: + \draw [help lines] (0,0) grid (4,3); + +\tzhelplines(1,1)(4,3) % works similarly to: + \draw [help lines] (1,1) grid (4,3); +\end{tztikz} + + +By default, |\tzhelplines| prints |grid| with |10| dots per |1cm|. +|\tzhelplines| with the option value |[tzdotted=<n>]| prints |<n>| dots per |1cm|. +(That is, the default value is |tzdotted=10|.) + +\begin{tzcode}{.3} +% \tzhelplines +\begin{tikzpicture} +\tzhelplines(2,2) +\draw [help lines] (3,0) grid (5,2); +\end{tikzpicture} +\end{tzcode} + + +\begin{tzcode}{.3} +% tzdotted: (default: 10 dots per 1cm) +\begin{tikzpicture} +\tzhelplines[thick](1,2) % 10 dots +\tzhelplines[thick,tzdotted=20](2,0)(3,2) % 20 dots +\tzhelplines[thick,tzdotted=5](4,0)(5,2) % 5 dots +\end{tikzpicture} +\end{tzcode} + +With the option value, |[tzdotted=<n>/<d>]|, |\tzhelplines| prints |<n>| dots per |<d>cm|. + +Similarly for |tzdashed|. + +\begin{tzcode}{.3} +% tzdotted, tzdashed +\begin{tikzpicture} +\tzhelplines[thick,tzdashed](4,2) +\tzhelplines[thick,step=.5](4,2) +\end{tikzpicture} +\end{tzcode} + +\begin{tzcode}{.3} +% scaled: 7 dots per .7cm (10 dots per hard 1cm) +\begin{tikzpicture}[scale=.7] +\tzhelplines[tzdashed](4,3) +\tzhelplines[step=.5](4,3) +\end{tikzpicture} +\end{tzcode} + +\begin{tzcode}{.3} +% scaled: 10/.7 means 10 dots per .7cm +\begin{tikzpicture}[scale=.7] +\tzhelplines[tzdashed=10/.7](4,3) %% +\tzhelplines[step=.5,tzdotted=10/.7](4,3) %% +\end{tikzpicture} +\end{tzcode} + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzbbox}: A bounding box} +\label{s:tzbbox} + +\icmd{\tzbbox} sets a bounding box. + +\begin{tzdef}{} +% syntax +\tzbbox(<coor1>)(<coor2>) +% defaults + (0,0)(<m>) +\end{tzdef} + +\begin{tztikz}{} +\tzbbox(-1,-1)(4,3) % is an abbreviation of: + \path [ use as bounding box ] (-1,-1) rectangle (4,3); +\end{tztikz} + +If only one coordinate is specified, the first coordinate is regarded as |(0,0)|. + +%%================================== +\chapter{Dots} +\label{c:dots} + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzcdot(*)}: A small circle} +\label{s:tzcdot} + +A dot is usually expressed by a small circle. +\icmd{\tzcdot} prints a circle dot \tikz \tzcdot(0,0);. + +The starred version \icmd{\tzcdot*} prints a filled circle dot \tikz \tzcdot*(0,0);. +The \xem{radius} of the circle is |1.2pt|, by default. + +\begin{tzdef}{} +% syntax: minimum +\tzcdot(<coor>) +% syntax: medium +\tzcdot*(<coor>){<label>}[<angle>](<radius>) +% syntax: full +\tzcdot*[<opt>]<shift coor>(<coor>){<label>}[<[label opt]angle>](<radius>) +% defaults + *[ solid,thin,tzcdot=1.2pt ]<>(<m>){}[](1.2pt) +% tzcdot is a predefined key (in this package). +% (<m>): mandatory +\end{tzdef} + +Here, |(|\ixxw{<m>}|)| stands for a \xem{mandatory} argument. All others are optional arguments. + +\paragraph{How to change the size} +There are three ways to change the \xem{radius} of a circle dot drawn by |\tzcdot|. + +\begin{enumerate} +\item The simplest way is to use the last parenthesis option, like |\tzcdot(0,0)(3pt)|. + +\begin{tztikz}{} +\tzcdot(0,0) % is an abbreviation of: + \draw (0,0) circle (1.2pt); % default radius=1.2pt +\end{tztikz} + +\begin{tztikz}{} +\tzcdot*(0,0)(3pt) % is an abbreviation of: + \draw [fill] (0,0) circle (3pt); +\end{tztikz} + +\item +You can use the key-value option |[tzcdot=<dim>]|, like |\tzcdot[tzcdot=3pt](0,0)|, to change the \xem{radius} of a circle dot. The |tzcdot| key is defined in the package. +If both the |tzcdot| key-value and the last parenthesis option are used, the former wins. + +\begin{tztikz}{} +\tzcdot*(1,1) % works like: + \draw [fill] (1,1) circle [radius=1.2pt]; % default radius=1.2pt +\end{tztikz} + +\begin{tztikz}{} +\tzcdot*[tzcdot=3pt] % works like: + \draw [fill] (0,0) circle [radius=3pt]; +\end{tztikz} + +\begin{tzcode}{.3} +% \tzcdot(*) +\begin{tikzpicture} +\tzhelplines(4,2) +\tzcdot(0,0) \tzcdot[tzcdot=4pt](1,1) +\tzcdot*(2,1)(2pt) \tzcdot*(3,0)(3pt) +\end{tikzpicture} +\end{tzcode} + +\item +Another way to change the radius is to use a macro, like |\settzcdotradius{3pt}|, +It is effective within the |tizpicture| environment unless changed by \icmd{\settzcdotradius} again. + +\begin{tzcode}{.3} +% \settzcdotradius +\begin{tikzpicture} +\tzhelplines(4,2) +\settzcdotradius{4pt} +\tzcdot(0,0) \tzcdot(1,1) +\tzcdot*(2,1)(2pt) \tzcdot*(3,0) +\end{tikzpicture} +\end{tzcode} + +\end{enumerate} + + +\paragraph{How to label} +You can add a label to a specified coordinate by adding the optional argument |{<label>}| immediately after |(<coor>)|. You can also change the |<label>| position by the option |[<angle>]|. +(Note that you \xem{cannot} use the abbreviations such as |a|, |r|, |bl|, etc. to place label nodes.) + +\begin{tztikz}{} +\tzcdot(0,0){A} % is an abbreviation of: + \draw (0,0) circle (1.2pt) node [label={:A}] {}; + +\tzcdot(0,0)(2pt){A}[[blue]0] % is an abbreviation of: + \draw (0,0) circle (2pt) node [label={[blue]0:A}] {}; +\end{tztikz} + +\begin{tzcode}{.3} +% \tzcdot: labels +\begin{tikzpicture} +\tzhelplines(4,3) +\tzcdot(0,0){A} % default position: 90 or above +\tzcdot[tzcdot=4pt](1,1){B}[0] +\tzcdot*(2,1){C}[45](2pt) +\tzcdot*(3,0){D}[-90](3pt) +\tzcdot(4,3){E}[-90](6pt) +\end{tikzpicture} +\end{tzcode} + +The label position does not depend on the size of circle dots. + +\paragraph{How to change colors} +With the first optional argument |[<opt>]|, you can change the color of a dot. +You can also change the color of a label, as shown in the following example. + +\begin{tzcode}{.3} +% \tzcdot(*) +\begin{tikzpicture} +\draw [help lines] (0,0) grid (4,3); +\tzcdot(0,0){A} +\tzcdot*[red](1,0){\textbf{B}}[45] +\tzcdot*[red,fill=green](2,1){green}[[blue]0](10pt) +\tzcdot[tzcdot=2*7pt](3,2){big}[center] +\tzcdot*[fill=red,text=blue](4,3){D}(2*3pt) +\end{tikzpicture} +\end{tzcode} + + +\paragraph{Shift} +Dots can be shifted by specifying the optional argument |<shift coor>| immediately before |(<coor>)|. The empty shift option |<>| is not allowed. + +\begin{tzcode}{.3} +% \tzcdot: shift +\begin{tikzpicture} +\draw [help lines] (0,0) grid (4,3); +\tzcdot(0,0){A} +\tzcdot*[red]<0,2>(1,0){\textbf{B}}[45] % shift +\tzcdot*[red,fill=green](2,1){green}[[blue]0](10pt) +\tzcdot[tzcdot=2*7pt]<1,-1>(3,2){big}[center] % shift +\tzcdot*[fill=red,text=blue](4,3){D}(2*3pt) +\end{tikzpicture} +\end{tzcode} + +\begin{tzcode}{.3} +% \tzcdot: repeated +\begin{tikzpicture} +\tzhelplines(4,2) +\foreach \x in {0,...,4} + { \foreach \A in {2,4,6,8} + { \tzcdot[blue] (\x,0)(\A pt) } } +\foreach \x in {0,...,4} + { \foreach \A in {2,4,6,8} + { \tzcdot[red]<1,1>(\x,0)(\A pt) } } % shift +\end{tikzpicture} +\end{tzcode} + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzcdots(*)}: Multiple circle dots} +\label{s:tzcdots} + +The macro \icmd{\tzcdots} takes an arbitrary number of coordinates as arguments to print multiple circle dots with the radius |1.2pt|, by default. +You need to indicate when the iteration of an arbitrary number of coordinates ends, by typing a \xem{semicolon} |;|. +Let us call this kind of macro a \iisw{semicolon version} macro. + +\remark +\begin{itemize} +\item DO NOT FORGET to enter `|;|' at the end of iteration. + \begin{itemize} + \item Tokens such as `|!|' and `|#|' other than the open parenthesis `|(|' work like the semicolon `|;|' to indicate the end of iteration. + But it is highly recommended to use `|;|' for consistency. + \end{itemize} +\item Without the semicolon |;|, the macro does nothing or a compile error occurs. +\end{itemize} + + +The starred version |\tzcdots*| prints multiple filled dots. + +\begin{tzdef}{} +% syntax: minimum +\tzcdots*(<coor>)(<coor>)..repeated..(<coor>) ; +% syntax: full +\tzcdots*[<opt>]<shift coor> (<coor>){<label>}[<[label opt]angle>] + ..repeated.. (){}[] ; (<dot radius>) +% defaults + *[tzcdot=1.2pt]<>(<m>){}[]..repeated..(){}[] ; (1.2pt) +\end{tzdef} + +\begin{tzcode}{.3} +% \tzcdots(*) +\begin{tikzpicture} +\tzhelplines(4,3) +\tzcdots(0,0)(1,1)(2,1)(3,2)(4,0); +\tzcdots*(0,3)(1,2)(2,2)(3,3)(4,3); +\end{tikzpicture} +\end{tzcode} + +\paragraph{How to label} + +Each coordinate can be followed by the optional arguments |{<label>}| and |[<angle>]| to label dots. So the repeating pattern is the triple |(<coor>){<label>}[<angle>]|. + +\begin{tzcode}{.3} +% \tzcdots: label +\begin{tikzpicture} +\tzhelplines(4,3) +\tzcdots(0,0){A} + (1,1) + (2,1){C}[0] + (3,2){D}[-90] + (4,0){E}; +\tzcdots*(0,3)(1,2){B}(2,2){C}[45](3,3)(4,3); +\end{tikzpicture} +\end{tzcode} + +\paragraph{How to change the size of dots} + +There are three ways of changing the \xem{radius} of dots. +\begin{enumerate} +\item The simplest way is to use the \xem{last} parenthesis optional argument, \xem{after the semicolon}. +\item Another way is to use the \ixxw{tzcdot} key, like |\tzcdots[tzcdot=3pt]...|. +If both options are used the key-value option wins. +\item You can also use the macro \icmd{\settzcdotradius}. +The effect remains within the |tikzpicture| environment unless it is changed again. +\end{enumerate} + +\begin{tzcode}{.3} +% \tzcdots: size (radius) +\begin{tikzpicture} +\tzhelplines(4,3) +\settzcdotradius{3pt} +\tzcdots(0,0)(1,0){3pt}; +\tzcdots*(1,1)(2,1){1pt};(1pt) % simplest +\tzcdots[tzcdot=5pt](2,2)(3,2){5pt}; +\tzcdots*(3,3)(4,3){3pt}; +\end{tikzpicture} +\end{tzcode} + + + +\paragraph{How to change colors} + +With the first optional argument |[<opt>]|, you can change the color of dots. +You can also change the color of all labels at once using the first optional argument, +like |\tzcdots[text=red]...| as shown in the following example. + +\begin{tzcode}{.3} +% \tzcdots: color +\begin{tikzpicture} +\tzhelplines(4,3) +\settzcdotradius{3pt} +\tzcdots*[red] + (0,0)(1,1){\textbf{Ben}}[[blue]-90](2,1)(3,0); +\tzcdots*[thick,blue,fill=green,text=red] + (1,2){A}(2,2){Ben}[[blue]-90](3,2){C}(4,2){D};(4pt) +\tzcdots*[blue] + (1,3){A}(2,3){B}(3,3){C}(4,3){D}; +\end{tikzpicture} +\end{tzcode} + +\paragraph{Shift} You can move the coordinates of dots by specifying |<shift coor>| option immediately before the first coordinate. + +\begin{tzcode}{.3} +% \tzcdots: shift +\begin{tikzpicture} +\tzhelplines(4,3) +\tzcdots[red] (0,0){A}(1,1)(2,1){C}(3,2){D}[0](4,0){E}; +\tzcdots*<0,1>(0,0){A}(1,1)(2,1){C}(3,2){D}[0](4,0){E}; +\end{tikzpicture} +\end{tzcode} + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzdot(*)}: A single node dot} +\label{s:tzdot} + +The macro \icmd{\tzdot} prints a small circle node \tikz \tzdot(0,0);, as a dot, with the \xem{diameter} (or |minimum size|) of |2.4pt|, by default. + +The starred version \icmd{\tzdot*} prints a filled dot \tikz \tzdot*(0,0);. + +\begin{tzdef}{} +% syntax: minimum +\tzdot(coor) +% syntax: medium +\tzdot*(<coor>){<label>}[<angle>](<dot size>) +% syntax: full +\tzdot*[<node opt>]<shift coor>(<coor>){<label>}[<[label opt]angle>](<dot size>) +% defaults + *[ tzdot=2.4pt ]<>(<m>){}[](2.4pt) +% the style tzdot is predefined +% (<m>): mandatory +\end{tzdef} + +|\tzdot(*)| accepts one mandatory argument, denoted by |(|\ixxw{<m>}|)|. All others are optional. + +The style \ixxw{tzdot} is defined as follows: + +\begin{tzsty}{} +% style: tzdot +\tikzset{ + tzdot/.style={draw,circle,solid,thin,inner sep=0pt,minimum size=#1}, + tzdot/.default=2.4pt +} +\end{tzsty} + + +\subsection{{\normalfont\scshape Three Ways} to change the size of node dots} +\label{ss:threeways} + +There are \iscw{Three Ways} to change the \xem{diameter} (or |minimum size|) of a node dot drawn by |\tzdot(*)|. + +\begin{enumerate} +\item Use the predefined style |tzdot| in the first optional agrument, like |\tzdot[tzdot=5pt](0,0)|, which gives the same result as |\tzdot[minimum size=5pt](0,0)|. + +\begin{tztikz}{} +\tzdot(0,0) % works like: + \path (0,0) node [tzdot=2.4pt] {}; % default size + % or equivalently + \node [tzdot,minimum size=2.4pt] at (0,0) {}; +\end{tztikz} + +\item The simplest way is to use the \xem{last} parenthesis optional argument, like |\tzdot(0,0)(5pt)|, which yields the same result as in |\tzdot[tzdot=5pt](0,0)|. +If both options are used, the |tzdot| (or |minimum size|) option overwrites the last parenthesis option. + +\begin{tzcode}{.3} +% \tzdot(*) +\begin{tikzpicture} +\tzhelplines(4,2) +\tzdot(0,0) \tzdot[tzdot=8pt](1,1) +\tzdot*(2,1)(4pt) \tzdot*(3,0)(6pt) +\end{tikzpicture} +\end{tzcode} + +\item To change the size of all node dots drawn by |\tzdot*|, you can use the macro |\settzdotsize|. Its effect remains valid until the end of |tikzpicture| environment unless changed again. + +\begin{tzcode}{.3} +% \settzdotsize +\begin{tikzpicture} +\tzhelplines(4,2) +\settzdotsize{8pt} +\tzdot(0,0) \tzdot(1,1) +\tzdot*(2,1)(4pt) \tzdot*(3,0) +\end{tikzpicture} +\end{tzcode} + +\end{enumerate} + +\subsection{How to label} +\label{ss:tzdot:label} + +You can add a label to a specified coordinate by specifying the optional argument |{<label>}| immediately after the coordinate |(<coor>)|. + +You can also change the label position by the option |[<angle>]| following |{<label>}|. + +\begin{tztikz}{} +\tzdot(0,0){A}(3pt) % works like: + \path (0,0) node [tzdot=3pt,label={:A}] {}; + +\tzdot*(0,0){A}[[red]0](3pt) % works like: + \path (0,0) node [fill,tzdot=3pt,label={[red]0:A}] {}; +\end{tztikz} + + +\begin{tzcode}{.3} +% \tzdot: labels +\begin{tikzpicture} +\tzhelplines(4,3) +\tzdot(0,0){A} +\tzdot(1,1){B}[0](8pt) +\tzdot*(2,1){C}[45](4pt) +\tzdot*(3,0){D}[-90](6pt) +\tzdot(4,3){E}[-90](12pt) +\end{tikzpicture} +\end{tzcode} + +Unlike |\tzcdot|, the |\tzdot|'s label position depends on the size of a circle node. In \Tikz\ jargon, |{<label>}| is in a \iisw{label node} for a \iisw{main node} that is a circle node with no text in it, so |<label>| moves accordingly as the main node dot gets bigger or smaller. + + +\subsection{How to change colors and shapes} +\label{ss:tzdot:color} + +With the first optional argument |[<node opt>]|, you can change of the color or shape of dots. +You can also change the label color using |[<label opt>]| as shown in the following example. + +\remark +\begin{itemize} +\item |[<node opt>]| is for options of \xem{main nodes}, |[<label opt>]| is for options of \xem{label nodes}. +\item |[<label opt>]| is used in the form of |[<[label opt]angle>]|. +\end{itemize} + +\begin{tzcode}{.3} +% \tzdot: color +\begin{tikzpicture} +\draw [help lines] (0,0) grid (4,3); +\tzdot(0,0){A} +\tzdot*[red](1,0){\textbf{B}}[45] +\tzdot*[red,fill=green](2,1){green}[[blue]0](2*10pt) +\tzdot[tzdot=4*7pt](3,2){big}[center] +\tzdot*[fill=red](4,3){D}(4*3pt) +\end{tikzpicture} +\end{tzcode} + + +\begin{tzcode}{.3} +% \tzdot: shape +\begin{tikzpicture} +\draw [help lines] (0,0) grid (4,3); +\tzdot[regular polygon](0,0){A}(10pt) +\tzdot*[red](1,0){\textbf{B}}[45] +\tzdot*[red,fill=green,rectangle](2,1){green}[0](2*10pt) +\tzdot[tzdot=4*7pt](3,2){big}[center] +\tzdot*[fill=red,star](4,3){D}(4*3pt) +\end{tikzpicture} +\end{tzcode} + + + +\subsection{How to move: \texttt{shift}} +\label{ss:tzdot:shift} + +Dots can be shifted by specifying the optional argument |<shift coor>| immediately before |(<coor>)|. The empty shift option |<>| is not allowed. + +\begin{tzcode}{.3} +% \tzdot: shift +\begin{tikzpicture} +\draw [help lines] (0,0) grid (4,3); +\tzdot[regular polygon](0,0){A}(10pt) +\tzdot*[red]<0,2>(1,0){\textbf{B}-shifted}[45] % shift +\tzdot*[red,fill=green,rectangle](2,1){green}[0](2*10pt) +\tzdot[tzdot=4*7pt]<1,-1>(3,2){big}[center] % shift +\tzdot*[fill=red,star](4,3){D}(4*3pt) +\end{tikzpicture} +\end{tzcode} + + +\begin{tzcode}{.3} +% \tzdot: repeated +\begin{tikzpicture} +\tzhelplines(4,2) +\foreach \x in {0,...,4} + { \foreach \A in {1,2,3,4} + { \tzdot[blue] (\x,0)(2*\A mm) } } +\foreach \x in {0,...,4} + { \foreach \A in {1,2,3,4} + { \tzdot[green]<1,1>(\x,0)(2*\A mm) } } % shift +\end{tikzpicture} +\end{tzcode} + + +\subsection{Comparison: \protect\cmd{\tzdot} and \protect\cmd{\tzcdot}} +\label{ss:tzdot:comparison} + +The most important difference between |\tzcdot| and |\tzdot| is that |\tzcdot| is affected by \Tikz's scaling factor, but |\tzdot| is not. +This is critical when |xscale| is not equal to |yscale|. + +\begin{tzcode}{.3} +\begin{tikzpicture}[xscale=1.6,yscale=.8] +\tzhelplines(3,3) +\tzcdot(0,0)(3pt) % dostorted +\tzdot(1,0)(6pt) +\tzcdots*(1,1)(2,1)(3,1);(2pt) % distorted +\tzdots*(1,2)(2,2)(3,2);(4pt) +\end{tikzpicture} +\end{tzcode} + +The following table further shows the differences between them. +%Everything else is the same for end-users. + +\begin{tzcode}[listing only,colback=green!10!white]{.3} +% concept % single % multi % size control % [key=default size] +node [circle] \tzdot \tzdots \settzdotsize [tzdot=2.4pt] % diameter +circle \tzcdot \tzcdots \settzcdotradius [tzcdot=1.2pt] % radius +\end{tzcode} + +\remark +\begin{itemize} +\item In \Tikz, a `node' is `not' affected by `scaling' unless the \Tikz\ option |transform shape| is used together. +|\tzdot| is also useful for labelling a large dot. + \begin{itemize} + \item In |\tzdot|, |<label>| is a label in a \iisw{label node} for a node dot (as a \iisw{main node}). + So if a main node dot gets larger or smaller, its label moves accordingly. + (Unlike, the labels with |\tzcdot| or |\tzcdots|.) + \item The position of |<label>| in |\tzcdot| does not depend on the size of dots. + \end{itemize} +\item The package |tzplot| takes |\tzdot| as a \xem{standard dot}, not |\tzcdot|. +So, you can apply the \threeways\ (on page \pageref{ss:threeways}) to change the size of any standard dots. +\end{itemize} + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzdots(*)}: Multiple node dots} +\label{s:tzdots} + +\icmd{\tzdots} takes an arbitrary number of coordinates as arguments to print multiple circle node dots with the \xem{diameter} (or |minimum size|) of |2.4pt|, by default. + +This is a \iisw{semicolon version} macro, with the repeating pattern |(<coor>){<label>}[<angle>]|, which means that you need to type a \xem{semicolon} `|;|' at the end of the coordinate repetition. The \xem{semicolon} says, ``\xem{The repetition ends here}." + +\remark +\begin{itemize} +\item DO NOT FORGET to enter `|;|' at the end of iteration. + \begin{itemize} + \item Tokens such as `|!|' and `|#|' other than the open parenthesis `|(|' work like the semicolon `|;|' to indicate the end of iteration. + But it is highly recommended to use `|;|' for consistency. + \end{itemize} +\item Without the semicolon |;|, the macro does nothing or a compile error occurs. +\end{itemize} + +The starred version \icmd{\tzdots*} prints multiple filled node dots. + +\begin{tzdef}{} +% syntax: minimum +\tzdots*(<coor>)(<coor>)..repeated..(<coor>) ; +% syntax: full +\tzdots*[<node opt>]<shift coor> (<coor>){<label>}[<[label opt]angle>] + ..repeated.. (){}[] ; (<dot size>) +% defaults + *[tzdot=2.4pt]<> (<m>){}[] ..repeated.. (){}[] ; (2.4pt) +\end{tzdef} + +\begin{tzcode}{.3} +% \tzdots(*) +\begin{tikzpicture} +\tzhelplines(4,3) +\tzdots(0,0)(1,1)(2,1)(3,2)(4,0); +\tzdots*(0,3)(1,2)(2,2)(3,3)(4,3); +\end{tikzpicture} +\end{tzcode} + +\paragraph{How to label} + +Each coordinate can be followed by the optional arguments |{<label>}| and |[<angle>]| to label dots. So the triple |(<coor>){<label>}[<angle>]| is the whole repeating pattern. + +\begin{tzcode}{.3} +% \tzdots: label +\begin{tikzpicture} +\tzhelplines(4,3) +\tzdots(0,0){A} + (1,1) + (2,1){C}[0] + (3,2){D}[-90] + (4,0){E}; +\tzdots*(0,3)(1,2){B}(2,2){C}[45](3,3)(4,3); +\end{tikzpicture} +\end{tzcode} + + +\paragraph{How to change the size of dots} + +There are \threeways\ of changing the \xem{diameter} of node dots, as discussed in Section \ref{ss:threeways} on page \pageref{ss:threeways}. + +\begin{enumerate} +\item The simplest way is to use the \xem{last} parenthesis optional argument, \xem{after the semicolon}. +\item Another way is to use the style \ixxw{tzdot}, like |\tzdots[tzdot=3pt]...|. +If both options are used the |tzdot| option style wins. +\item You can also use the macro \icmd{\settzdotsize}. +The effect remains within the |tikzpicture| environment unless it is changed again. +\end{enumerate} + +\begin{tzcode}{.3} +% \tzdots: size (diameter) +\begin{tikzpicture} +\tzhelplines(4,3) +\settzdotsize{3mm} +\tzdots(0,0)(1,0){3mm}; +\tzdots*(1,1)(2,1){2mm};(2mm) % simplest +\tzdots[tzdot=4mm](2,2)(3,2){4mm}; +\tzdots*(3,3)(4,3){3mm}; +\end{tikzpicture} +\end{tzcode} + + + +\paragraph{How to change colors} + +With the first optional argument |[<node opt>]| you can change the color of node dots. +You can also change the color of each label by |[<label opt>]|. + +\begin{tzcode}{.3} +% \tzdots: color +\begin{tikzpicture}[->] +\tzhelplines(4,3) +\settzdotsize{6pt} +\tzdots*[red] + (0,0)(1,1){\textbf{Ben}}[[blue]-90](2,1)(3,0); +\tzdots*[thick,blue,fill=green] + (1,2){A}(2,2){Ben}[[red]-90](3,2){C}(4,2){D};(8pt) +\tzdots*[blue] + (1,3){A}(2,3){B}(3,3){C}(4,3){D}; +\end{tikzpicture} +\end{tzcode} + +\remark +\begin{itemize} +\item |[<node opt>]| is the option of a \iisw{main node} and |[<label opt>]| is the option of a \iisw{label node}. +\item |[<label opt>]| is used in the form of |[<[label opt]angle>]|, like |[[red]90]|. +\item You can control all labels together using |every label/.style| as in the following examples: +\end{itemize} + +\begin{tzcode}{.3} +% \tzdots: every label/.style +\begin{tikzpicture} +\tzhelplines(4,3) +\settzdotsize{6pt} +\tzdots*[red] + (0,0)(1,1){\textbf{Ben}}[[blue]-90](2,1)(3,0); +\tzdots*[thick,blue,fill=green] + (1,2){A}(2,2){Ben}[[red]-90](3,2){C}(4,2){D};(8pt) +\tikzset{every label/.style={draw,text=red}} %% +\tzdots*[blue] + (1,3){A}(2,3){B}(3,3){C}(4,3){D}[0]; +\end{tikzpicture} +\end{tzcode} + + +\begin{tzcode}{.3} +% every label/.style +\begin{tikzpicture}[every label/.style={draw,text=red}] +\tzhelplines(4,3) +\tzdots* + (0,0){Ace}[[font=\LARGE\ttfamily]-90] + (2,1){\textbf{Bob}}[[blue]135] + (3,2){$C_1$\\$N_o$}[[align=center]0]; +\end{tikzpicture} +\end{tzcode} + + +\paragraph{Shift} You can move the coordinates of dots by specifying |<shift coor>| option immediately before the first coordinate. +The empty shift option |<>| is not allowed. + +\begin{tzcode}{.3} +% \tzdots: shift +\begin{tikzpicture} +\tzhelplines(4,3) +\tzdots[red] (0,0){A}(1,1)(2,1){C}(3,2){D}[0](4,0){E}; +\tikzset{every label/.style={red}} +\tzdots*<0,1>(0,0){A}(1,1)(2,1){C}(3,2){D}[0](4,0){E}; +\end{tikzpicture} +\end{tzcode} + + +%%================================== +\chapter{Coordinates} +\label{c:coordinates} + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzcoor} and \protect\cmd{\tzcoor*}} +\label{s:tzcoor} + +\subsection{\protect\cmd{\tzcoor}} +\label{ss:tzcoor} + +For example, \icmd{\tzcoor}|(0,0)(A)| means that the coordinate |(0,0)| is named |(A)|. + +\begin{tztikz}{} +\tzcoor(0,0)(A) % is an abbreviation of: + \path (0,0) coordinate (A); + % or + \coordinate (A) at (0,0); +\end{tztikz} + +\begin{tzdef}{} +% syntax: minimum +\tzcoor(<coor>)(<name>) +% syntax: medium +\tzcoor(<coor>)(<name>){<label>}[<angle>] +% syntax: full +\tzcoor<shift coor>(<coor>)(<name>){<label>}[<[label opt]angle>] +% defaults + <>(<m>)(<m>){}[] +\end{tzdef} + +Here, |<m>| stands for `mandatory.' |\tzcoor| takes two mandatory arguments in parenthesis. + +\paragraph{How to label} +You can put a label to a coordinate by specifying the optional arguments |{<label>}| and |[<angle>]| immediately after |(<name>)|. + +\begin{tztikz}{} +\tzcoor(0,0)(A){$A$}[0] % works like: + \path (0,0) coordinate [label={0:$A$}] (A); +\end{tztikz} + +\begin{tzcode}{.3} +% \tzcoor +\begin{tikzpicture} +\tzhelplines(4,3) +\tzcoor(0,0)(A){$A_1$} % TikZ default: 90 or above +\tzcoor(2,1)(B){$B_2$\\ending point}[[align=left,red]0] +\draw (A) -- (B); +\end{tikzpicture} +\end{tzcode} + +\paragraph{Shift} +You can move the coordinate by specifying the optional argument |<shift coor>| before |(<coor>)|. +The empty shift option |<>| is not allowed. + +\begin{tzcode}{.3} +% \tzcoor: shift +\begin{tikzpicture} +\tzhelplines(4,3) +\tzcoor<0,1>(0,0)(A){$A_1$} %% +\tzcoor(2,1)(B){$B_2$\\ending point}[[align=left,red]0] +\tzline(A)(B) +\end{tikzpicture} +\end{tzcode} + + +\subsection{\protect\cmd{\tzcoor*}} +\label{ss:tzcoor*} + +The starred version \icmd{\tzcoor*} works like |\tzcoor| with one exception. It prints a `node dot' of the size |2.4pt|, by default, at a specified coordinate. + +\begin{tzdef}{} +% syntax: minimum +\tzcoor*(<coor>)(<coor name>) +% syntax: medium +\tzcoor*(<coor>)(<coor name>){<label>}[<angle>] +% syntax: full +\tzcoor*[<dot opt>]<shift coor> + (<coor>)(<name>){<label>}[[<label opt>]<angle>](<dot size>) +% defaults + *[]<>(<m>)(<m>){}[](2.4pt) +\end{tzdef} + + +\begin{tztikz}{} +\tzcoor*(0,0)(A) % works like: + \path (0,0) coordinate (A); + \tzdot*(0,0) +\end{tztikz} + +\begin{tztikz}{} +\tzcoor(0,0)(A){$A$}[right] % works like: + \path (0,0) coordinate (A); + \tzdot*(0,0){$A$}[right] +\end{tztikz} + +\begin{tzcode}{.3} +% \tzcoor* +\begin{tikzpicture} +\tzhelplines(4,3) +\tzcoor*(0,0)(A){$A_1$} % TikZ default: 90 or above +\tzcoor*(30:3cm)(B){$B_2$}[[draw,blue]0] +\draw (A) -- (B); +\end{tikzpicture} +\end{tzcode} + +\paragraph{Changing the color and size of a dot} + +You can change the color of a dot by specifying |[<dot opt>]|, which is, in fact, \Tikz's |node| option. +To change the size of dots, you can apply the \threeways\ (see Subsection \ref{ss:threeways} on page \pageref{ss:threeways}). + +\begin{tzcode}{.3} +% \tzcoor*: color, size +\begin{tikzpicture} +\tzhelplines(4,3) +\tzcoor(1,1)(A){A} +\tzcoor*(2,1)(B){B}[0] +\tzcoor*[red](1,2)(C){C}[180] +\tzcoor*[fill=none,tzdot=5pt](3,2)(D){D}[45] +\tzcoor*[blue,thick,fill=green](4,0)(E){E}[180](6pt) +\end{tikzpicture} +\end{tzcode} + +\paragraph{Shift} The optional argument |<shift coor>| works just like in |\tzcoor|. +The empty shift option |<>| is not allowed. + +\begin{tzcode}{.3} +% \tzcoor*: shift +\begin{tikzpicture} +\tzhelplines(4,3) +\tzcoor*<0,1>(0,0)(A){$A_1$} %% +\tzcoor*(2,1)(B){$B_2$\\end point}[[align=left,red]0] +\tzline(A)(B) +\end{tikzpicture} +\end{tzcode} + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzcoors} and \protect\cmd{\tzcoors*}: Semicolon versions} +\label{s:tzcoors} + +\subsection{\protect\cmd{\tzcoors}} +\label{ss:tzcoors} + +The macro \icmd{\tzcoors} takes an arbitrary number of pairs of coordinates and their names as arguments. +For example, |\tzcoors(0,0)(A) (1,1)(B) (2,2)(C);| means that the coordinate |(0,0)| is represented by the name |(A)|, |(1,1)| by |(B)|, and |(2,2)| by |(C)|. + +\begin{tzdef}{} +% syntax: minimum +\tzcoors(<coor>)(<name>..repeated..(<coor>)(<name>) ; +% syntax: full +\tzcoors <shift coor>(<coor>)(<name>){<label>}[<[label opt]angle>] + ..repeated.. ()(){}[] ; +% defaults + <> (<m>)(<m>){}[] ..repeated.. ()(){}[] ; +\end{tzdef} + +This is a \xem{semicolon version} macro. The quadruple |(<coor>)(<name>){<label>}[<angle>]| is the whole repeating pattern. +It is required to type a \xem{semicolon} `|;|' to indicate when the coordinate repetition ends. + + +\begin{tztikz}{} +\tzcoors (0,0)(A) (1,1)(B) (2,1)(C) (3,0)(D) ; % works like: + \path (0,0) coordinate (A) + (1,1) coordinate (B) + (2,1) coordinate (C) + (3,0) coordinate (D); +\end{tztikz} + +\begin{tztikz}{} +\tzcoors (0,0)(A) (1,1)(B) (2,1)(C){C}[0] (3,0)(D){D}[90]; % works like: + \path (0,0) coordinate (A) + (1,1) coordinate (B) + (2,1) coordinate [label={0:C}] (C) + (3,0) coordinate [label={90:D}] (D); +\end{tztikz} + +You can add a label to each specified coordinate by adding the optional arguments |{<label>}| and |[<angle>]| immediately after |(<name>)|. + +\begin{tzcode}{.3} +% \tzcoors +\begin{tikzpicture} +\tzcoors (0,0)(A){Ace}[[font=\LARGE\ttfamily]-90] + (2,1)(B){\textbf{Bob}}[[blue]135] + (3,2)(C){$C_1$\\$N_o$}[[align=center]0]; +\draw (A) -- (B) -- (C); +\end{tikzpicture} +\end{tzcode} + +By the option |<shift coor>|, all specified coordinates are shifted. +The empty shift option |<>| is not allowed. + +\begin{tzcode}{.3} +% \tzcoors +\begin{tikzpicture} +\tzhelplines(4,3) +\tzcoors (0,0)(A) (1,1)(B) (2,1)(C){C} (3,0)(D); +\tzlines(A)(B)(C)(D); +% shift +\tzcoors <1,1> (0,0)(A) (1,1)(B) (2,1)(C){C} (3,0)(D); +\tzlines[dashed](A)(B)(C)(D); +\end{tikzpicture} +\end{tzcode} + +\subsection{\protect\cmd{\tzcoors*}} +\label{ss:tzcoors*} + +The starred version \icmd{\tzcoors*} takes an arbitrary number of coordinates as arguments to print node dots at the coordinates. Full repeating pattern is |(<coor>)(<name>){<label>}[<angle>]|. It is required to type a \xem{semicolon} `|;|' to indicate when the iteration of coordinates ends. + +\begin{tzdef}{} +% syntax: minimum +\tzcoors*(<coor>)(<name>)..repeated..(<coor>)(<name>) ; +% syntax: full +\tzcoors*[<dot opt>]<shift coor>(<coor>)(<name>){<label>}[<[label opt]angle>] + ..repeated.. ()(){}[] ; (<dot size>) +% defaults + *[]<> (<m>)(<m>){}[] ..repeated.. ()(){}[] ; (2.4pt) +\end{tzdef} + +You can label each dot by specifying the optional arguments |{<label>}| and |[<angle>]| after the pair |(<coor>)(<name>)|. + +\begin{tzcode}{.3} +% \tzcoors* +\begin{tikzpicture} +\tzhelplines(4,3) +\tzcoors*(0,0)(A) + (1,1)(B){B} + (2,1)(C) + (3,3)(D){D}[0] ; +\end{tikzpicture} +\end{tzcode} + +You can change the dot color by |[<dot opt>]| and the label color by |[<label opt>]|. +You can apply the \threeways\ (on page \pageref{ss:threeways}) to change the dot size. The simplest way of changing the dot size is to specify the \xem{last} (even after the semicolon) parenthesis option |(<dot size>)|. + +\begin{tzcode}{.3} +% \tzcoors* +\begin{tikzpicture} +\tzhelplines(4,3) +\tzcoors*[red](0,0)(A) + (1,1)(B){B} + (2,1)(C) + (3,3)(D){D}[[blue]0] ; (6pt) +\end{tikzpicture} +\end{tzcode} + +By specifying the optional argument |<shift coor>| immediately before the first coordinate, you can move all specified coordinates. +The empty shift option |<>| is not allowed. + +\begin{tzcode}{.3} +% \tzcoors*: shift +\begin{tikzpicture} +\tzhelplines(4,3) +\settzdotsize{6pt} +\tzcoors*[red] (0,0)(A)(1,1)(B)(2,1)(C)(3,3)(D); +\settzdotsize{4pt} +\tzcoors*[blue]<.5,0>(0,0)(A)(1,1)(B)(2,1)(C)(3,3)(D); +\end{tikzpicture} +\end{tzcode} + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzcoorsquick} and \protect\cmd{\tzcoorsquick*}} +\label{s:tzcoorsquick} + +\subsection{\protect\cmd{\tzcoorsquick}} +\label{ss:tzcoorsquick} + +You can see the coordinate array at a glance using \icmd{\tzcoorsquick}, which displays specified names as text at the |center| of the coordinates, by default. + +\begin{tzdef}{} +% syntax: minimum +\tzcoorsquick(<coor>)(<name>)..repeated..(<coor>)(<name>) ; +% syntax: full +\tzcoorsquick<shift coor>(<coor>)(<name>){<label>}[<[label opt]angle>] + ..repeated.. ()(){}[] ; +% defaults + <> (<m>)(<m>){}[center] ..repeated.. ()(){}[] ; +\end{tzdef} + +\begin{tzcode}{.3} +% \tzcoorsquick +\begin{tikzpicture} +\tzhelplines(4,3) +\tzcoorsquick(0,0)(A) + (1,1)(Ben) + (2,1)(Cate) + (3,2)(Daniel); +\end{tikzpicture} +\end{tzcode} + +A label can be suppressed by the empty braces |{}|. +You can move the coordinates by specifying |<shift coor>| immediately before the first coordinate. The empty option |<>| is not allowed. + +\begin{tzcode}{.3} +% \tzcoorsquick: shift, color +\begin{tikzpicture} +\tzhelplines(4,3) +\tzcoorsquick + (0,0)(A) (1,1)(Ben) (2,1)(Cate){} (3,2)(Daniel); +\tikzset{every label/.style={blue}} +\tzcoorsquick <0,1> + (0,0)(A) (1,1)(Ben) (2,1)(Cate){} (3,2)(Daniel); +\end{tikzpicture} +\end{tzcode} + + +\subsection{\protect\cmd{\tzcoorsquick*}} +\label{ss:tzcoorsquick*} + +The starred version \icmd{\tzcoorsquick*} prints node dots on the coordinates and displays the names |above| (or |90| degree from) the dots, by default. + +\begin{tzdef}{} +% syntax: minimum +\tzcoorsquick*(<coor>)(<name>)..repeated..(<coor>)(<name>) ; +% syntax: full +\tzcoorsquick*[<dot opt>]<shift coor>(<coor>)(<name>){<label>}[<[label opt]angle>] + ..repeated.. ()(){}[] ; +% defaults + *[ tzdot=1.2pt ]<> (<m>)(<m>){}[] ..repeated.. ()(){}[] ; +\end{tzdef} + +\begin{tzcode}{.3} +% \tzcoorsquick* +\begin{tikzpicture} +\tzhelplines(4,3) +\tzcoorsquick*(0,0)(A) (1,1)(Ben) + (2,1)(Cate) (3,2)(Daniel); +\end{tikzpicture} +\end{tzcode} + +A label can be suppressed by the empty braces |{}|. +You can change the dot size using the \threeways\ (on page \pageref{ss:threeways}). +You can shift the coordinate by specifying |<shift coor>| immediately before the first coordinate. The empty shift option |<>| is not allowed. + +\begin{tzcode}{.3} +% \tzcoorsquick*: size, color, shift +\begin{tikzpicture} +\tzhelplines(4,3) +\tzcoorsquick* + (0,0)(A) (1,1)(Ben) (2,1)(Cate){} (3,2)(Daniel); +\tikzset{every label/.style={blue}} +\tzcoorsquick*[blue]<0,1> + (0,0)(A) (1,1)(Ben) (2,1)(Cate){} (3,2)(Daniel);(6pt) +\end{tikzpicture} +\end{tzcode} + +\remark +The first optional argument of |\tzcoorsquick*| is for only dots. +You can use the \Tikz\ option |every label/.style={...}| to control all the labels together. +You can also control each labels using |[<label opt>]| for each coordinate. + +\begin{tzcode}{.3} +% \tzcoorsquick* +\begin{tikzpicture}[every label/.style={draw,red}] +\tzhelplines(4,3) +\tzcoorsquick*[fill=none,blue,very thick] + (0,0)(A)(1,1)(B-1)(2,1)(C)(3,3)(D)[[blue]0];(8pt) +\end{tikzpicture} +\end{tzcode} + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzgetxyval}} +\label{s:tzgetxyval} + +\icmd{\tzgetxyval} extracts the values of x-coordinate and the y-coordinate \xem{in the unit of centimeter} from a specified coordinate and saves the values in the user-defined macros, so that you can use them later. +For example, |\tzgetxyval(3,2){\xval}{\yval}| results in |\xval=3| and |\yval=2|. + +\begin{tzdef}{} +% syntax +\tzgetxyval(<coor>){<\macroXval>}{<\macroYval>} +% default +(<m>){<m>}{<m>} +\end{tzdef} + +\begin{tzcode}{.3} +\begin{tikzpicture} +\tzhelplines(4,3) +\tzfn"dem"{3-(3/4)*\x}[0:4] +\tzfn"sup"{\x}[0:4] +% intersection point: (E) +\tzXpoint*{dem}{sup}(E)(5pt) +% extract x/y-coordinate from (E) +\tzgetxyval(E){\Ex}{\Ey} +\tzdots*(\Ex,\Ey){E}(\Ex+1,\Ey){F}(\Ex,\Ey+1){G}; +\tzdot(E)(10pt) +\tznodeframe(2,0){x\;=\;\Ex\,cm\\ y\;=\;\Ey\,cm} + [font=\ttfamily\scriptsize,align=left] +\end{tikzpicture} +\end{tzcode} + + +%%================================== +\chapter{Plot Coordinates: \protect\cmd{\tzplot}: Semicolon Versions} +\label{c:plotcoordinates} + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzplot} and \protect\cmd{\tzplot*}: Syntax} +\label{s:tzplot} + +\icmd{\tzplot} takes an arbitrary number of coordinates as arguments. +Each |(<coor>)| can be followed by the optional arguments |{<label>}| and |[<angle>]| to label the coordinate. This is a \xem{semicolon version} and the whole repeating pattern is the triple |(<coor>){<label>}[<angle>]|. It is required to type a semicolon `|;|' to indicate when the coordinate iteration ends. + +The macro |\tzplot| draws connected line segments that link specified coordinates. + +\begin{tzdef}{} +% syntax: minimum +\tzplot(<coor>)(<coor>)..repeated..(<coor>) ; +% syntax: medium +\tzplot(<coor>){<label>}[<angle>]..repeated..(<coor>){<label>}[<angle>] ; +% syntax:full +\tzplot[<opt>]{<tension>} [<plot opt>]<shift coor>"<path name>" + (<coor>){<label>}[<[label opt]angle>] + ..repeated.. + (){}[] ; (<mark size>) <code.append> +% defaults + [tzmark=2pt]{0}[smooth] <>"" (<m>){}[] ..repeated.. (){}[] ; (2pt) <> +\end{tzdef} + +The style \ixxw{tzmark} is defined as follows: + +\begin{tzsty}{} +% style: tzmark +\tikzset{ + tzmark/.style= + {mark options={solid,thin},mark size=#1}, + tzmark/.default=\tzmarksize +} +\end{tzsty} + +\icmd{\tzmarksize} is the \xem{radius} of a |mark| and the default is |2pt| as in \Tikz. +The value of |\tzmarksize| can be changed by the macro \icmd{\settzmarksize}, like |\settzmarksize{3pt}|. + + +The starred version |\tzplot*| prints dot marks at specified coordinates, without drawing line segments connecting the coordinates, by default. + + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzplot*}: Dots and marks} +\label{s:tzplot-dots} + +The starred version |\tzplot*| prints \Tikz\ marks (|*| by default) at specified coordinates. +You can change the mark color and mark style using the first bracket optional argument. + +\begin{tztikz}{} +\tzplot*(0,0)(1,2)(2,2)(3,3); % works like: + \draw [draw=none,mark=*] plot coordinates { (0,0)(1,1)(2,2)(3,3) } ; +\end{tztikz} + + +\begin{tzcode}{.3} +% \tzplot* +\begin{tikzpicture}[scale=.8] +\tzhelplines(4,3) +\tzplot*(0,0)(1,1)(2,1)(3,3); +\tzplot*[mark=o](0,3)(1,3)(2,2)(3,1); +\tzplot*[red](0,2)(1,2)(2,0)(3,2); +\end{tikzpicture} +\end{tzcode} + +\paragraph{Labels, marks, and mark size} +You can also add labels to specified coordinates with the optional arguments |{<label>}| and |[<angle>]| immediately after each |(<coor>)|. + +\begin{tztikz}{} +\tzplot*(0,0){A}[90](1,2)(2,2)(3,3){D}[0]; % works like: + \draw [draw=none,mark=*] plot coordinates { (0,0)(1,1)(2,2)(3,3) } + node (0,0) [label={90:D}] {} + node (3,3) [label={0:D}] {} ; +\end{tztikz} + +There are three ways to change the mark size. + +\begin{enumerate} +\item The simplest way is to use the parenthesis optional argument |(<mark size>)|, \xem{immediately after the semicolon}. +\item You can use the style |tzmark|, like |tzmark=3pt|. +\item You can also use the macro |\settzmarksize|, which is effective until the end of |tikzpicture| environment. +\end{enumerate} + +\begin{tzcode}{.3} +% \tzplot*: label, size +\begin{tikzpicture}[scale=.8] +\tzhelplines(4,3) +\tzplot*(0,0){A}(1,1)(2,1)(3,3){D}[[blue]0];(1mm) +\tzplot*[mark=o,tzmark=6pt](0,3)(1,3)(2,2)(3,1); +\settzmarksize{4pt} +\tzplot*[red](0,2){A}(1,2){B}(2,0){C}[[blue]0](3,2){D}; +\end{tikzpicture} +\end{tzcode} + +With |\tzplot*|, you can draw line segments by giving the \Tikz's option |draw| in the first bracket optional argument, like |\tzplot*[draw]|. + +\begin{tzcode}{.3} +% \tzplot*: line, more marks, size +\begin{tikzpicture}[scale=1] +\tzhelplines(4,3) +\settzmarksize{3pt} +\tzplot*[draw,mark=x](0,0)(1,1)(2,1)(3,3); +\tzplot*[blue,mark=diamond*](0,3)(1,3)(2,2)(3,1);(10pt) +\tzplot*[draw,dashed,red,mark=heart](0,2)(1,2)(2,0)(3,2); +\end{tikzpicture} +\end{tzcode} + +\remark In \Tikz, the |mark| shapes are affected by |scale|, |xscale|, and |yscale|. + +\begin{tzcode}{.3} +% \tzplot*: marks: distorted +\begin{tikzpicture}[yscale=.5] +\tzhelplines(4,3) +\settzmarksize{3pt} +\tzplot*[draw,mark=x](0,0)(1,1)(2,1)(3,3); +\tzplot*[blue,mark=diamond*](0,3)(1,3)(2,2)(3,1);(10pt) +\tzplot*[draw,dashed,red,mark=heart](0,2)(1,2)(2,0)(3,2); +\end{tikzpicture} +\end{tzcode} + +\paragraph{Shift} +You can move specified coordinates using the option |<shift coor>| before the first coordinate (to be precise, immediately before the option |"<path name>"| if it exists). +The empty shift option |<>| is not allowed. + +\begin{tzcode}{.3} +% \tzplot*: shift +\begin{tikzpicture} +\tzhelplines(4,3) +\tzplot*[draw] (1,3){A}(2,3)(3,3)(4,3){D}[0]; +\tzplot*[draw,red]<-1,-1>(1,3){A}(2,3)(3,3)(4,3){D}[0]; +\tzplot*[draw,blue]<0,-3>(1,3){A}(2,3)(3,3)(4,3){D}[0]; +\end{tikzpicture} +\end{tzcode} + + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzplot}: Lines} +\label{s:tzplot-lines} + +|\tzplot| draws connected line segments connecting specified coordinates. +(By default, |tension=0|.) + +\begin{tztikz}{} +\tzplot(0,0)(1,2)(2,2)(3,3); % works like: + \draw [tension=0] plot [smooth] coordinates { (0,0)(1,1)(2,2)(3,3) } ; +\end{tztikz} + + +\paragraph{Options: draw, mark, mark options, etc.} +You can use the optional argument |[<opt>]| to change the style of lines and marks. + +\begin{tzcode}{.3} +% \tzplot: line +\begin{tikzpicture}[scale=.8] +\tzhelplines(4,3) +\tzplot (0,0)(1,1)(2,1)(3,3); +\tzplot[dashed,mark=o](0,3)(1,3)(2,2)(3,1); +\tzplot[red,mark=ball,mark options={ball color=purple}] + (0,1)(1,2)(2,0)(3,2); +\end{tikzpicture} +\end{tzcode} + +To close the path of |\tzplot| you can use the option |smooth cycle| in the first bracket optional argument |[<opt>]| or in the second bracket optional argument |[<plot opt>]|. + +\begin{tzcode}{.3} +% \tzplot: smooth cycle +\begin{tikzpicture}[scale=.8] +\tzhelplines(4,3) +\tzplot (0,0)(1,1)(2,1)(3,3); +\tzplot[dashed,mark=o,smooth cycle] + (0,3)(1,3)(2,2)(3,1); +\tzplot[red,mark=*,mark options={blue}] + [smooth cycle] %% + (0,1)(1,2)(2,0)(3,2); +\end{tikzpicture} +\end{tzcode} + + + +\paragraph{Labels} You can label specified coordinates with the options |{<label>}| and |[<angle>]| immediately after each |(<coor>)|. + +\begin{tzcode}{.3} +% \tzplot: label +\begin{tikzpicture}[scale=.8] +\tzhelplines(4,3) +\tzplot(0,0){A}(1,1){B}[-90](2,1)(3,3){Da}[[draw]0]; +\tzplot[mark=o](0,3)(1,3){B}(2,2)(3,1){Db}[0]; +\tzplot[red,mark=*,draw=blue] + (0,1)(1,2){B}(2,0)(3,2){Dc}[[blue]0]; +\end{tikzpicture} +\end{tzcode} + +\paragraph{Shift} You can also move the line segments by specifying the option |<shift coor>| before the first coordinate (to be precise, immediately before the option |"<path name>"| if it exists). +The empty shift option |<>| is not allowed. + +\begin{tzcode}{.3} +% \tzplot: shift +\begin{tikzpicture}[scale=.8] +\tzhelplines(4,3) +\tzplot <1,0>(0,0)(1,1)(2,1)(3,3){Da}[0]; +\tzplot[mark=o] <1,0>(0,3)(1,3)(2,2)(3,1){Db}[0]; +\tzplot*[draw,red]<1,0>(0,1)(1,2)(2,0)(3,2){Dc}[0]; +\end{tikzpicture} +\end{tzcode} + +\paragraph{\texttt{name path} for intersections} + +To find the intersection points of two lines, you may want to name the paths first, like |[name path=<path name>]| in \Tikz. With |\tzplot|, you can do it by specifying the quote optional argument |"<path name>"| immediately before the first coordinate. + +\begin{tzcode}{.3} +% \tzplot: "path name" +\begin{tikzpicture}[scale=.8] +\tzhelplines(4,3) +\tzplot[name path=Da] (0,0)(1,1)(2,1)(3,3){Da}[0]; +\tzplot[mark=o] "Db"(0,3)(1,3)(2,2)(3,1){Db}[0]; +\tzplot*[draw,red]"Dc"(0,1)(1,2)(2,0)(3,2){Dc}[0]; +% intersection points +\tzXpoint*[gray]{Da}{Db} +\tzXpoint*[blue]{Da}{Dc} +\end{tikzpicture} +\end{tzcode} + +\paragraph{Extending the path} +In order to \xem{extend a path}, formed by |\tzplot|, \xem{from the last coordinate}, you can write \Tikz\ code in the very last optional argument |<code.append>|, \xem{after the semicolon}. + +\begin{tzcode}{.3} +% \tzplot: "path name" +\begin{tikzpicture}[scale=.8] +\tzhelplines(6,4) +\tzplot(0,0)(1,1)(2,1)(3,3){Da}[0];< -- (6,4) > +\tzplot[mark=o](0,3)(1,3)(2,2)(3,1){Db}[0];(4pt) +\tzplot[mark=ball,red](0,1)(1,2)(2,0)(3,2){Dc}[0]; + (5pt)< to [bend left] ++(2,-2) node {ends here!} > +\end{tikzpicture} +\end{tzcode} + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzplot}: Curves} +\label{s:tzplot:curves} + +With |\tzplot|, the default value of |tension| is |0|. +You can draw a curve with |\tzplot|, by specifying the optional argument |{<tension>}| before the coordinates or between the first and second bracket options (if they exist). + +\begin{tztikz}{} +\tzplot[blue,smooth cycle]{1}(0,0)(1,2)(2,2)(3,3); % works like: + \draw [blue,tension=1] plot [smooth cycle] coordinates { (0,0)(1,1)(2,2)(3,3) } ; +\end{tztikz} + +\begin{tzcode}{.3} +\begin{tikzpicture}[scale=.8] +\tzhelplines(4,3) +\tzplot[tension=1](0,0)(1,1)(2,1)(3,3); +\tzplot[mark=o] (0,3)(1,3)(2,2)(3,1); % tension=0 +\tzplot*[draw,red,smooth cycle]{1} + (0,1)(1,2)(2,0)(3,2); +\end{tikzpicture} +\end{tzcode} + +To plot curves, the macro |\tzplotcurve| is provided. +Basically, |\tzplotcurve| is the |tension=1| version of |\tzplot|. +(See Section \ref{s:tzplotcurve} on page \pageref{s:tzplotcurve}.) + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzplot}: Bars and combs} +\label{s:tzplot-bars} + +With |\tzplot|, you can draw bars or combs, using the \Tikz\ options |ybar|, |xbar|, |ycomb|, and |xcomb|. + +\begin{tzcode}{.3} +\begin{tikzpicture}[scale=.8] +\tzhelplines(4,3) +\tzplot*[draw](0,0)(1,1)(2,1)(3,3); +\tzplot[ybar](0,3)(1,3)(2,2)(3,1); +\tzplot[dashed,red,mark=heart](0,1)(1,2)(2,0)(3,2);%(5pt) +\end{tikzpicture} +\end{tzcode} + +\begin{tzcode}{.3} +\begin{tikzpicture}[scale=.8] +\tzhelplines(4,3) +\tzplot[xbar](.5,2.5)(1,3)(2,2)(3,1); +\tzplot[xbar,bar width=2mm,fill,red!50] + (1,2.5)(1.5,2)(2,0)(3,1.5);(3pt) +\end{tikzpicture} +\end{tzcode} + + +\begin{tzcode}{.3} +\begin{tikzpicture}[yscale=1.5] +\tzhelplines(0,-1)(4,1) +\tzplot[ycomb,mark=*,very thick,blue] + (.5,.1)(1,.3)(1.5,.4)(2,.5) + (4,-.1)(3.5,-.3)(3,-.4)(2.5,-.5); +\end{tikzpicture} +\end{tzcode} + +\begin{tzcode}{.3} +\begin{tikzpicture}[scale=.8] +\tzhelplines(4,3) +\tzplot[xcomb,mark=*,very thick] + (1,2.5)(1.5,2)(2,0)(3,1.5); +\end{tikzpicture} +\end{tzcode} + +\remark +\begin{itemize} +\item +Do not use |<shift coor>| for plotting bars or combs to avoid getting unexpected results. It gives you wrong bars because |<shift coor>| moves coordinates but not bars. + +%\item Use the option |shift={(coor)}| to move bars. +%\begin{tzcode}{.3} +%% shift : shift={(1,1)} +%\begin{tikzpicture}[scale=1] +%\tzhelplines(4,3) +%\tzplot*[draw]<1,1>(0,0)(1,1)(2,1)(3,3); +%\tzplot[ybar,shift={(1,1)}](0,3)(1,3)(2,2)(3,1); %% +%\tzplot[red,mark=heart]<1,1>(0,2)(1,2)(2,0)(3,2); +%\end{tikzpicture} +%\end{tzcode} + +\item +It can be a mess when using the \Tikz\ option |shift={(coor)}| with the type of mixed coordinates: native and named coordinates. + +%\begin{tzcode}{.3} +%% \tzplot(*) +%% shift : mixed coor : shift={(1,1)} : chaos +%\begin{tikzpicture}[scale=1] +%\tzhelplines(4,3) +%\tzcoors(0,3)(A)(1,3)(B)(2,2)(C)(3,1)(D); +%\tzcoors(0,2)(a)(1,2)(b)(2,0)(c)(3,2)(d); +%\tzplot*[draw]<1,1>(0,0)(1,1)(2,1)(3,3); +%\tzplot[ybar,shift={(1,1)}](A)(1,3)(C)(D); %% +%\tzplot[dashed,red,mark=heart]<1,1>(a)(1,2)(c)(d); +%\end{tikzpicture} +%\end{tzcode} + +\end{itemize} + + + +%%----------------------------------- +%%------------------------------------------------------------ +\section{\protect\cmd{\tzplotcurve(*)}} +\label{s:tzplotcurve} + +\icmd{\tzplotcurve} draws a curve connecting specified coordinates with |tension=1|, by default. Basically, it is equivalent to |\tzplot| with |[tension=1]|. + +The starred version \icmd{\tzplotcurve*} draws a curve and displays marks |*|, by default. +Basically, this is equivalent to |\tzpolot*[draw,tension=1]|. + +\begin{tzdef}{} +% syntax: minimum +\tzplotcurve(<coor>)(<coor>)..repeated..(<coor>) ; +% syntax: full +\tzplotcurve*[<opt>]{<tension>} [<plot opt>]<shift coor>"<path name>" + (<coor>){<label>}[<[label opt]angle>] + ..repeated.. + (){}[] ; (<mark size>) <code.append> +% defaults + *[tzmark=2pt]{1}[smooth] <>"" (<m>){}[] ..repeated.. (){}[] ; (2pt) <> +\end{tzdef} + +\begin{tztikz}{} +\tzplotcurve(0,0)(1,2)(2,2)(3,3); % works like: + \draw [tension=1] plot [smooth] coordinates { (0,0)(1,1)(2,2)(3,3) } ; +\end{tztikz} + +\begin{tztikz}{} +\tzplotcurve[blue,smooth cycle]{2}(0,0)(1,2)(2,2)(3,3); % works like: + \draw [blue,tension=2] plot [smooth cycle] coordinates { (0,0)(1,1)(2,2)(3,3) } ; +\end{tztikz} + +Since |\tzplotcurve| is a \xem{semicolon version}, you need to enter a semicolon to indicate when the coordinate iteration ends. +In repeating coordinates, each mandatory coordinate can have a label. +So the whole repeating pattern is the triple |(<coor>){<text>}[<pos>]|. +For example, |(A){here}[above]| represents |(A) node [above] {here}| in \Tikz. + +\paragraph{Options: lines, labels, colors, smooth cycle} +Use the first bracket option to control the colors of lines or labels. + +\begin{tztikz}{} +\tzplotcurve(0,0)(1,2)(2,2){A}[below](3,3){B}[right]; % works like: + \draw [tension=1] plot [smooth] coordinates { (0,0)(1,1)(2,2)(3,3) } + (2,2) node [below] {A} + (3,3) node [right] {B} ; +\end{tztikz} + +You can change the color of all labels together by adding |[text=<color>]| to the first bracket option list. + +\begin{tzcode}{.3} +% \tzplotcurve(*) +\begin{tikzpicture} +\tzhelplines(4,3) +\tzplotcurve*[red,text=blue] + (0,0)(1,2){B}(2,2)(3,3)(4,1){E}[0]; +\tzplotcurve(1,.5)(2,3)(3,2)(2,1)(3,1); +\end{tikzpicture} +\end{tzcode} + +The simplest way to change the mark size is to specify |(<mark size>)| immediately after the semicolon |;|. +To close the path of |\tzplotcurve|, you can use the \Tikz\ option |smooth cycle| in the first bracket option or in the second bracket option. + +\begin{tzcode}{.3} +% \tzplotcurve(*): smooth cycle, mark size +\begin{tikzpicture} +\tzhelplines(4,3) +\tzplotcurve*[red,text=blue][smooth cycle] + (0,0)(1,2){B}(2,2)(3,3)(4,1){E}[0];(3pt) %% +\tzplotcurve*[smooth cycle](1,.5)(2,3)(3,2)(2,1)(3,1); +\end{tikzpicture} +\end{tzcode} + +\paragraph{Tension} +You can change the value of |tension| (|tension=1| by default) by specifying the option |{<tension>}| before the coordinates or between the two bracket options if they exist. + +\begin{tzcode}{.3} +% \tzplotcurve: tension +\begin{tikzpicture} +\tzhelplines(4,3) +\tzcoor(.5,.5)(A) +\tzplotcurve[blue]{2}(1,3)(A)(4,0); +\tzplotcurve[thick](1,3)(A)(4,0); % default: tension=1 +\tzplotcurve[red]{.5}(1,3)(A)(4,0); +\tzplotcurve[dashed]{0}(1,3)(A)(4,0); +\end{tikzpicture} +\end{tzcode} + + +\paragraph{Shift} Use the optional argument |<shift coor>| before the first coordinate (to be precise, immediately before |"<path name>"|, if exists). +The empty shift option |<>| is not allowed. + +\begin{tzcode}{.3} +% \tzplotcurve(*): shift +\begin{tikzpicture} +\tzhelplines(4,3) +\tzplotcurve*[red,text=blue,smooth cycle] + <0,1>(0,0)(1,2){B}(2,2)(3,3)(4,1){E}[0];(3pt) %% +\tzplotcurve*[smooth cycle] + (1,.5)(2,3)(3,2)(2,1)(3,1); +\end{tikzpicture} +\end{tzcode} + + +\paragraph{Extending the path} In order to extend the path created by |\tzplotcurve(*)| from the last coordinate, you can directly write \Tikz\ code in the very last optional argument |<code.append>|, after the semicolon. + +\begin{tzcode}{.3} +% \tzplotcurve(*): <code.append> +\begin{tikzpicture} +\tzhelplines(4,3) +\tzplotcurve*[red,text=blue,thick] + (0,0)(1,2){B}(2,2)(3,3)(4,1){E}[-45];(3pt) + < arc (-90:90:1cm) node [above] {up} > %% +\tzplotcurve[dashed] + (1,.5)(2,3)(3,2)(2,1)(3,1); + < -- ++(-1,-1) node [below] {down} > %% +\end{tikzpicture} +\end{tzcode} + +You can also use |<--cycle>| to \xem{close} the path \xem{with a straight line} from the last coordinate to the first coordinate. + +\begin{tzcode}{.3} +% \tzplotcurve(*): <--cycle> +\begin{tikzpicture} +\tzhelplines(4,3) +\tzplotcurve*[red,text=blue] + (0,0)(1,2)(2,2)(3,3)(4,1){A}[right] ; (3pt)<--cycle> +\tzplotcurve + (1,.5)(2,3)(3,2)(2,1)(3,1) ; <--cycle> +\end{tikzpicture} +\end{tzcode} + +\paragraph{\texttt{name path} for intersection points} +You can name the path of |\tzplotcurve| by specifying the option |"<path name>"| immediately before the first coordinate. + +\begin{tzcode}{.3} +% \tzplotcurve(*): name path +\begin{tikzpicture} +\tzhelplines(4,3) +\tzplotcurve[blue] + "IC"(.5,3)(1.5,1.2)(4,.5){$u$}[0]; +\tzplot[draw=red] + "bgt"(0,3)(4,0){budget}[-90]; +% intersection points +\tzXpoint{IC}{bgt}(K) +\tzdots*(K){$A_1$}[30](K-2){$A_2$}; +\end{tikzpicture} +\end{tzcode} + + +%%================================== +\chapter{Nodes} +\label{c:nodes} + +%%------------------------------------------------------------ +\section{\protect\cmd{\tznode} and \protect\cmd{\tznode*}} +\label{s:tznode} + +The macro \icmd{\tznode} allows you to put text at specified coordinates. +You can also optionally name a node so you can refer to the \iisw{node coordinate} later. + +The starred version \icmd{\tznode*} is equivalent to |\tznode[draw]|, which draws the perimeter of the specified node. The default node shape is a |rectangle|. + +\begin{tzdef}{} +% syntax: minimal +\tznode(<coor>){<text>} +% syntax: full +\tznode[<opt>]<shift coor>(<coor>)(<node name>){<text>}[<node opt>] +% defaults + []<>(<m>)(){}[] +\end{tzdef} + +\begin{tztikz}{} +\tznode(0,0){text} % works like: + \path (0,0) node {text}; + % or + \node at (0,0) {text}; +\end{tztikz} + +\begin{tztikz}{} +\tznode[draw] (0,0)(A){text}[above right] % works like: + \node [draw] (A) at (0,0) [above right] {text}; +\end{tztikz} + +|\tznode*| prints the perimeter of a node, which is a |rectangular| by default. + +\begin{tzdef}{} +% syntax: minimal +\tznode*(<coor>){<text>} +% syntax: full +\tznode*[<opt>]<shift coor>(<coor>)(<name>){<text>}[<node opt>]<code.append> +% defaults + *[draw]<>(<m>)(){}[]<> +\end{tzdef} + +\begin{tztikz}{} +\tznode* (0,0)(A){text}[above right] % works like: + \node [draw] (A) at (0,0) [above right] {text}; +\end{tztikz} + +\paragraph{Putting text} You can use \Tikz\ options in the first bracket optional argument |[<opt>]| or the second bracket option |[<node opt>]| to put text with different colors, fonts, and so on. + +\begin{tzcode}{.3} +% \tznode(*) +\begin{tikzpicture} +\tzhelplines(4,3) +\tznode(1,1){text} +\tznode(2,2){another\\text}[align=left] +\tznode*(3,1){\textbf{text}} +\tznode*[blue](3,0){\scshape Text}[r] % right +\tznode*(4,2){another\\text}[align=center,font=\itshape] +\end{tikzpicture} +\end{tzcode} + +\paragraph{Abbreviations} You can use \xem{abbreviations} such as |a| for |above|, |l| for |left|, |ar| for |above right|, |bl| for |below left|, and so on to indicate where the \xem{text} of a \xem{main node} is placed. (See also Section \ref{s:stylenames} on page \pageref{s:stylenames}.) + +\begin{quote} +\warning +A \iisw{main node} is placed by the placement words, while a \iisw{label node} is placed by the placement words or the |<angle>| expression. +\begin{itemize} +\item You CANNOT use the abbreviations to place a \xem{label node} for \xem{points} or \xem{dots} or \xem{coordinates}. +\item +Instead, use |<angle>| or the original (unabridged) placement words such as |right| and |below left| to place |<label>|. +\item +Note that, on the other hand, you CANNOT use the |<angle>| option to place a \xem{main node}. +\end{itemize} +\end{quote} + + +\begin{tzcode}{.3} +% \tznode(*): main node, label node +\begin{tikzpicture} +\tzhelplines(4,3) +\tzdot*(1,1) +\tznode*(1,1){A}[ar] +\tznode*[red](1,1){B}[b] +\tznode(1,1){C}[l] +\tznode*[inner sep=0pt,text=blue,scale=2] + (3,2){Text}[label=180:Left,pin=45:Above Right] +\tznode*[inner sep=0pt,text=red,scale=2] + (3,2){Text}[b=2cm] %% below=2cm +\end{tikzpicture} +\end{tzcode} + +\paragraph{Naming nodes} +You can name a node at a specified coordinate |(<coor>)| by specifying |(<name>)| immediately after the coordinate. You can use the node name as a \iisw{node coordinate}. + +\begin{tzcode}{.3} +% \tznode(*): name nodes +\begin{tikzpicture} +\tzhelplines(4,3) +\tznode*(1,1)(A){A} +\tznode*[fill=blue,text=yellow](2,3)(B){B} +\tznode*[circle,text=red](4,1)(C){C} +\tzline[->](A)(B) +\tzto[->,bend left,dashed](B)(C) +\end{tikzpicture} +\end{tzcode} + +\paragraph{Shift} +You can move the coordinates by specifying the option |<shift coor>| immediately before the coordinate |(<coor>)|. +The empty shift option |<>| is not allowed. + +\begin{tzcode}{.3} +% \tznode(*): shift +\begin{tikzpicture} +\tzhelplines(4,3) +\tznode*<-1,0>(1,1)(A){A} +\tznode*[fill=blue,text=yellow]<1,-1>(2,3)(B){B} +\tznode*[circle,text=red]<-2,-1>(4,1)(C){C} +\tzline[->](A)(B) +\tzto[->,bend left,dashed](B)(C) +\end{tikzpicture} +\end{tzcode} + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tznodedot(*)}} +\label{s:tznodedot} + +\icmd{\tznodedot} names a node and prints a circle node dot. +|\tznodedot| is basically the same as |\tzdot|, except for one thing. +|\tznodedot| names a node. + +The starred version \icmd{\tznodedot*} prints a filled circle node dot (of the size |2.4pt|, by default), just like |\tzdot*|. But it optionally names a node. + +\begin{tzdef}{} +% syntax: medium +\tznodedot(<coor>)(<node name>){<label>}[<angle>] +% syntax: full +\tznodedot*[<opt>]<shift coor> + (<coor>)(<node name>){<label>}[<[label opt]angle>] (<dot size>) +% defaults + *[]<>(<m>)(){}[](2.4pt) +\end{tzdef} + +Since |\tznodedot(*)| prints a node dot, its |<label>| is placed by |<angle>|. + +\begin{tzcode}{.3} +% \tznodedot(*): label, color +\begin{tikzpicture} +\tzhelplines(4,3) +\tznodedot(1,1)(A){A}[180] +\tznodedot*(2,3)(B){\textbf{B}} +\tznodedot[rectangle](4,1)(C){C}[[red]0] +\tzline[->](A)(B) +\tzto[->,bend left,dashed](B)(C) +\end{tikzpicture} +\end{tzcode} + +You can apply the \threeways\ (on page \pageref{ss:threeways}) to change the size of node dots. +The simplest way is to use the last parenthesis option |(<dot size>)|. + +\begin{tzcode}{.3} +% \tznodedot(*): size +\begin{tikzpicture} +\tzhelplines(4,3) +\settzdotsize{5pt} %% +\tznodedot(1,1)(A){A}[180] +\tznodedot*(2,3)(B){B} +\tznodedot[rectangle](4,1)(C){C}[0](10pt) %% +\tzline[->](A)(B) +\tzto[->,bend left,dashed](B)(C) +\end{tikzpicture} +\end{tzcode} + + +You can move the coordinates of dots by specifying the |<shift coor>| option immediately before the coordinate. +The empty shift option |<>| is not allowed. + +\begin{tzcode}{.3} +% \tznodedot(*): shift +\begin{tikzpicture} +\tzhelplines(4,3) +\settzdotsize{5pt} +\tznodedot(1,1)(A){A}[180] +\tznodedot*(2,3)(B){B} +\tznodedot[rectangle]<-1,-1>(4,1)(C){C}[0](10pt) %% +\tzline[->](A)(B) +\tzto[->,bend left,dashed](B)(C) +\end{tikzpicture} +\end{tzcode} + + + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tznodeframe} and \protect\cmd{\tznodeframe*}} +\label{s:tznodeframe} + +\icmd{\tznodeframe} draws and names a rectangle node with text in it. + +%\icmd{\tznoderectangle} and \icmd{\tznodebox} are aliases of |\tznodeframe|. + +\begin{tzdef}{} +% syntax: +\tznodeframe[<opt>](<coor>)(<node name>){<text>}[<node opt>] +% defaults + []<>(<m>)(){}[text=black] +\end{tzdef} + + +\begin{tzcode}{.3} +% \tznodeframe +\begin{tikzpicture} +\tzhelplines(4,3) +\tznodeframe(0,0)(A) +\tznodeframe(4,2)(B)[circle] +\tzline[blue,thick](A)(B) +\tznodeframe[scale=1.5](2,1){Node frame} + [label=180:Left, pin=-45:pin] +\end{tikzpicture} +\end{tzcode} + +\begin{tzcode}{.3} +% \tznodeframe: fill (opacity=1) +\begin{tikzpicture} +\tzhelplines(4,3) +\tznodeframe(0,3) +\tznodeframe(0,0)(A) +\tznodeframe(4,2)(B)[circle] +\tzline[blue,thick](A)(B) +\tznodeframe[fill=green,scale=1.5](2,1){Node frame} + [label=180:Left, pin=-45:pin] +\end{tikzpicture} +\end{tzcode} + +The starred version |\tznodeframe*| fills the rectangle with color (|black!50| by default) with |fill opacity=.3| but with |text opacity=1|, by default. + +%\icmd{\tznoderectangle*} and \icmd{\tznodebox*} are aliases of |\tznodeframe*|. + +\begin{tzdef}{} +% syntax: +\tznodeframe*[<opt>]<shift coor> + (<coor>)(<node name>){<text>}[<node opt>]{<fill opacity>} +% defaults + *[fill=black!50,fill opacity=.3,text opacity=1] <> + (<m>)(){}[draw=black,text=black]{.3} +\end{tzdef} + +\remark +|\tznodeframe| works very similar to |\tznode|, but their `starred versions' work differently. +While |\tznode*| draws the perimeter of a node, |\tznodeframe*| fills a node with color. + +\begin{tzcode}{.3} +% \tznodeframe*: opacity=.3 (by default) +\begin{tikzpicture} +\tzhelplines(4,3) +\tznodeframe(0,0)(A) +\tznodeframe(4,2)(B)[circle] +\tzline[blue,thick](A)(B) +\tznodeframe*[green,scale=1.5](2,1){Node frame} + [label=180:Left, pin=-45:pin] +\end{tikzpicture} +\end{tzcode} + +You can change the |fill opacity| of |\tznodeframe*| by specifying the last curly brace option |{<fill opacity>}|. You can also move the node by specifying the |<shift coor>| option immediately before the coordinate. +(The empty shift coor |<>| is not allowed.) + +\begin{tzcode}{.3} +% \tznodeframe(*): opacity, shift +\begin{tikzpicture} +\tzhelplines[solid](4,3) +\tznodebox(0,0) +\tznodeframe*(1,2)(A){A}{.1} % opacity +\tznodeframe[fill=yellow](2,2)(B){B} +\tznodeframe*[red](3,2)(C){Cat} +\tznodeframe[fill=green]<-1,-2>(4,2)(D){Dog} % shift +\tzto[->,bend left=45](A.north)(C.90) +\tzto[->,bend right=45,dashed](B.-135)(D.west) +\end{tikzpicture} +\end{tzcode} + +\remark +In addition to using the option |{<fill opacity>}|, you can use a macro to change the default value. +\begin{itemize} +\item The default fill opacity can be changed by the macro \icmd{\settzfillopacity}. +\item +The default fill color is |black!50|. You can use the macro \icmd{\settzfillcolor} to change the default fill color. +\item With |\tznodeframe|, you can change the color of the perimeter and text with the second bracket option |[<node opt>]|. +\end{itemize} + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tznodecircle} and \protect\cmd{\tznodecircle*}} +\label{s:tznodecircle} + +\icmd{\tznodecircle} works just like |\tznodeframe| but with a circle node. + +\begin{tzdef}{} +% syntax +\tznodecircle[<opt>]<shift coor>(<coor>)(<node name>){<text>}[<node opt>] +% defaults + [circle]<>(<m>)(){}[text=black] +\end{tzdef} + +\icmd{\tznodecircle*} works just like |\tznodeframe*| but with a circle node. + +\begin{tzdef}{} +% syntax +\tznodecircle*[<opt>]<shift coor> + (<coor>)(<node name>){<text>}[<node opt>]{<fill opacity>} +% defaults + *[circle,fill=black!50,fill opacity=.3,text opacity=1] <> + (<m>)(){}[draw=black,text=black]{.3} +\end{tzdef} + +\begin{tzcode}{.3} +% \tznodecircle +\begin{tikzpicture} +\tzhelplines(4,3) +\tznodecircle(0,0)(A) +\tznodecircle(4,2)(B)[circle] +\tzline[blue,thick](A)(B) +\tznodecircle[scale=1.5](2,1){Node frame} + [label=180:Left, pin=-45:pin] +\end{tikzpicture} +\end{tzcode} + +You can change the |fill opacity| of |\tznodecircle*| by specifying the last curly brace option |{<fill opacity>}| or using |\settzfillopacity|. You can also move the node by specifying the |<shift coor>| option immediately before the coordinate. +(The empty shift coor |<>| is not allowed.) + +\begin{tzcode}{.3} +% opacity, shift +\begin{tikzpicture} +\tzhelplines[solid](4,3) +\tznodecircle(0,0) +\tznodecircle*(1,2)(A){A}{.1} % opacity +\tznodecircle[fill=yellow](2,2)(B){B} +\tznodecircle*[red](3,2)(C){Cat} +\tznodecircle[fill=green]<-1,-2>(4,2)(D){Dog} % shift +\tzto[->,bend left=45](A.north)(C.90) +\tzto[->,bend right=45,dashed](B.-135)(D.west) +\end{tikzpicture} +\end{tzcode} + + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tznodeellipse} and \protect\cmd{\tznodeellipse*}} +\label{s:tznodeellipse} + +\icmd{\tznodeellipse} works just like |\tznodeframe| but with an ellipse node. + +\begin{tzdef}{} +% syntax: +\tznodeellipse[<opt>]<shift coor>(<coor>)(<node name>){<text>}[<node opt>] +% defaults + [ellipse]<>(<m>)(){}[text=black] +\end{tzdef} + +The starred version \icmd{\tznodeellipse*} works just like |\tznodeframe*| but with an ellipse node. + +\begin{tzdef}{} +% syntax: +\tznodeellipse*[<opt>]<shift coor> + (<coor>)(<node name>){<text>}[<node opt>]{<fill opacity>} +% defaults + *[ellipse,fill=black!50,fill opacity=.3,text opacity=1] <> + (<m>)(){}[draw=black,text=black]{.3} +\end{tzdef} + +\begin{tzcode}{.3} +% \tznodeellipse +\begin{tikzpicture} +\tzhelplines(4,3) +\tznodeellipse(0,3) +\tznodeellipse(0,0)(A) +\tznodeellipse(4,2)(B)[circle] +\tzline[blue,thick](A)(B) +\tznodeellipse[scale=1.5](2,1){Node frame} + [label=180:Left, pin=-45:pin] +\end{tikzpicture} +\end{tzcode} + +You can change the |fill opacity| of |\tznodeellipse*| by specifying the last curly brace option |{<fill opacity>}|. You can also move the node by specifying the |<shift coor>| option immediately before the coordinate. +(The empty shift coor |<>| is not allowed.) + +\begin{tzcode}{.3} +% opacity, shift +\begin{tikzpicture} +\tzhelplines[solid](4,3) +\tznodeellipse(0,0) +\tznodeellipse*(1,2)(A){A}{.1} % opacity +\tznodeellipse[fill=yellow](2,2)(B){B} +\tznodeellipse*[red](3,2)(C){Cat} +\tznodeellipse[fill=green]<-1,-2>(4,2)(D){Dog} % shift +\tzto[->,bend left=45](A.north)(C.90) +\tzto[->,bend right=45,dashed](B.-135)(D.west) +\end{tikzpicture} +\end{tzcode} + + +%%================================== +\chapter{Lines} +\label{c:lines} + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzline}: Connecting two points} +\label{s:tzline} + +\icmd{\tzline} connects two points with a straight line. + +\begin{tzdef}{} +% syntax: miminum +\tzline(<coor1>)(<coor2>) +% syntax: medium +\tzline[<opt>](<coor1>){<text1>}[<node opt1>] + (<coor2>){<text2>}[<node opt2>] +% syntax: full +\tzline[<opt>]<shift coor>"<path name>" + (<coor1>){<text1>}[<node opt1>] + (<coor2>){<text2>}[<node opt2>]<code.append> +% defaults + []<>""(<m>){}[above](<m>){}[]<> +\end{tzdef} + + +\begin{tztikz}{} +\tzline(0,1)(2,1) % works like: + \draw (0,1) -- (2,1); +\end{tztikz} + + +\subsection{Line styles} +\label{ss:tzline:linestyles} + +You can use the first optional argument |[<opt>]| to control the line styles. + +\begin{tztikz}{} +\tzline[blue](0,1)(2,1) % works like: + \draw [blue] (0,1) -- (2,1); +\end{tztikz} + +\begin{tzcode}{.3} +% \tzline +\begin{tikzpicture} +\tzhelplines(4,3) +\tzline[blue,->](0,0)(3,3) +\tzline[*-o](0,2)(3,0) +\tzline[dashed](1,2)(4,0) +\tzdots*(1,2)(4,0); +\end{tikzpicture} +\end{tzcode} + +\subsection{Adding text} +\label{ss:tzline:addingtext} + +You can add text by specifying the optional arguments |{<text>}| and |[<node opt>]|. + +\paragraph{Text next to the line} +With the options |{<text1>}[<node opt1>]| \xem{in-between} two coordinates, you can add text next to the line, with the option |[above,midway]| by default. + +\begin{tztikz}{} +\tzline[blue](0,1){my line}[sloped](2,1) % works like: + \draw [blue] (0,1) -- node [above,sloped] {my line} (2,1) ; +\end{tztikz} + +\begin{tzcode}{.3} +% \tzline: text next to line +\begin{tikzpicture} +\tzhelplines(4,3) +\tzline(0,0){Above}(4,0) % default [above] +\tzline[blue](0,1){Near end}[b,near end](4,1) % below +\tzline[->](0,2){Sloped}[sloped](3,3) % default [above] +\end{tikzpicture} +\end{tzcode} + +You can use the \xem{abbreviations} of \Tikz\ basic placement options such as |a| for |above|, |bl| for |below left|, and so on. (For more details, see page \pageref{abbreviations}.) + + +\paragraph{Text at or around the last coordinate} + +You can also add text at (by default) or around the second coordinate by specifying |{<text2>}| and |[<node opt2>]| immediately \xem{after} the second coordinate. + +\begin{tztikz}{} +\tzline[blue](0,1)(2,1){my line}[right] % works like: + \draw [blue] (0,1) -- (2,1) node [right] {my line}; +\end{tztikz} + + +\begin{tzcode}{.3} +% \tzline +\begin{tikzpicture} +\tzhelplines(4,3) +\tzline[blue,->](0,0)(3,3){\textbf{line A}}[r] +\tzline[*-o](0,2)(3,0){line B}[red,draw=blue,b=1mm] +\tzline[dashed](1,2){dashed}[sloped](4,0){line C}[ar] +\tzdots*(1,2)(4,0); +\end{tikzpicture} +\end{tzcode} + +%\subsection{Relative coordinates: \texttt{+} or \texttt{++}} +%\label{ss:tzline:relative} +% +%You can make the second coordinate relative to the first. +%You can even select `|+| relative' or `|++| relative' by specifying the option |<+>| or |<++>| immediately before the second coordinate. +% +%\begin{tztikz}{} +%\tzline+(0,0)<+>(2,1) % works like: +% \draw (1,1) -- + (2,1); +%\end{tztikz} +% +%\begin{tzcode}{.3} +%% \tzline +%\begin{tikzpicture} +%\tzhelplines(4,3) +%\tzline[blue,->](0,0) (3,3) {A}[r] +%\tzline[*-o] (0,2){b} <+>(3,-2){B}[r] +%\tzline[dashed] (1,2){c}<++>(3,-2){C}[r] +%\tzdots*(1,2)(4,0); +%\end{tikzpicture} +%\end{tzcode} +% +%Notice that, with |\tzline|, |<+>| and |<++>| make no difference. +%But with the macro |\tzlines| it is not the case. +% +%\remark +%Notice that using |<+>| and |<++>| makes no difference in |\tzline|. +%But it is not the case with the macro |\tzlines| that connects multiple coordinates. + +\subsection{Moving the line: \texttt{shift}} +\label{ss:tzline:shift} + +You can move the line generated by |\tzline| by specifying the option |<shift coor>| before the first coordinate (to be precise, immediately before the option |"<path name>"|, which is put immediately before the first coordinate, if it exists). +The empty shift coor |<>| is not allowed. + +\begin{tzcode}{.3} +% \tzline: shift +\begin{tikzpicture} +\tzhelplines(4,3) +\tzline[blue,->] (0,0)(3,3){A}[r] +\tzline[blue] <1,0>(0,0)(3,3){A}[r] +\tzline[dashed] (1,2)(4,0){C}[r] +\tzline[dashed]<-.5,-.5>(1,2)(4,0){C}[r] +\tzdots*(1,2)(4,0); +\end{tikzpicture} +\end{tzcode} + + + +\subsection{Extending the path} +\label{ss:tzline:extendingpath} + +You can extend the path of |\tzline| from the last coordinate, by writing \Tikz\ code in the last optional argument |<code.append>|. + +\begin{tzcode}{.3} +% \tzline: shift +\begin{tikzpicture} +\tzhelplines(4,3) +\tzline[blue,->](0,0)(3,3)<arc(0:-60:1cm)> +\tzline[dashed,->](1,2)(4,0) + <to[bend left] ++(-4,1) node [a] {ends here!}> +\end{tikzpicture} +\end{tzcode} + + +\subsection{Naming the path: Intersection points} +\label{ss:tzline:namepath} + +When you specify the option |"<path name>"| immediately before the first coordinate, it works like |[name path=<path name>]| in the option list of |[<opt>]|. +You can use this name of path to find intersection points. + +\begin{tzcode}{.3} +% \tzline+: name path +\begin{tikzpicture} +\tzhelplines(4,3) +\tzline[blue,->] "dem" (0,0)(3,3){demand}[r] +\tzline[dashed,->]"supp"(1,2)(4,0){supply}[ar] +% intersection point +\tzXpoint*{dem}{supp} +\end{tikzpicture} +\end{tzcode} + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzline+}: Relative coordinates} +\label{s:tzline+} + +The \iisw{plus version} \icmd{\tzline+} takes the second coordinate |(<coor2>)| relative (with |++|) to the first coordinate |(<coor1>)|. +%That is, |\tzline+(A)(B)| is equivalent to |\tzline(A)<++>(B)|. + +\xem{Everything else is the same as in} |\tzline|. + +\begin{tzdef}{} +% syntax: full +\tzline+[<opt>]<shift coor>"<path name>" + (<coor1>){<text1>}[<node opt1>] + (<coor2>){<text2>}[<node opt2>]<code.append> +% defaults + +[]<>""(<m>){}[above](<m>){}[]<> +\end{tzdef} + + +\begin{tztikz}{} +\tzline+(0,1)(2,1) % works like: + \draw (0,1) -- ++ (2,1); +\end{tztikz} + +\begin{tztikz}{} +\tzline+[dashed]"AA"(0,1){A}[red](2,1){B}[right,blue] % works like: + \draw [dashed,name path=AA] + (0,1) -- node [red] {A} ++ (2,1) node [right,blue] {B}; +\end{tztikz} + + +\begin{tzcode}{.3} +% \tzline+ +\begin{tikzpicture} +\tzhelplines(4,3) +\tzline+[blue,->](0,1)(3,2) {A}[r] +\tzline+[*-o] (0,2){b}(3,-2){B}[r] +\tzline+[dashed]<1,0>(0,2){b}(3,-2){B}[r] +\end{tikzpicture} +\end{tzcode} + + +\begin{tzcode}{.3} +% \tzline+: name path +\begin{tikzpicture} +\tzhelplines(4,3) +\tzline+[blue,->] "dem" (0,0)(3,3){demand}[r] +\tzline+[dashed,->]"supp"(1,2)(3,-2){supply}[ar] +% intersection point +\tzXpoint*{dem}{supp} +\end{tikzpicture} +\end{tzcode} + + +%%------------------------------------------------------------ +\section{Styles: \texttt{tzshorten} and \texttt{tzextend}} +\label{s:tzshorten} + +The styles \ixxw{tzshorten} and \ixxw{tzextend} are defined as follows. + +\begin{tzsty}{} +% tzshorten +\tikzset{% + tzshorten/.style 2 args ={shorten <=#1, shorten >=#2}, + tzshoretn/.default={2pt}{2pt} +} + +% tzextend (negative tzshorten) +\tikzset{% + tzextend/.style 2 args ={shorten <=-#1, shorten >=-#2}, + tzextend/.default={2pt}{2pt} +} +\end{tzsty} + +For example, |[tzshorten={2mm}{1mm}]| is equivalent to |[shorten <=2mm,shorten >=1mm]| in \Tikz. Simple |[tzshorten]| means that |[tzshorten={2pt}{2pt}]| by default. + +The style |tzextend| is a negative |tzshorten|. For example, |tzextend{2mm}{1mm}| is equivalent to |tzshorten{-2mm}{-1mm}|. + + +\begin{tzcode}{.3} +% tzshorten, tzextend +\begin{tikzpicture} +\tzhelplines(4,3) +\tzdots(0,0)(3,0); \tzline(0,0)(3,0) +\tzdots(0,1)(3,1); +\tzline[->,thick,blue,tzshorten={2mm}{1mm}](0,1)(3,1) +\tzdots(1,2)(3,2); +\tzline[<->,thick,red,tzextend={1cm}{1cm}](1,2)(3,2) +\end{tikzpicture} +\end{tzcode} + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzlines}: Connecting multiple points: Semicolon version} +\label{s:tzlines} + +\icmd{\tzlines} connects two or more points with connected line segments. +Since |\tzlines| takes an arbitrary number of coordinates as arguments, it is a \xem{semicolon version}. So, you need to enter a semicolon `|;|' to indicate when the coordinate iteration ends. + +\begin{tzdef}{} +% syntax: minimum +\tzlines(<coor>)(<coor>)..repeated..(<coor>) ; +% syntax: medium +\tzlines(<coor>){<text>}[<node opt>]..repeatd..(<coor>){<text>}[<node opt>] ; +% syntax: full +\tzlines[<opt>]<shift coor>"<path name>" + (<coor>){<text>}[<node opt>] + ..repeated.. (){}[] ; <code.append> +% defaults + []<>"" (<m>){}[] ..repeated.. (){}[] ; <> +\end{tzdef} + + +\begin{tztikz}{} +\tzlines(1,1)(2,2)(3,1)(4,3); % works like: + \draw (1,1) -- (2,2) -- (3,1) -- (4,3); +\end{tztikz} + +The whole repeating pattern in |\tzlines| is the triple |(<coor>){<text>}[<node opt>]|. +%Any |<+ or ++>| after the last coordinate, if any, is ignored. + +\begin{tztikz}{} +\tzlines(1,1)(2,2)(3,1){C}(4,3){D}[r]; % works like: + \draw (1,1) -- (2,2) -- (3,1) -- node {C} (4,3) node [right] {D}; +\end{tztikz} + +\paragraph{Line styles} +Use the first optional argument |[<opt>]| to control the style of the connected line drawn by |\tzlines|. + +\begin{tzcode}{.3} +% \tzlines: line style +\begin{tikzpicture} +\tzhelplines(4,3) +\tzlines[blue,<->](0,1)(1,2)(3,1)(4,3); +\tzlines[dashed](0,0)(1,1)(2,1)(3,0); +\end{tikzpicture} +\end{tzcode} + +\paragraph{Adding text} + +You can add text in the |midway|, by default, of each line segment by specifying the options |{<text>}| and |[<node opt>]| immediately after each coordinate (except the last one). +The options |{<text>}| and |[<node opt>]| after the last coordinate put |<text>| at or around the last coordinate. + + +\begin{tzcode}{.3} +% \tzlines: adding text +\begin{tikzpicture} +\tzhelplines(4,3) +\tzlines[red,thick,<->,text=blue] + (0,1){Up} + (1,2){Down}[a,sloped] + (3,1){Up} + (4,3){line A} ; +\tzlines[dashed](0,0)(1,1)(2,1)(3,0){line B}[r]; +\end{tikzpicture} +\end{tzcode} + +%\paragraph{Relative coordinates: \texttt{+} and \texttt{++}} +% +%You can make the coordinates (from the second coordinate) relative to the previous one by specifying the option |<+>| and |<++>| immediately before the coordinates. +%(In \Tikz, only |<++>| refreshes the \xem{current point} to new one.) +% +%\begin{tzcode}{.3} +%% \tzlines +%\begin{tikzpicture} +%\tzhelplines(4,3) +%\tzlines[red,thick,<->,text=blue] +% (0,1){Up} +% <+>(1,1){Down}[a,sloped] % current point: (0,1) +% <++>(3,0){Up} % new current point: (3,1) +% <++>(1,2){line A} ; +%\tzlines[dashed](0,0)(1,1)(2,1)<++>(1,-1){line B}[r]; +%\end{tikzpicture} +%\end{tzcode} + +\paragraph{Shift} +You can move the connected line by specifying |<shift coor>| before the first coordinate or immediately before the option |"<path name>"| if it exists. +(The empty shift option |<>| is not allowed.) + +\begin{tzcode}{.3} +% \tzlines: shift +\begin{tikzpicture} +\tzhelplines(4,3) +\tzlines[red,thick,<->,text=blue] + <0,-1>(0,1) + (1,2) + (3,1) + (4,3){shifted\\line A}[align=left,ar] ; +\tzlines[dashed]<1,0>(0,0)(1,1)(2,1)(3,0){line B}[r] ; +\end{tikzpicture} +\end{tzcode} + +\paragraph{Naming paths} +You can name the path of |\tzlines| by specifying the option |"<path name>"| immediately before the first coordinate. + +\begin{tzcode}{.3} +% \tzlines: shift, intersection +\begin{tikzpicture} +\tzhelplines(4,3) +\tzlines[red,thick,<->,text=blue] + <0,-1>"AA"(0,1) + (1,2)(3,1)(4,3){shifted\\line A}[align=left,ar] ; +\tzlines[dashed] + <1,0>"BB"(0,0)(1,1)(2,1)(3,0){line B}[r] ; +% intersection points +\tzXpoint*{AA}{BB}(X){X1}[-90] % [<angle>] for point +\tzdot(X-2){X2}[0] % [<angle>] for dot +\end{tikzpicture} +\end{tzcode} + +\paragraph{Extending the path} +You can extend the path of |\tzlines| by writing \Tikz\ code in the last (even \xem{after the semicolon}) optional argument |<code.append>|. + +\begin{tzcode}{.3} +% \tzlines: <code.append> +\begin{tikzpicture} +\tzhelplines(4,3) +\tzlines[red,thick,<->,text=blue] + (0,1){Up} + (1,2){Down}[a,sloped] + (3,1){Up} + (4,3) ; + <arc(0:90:1cm)> +\tzlines[dashed] + (0,0)(1,1)(2,1)(3,0) ; + <to[bend right] ++(2,2) node{Here!}> +\end{tikzpicture} +\end{tzcode} + +You can close the path with a straight line by |<--cycle>|. + +\begin{tzcode}{.3} +% \tzlines: closed path +\begin{tikzpicture} +\tzhelplines(4,3) +\tzlines[red,thick,<->,text=blue] + (0,1){Up} + (1,2){Down}[a,sloped] + (3,1){Up} + (4,3){line A} ; <--cycle> +\tzlines[dashed] + (0,0)(1,1)(2,1)(3,0){line B}[r] ; <--cycle> +\end{tikzpicture} +\end{tzcode} + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzlines+}: Relative coordinates: Semicolon version} +\label{s:tzlines+} + +The \iisw{plus version} \icmd{\tzlines+} connects two or more points with connected line segments, but each coordinate (except the first one) is \xem{relative} to the previous coordinate. +%For example, |\tzline+(A)(B)(C)(D);| is equivalent to |\tzline(A)<++>(B)<++>(C)<++>(D);|. + +\xem{Everything else is the same as in} |\tzlines|. +It is also required to enter a \xem{semicolon} to indicate when the coordinate iteration ends. + + +\begin{tzdef}{} +% syntax: full +\tzlines+[<opt>]<shift coor>"<path name>" + (<coor>){<text>}[<node opt>] + ..repeated.. (){}[] ; <code.append> +% defaults + []<>"" (<m>){}[] ..repeated.. (){}[] ; <> +\end{tzdef} + + +\begin{tztikz}{} +\tzlines+(0,1)(1,1)(2,-1)(1,2); % works like: + \draw (0,1) -- ++(1,1) -- ++(2,-1) -- ++(1,2); +\end{tztikz} + + +\begin{tztikz}{} +\tzlines+[dashed]"AA"(0,1){A}(1,1){B}(2,-1){C}(1,2){D}[right]; % works like: + \draw [dashed,name path=AA] + (0,1) -- node {A} ++(1,1) + -- node {B} ++(2,-1) + -- node {C} ++(1,2) node [right] {D} ; +\end{tztikz} + + +\begin{tzcode}{.3} +% \tzlines+ +\begin{tikzpicture} +\tzhelplines(4,3) +\tzlines+[red,thick,<->,text=blue] + (0,1){Up} + (1,1){Down}[a,sloped] + (2,-1){Up} + (1,2){line A} ; +\tzlines+[dashed,auto,text=red] + (0,0){A} + (1,1){B} + (1,0){C} + (1,-1){line B}[blue,draw,r] ; +\end{tikzpicture} +\end{tzcode} + + + +%%================================== +\chapter{Connecting Points} +\label{c:tzto} + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzto}: Two points} +\label{s:tzto} + +\icmd{\tzto} connects two points with a straight or curved line, using \Tikz's |to| operation. +So |\tzto| is more general than |\tzline|, which connects points only with a straight line. + +\begin{tzdef}{} +% syntax: minimum +\tzto(<coor>)(<coor>) +% syntax: medium +\tzto[<opt>](<coor>){<text>}[<node opt>](<coor>){<text>}[<node opt>] +% syntax: full +\tzto[<opt>]<shift coor>"<path name>" + (<coor>){<text>}[<node opt>] + (<coor>){<text>}[<node opt>]<code.append> +% defaults + []<>""(<m>){}[above](<m>){}[]<> +\end{tzdef} + + +\begin{tztikz}{} +\tzto[dashed](1,1)(3,2) % works like: + \draw [dashed] (1,1) to (3,2); +\end{tztikz} + + +\paragraph{Line styles} +You can control line styles with the first optional argument |[<opt>]|. + +\begin{tzcode}{.3} +% \tzto +\begin{tikzpicture} +\tzhelplines(4,3) +\tzto[blue,thick,->](0,1)(3,3) +\tzto[out=0](0,0)(4,2) +\tzto[bend right,dashed](2,0)(4,1) +\end{tikzpicture} +\end{tzcode} + +\paragraph{Adding text} + +You can add text \xem{next to the line} (|[midway,above]|, by default) by specifying the options |{<text>}| and |[<node opt>]| \xem{in-between} the two coordinates. + +\begin{tztikz}{} +\tzto[->,bend right](1,1){A}[near start](3,2) % works like: + \draw [->,bend right] (1,1) to node [near start] {A} (3,2); + +\tzto[->,bend right](1,1){A}[near start](3,2){B}[right] % works like: + \draw [->,bend right] (1,1) to node [near start] {A} + (3,2) node [right] {B}; +\end{tztikz} + + +You can also add text \xem{at or around} the last coordinate by the options |{<text>}| and |[<node opt>]| \xem{immediately after} the last coordinate. + +\begin{tzcode}{.3} +% \tzto: adding text +\begin{tikzpicture} +\tzhelplines(4,3) +\tzto[blue,thick,->](0,1){line}[sloped](3,3) +\tzto[out=0](0,0){curve}[pos=.8](4,2){line B}[r] +\tzto[bend right,dashed](2,0)(4,1){line C}[red,r] +\end{tikzpicture} +\end{tzcode} + +\paragraph{Shift} +You can move the line by specifying the option |<shift coor>| before the first coordinate or immediately before the option |"<path name>"| if it exists. +(The empty shift option |<>| is not allowed.) + +\begin{tzcode}{.3} +% \tzto: shift +\begin{tikzpicture} +\tzhelplines(4,3) +\tzto[blue,thick,->]<0,1>(0,1){line}[sloped](3,3) +\tzto[out=0]<1,1>(0,0){curve}[pos=.8](4,2){line B}[r] +\tzto[bend right,dashed]<-1,0>(2,0)(4,1){line C}[red,r] +\end{tikzpicture} +\end{tzcode} + +\paragraph{Naming paths: Intersections} +You can name the path of |\tzto| by specifying the option |"<path name>"| immediately before the first coordinate. + +\begin{tzcode}{.3} +% \tzto: name path +\begin{tikzpicture} +\tzhelplines(4,3) +\tzto[bend right=45,blue,thick,->]"curveA"(1,3)(4,0) +\tzto[out=0]"curveB"(0,0)(4,2){line B}[r] +% intersection point +\tzXpoint*{curveA}{curveB} +\end{tikzpicture} +\end{tzcode} + +\paragraph{Extending the path} +You can extend the path of |\tzto| by writing \Tikz\ code in the last optional argument |<code.append>|. + +\begin{tzcode}{.3} +% \tzto: extending path +\begin{tikzpicture} +\tzhelplines(4,3) +\tzto[bend right=45,blue,thick,->] + (1,3)(4,0)<--([turn]0:1cm) node [b] {extended}> +\tzto[out=0] + (0,0)(4,2)<--([turn]0:1cm) node [r] {extended}> +\end{tikzpicture} +\end{tzcode} + + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzto+}: Relative coordinates} +\label{s:tzto+} + +The \iisw{plus version} \icmd{\tzto+} uses the second coordinate relative to the first coordinate. + +\xem{Everything else is the same as in} |\tzto|. + +\begin{tztikz}{} +\tzto+(1,1)(3,2) % works like: + \draw (1,1) to ++(3,2); +\end{tztikz} + +\begin{tzcode}{.3} +% \tzto+ +\begin{tikzpicture} +\tzhelplines(4,3) +\tzto+[blue,thick,->](0,1){line}[sloped](3,2) +\tzto+[out=0](0,0){curve}[pos=.8](4,2){line B}[r] +\tzto+[bend right,dashed](2,0)(2,1){line C}[red,r] +\end{tikzpicture} +\end{tzcode} + +\begin{tzcode}{.3} +% \tzto+ +\begin{tikzpicture} +\tzhelplines(4,3) +\tzto+[bend right=45,blue,thick,->] + (1,3)(3,-3)<--([turn]0:1cm) node [b] {extended}> +\tzto+[out=0] + (0,0)(4,2)<--([turn]0:1cm) node [r] {extended}> +\end{tikzpicture} +\end{tzcode} + + + + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tztos}: Multiple points: Semicolon version} +\label{s:tztos} + +\icmd{\tztos} takes an arbitrary number of coordinates as arguments to connect them by \Tikz's |to| operation. Since this is a \xem{semicolon version}, you need to enter a \xem{semicolon} to indicate when the coordinate iteration ends. + +\begin{tzdef}{} +% syntax +\tztos[<opt>]<shift coor>"<path name>" + (<coor1>)[<to opt>]{<text>}[<node opt>]..repeated..()[]{}[] ; <code.append> +% defaults + []<>""(<m>)[]{}[]..repeated..()[]{}[]<> +\end{tzdef} + +The quadruple |(<coor>)[<to opt>]{<text>}[<node opt>]| is +the whole repeating pattern. +Here, |[<to opt>]| is for the options of \Tikz's |to| operation such as |[bend right]|, |[bend left]|, |[bend left=<angle>]|, |[out=<angle>,in=<angle>]| and so on. + +\begin{tztikz}{} +\tztos(0,0)(1,2)(3,1); % works like: + \draw (0,0) to (1,2) to (3,1); +\end{tztikz} + +\begin{tztikz}{} +\tztos[blue] (0,0) [bend right] (1,2) [out=-60,in=45] (3,1); % works like: + \draw[blue] (0,0) to [bend right] (1,2) to [out=-60,in=45] (3,1); +\end{tztikz} + +\paragraph{How to connect coordinates} +You can use the options of \Tikz's |to| operation to connect the coordinates with different types of curves. + +\begin{tzcode}{.3} +% \tztos +\begin{tikzpicture} +\tzhelplines(4,3) +\tztos[blue,<->](0,1)(1,2)(3,1)(4,3); +\tztos[red,thick] + (0,0)[bend right] + (1,1) + (2,1)[out=-135,in=45] + (3,0); +\end{tikzpicture} +\end{tzcode} + +\paragraph{Adding text} +You can add text next to lines or curves by specifying the options |{<text>}| and |[<node opt>]| \xem{in-between} coordinates or \xem{after} the option |[<to opt>]|, if it exists. +You can also add text at or around the last coordinate by the last options |{<text>}| and |[<node opt>]|. + +\begin{tzcode}{.3} +% \tztos: adding text +\begin{tikzpicture} +\tzhelplines(4,3) +\tztos(0,1)[bend right]{A} + (1,2) {Ben}[red,sloped,a] + (3,1)[bend right]{Cate}[sloped,near end] + (4,3) {Name}[draw,blue,a] ; +\end{tikzpicture} +\end{tzcode} + +\paragraph{Shift} +You can move the line or curve of |\tztos| +using the option |<shift coor>| before the first coordinate or immediately before the option |"<path name">|, if any. +(The empty shift option |<>| is not allowed.) + +\begin{tzcode}{.3} +% \tztos: shift +\begin{tikzpicture} +\tzhelplines(4,3) +\tztos[blue,<->](0,1)(1,2)(3,1)(4,3); +\tztos[red,thick] + <1,1>(0,0)[bend right] + (1,1) + (2,1)[out=-135,in=45] + (3,0); +\end{tikzpicture} +\end{tzcode} + + + +\paragraph{\texttt{name path} for intersections} +You can name the path of |\tztos| by specifying |"<path name>"| immediately before the first mandatory coordinate. + +\begin{tzcode}{.3} +% \tztos: name path, intersection points +\begin{tikzpicture} +\tzhelplines(4,3) +\tztos[blue,<->]"AA"(0,1)(1,2)(3,1)(4,3); +\tztos[red,thick] + <1,1>"BB"(0,0)[bend right] + (1,1) + (2,1)[out=-135,in=45] + (3,0); +% intersection points +\tzXpoint*{AA}{BB}(X) +\tzdot(X-2)(4pt) +\end{tikzpicture} +\end{tzcode} + + +\paragraph{Extending paths} +You can extend the path of |\tztos| from the last coordinate, +by writing \Tikz\ code in the last (after the semicolon) optional argument |<code.append>|. + +\begin{tzcode}{.3} +% \tztos +\begin{tikzpicture} +\tzhelplines(4,3) +\tztos[blue,<->](0,1)(1,2)(3,1)(4,3);<--cycle> +\tztos[red,thick] + (0,0)[bend right] + (1,1) + (2,1)[out=-135,in=45] + (3,0); < to ([turn]0:1.5cm) > +\end{tikzpicture} +\end{tzcode} + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tztos+}: Relative coordinates: Semicolon version} +\label{s:tztos+} + +The \iisw{plus version} \icmd{\tztos+} takes each coordinate (except the first coordinate) relative (with |++|) to the previous coordinate. + +\xem{Everything else is the same as in} |\tztos|. + +\begin{tzcode}{.3} +% \tztos+ +\begin{tikzpicture} +\tzhelplines(4,3) +\tztos+[blue,<->](0,1)(1,1)(2,-1)(1,2);<--cycle> +\tztos+[red,thick] + (0,0)[bend right] + (1,1) + (1,0)[out=-135,in=45] + (1,-1); < to ([turn]0:1.5cm) > +\end{tikzpicture} +\end{tzcode} + + +%%================================== +\chapter{Filling Area} +\label{c:fillingarea} + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzpath}: Semicolon version} +\label{s:tzpath} + + +\icmd{\tzpath} creates a path connecting an arbitrary number of coordinates, but it does not stroke the path. You can visualize the path with |\tzpath[draw]|. +Since |\tzpath| is a \iisw{semicolon version} macro, you need to enter a \xem{semicolon} `|;|' to indicate where the coordinate iteration ends. + + +\begin{tzdef}{} +% syntax: minimal +\tzpath (<coor>)(<coor>) ..repeated.. (<coor>) ; +% syntax: full +\tzpath{<path style>}[<opt>]<shift coor>"<path name>" + (<coor>)[<path style>]{<text>}[<node opt>] + ..repeated.. ()[]{}[] ; {<fill opacity>} <code.append> +% defaults: \tzpath + {to}[]<>"" (<m>)[]{}[] ..repeated.. ()[]{}[] ; {}<> +\end{tzdef} + +The main purpose of |\tzpath| is to fill an enclosed area with color or pattern. +You can use |\tzpath[fill]| or |\tzpath[pattern=<...>]| to do it. + + +\paragraph{Path construction operation} +(If you are not an experienced user of \Tikz\, just skip this part.) + +|\tzpath| is similar to |\tztos|, but it is more flexible in constructing paths. +|\tzpath| allows you to choose how to construct a path using the |[<path style>]| option \xem{in-between} coordinates. \xem{Path extension operation} can be selected from `|--|', `|to|', `\verb+|-+', `\verb+-|+', etc. +You can use \xem{the first brace option} |{<path style>}| to change all the |<path style>| in-between coordinates. + + +\begin{tzcode}{.3} +% \tzpath: path construction +\begin{tikzpicture} +\tzhelplines(4,3) +\tzpath[draw](0,1)(1,2)[-|](3,1)(4,3); +\tzpath[draw] + (0,0)[to[bend right]] + (1,1) + (2,1)[to[out=-135,in=45]] + (3,0); +\end{tikzpicture} +\end{tzcode} + +The default path style is `|to|' and can also be changed by \icmd{\settzpathstyle}, like, for example, |\settzpathstyle{--}|. The effect remains valid until the end of |tikzpicture| environment unless changed again. + +\begin{tzcode}{.3} +% \tzpath: \settzpathstyle +\begin{tikzpicture} +\tzhelplines(4,3) +\settzpathstyle{to[bend right]} +\tzpath[draw](0,1)(1,2)[-|](3,1)(4,3); +\tzpath[draw] + (0,0)[to[bend right]] + (1,1) + (2,1)[to[out=-135,in=45]] + (3,0); +\end{tikzpicture} +\end{tzcode} + +You can extend the path of |\tzpath| by writing \Tikz\ code in the last (after the semicolon) optional argument |<code.append>|. +So |<--cycle>| closes the path with a straight line. + +\begin{tzcode}{.3} +% \tzpath: <code.append> +\begin{tikzpicture} +\tzhelplines(4,3) +\tzpath[draw](0,1)(1,2)[-|](3,1)(4,3); + < to [bend right=60] (0,1) > +\tzpath[fill] + (0,0)[to[bend right]] + (1,1) + (2,1)[to[out=-135,in=45]] + (3,0); <--cycle> +\end{tikzpicture} +\end{tzcode} + +\section{\protect\cmd{\tzpath*}: Semicolon version} +\label{s:tzpath*} + +The starred version \icmd{\tzpath*} additionally fills the interior of |\tzpath| with |black!50| with |fill opacity=.3| and |text opacity=1|, by default. + +|\tzpath*| works like |\tzpath[fill=black!50,fill opacity=.3,text opacity=1]|. +You can change the defaults by \icmd{\settzfillcolor} and \icmd{\settzfillopacity}. + +\begin{tzdef}{} +% syntax: minimal +\tzpath*(<coor>)(<coor>) ..repeated.. (<coor>) ; {<fill opacity>} +% syntax: full +\tzpath*{<path style>}[<opt>]<shift coor>"<path name>" + (<coor>)[<path style>]{<text>}[<node opt>] + ..repeated.. ()[]{}[] ; {<fill opacity>} <code.append> +% defaults: \tzpath* + *{to}[fill=black!50,fill opacity=.3,text opacity=1]<>"" + (<m>)[]{}[] ..repeated.. ()[]{}[] ; {.3}<> +\end{tzdef} + + +\paragraph{Filling the interior} + +You can optionally change the opacity of fill color using the \Tikz\ option |fill opacity|. + +\begin{tzcode}{.3} +% \tzpath: fill, fill opacity +\begin{tikzpicture} +\tzhelplines(4,3) +\tzline[red,very thick](0,3)(4,0) +\tzpath[fill](0,0)(3,1)(2,3)(0,2); % default opacity=1 +\tzpath[fill,green,fill opacity=.5] + <1,-1>(0,0)(3,1)(2,3)(0,2); +\end{tikzpicture} +\end{tzcode} + +You can also change the fill opacity by specifying the \xem{last} curly brace optional argument |{<fill opacity>}|, \xem{after the semicolon}. + +\begin{tzcode}{.3} +% \tzpath* +\begin{tikzpicture} +\tzhelplines(4,3) +\tzline[red,very thick](0,3)(4,0) +\tzpath*(0,0)(3,1)(2,3)(0,2); +\tzpath*[fill=green] + <1,-1>(0,0)(3,1)(2,3)(0,2); {.5} %% +\end{tikzpicture} +\end{tzcode} + +You can also use the macros |\settzfillcolor| and |\settzfillopacity| to change the defaults. +The effect remains valid until the end of the |tikzpicture| environment, unless changed again. + +\begin{tzcode}{.3} +% \tzpath*: \settzfillcolor +\begin{tikzpicture} +\tzhelplines(4,3) +\settzfillcolor{red} +\tzpath*[blue](0,1)(1,2)[-|](3,1)(4,3); + < to [bend right=60] (0,1) > +\tzpath* + (0,0)[to[bend right]] + (1,1) + (2,1)[to[out=-135,in=45]] + (3,0); <--cycle> +\end{tikzpicture} +\end{tzcode} + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzpath+} and \protect\cmd{\tzpath*+}: Relative coordinates: Semicolon versions} +\label{s:tzpath+} + +The \iisw{plus version} \icmd{\tzpath+} uses each coordinate (except for the first coordinate) relative (with |++|) to the previous coordinate. + +\xem{Everything else is the same as in} |\tzpath|. + +\icmd{\tzpath*+} is simply the plus version of |\tzpath*|. + +\begin{tzcode}{.3} +% \tzpath+ +\begin{tikzpicture} +\tzhelplines(4,3) +\tzline[red,very thick](0,3)(4,0) +\tzpath+[pattern=bricks,preaction={fill=brown}] + (0,0)(3,1)(-1,2)(-2,-1); +\tzpath+[pattern=north east lines,opacity=.5] + <1,-1>(0,0)(3,1)(-1,2)(-2,-1); +\end{tikzpicture} +\end{tzcode} + +\begin{tzcode}{.3} +% \tzpath*+ +\begin{tikzpicture} +\tzhelplines(4,3) +\tzline[red,very thick](0,3)(4,0) +\tzpath*+(0,0)(3,1)(-1,2)(-2,-1); +\tzpath*+[fill=green] + <1,-1>(0,0)(3,1)(-1,2)(-2,-1); {.5} %% +\end{tikzpicture} +\end{tzcode} + + +%%======================================= +%%================================== +\chapter{Curves} +\label{c:curves} + +There are many ways to draw curves. + +%%----------------------------------- +%%------------------------------------------------------------ +\section{B\'{e}zier curves} +\label{s:beziercurves} + +\icmd{\tzbezier} draws a B\'{e}zier curve with one or two control points. + +\subsection{\protect\cmd{\tzbezier}} +\label{ss:tzbezier} + +\begin{tzdef}{} +% syntax: minimal +\tzbezier(<start-coor>)(cntl-coor>)(<last-coor>) +\tzbezier(<start-coor>)(cntl-coor>)(<cntl-coor>)(<last-coor>) +% syntax: full +\tzbezier[<draw opt>]<shift coor>"<name path>" + (<start-coor>)(cntl-coor>)(<cntl-coor>)(<last-coor>) + {<text>}[<node opt>]<code.append> +% defaults + []<>""(<m>)(<m>)()(<m>){}[]<> +\end{tzdef} + +\paragraph{Control points} + +You can specify one or two control points, |(<cntl-coor>)|. +So |\tzbezier| accepts three or four coordinates as arguments. + +\begin{tztikz}{} +% three coordinates: one control point +\tzbezier(0,1)(1,0)(4,3) % works like: + \draw (0,0) ..controls (1,0).. (4,3); +\end{tztikz} + +\begin{tztikz}{} +% four coordinates: two control points +\tzbezier(0,1)(1,0)(2,4)(4,3) % works like: + \draw (0,0) ..controls (1,0) and (2,4).. (4,3); +\end{tztikz} + +\begin{tzcode}{.3} +% \tzbezier +\begin{tikzpicture} +\tzhelplines(4,4) +\tzbezier[red](0,3)(1,2)(2,4)(4,3) +\tzbezier[blue](0,2)(1,.5)(4,0) +\end{tikzpicture} +\end{tzcode} + +The style \ixxw{tzshowcontrols} displays the control points by drawing dotted lines, by default. +You can also change the dotted line style, like |tzshowcontrols={dashed,green}|. + + +\begin{tzcode}{.3} +% \tzbezier: tzshowcontrols +\begin{tikzpicture} +\tzhelplines(4,4) +\tzbezier[blue,tzshowcontrols](0,2)(1,.5)(4,0) +\tzdots*[blue](0,2)(1,.5)(4,0); +\tzbezier[red,tzshowcontrols={green,dashed}] + (0,3)(1,2)(2,4)(4,3) +\tzdots*[red](0,3)(1,2)(2,4)(4,3); +\end{tikzpicture} +\end{tzcode} + +\paragraph{Adding text} +You can add text next to the curve or at the last coordinate +by specifying the options |{<text>}| and |[<node opt>]| immediately after the last coordinate. + + +\begin{tzcode}{.3} +% \tzbezier: adding text +\begin{tikzpicture} +\tzhelplines(4,4) +\tzbezier[blue](0,2)(1,.5)(4,0){curve}[draw,black,r] +\tzbezier[red](0,3)(1,2)(2,4)(4,3){bezier}[near end,a] +\end{tikzpicture} +\end{tzcode} + +\paragraph{Shift} +You can move the curve of |\tzbezier| by specifying the option |<shift coor>| before the first coordinate or immediately before the option |"<path name>"|, if any. +The empty shift option |<>| is not allowed. + +\begin{tzcode}{.3} +% \tzbezier: shift +\begin{tikzpicture} +\tzhelplines(4,4) +\tzbezier[blue] + (0,2)(1,.5)(4,0){curve}[draw,black,r] +\tzbezier[blue,dashed] + <1,1>(0,2)(1,.5)(4,0){curve}[r] +\tzbezier[red] + (0,3)(1,2)(2,4)(4,3){bezier}[near end,a] +\tzbezier[red,dashed] + <0,-1>(0,3)(1,2)(2,4)(4,3){bezier}[blue,near end,a] +\end{tikzpicture} +\end{tzcode} + +\paragraph{\texttt{name path}} +You can name the path of |\tzbezier| by specifying the option |"<path name>"| immediately before the first coordinate. + +\begin{tzcode}{.3} +% \tzbezier: name path, intersection +\begin{tikzpicture} +\tzhelplines(4,4) +\tzbezier[blue,dashed,thick]<1,1>"curve" + (0,2)(1,.5)(4,0){curve}[r] +\tzbezier[red,dashed,thick]<0,-1>"bezier" + (0,3)(1,2)(2,4)(4,3){bezier}[blue,near end,a] +% intersection point +\tzXpoint*{curve}{bezier}(X){X}[-90] % <angle> +\end{tikzpicture} +\end{tzcode} + +\paragraph{Extending paths} +You can extend the path of |\tzbezier| from the last coordinate, by writing \Tikz\ code +in the last optional argument |<code.append>|. + +\begin{tzcode}{.3} +% \tzbezier: extending path +\begin{tikzpicture} +\tzhelplines(4,4) +\tzbezier[red](0,3)(1,2)(2,4)(4,3){bezier}[near end,a] + < to [bend right] ++(-1,-1) node [below] {A} > +\tzbezier[blue,->](0,2)(1,.5)(4,0) + < |- ++(-2,1) node [above] {B} > +\end{tikzpicture} +\end{tzcode} + + + +\subsection{\protect\cmd{\tzbezier+}: Relative coordinates} +\label{ss:tzbezier+} + +For the \iisw{plus version} |\tzbezier+(A)(B)(C)|, |(B)| and |(C)| are relative to |(A)|, as in \Tikz. + +For |\tzbezier+(A)(B)(C)(D)|, |(B)| and |(D)| are relative to |(A)|, and |(C)| is relative to |(D)|, as in \Tikz. + +\begin{tztikz}{} +% three coordinates +\tzbezier+(0,1)(1,-1)(4,3) % works like: + \draw (0,1) ..controls +(1,-1).. ($(0,1)+(4,3)$); +\end{tztikz} + +\begin{tztikz}{} +% four coordinates +\tzbezier+(0,1)(1,-1)(-2,1)(4,3) % works like: + \draw (0,1) ..controls +(1,-1) and +(-2,1).. ($(0,1)+(4,3)$); +\end{tztikz} + +\begin{tzcode}{.3} +% \tzbezier+ +\begin{tikzpicture} +\tzhelplines(4,4) +\tzbezier+(0,3)(1,-1)(-2,1)(4,0){bezier}[near end,a] + < to [bend right] ++(-1,-1) node [below] {A} > +\tzbezier+[blue,->](0,2)(1,-1.5)(4,-2) + < |- ++(-2,1) node [above] {B} > +\end{tikzpicture} +\end{tzcode} + + +%%----------------------------------- +%%------------------------------------------------------------ +\section{Parabolas} +\label{s:parabolas} + + +\subsection{\protect\cmd{\tzparabola}} +\label{ss:tzparabola} + +\icmd{\tzparabola} draws a parabola going through specified coordinates. +It accepts two or three coordinates. +In the case of three coordinates, the parabola bends at the second coordinate. + +\begin{tztikz}{} +% two coordinates +\tzparabola(0,0)(3,2) % works like: + \draw (0,0) parabola (3,2); +\end{tztikz} + +\begin{tztikz}{} +% three coordinates +\tzparabola(0,0)(1,1)(3,2) % works like: + \draw (0,0) parabola bend (1,1) (3,2); +\end{tztikz} + +\begin{tzdef}{} +% syntax: minimal +\tzparabola(<coor>)(<coor>) +\tzparabola(<coor>)(<coor>)(<coor>) +% syntax: full +\tzparabola[<opt1>]<shift coor>"<path name>" + (<coor>)(<coor>)(<coor>){<text>}[<node opt>]<code.append> +% default + []<>""(<m>)()(<m>){}[]<> +\end{tzdef} + +\paragraph{Parabolas} +|\tzplot| draws the graph of a quadratic function $f(x)=ax^2+bx+c$ for appropriate values of $a$, $b$, and $c$. + +\begin{tzcode}{.3} +% \tzparabola: two coordinates +\begin{tikzpicture} +\tzhelplines(4,3) +\tzparabola[thick](0,0)(2,2) +\tzparabola[bend at end,dashed](0,0)(2,2) +\tzparabola[red,thick,bend pos=.5](2,0)(4,3) +\tzparabola[blue,parabola height=-2cm](2,3)(4,2) +\end{tikzpicture} +\end{tzcode} + +\begin{tzcode}{.3} +% \tzparabola: three coordinates +\begin{tikzpicture} +\tzhelplines(4,3) +\tzparabola[thick](0,2)(1,0)(2,2) +\tzparabola[blue](0,3)(2,1)(4,2) +\tzparabola[red,thick](2,0)(3,2)(4,3) +\end{tikzpicture} +\end{tzcode} + +\paragraph{Adding text} +You can add text at or around the last coordinate by specifying the options |{<text>}| and |[<node opt>]| immediately after the last coordinate. + +\begin{tzcode}{.3} +% \tzparabola: adding text +\begin{tikzpicture} +\tzhelplines(4,3) +\tzparabola[thick](0,0)(2,2){parabola}[blue,draw,a] +\tzparabola[blue](0,3)(2,1)(4,2){AC}[r] +\tzparabola[red,thick,bend pos=.5](2,0)(4,3){C}[ar] +\end{tikzpicture} +\end{tzcode} + +\paragraph{Shift} +You can move the parabola by specifying the option |<shift coor>| before the first coordinate or immediately before the option |"<path name>"|, if any. +The empty shift option |<>| is not allowed. + +\begin{tzcode}{.3} +% \tzparabola: shift +\begin{tikzpicture} +\tzhelplines(4,3) +\tzparabola[blue] (0,3)(2,1)(4,2){AC}[r] +\tzparabola[dashed]<0,-.5>(0,3)(2,1)(4,2){AC}[r] +\tzparabola[dotted]<0,-1> (0,3)(2,1)(4,2){AC}[r] +\end{tikzpicture} +\end{tzcode} + +\paragraph{\texttt{name path}} +You can name the path of |\tzparabola| by specifying the option |"<path name>"| immediately before the first coordinate. + +\begin{tzcode}{.3} +% \tzparabola: name path, intersection +\begin{tikzpicture} +\tzhelplines(4,3) +\tzparabola[blue]"AC"(0,3)(2,1)(4,2){AC}[r] +\tzparabola"BB"(1,0)(2,2)(3,0) +% intersection points +\tzXpoint*{AC}{BB}(X) +\tzdot(X-2)(3pt) +\end{tikzpicture} +\end{tzcode} + +\paragraph{Extending paths} +You can extend the path of |\tzparabola| from the last coordinate by writing \Tikz\ code in the last optional argument |<code.append>|. + +\begin{tzcode}{.3} +% \tzparabola: extending path +\begin{tikzpicture} +\tzhelplines(4,3) +\tzparabola[blue,->]"AC"(0,3)(2,1)(4,2) + < -- ++ (-1,1) > +\tzparabola"BB"(1,0)(2,2)(3,0) + < -| ++ (1,1) node [right] {K!} > +\end{tikzpicture} +\end{tzcode} + + + +\subsection{\protect\cmd{\tzparabola+}: Relative coordinates} +\label{ss:tzparabola+} + +For the \iisw{plus version} \icmd{\tzparabola+}, the second and the third coordinates are relative to the first coordinate. + +\xem{Everything else is the same as in} |\tzparabola|. + +\begin{tztikz}{} +% two coordinates +\tzparabola+(0,1)(3,2) % works like: + \draw (0,1) parabola ($(0,1)+(1,2)$); +\end{tztikz} + + +\begin{tztikz}{} +% three coordinates +\tzparabola+(0,1)(1,1)(3,-1) % works like: + \draw (0,1) parabola bend +(1,1) ($(0,1)+(3,-1)$); +\end{tztikz} + +\begin{tzcode}{.3} +% \tzparabola+ +\begin{tikzpicture} +\tzhelplines(4,3) +\tzparabola+[thick](0,0)(2,2){parabola}[blue,draw,a] +\tzparabola+[blue](0,3)(2,-2)(4,-1){AC}[r] +\tzparabola+[red,thick,bend pos=.5](2,0)(2,3){C}[ar] +\end{tikzpicture} +\end{tzcode} + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzplotcurve}} +\label{s:tzplot} + +See Section \ref{s:tzplotcurve} on page \pageref{s:tzplotcurve}, for more details on |\tzplotcurve|. + + + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzto}, \protect\cmd{\tztos}} +\label{s:curves:tzto} + +See Section \ref{s:tzto} on page \pageref{s:tzto}, for more details on |\tzto|. + +See Section \ref{s:tztos} on page \pageref{s:tztos}, for more details on |\tztos|. + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzfn}} +\label{s:curves:tzfn} + +With \icmd{\tzfn}, you can plot functions such as $f(x)=\frac13(x-1)^3+1$, $g(x)=\sin x$, $h(x)=\sqrt{x-1}$, and so on. +See Section \ref{s:tzfn} on page \pageref{s:tzfn}, for more details on |\tzfn|. + + + + +%%================================== +\chapter{Polygons and Circles} +\label{c:polygons} + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzpolygon}: Semicolon verion} +\label{s:tzpolygon} + +\icmd{\tzpolygon} connects an arbitrary number of coordinates to draw a polygon, a closed figure. |\tzpolygon| is equivalent to a closed |\tzlines|. Since |\tzpolygon| is a \xem{semicolon version}, you need to enter a \xem{semicolon} to indicate when the coordinate repetition ends. + + +\begin{tzdef}{} +% syntax: minimum +\tzpolygon(<coor>)(<coor>)..repeated..(<coor>) ; +% syntax: medium +\tzpolygon (<coor>){<text>}[<node opt>]..repeated..(<coor>){<text>}[<node opt>] ; +% syntax: full +\tzpolygon[<opt>]<shift coor>"<path name>" + (<coor>){<text>}[<node opt>] + ..repeated.. (){}[] ; <code.append> +% defaults + []<>""(<m>){}[] ..repeated.. (){}[] ; <> +\end{tzdef} + +\begin{tztikz}{} +\tzpolygon(1,1)(2,2)(3,1)(4,3); % works like: + \draw (1,1) -- (2,2) -- (3,1) -- (4,3) -- cycle; +\end{tztikz} + +You can add text next to lines by specifying the options |{<text>}| and |[<node opt>]| \xem{in-between} coordinates. + +\begin{tzcode}{.3} +% \tzpolygon +\begin{tikzpicture} +\tzhelplines(4,3) +\tzpolygon[fill,blue,auto] + (0,1){Side A}[sloped,red] + (1,3){B} + (2,3) + (3,2){Side D}[swap,sloped] + (1,0); +\end{tikzpicture} +\end{tzcode} + +You can also move the polygon by specifying the option |<shift coor>| before the first coordinate. +The empty shift option |<>| is not allowed. + +\begin{tzcode}{.3} +% \tzpolygon: shift +\begin{tikzpicture} +\tzhelplines(4,3) +\tzpolygon[blue,auto] + (0,1){Side A}[sloped,red] + (1,3){B} + (2,3) + (3,2){Side D}[swap,sloped] + (1,0); +\tzpolygon[auto,dashed]<1,-.5> + (0,1)(1,3)(2,3){C}(3,2)(1,0); +\end{tikzpicture} +\end{tzcode} + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzpolygon*}: Semicolon version} +\label{s:tzpolygon*} + +\icmd{\tzpolygon*} paints the interior of the polygon with |black!50| with |fill opacity=.3| but with |text opacity=1|, by default. + +\begin{tzdef}{} +% syntax: minimum +\tzpolygon*(<coor>)(<coor>)..repeated..(<coor>) ; +% syntax: medium +\tzpolygon*(<coor>){<text>}[<node opt>]..repeated..(<coor>){<text>}[<node opt] ; +% syntax: full +\tzpolygon*[<opt>]<shift coor>"<path name>" + (<coor>){<text>}[<node opt>] + ..repeated.. (){}[] ; {<fill opacity>} <code.append> +% defaults + *[fill=black!50,fill opacity=.3,text opacity=1]<>"" + (<m>){}[] .. repeated.. (){}[] ; {} <> +\end{tzdef} + +You can change the fill opacity by specifying the the last curly brace option |{<fill opacity>}| immediately \xem{after the semicolon}. + +\begin{tzcode}{.3} +% \tzpolygon: shift +\begin{tikzpicture} +\tzhelplines(4,3) +\tzpolygon*[draw=blue,auto] + (0,1){Side A}[sloped,red] + (1,3){B} + (2,3) + (3,2){Side D}[swap,sloped] + (1,0); +\tzpolygon*[green,auto,dashed,text=black]<1,-.5> + (0,1)(1,3)(2,3){C}(3,2)(1,0); {.7} +\end{tikzpicture} +\end{tzcode} + +You can also change the defaults using |\settzfillcolor| and |\sttzfillopacity|. + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzpolygon+} and \protect\cmd{\tzpolygon*+}: Relative coordinates: Semicolon verion} +\label{s:tzpolygon} + +The plus version \icmd{\tzpolygon+} uses each coordinate (except the first one) relative (with |++|) to the previous coordinate. + +\xem{Everything else is the same as in} |\tzpolygon|. + +\icmd{\tzpolygon*+} is just a plus version of |\tzpolygon*|. + +\begin{tztikz}{} +\tzpolygon+(1,1)(2,2)(3,1)(4,3); % works like: + \draw (1,1) -- ++(2,2) -- ++(3,1) -- ++(4,3) -- cycle; +\end{tztikz} + +\begin{tztikz}{} +\tzpolygon+[dashed]"AA"(1,1)(2,2){A}(3,1){B}[below]; % works like: + \draw [dashed,name path=AA] (1,1) + -- ++(2,2) + -- ++(3,1) node {A} + -- ++(4,3) node [below] {B} + -- cycle; +\end{tztikz} + +\begin{tzcode}{.3} +% \tzpolygon: shift +\begin{tikzpicture} +\tzhelplines(4,3) +\tzpolygon*+[blue,auto] + (0,1){Side A}[sloped,red] + (1,2){B} + (1,0) + (1,-1){Side D}[swap,sloped] + (-2,-2); +\tzpolygon*+[green,auto,dashed,text=black]<1,-.5> + (0,1)(1,2)(1,0){C}(1,-1)(-2,-2); {.7} +\end{tikzpicture} +\end{tzcode} + + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzframe} and \protect\cmd{\tzframe*}} +\label{s:tzframe} + +\icmd{\tzframe} accepts two coordinates draws a rectangle. + +\begin{tzdef}{} +% syntax: minimum +\tzframe(<coor>)(<coor>) +% syntax: full +\tzframe[<opt>]<shift coor>"<path name>"(<coor1>)(<coor2>)<code.append> +% defaults + []<>""(<m>)(<m>)<> +\end{tzdef} + +\icmd{\tzrectangle} is an alias of |\tzframe|. + +\begin{tztikz}{} +\tzframe(0,1)(3,2) % works like: + \draw (0,1) rectangle (3,2); +\end{tztikz} + + +The plus version \icmd{\tzframe+} uses the second coordinate as the coordinate relative (with |++|) to the first. \icmd{\tzrectangle+} is an alias of |\tzframe+|. + +\begin{tztikz}{} +\tzframe+(0,1)(3,2) % works like: + \draw (0,1) rectangle ++(3,2); +\end{tztikz} + +\begin{tzcode}{.3} +% \tzframe, \tzframe+ +\begin{tikzpicture} +\tzhelplines(4,3) +\tzframe(0,0)(3,2) +\tzframe+[blue,rounded corners=2mm](1,3)(1,-2) +\end{tikzpicture} +\end{tzcode} + +The starred version \icmd{\tzframe*} fills the interior +with |black!50| with |fill opacity=.3|, by default. +(\icmd{\tzrectangle*} is an alias of |\tzframe*|.) + +|\tzframe+| has also its starred version \icmd{\tzframe*+}. +(\icmd{\tzrectangle*+} is an alias of |\tzframe*+|.) + +\begin{tzdef}{} +% syntax +\tzframe*[<opt>]<shift coor>"<path name>" + (<coor1>)(<coor2>){<fill opacity>}<code.append> +% defaults + *[fill=black!50,fill opacity=.3]<>""(<m>)(<m>){.3}<> +\end{tzdef} + +With the starred versions, you can change the fill opacity using the last option |{<fill opacity>}|. + +\begin{tzcode}{.3} +% \tzframe*(+) +\begin{tikzpicture} +\tzhelplines(4,3) +\tzframe[fill](0,0)(3,2) +\tzframe*+[green,rounded corners=2mm](1,3)(1,-2){.7} %% +\end{tikzpicture} +\end{tzcode} + +You can move |\tzframe| and its variants by specifying the option |<shift coor>| immediately before the first mandatory coordinate. +The empty shift option |<>| is not allowed. + +\begin{tzcode}{.3} +% \tzframe(*)(+): shift +\begin{tikzpicture} +\tzhelplines*(4,4) +\tzframe(0,0)(3,2) +\tzframe[blue,dashed]<1,1>(0,0)(3,2) +\tzcoors(1,3)(A)(1,-2)(B); +\tzframe*+[blue,rounded corners=2mm](A)(B) +\tzframe*+[red,rounded corners=2mm]<-.5,-.5>(A)(B) +\tzframe*+[green,rounded corners=2mm]<1,1>(A)(B) +\end{tikzpicture} +\end{tzcode} + +You can extend the path by the option |<code.append>|. + +\begin{tzcode}{.3} +% \tzframe(*), \tzrectangle(*): <code.append> +\begin{tikzpicture} +\tzhelplines(4,4) +\tzcoors(2,2)(A)(3,1)(B); +\tzrectangle*[blue,even odd rule](0,0)(3,2) + <(.5,.5) rectangle (2.5,1.5)> +\tzframe[fill=green,even odd rule](2,1)(4,4) + <(2.3,1.2) rectangle (3.5,3.6)> +\end{tikzpicture} +\end{tzcode} + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzcircle} and \protect\cmd{\tzcircle*}} +\label{s:tzcircle} + +\icmd{\tzcircle} draws a circle around a specified coordinate with a specified radius. +The coordinate and the radius are mandatory. + +\begin{tzdef}{} +% syntax +\tzcircle[<opt>]<shift coor>"<path name>"(<coor>)(<radius>)<code.append> +% defaults + []<>""(<m>)(<m>)<> +\end{tzdef} + +\begin{tztikz}{} +\tzcircle(0,0)(1cm) % works like: + \draw (0,0) circle (1cm); +\end{tztikz} + +The starred version \icmd{\tzcircle*} fills the interior +with |black!50| with |fill opacity=.3|, by default. +You can change the fill opacity using the last option |{<fill opacity>}|. + +\begin{tzdef}{} +% syntax +\tzcircle*[<opt>]<shift coor>"<path name>" + (<coor>)(<radius>){<fill opacity>}<code.append> +% defaults + *[fill=black!50,fill opacity=.3]<>""(<m>)(<m>){.3}<> +\end{tzdef} + +\begin{tzcode}{.3} +% \tzcircle(*) +\begin{tikzpicture} +\tzhelplines(4,3) +\tzcircle(2,2)(1) +\tzcircle[fill=red](3,1)(.5cm) +\tzcircle*[blue](2,1)(1){.5} +\tzcircle*[green](3,.5)(.5cm) +\end{tikzpicture} +\end{tzcode} + +You can move the circle by specifying the option |<shift coor>| immediately before the center coordinate. +The empty shift option |<>| is not allowed. + +\begin{tzcode}{.3} +% \tzcircle(*): shift +\begin{tikzpicture} +\tzhelplines(4,4) +\tzcoors(2,2)(A)(3,1)(B); +\tzcircle(2,2)(1) +\tzcircle[blue,dashed]<-.5,0>(A)(1) +\tzcircle*(3,1)(.5cm) +\tzcircle*[blue]<.5,0>(B)(.5cm) +\end{tikzpicture} +\end{tzcode} + +You can extend the path by the option |<code.append>|. + +\begin{tzcode}{.3} +% \tzcircle(*): <code.append> +\begin{tikzpicture} +\tzhelplines(4,4) +\tzcoors(2,2)(A)(3,1)(B); +\tzcircle*[blue,even odd rule](2,2)(1) + <(2,2) circle (1.5)> +\tzcircle[fill=green,even odd rule](3,1)(1) + <(3,1) circle (.7)> +\end{tikzpicture} +\end{tzcode} + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzellipse} and \protect\cmd{\tzellipse*}} +\label{s:tzellipse} + +\icmd{\tzellipse} draws an ellipse around a specified coordinate with the specified x-radius and y-radius. + +\begin{tzdef}{} +% syntax +\tzellipse[<opt>]<shift coor>"<path name>"(<coor>)(<x and y radius>)<code.append> +% defaults + []<>""(<m>)(<m>)<> +\end{tzdef} + +\icmd{\tzoval} is an alias of |\tzellipse|. + +\begin{tztikz}{} +\tzellipse(0,0)(1 and .5) % works like: + \draw (0,0) ellipse (1 and .5); +\end{tztikz} + +The starred version \icmd{\tzellipse*} fills the interior +with |black!50| with |fill opacity=.3|, by default. +You can change the fill opacity using the last option |{<fill opacity>}|. + +\begin{tzdef}{} +% syntax +\tzellipse*[<opt>]<shift coor>"<path name>" + (<coor>)(<x and y radius>){<fill opacity>}<code.append> +% defaults + *[fill=black!50,fill opacity=.3]<>""(<m>)(<m>){.3}<> +\end{tzdef} + +\begin{tzcode}{.3} +% \tzellipse(*) +\begin{tikzpicture} +\tzhelplines(4,3) +\tzellipse(2,2)(1.5 and 1) +\tzellipse[fill=red](3,1)(1cm and .5cm) +\tzellipse*[blue](2,1)(1 and 1.5){.5} +\tzellipse*[green](3,.5)(1cm and .5cm) +\end{tikzpicture} +\end{tzcode} + +You can move the ellipse by specifying the option |<shift coor>| immediately before the mandatory coordinate. +The empty shift option |<>| is not allowed. + +\begin{tzcode}{.3} +% \tzellipse(*): shift +\begin{tikzpicture} +\tzhelplines(4,4) +\tzcoors(2,2)(A)(3,1)(B); +\tzellipse(2,2)(1.5 and 1) +\tzellipse[blue,dashed]<-.5,0>(A)(1.5 and 1) +\tzellipse*(3,1)(1cm and .5cm) +\tzellipse*[blue]<.5,0>(B)(1cm and .5cm) +\end{tikzpicture} +\end{tzcode} + +You can extend the path by the option |<code.append>|. +Note also that \icmd{\tzoval*} is an alias of |\tzellipse*|. + +\begin{tzcode}{.3} +% \tzellipse(*), \tzoval(*): <code.append> +\begin{tikzpicture} +\tzhelplines(4,4) +\tzcoors(2,2)(A)(3,1)(B); +\tzoval*[blue,even odd rule](2,2)(1.5 and 1) + <(2,2) ellipse (2 and 1.5)> +\tzellipse[fill=green,even odd rule](3,1)(1 and 1) + <(3,1) ellipse (.5 and .8)> +\end{tikzpicture} +\end{tzcode} + + +%%================================== +\chapter{Arcs and Wedges} +\label{c:arcs} + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzarc(')}: Centered arcs} +\label{s:tzarc} + +\subsection{Arcs} +\label{ss:tzarc} + +\icmd{\tzarc} draws an arc around a specified center coordinate. + +\begin{tzdef}{} +% syntax: minimum +\tzarc(<coor>)(<angA:angB:radius>) +% syntax: full +\tzarc[<opt>]<shift coor>"<path name>" + (<coor>)(<angA:angB:radius>){<text>}[<node opt>]<code.append> +% defaults + []<>""(<m>)(<m>){}[]<> +\end{tzdef} + + +\begin{tztikz}{} +\tzarc(1,1)(30:120:1) % works like: + \draw (1,1) ++(30:1) arc (30:120:1); +\end{tztikz} + +The \iisw{swap version} \icmd{\tzarc'} switches its drawing direction from \ixxw{counterclockwise} to \ixxw{clockwise} and vice versa. + +\begin{tztikz}{} +\tzarc'(1,1)(30:120:1) % works like: + \draw (1,1) ++(30:1) arc (30:120-360:1); +\end{tztikz} + + +\begin{tzcode}{.3} +% \tzarc, \tzarc' +\begin{tikzpicture} +\tzhelplines(4,3) +\tzdots*(1,1)(3,2); +\tzarc [blue,->] (1,1)(-45:180:1) +\tzarc'[dashed,->] (1,1)(-45:180:1) +\draw [->](3,2) ++(-45:1) arc (-45:180:1); +\draw [dashed,->](3,2) ++(-45:1) arc (-45:180-360:1); +\end{tikzpicture} +\end{tzcode} + +You can add text along the arc by specifying the options |{<text>}| and |[<node opt>]| immediately after the two mandatory arguments. + + +\begin{tzcode}{.3} +% \tzarc('): adding text +\begin{tikzpicture} +\tzhelplines(4,3) +\tzarc [blue,->] (1,1)(-45:180:1){A}[r] +\tzarc'[dashed,->](1,1)(-45:180:1) +\tzarc[->] (3,2)(-45:180:1){arc}[midway,sloped] +\tzarc'[dashed,->](3,2)(-45:180:1) +\end{tikzpicture} +\end{tzcode} + +You can move arcs by specifying the option |<shift coor>| just before the center coordinate. + +\begin{tzcode}{.3} +% \tzarc('): shift +\begin{tikzpicture} +\tzhelplines(4,3) +\tzarc [blue,->] (1,1)(-45:180:1){A}[r] +\tzarc'[dashed,->] (1,1)(-45:180:1) +\tzarc [blue,->] <2,1>(1,1)(-45:180:1){A-shifted}[r] +\tzarc'[dashed,->]<2,1>(1,1)(-45:180:1) +\end{tikzpicture} +\end{tzcode} + +You can also extend the path of |\tzarc| by specifying the last option |<code.append>| with \Tikz\ code written in it. For example, |<--cycle>| makes a closed path. + + +\begin{tzcode}{.3} +% \tzarc('): <code.append> +\begin{tikzpicture} +\tzhelplines(4,3) +\tzarc [blue,->](1,1)(-45:180:1)<--++(1,2)> +\tzarc'[dashed,->] (1,1)(-45:180:1) +\tzarc [blue,->] <2,1>(1,1)(-45:180:1)<--cycle> +\end{tikzpicture} +\end{tzcode} + + + +\subsection{Elliptical arcs} +\label{ss:ellipticalarc} + +|\tzarc| draws an elliptical arc if you specify |x-radius| and |y-radius|. + +\begin{tzcode}{.3} +% \tzarc: elliptical +\begin{tikzpicture} +\tzhelplines(4,4) +\tzarc[->,red](1,1)(30:270:1.5 and 0.5) +\tzarc'[->,dotted](1,1)(30:270:1.5 and 0.5) +\tzdots*(1,1)(2,2); +\tzarc[->,blue,dashed](2,2)(0:-270:1 and 2) +\tzarc'[->](2,2)(0:-270:1 and 2) +\end{tikzpicture} +\end{tzcode} + + +\begin{tzcode}{.3} +% \tzarc: elliptical +\begin{tikzpicture} +\tzhelplines(4,4) +\tzarc[->,red](1,1)(30:270:1.5 and 0.5) +\tzdots*(1,1)(2,2); +\tzarc[->,blue,dashed,fill=green,fill opacity=.3] + (2,2)(0:-270:1 and 2)<--(2,2)> % code.append +\tzarc[->,blue,dashed] + <1,0>(2,2)(0:-270:1 and 2) % shift +\end{tikzpicture} +\end{tzcode} + + + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzarcfrom(')}: Arcs as in \Tikz} +\label{s:tzarcfrom} + +\icmd{\tzarcfrom} draws an arc starting from a specified point, like \Tikz\ does. + +\begin{tzdef}{} +% syntax: minimum +\tzarcfrom(<coor>)(<angA:angB:radius>) +% syntax: full +\tzarcfrom[<opt>]<shift coor>"<path name>" + (<coor>)(<angA:angB:radius>){<text>}[<node opt>]<code.append> +% defaults + []<>""(<m>)(<m>){}[]<> +\end{tzdef} + + +\begin{tztikz}{} +\tzarcfrom(1,1)(30:120:1) % works like: + \draw (1,1) arc (30:120:1); +\end{tztikz} + +\xem{Everything else is the same as in }|\tzarc|. + +\icmd{\tzarcfrom'} is the \iisw{swap version} of |\tzarcfrom|. + + +\begin{tzcode}{.3} +% \tzarcfrom +\begin{tikzpicture} +\tzhelplines(4,3) +\tzdots*(1,1)(3,2); +\tzarcfrom [blue,->] (1,1)(-45:180:1){A}[r] +\tzarcfrom'[dashed,->](1,1)(-45:180:1) +\tzarcfrom[->](3,2)(-45:180:1){arc}[midway,sloped] +\tzarcfrom'[dashed,->](3,2)(-45:180:1) +\end{tikzpicture} +\end{tzcode} + + + +%%------------------------------------------------------------ +\section{\protect\cmd{\tzarcsfrom}: Connected arcs: Semicolon version} +\label{s:tzarcsfrom} + +The macro \icmd{\tzarcsfrom} (i.e. |\tzarcs + from|) accepts an arbitrary number of parenthesis arguments in the form of |(<angA:AngB:radius>)| following the start coordinate. You need to enter a \xem{semicolon} to indicate when the repetition ends. + +\begin{tzdef}{} +% syntax: minimum +\tzarcsfrom(<start coor>) + (<angA:angB:radius>)..repeated..(<angA:angB:radius>) ; +% syntax: full +\tzarcsfrom[<opt>]<shift coor>"<path name>" + (<start coor>)(<angA:angB:radius>){<text>}[<node opt>] + ..repeated..(){}[] ; <code.append> +% defaults + []<>""(<m>)(<m>){}[]..repeated..(){}[] ; <> +\end{tzdef} + + +\begin{tzcode}{.4} +% \tzarcfrom: adding text, <code.append> +\begin{tikzpicture} +\tzhelplines(4,4) +\tzcoor*(3,2)(A) +\tzarcsfrom[->,auto](A) + (0:180:1){1}[midway] + (180:360:1.2){2}[midway] + (0:180:1.4){3}[midway,swap] + (180:360:1.6){4}[midway,swap]; + < node [right,blue] {End!} > +\end{tikzpicture} +\end{tzcode} + + + +\begin{tzcode}{.4} +% \tzarcfrom: shift +% flag: step 1 +\begin{tikzpicture} +\tzhelplines(-2,-2)(2,2) +\tzdot*(0,0) +\edef\x{atan(2/3)} +\tzarcsfrom[red,->](0,0) + (-\x:-\x-180:1){red 1}[midway]; +\tzarcsfrom[blue,->](0,0) + (180-\x:-\x:1){blue 1}[midway]; +\tzarcsfrom[dashed,->]<.5,.5>(0,0) + (180-\x:-\x:1){blue 1}[midway]; +\end{tikzpicture} +\end{tzcode} + + +\begin{tzcode}{.4} +% flag: step 2 +\begin{tikzpicture} +\edef\x{atan(2/3)} +\tzarcsfrom[red](0,0) + (-\x:-\x-180:1){1}[midway] + (-\x+180:-\x:2){2}[midway]; +\tzarcsfrom[blue](0,0) + (180-\x:-\x:1){1}[midway] + (-\x:-\x-180:2){2}[midway]; +\end{tikzpicture} +\end{tzcode} + + +\begin{tzcode}{.4} +% flag: step 3 +\definecolor{flagred}{RGB}{205,48,57} +\definecolor{flagblue}{RGB}{17,73,156} +\begin{tikzpicture}[scale=1] +\edef\x{atan(2/3)} +\tzarcsfrom[draw=none,fill=flagred](0,0) + (-\x:-\x-180:1) + (-\x+180:-\x:2) + (-\x:-\x+180:1);<-- cycle> +\tzarcsfrom[draw=none,fill=flagblue](0,0) + (180-\x:-\x:1) + (-\x:-\x-180:2) + (-\x+180:-\x+360:1);<-- cycle> +\end{tikzpicture} +\end{tzcode} + + +\begin{tzcode}{.4} +% flag: shift +\definecolor{flagred}{RGB}{205,48,57} +\definecolor{flagblue}{RGB}{17,73,156} +\begin{tikzpicture}[scale=1] +\edef\x{atan(2/3)} +\tzarcsfrom[draw=none,fill=flagred]<.1,.3>(0,0) + (-\x:-\x-180:1) + (-\x+180:-\x:2) + (-\x:-\x+180:1);<-- cycle> +\tzarcsfrom[draw=none,fill=flagblue](0,0) + (180-\x:-\x:1) + (-\x:-\x-180:2) + (-\x+180:-\x+360:1);<-- cycle> +\end{tikzpicture} +\end{tzcode} + + + +%%------------------------------------------------------------ +\section{Wedges} +\label{s:wedges} + +\subsection{\protect\cmd{\tzwedge(')}} +\label{ss:tzwedge} + +\icmd{\tzwedge} draws a wedge around a specified center coordinate. + +|\tzwedge| works similarly to |\tzarc|, but it forms a closed path from the center coordinate. + +\begin{tzdef}{} +% syntax +\tzwedge[<opt>]<shift coor>"<path name>" + (<coor>)(<angA:angB:radius>){<text>}[<node opt>] +% defaults + []<>""(<m>)(<m>){}[midway] +\end{tzdef} + + +\begin{tztikz}{} +\tzwedge(1,1)(30:120:1) % works like: + \draw (1,1) -- ++(30:1) arc (30:120:1) -- cycle; +\end{tztikz} + +The macro \icmd{\tzwedge'} is the \iisw{swap version} of \icmd{\tzwedge}. +It switches the drawing direction from \ixxw{counterclockwise} to \ixxw{clockwise} and vice versa. + + +\begin{tztikz}{} +\tzwedge'(1,1)(30:120:1) % works like: + \draw (1,1) -- ++(30:1) arc (30:120-360:1) -- cycle; +\end{tztikz} + +\begin{tzcode}{.3} +% \tzwedge, \tzwedge' +\begin{tikzpicture} +\tzcoor*(2,1)(A)(3pt) +\tzhelplines(4,3) +\tzwedge[blue,very thick](A)(30:120:1.5) +\tzarc[->,green] (A)(30:120:1.3) +\tzwedge'[dashed](A)(0:135:1.5){clockwise}[sloped,red] +\tzarc'[->,green](A)(0:135:1.3) +\tzwedge'[fill](A)(-60:240:1) +\end{tikzpicture} +\end{tzcode} + +\begin{tzcode}{.3} +% \tzwedge('): shift +\begin{tikzpicture} +\tzcoor*(2,1)(A) +\tzhelplines(4,3) +\tzwedge[blue,very thick]<.1,.1>(A)(30:120:1.5) % shift +\tzarc[->,lightgray]<.1,.1>(A)(30:120:1.3) % shift +\tzwedge'[dashed](A)(0:135:1.5){clockwise}[sloped,red] +\tzarc'[->,lightgray](A)(0:135:1.3) +\tzwedge'[fill]<2,0>(A)(-60:240:1) % shift +\end{tikzpicture} +\end{tzcode} + + + + + +\subsection{\protect\cmd{\tzwedge*(')}} +\label{ss:tzwedge*} + +The starred version \icmd{\tzwedge*} works just like |\tzwedge|, but it fills wedges with |black!50| with |fill opacity=.3| and |fill opacity=1|, by default. +You can change the defaults with |\settzfillcolor| and |\settzfillopacity|. +You can also change the fill opacity by specifying the last optional argument |{<fill opacity>}|. + +\begin{tzdef}{} +% syntax +\tzwedge*[<opt>]<shift coor>"<path name>" + (<coor>)(<angA:angB:radius>){<text>}[<node opt>]{<fill opacity>} +% defaults + [fill=black!50,fill opacity=.3,text opacity=1]<>""(<m>)(<m>){}[midway]{.3} +\end{tzdef} + +\icmd{\tzwedge*'} is the \iisw{swap version} of |\tzwedge*|. + +\begin{tzcode}{.3} +% \tzwedge*, \tzwedge*' +\begin{tikzpicture}[->,>=stealth] +\tzhelplines(3,3) +\tzwedge[very thick,blue](1,1)(30:120:1.5) +\tzwedge*[-,very thick,blue,fill=red](1,1)(30:120:1) +\tzwedge'[dashed](1,1)(30:120:1.5){clockwise}[pos=.45] +\tzwedge*'[dashed,fill=green](1,1)(-90:180:1) +\tzdot*(1,1) +\end{tikzpicture} +\end{tzcode} + +\begin{tzcode}{.3} +% \tzwedge*('): shift, fill opacity +\begin{tikzpicture} +\tzdot*(1,1) +\tzhelplines(3,3) +\tzwedge[blue,very thick](1,1)(30:120:1.5) +\tzwedge[red,very thick]<.5,.5>(1,1)(30:120:1.5) +\tzwedge'[dashed](1,1)(0:135:1.5) +\tzwedge*[fill=blue](1,1)(300:240:1){B}[b] +\tzwedge*[blue]<2,0>(1,1)(300:240:1){B}[b]{.7} +\end{tikzpicture} +\end{tzcode} + + |