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diff --git a/Master/texmf-dist/doc/generic/pstricks/pst-fill-doc.tex b/Master/texmf-dist/doc/generic/pstricks/pst-fill-doc.tex new file mode 100644 index 00000000000..dbface7370c --- /dev/null +++ b/Master/texmf-dist/doc/generic/pstricks/pst-fill-doc.tex @@ -0,0 +1,1362 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -*- Mode: Latex -*- %%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% doc-fill.tex --- Documentation for `pst-fill PSTricks package +%% +%% Author : Denis GIROU (CNRS/IDRIS - France) <Denis.Girou@idris.fr> +%% Created the : Wed Oct 29 18:39:29 1997 +%% Last mod. by : Herbert Voss <voss _at_ pstricks.de> +%% Last mod. the : Aug 17 2004 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +% If there is not `ctandir' installed (from `ltugboat' package) +\begin{filecontents}{ctandir.sty} +%% LaTeX2e file `ctandir.sty' +%% generated by the `filecontents' environment +%% from source `ltubguid' on 1997/06/12. +%% +% +% Experimental CTAN location information macros for use with Donald +% Arseneau's |url.sty| +% +% we need url.sty; we can rely on it to demand anything it needs of +% LaTeX +\IfFileExists{url.sty}% + {\RequirePackage{url}}% + {\PackageWarning{ctandir}{You should acquire a copy of url.sty}% + \newcommand\urldef[3]{\def#1{\texttt{#3}}}% + \let\url\texttt + } +% +\newcommand\CTANdirectory[1]{\expandafter\urldef + \csname CTAN@#1\endcsname\path} +\newcommand\CTANfile[1]{\expandafter\urldef + \csname CTAN@#1\endcsname\path} +% +% Use the standard label-referencing mechanism to get the warning for +% an undefined label +\newcommand\CTANref[1]{\expandafter\@setref\csname CTAN@#1\endcsname + \relax{#1}} +\end{filecontents} + +\documentclass{article} +\usepackage[T1]{fontenc} +\usepackage{geometry} +\usepackage[hang]{caption} % Improved captions +\usepackage{ctandir} % For CTAN references +\usepackage{fancyvrb} % Fancy verbatims +\usepackage{graphicx} % `graphicx' LaTeX standard package +\usepackage{mflogo} % For the MetaFont and MetaPost logos +\input{random.tex} % Random macros from Donald Arseneau +\usepackage{url} % URLs convenient typesetting +\usepackage{multido} % General loop macro +\usepackage{pstricks} % PSTricks with the `color' extension +\usepackage{pst-char} % PSTricks package for character path +\usepackage[tiling]{pst-fill} % PSTricks package for filling/tiling +\usepackage{pst-grad} % PSTricks package for gradient filling +\usepackage{pst-node} % PSTricks package for nodes + +% To extend the height used for the text +%\setlength{\textheight}{25cm} +%\setlength{\topmargin}{-1.5cm} + +% Aligned labels in a description environment +\newenvironment{Description}[1]{% +\begin{list}{nothing}{\setlength{\leftmargin}{#1} +\setlength{\labelwidth}{\leftmargin}\setlength{\labelsep}{1mm}}} +{\end{list}} + +% For macro names +\DeclareRobustCommand\cs[1]{\texttt{\char`\\#1}} + +% Define CTAN addresses using the commands of the |ctandir| package +\CTANdirectory{mpattern}{graphics/metapost/macros/mpattern} +\CTANdirectory{pstricks}{graphics/pstricks} +\CTANdirectory{pst-fill.sty}{graphics/pstricks/latex/pst-fill.sty} +\CTANdirectory{pst-fill}{graphics/pstricks/generic/pst-fill.tex} +\CTANdirectory{Roegel}{graphics/metapost/contrib/macros/truchet} +\CTANdirectory{xypic}{macros/generic/diagrams/xypic} + +% From ltugboat.cls +% For references +\makeatletter +\newcommand\acro[1]{\textsc{#1}\@} +\def\CTAN{\acro{CTAN}} +\let\texttub\textsl % redefined in other situations +\def\TUB{\texttub{TUGboat}} +\def\TUG{\TeX\ \UG} +\def\tug{\acro{TUG}} +\def\UG{Users Group} +% For the bibliography +\let\@internalcite\cite +\def\cite{\def\@citeseppen{-1000}% + \def\@cite##1##2{(##1\if@tempswa , ##2\fi)}% + \def\citeauthoryear##1##2##3{##1, ##3}\@internalcite} +\def\etal{et\,al.\@} +\makeatother + +% Personal macros (D.G.) +% ---------------------- + +% Some colors used +\definecolor{LemonChiffon}{rgb}{1.,0.98,0.8} +\definecolor{LightBlue} {rgb}{0.8,0.85,0.95} +\definecolor{PaleGreen} {rgb}{0.88,1,0.88} +\definecolor{PeachPuff} {rgb}{1.0,0.85,0.73} + +% To define a unique string for TeX and LaTeX +\newcommand{\AllTeX}{% +{\rm(L\kern-.36em\raise.3ex\hbox{\sc a}\kern-.15em)% +T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}} + +% Bibliography style +\bibliographystyle{ltugbib} + +% Name macros +\newcommand{\FillPackage}{\textsf{`pst-fill'}} +\newcommand{\XYpic}{% +\leavevmode\hbox{\kern-.1em X\kern-.3em\lower.4ex\hbox{Y\kern-.15em}-pic}} + +\makeatletter + +% Example environments +% (do not use in them the four JXYZ characters, that we will use +% as escape characters!) + +% For highlighting some verbatim sequences (array names, macro names and comments) +\def\HLComment#1{\textit{#1}} +\def\HLEmph#1{\textit{#1}} +\def\HLTeletype#1{\texttt{#1}} +\def\HLReverse#1{{% +\setlength{\fboxsep}{1pt}% +\colorbox{black}{\textcolor{white}{\textbf{#1}}}}} + +\def\Example{\FV@Environment{}{Example}} +\def\endExample{% +\end{VerbatimOut} +\Below@Example{\input{\jobname.tmp}} +\endgroup} + +\def\CenterExample{\FV@Environment{}{Example}} +\def\endCenterExample{% +\end{VerbatimOut}% +\begin{center} +\Below@Example{\input{\jobname.tmp}} +\end{center} +\endgroup} + +\def\SideBySideExample{\FV@Environment{}{Example}} +\def\endSideBySideExample{% +\end{VerbatimOut}% +\SideBySide@Example{\input{\jobname.tmp}} +\endgroup} + +\def\FVB@Example{% +\begingroup +\FV@UseKeyValues +\parindent=0pt +\multiply\topsep by 2 +\VerbatimEnvironment +\begin{VerbatimOut}[codes={\catcode`\Z=12}]{\jobname.tmp}} + +\def\Below@Example#1{% +\VerbatimInput[gobble=0,commentchar=Z,commandchars=JXY,numbersep=3pt, + frame=single,numbers=left]% + {\jobname.tmp} +\catcode`\Z=9\relax% +% We suppress the effect of the highlighting macros +\catcode`\J=0\relax% +\catcode`\X=1\relax% +\catcode`\Y=2\relax% +\def\HLComment##1{##1}% +\def\HLEmph##1{##1}% +\def\HLTeletype##1{##1}% +\def\HLReverse##1{##1}% +#1\par} + +\def\SideBySide@Example#1{% +\@tempdimb=\FV@XRightMargin +\advance\@tempdimb -5mm +\begin{minipage}[c]{\@tempdimb} + \fvset{xrightmargin=0pt} + \catcode`\Z=9\relax% + % We suppress the effect of the highlighting macros + \catcode`\J=0\relax% + \catcode`\X=1\relax% + \catcode`\Y=2\relax% + \def\HLComment##1{##1}% + \def\HLEmph##1{##1}% + \def\HLTeletype##1{##1}% + \def\HLReverse##1{##1}% + #1 +\end{minipage}% +\@tempdimb=\textwidth +\advance\@tempdimb -\FV@XRightMargin +\advance\@tempdimb 5mm +\begin{minipage}[c]{\@tempdimb} + \VerbatimInput[gobble=0,commentchar=Z,commandchars=JXY, + numbersep=3pt,frame=single,numbers=left, + xleftmargin=5mm,xrightmargin=0pt]{\jobname.tmp} +\end{minipage}} + +\makeatother + +% Example environments are numbered, framed and indented by 2 spaces +\fvset{gobble=2,frame=single,fontfamily=tt,numbers=left,numbersep=3pt} + +% Default PSTricks parameters +\psset{dimen=middle} + +% Translation in PSTricks from the one drawn by Emmanuel Chailloux and +% Guy Cousineau for the MLgraph system +% (see /ftp.ens.fr:/pub/unix/lang/MLgraph/version-2.1/MLgraph-refman.ps.gz) +% The kangaroo itself is reproduce from an original picture from Raoul Raba +\newcommand{\DimX}{2.47} +\newcommand{\DimY}{4.8} +\newcommand{\DimXDivTwo}{1.235} + +\newcommand{\KangarooItself}[1]{% +% Body +\pspolygon[fillstyle=solid,fillcolor=#1]% + (52.5,68)(55,72.5)(55.8,76.5)(56.8,79.8)(58.2,83)(60,85.8)(61.5,86.5) + (64,87)(66,87.5)(67.8,87.3)(70,87)(71.5,87.3)(73,88)(74.7,88.5) + (76,90.3)(77,91.5)(72.8,93.8)(69,96)(64.5,99)(59.4,103)(56.2,106.3) + (53,110.5)(49.5,115.5)(47.2,119.9)(45.7,126)(43.2,123)(41.5,121)(37.5,125) + (37,122.5)(36.8,120)(37,117)(37.6,113.5)(38.6,110)(40,106.3)(42,102.3) + (43.5,99.5)(45,97)(46.2,94)(46.8,91.7)(47.2,88)(47,83.5)(46.3,80.8) + (45.3,78.5)(42.5,76.5)(39.5,75.8)(36,75.9)(33,75.9)(29,76.2)(26,77) + (22.3,77.5)(18,78.4)(12.8,79.3)(8.6,80)(5.5,80.3)(3,80.5)(0,80) + (-5.2,78.5)(-9,76.3)(-11.2,74.8)(-13,72.5)(-16.5,68)(-16.5,68)(-19.5,62.5) + (-22,58)(-25.5,53)(-29,48.5)(-32.5,45)(-36,42)(-39,39.5)(-44,37) + (-49,35)(-51,34)(-53.5,34.5)(-55.5,36)(-56.5,38)(-56.5,40.5)(-55,41.5) + (-53.5,41)(-51.5,41)(-50.5,43)(-50.5,44.5)(-51,47)(-51.5,47.2)(-56.5,47) + (-58.5,46.5)(-60,44.7)(-62,42.3)(-63,39.5)(-63.5,36.3)(-63.5,33)(-63.1,29.5) + (-61.5,26)(-58,23.6)(-54,22.2)(-50.7,22)(-47.5,22)(-44.5,22.3)(-41,23.5) + (-36.8,25.8)(-33,28)(-28.5,31)(-23.4,35)(-20.2,38.3)(-17,42.5)(-13.5,47.5) + (-11.2,51.9)(-9.7,58)(-7.2,55)(-5.5,53)(-1.5,57)(-1,54.5)(-0.8,52) + (-1,49)(-1.6,45.5)(-2.6,42)(-4,38.3)(-6,34.3)(-7.5,31.5)(-9,29) + (-10.2,26)(-10.8,23.7)(-11.2,20)(-11,15.5)(-10.3,12.8)(-9.3,10.5)(-6.5,8.5) + (-3.5,7.8)(0,7.9)(3,7.9)(7,8.2)(10,9)(13.7,9.5)(18,10.4) + (23.2,11.3)(27.4,12)(30.5,12.3)(33,12.5)(36,12)(41.2,10.5)(45,8.3) + (47.2,6.8)(49,4.5)(52.5,0)(50,4.5)(49.2,8.5)(48.2,11.8)(46.8,15) + (45,17.8)(43.5,18.5)(41,19)(39,19.5)(37.2,19.3)(35,19)(33.5,19.3) + (32,20)(30.3,20.5)(29,22.3)(28,23.5)(28,23.5)(24.5,22.3)(21.5,22) + (18.3,22)(15,22.2)(11,23.6)(7.5,26)(5.9,29.5)(5.5,33)(5.5,36.3) + (6,39.5)(7,42.3)(9,44.7)(10.5,46.5)(12.5,47)(17.5,47.2)(18,47) + (18.5,44.5)(18.5,43)(17.5,41)(15.5,41)(14,41.5)(12.5,40.5)(12.5,38) + (13.5,36)(15.5,34.5)(18,34)(20,35)(25,37)(30,39.5)(33,42) + (36.5,45)(40,48.5)(43.5,53)(47,58)(49.5,62.5)(52.5,68) +% Eye +\pscircle*[linecolor=white](58.2,98.3){2\psxunit} +\pscircle*(58.2,97.3){\psxunit} +% Mouth +\psline(71.5,88)(70,89.3)(68.5,90.3)(67,91.9) +% Tear +\psline(42,121)(45,118)(47,115.3)(48.5,112.7)(50,110)(51.8,106.5) + (52.5,103.7)(53,100.5) +\pspolygon(41.2,115.8)(43.2,114.7)(45,112.5)(47,109.8)(48,107)(49.5,104.2) + (50.5,101.6)(51,98.5)(47.7,100.6)(46,102.2)(44.8,104)(43.5,106) + (42.5,108)(41.7,110.5)(41,113.2) +} + +\newcommand{\Kangaroo}[1]{% +\begin{pspicture}(\DimX,\DimY) +\psset{unit=0.035278} +\KangarooItself{#1} +\end{pspicture}} + +\newcommand{\KangarooPstChart}[1]{{% +\psset{xunit=0.006784,yunit=0.00735,linewidth=0.01} +\begin{pspicture}(-65.5,0)(82,126) +\KangarooItself{#1} +\end{pspicture}}} + +\begin{document} + +\title{\FillPackage\\A PSTricks package for filling and tiling areas} +\author{Timothy van \textsc{Zandt}\thanks{INSEAD, +Economics and Political Science, Fontainebleau, France --- +\mbox{\texttt{<tvz@econ.insead.fr>}}.}\hspace{2mm}{\small (documentation by +Denis \textsc{Girou}\thanks{CNRS/IDRIS --- Centre National de la Recherche +Scientifique / Institut du D\'eveloppement et des Ressources en Informatique +Scientifique, Orsay , France --- \mbox{\texttt{<Denis.Girou@idris.fr>}}.}% +\hspace{1.5mm})}} + +\date{\shortstack{December 12, 1997 --- Version 97 patch 2\\ + {\small Documentation revised June 30, 2000}}} +\maketitle + +\begin{center} +\psframebox[framearc=0.3,framesep=5mm,linewidth=0.7mm]{% + \parbox{11cm}{% + {\Large\textbf{Abstract}}: + \FillPackage{} is a PSTricks \cite{vanZandt93}, \cite{Girou94}, + \cite{vanZandtGirou94}, \cite{Hoenig97}, \cite{LGC97} package to draw easily + various kinds of filling and tiling of areas. It is also a good example of + the great power and flexibility of PSTricks, as in fact it is a very short + program (it body is around 200~lines long) but nevertheless really powerful. + + \hspace{5mm} It was written in 1994 by Timothy \textsc{van Zandt} but + publicly available only in PSTricks 97 and without any documentation. + We describe here the version \emph{97 patch 2} of December 12, 1997, which + is the original one modified by myself to manage \emph{tilings} in the + so-called \emph{automatic} mode. This article would like to serve both of + reference manual and of user's guide. + + \hspace{5mm} This package is available on \CTAN{} in the + \texttt{graphics/pstricks} directory (files \texttt{latex/pst-fill.sty} and + \texttt{generic/pst-fill.tex}). +}} +\end{center} + +\section{Introduction} + + Here we will refer as \emph{filling} as the operation which consist to fill +a defined area by a pattern (or a composition of patterns). We will refer as +\emph{tiling} as the operation which consist to do the same thing, but with +the control of the starting point, which is here the upper left corner. +The pattern is positioned relatively to this point. This make an essential +difference between the two modes, as without control of the starting point we +can't draw \emph{tilings} (sometimes called \emph{tesselations}) as used in +many fields of Art and Science% +\footnote{For an extensive presentation of tilings, in their history and usage +in many fields, see the reference book \cite{GS87}. + + In the \TeX{} world, few work was done on tilings. You can look at the +\emph{tile} extension of the \XYpic{} package \cite{XYpic}, at the articles of +Kees \textsc{van der Laan} \cite[paragraph 7]{LAAN96} (the tiling was in +fact directly done in PostScript) and \cite{LAAN97}, at the \MP{} program +(available on \CTANref{Roegel}) by Denis \textsc{Roegel} for the +\textsc{Truchet} contest in 1995 \cite{EsperetGirou98} and at the \MP{} +package \cite{Bolek98} to draw patterns, which have a strong connection with +tilings.}. + + Nevertheless, as tilings are a wide and difficult field in mathematics, this +package is limited to simple ones, mainly \emph{monohedral} tilings with one +prototile (which can be composite, see section \ref{sec:KindTiles}). With some +experience and wiliness we can do more and obtained easily rather +sophisticated results, but obviously hyperbolic tilings like the famous +\textsc{Escher} ones or aperiodic tilings like the \textsc{Penrose} ones are +not in the capabilities of this package. For more complex needs, we must used +low level and more painfull technics, with the basic \cs{multido} +and \cs{multirput} macros. + +\section{Package history and description of it two different modes} + + As already said, this package was written in 1994 by Timothy \textsc{van +Zandt}. Two modes were defined, called respectively \emph{manual} and +\emph{automatic}. For both, the pattern is generated on contiguous positions in +a rather large area which include the region to fill, later cut to the +required dimensions by clipping mechanism. In the first mode, the pattern is +explicitely inserted in the PostScript file each time. In the second one, the +result is the same but with an unique explicit insertion of the pattern and a +repetition done by PostScript. Nevertheless, in this method, the control of +the starting point was loosed, so it allowed only to \emph{fill} a region and +not to \emph{tile} it. + + See the difference between the two modes, \emph{tiling}: +{\psset{unit=0.5} + \psboxfill{\begin{pspicture}(1,1)\psframe[dimen=middle](1,1)\end{pspicture}} + \begin{pspicture}(3,3.3) + \psframe[fillstyle=boxfill](3,3) + \end{pspicture} +} +and \emph{filling}: +{% + \makeatletter +\pst@def{BoxFill}<% + gsave + gsave \tx@STV CM grestore dtransform CM idtransform + abs /h ED abs /w ED + pathbbox + h div round 2 add cvi /y2 ED + w div round 2 add cvi /x2 ED + h div round 2 sub cvi /y1 ED + w div round 2 sub cvi /x1 ED + /y2 y2 y1 sub def + /x2 x2 x1 sub def + CP + y1 h mul sub neg /y1 ED + x1 w mul sub neg /x1 ED + clip + y2 { + /x x1 def + x2 { + save CP x y1 T moveto Box restore + /x x w add def + } repeat + /y1 y1 h add def + } repeat + currentpoint currentfont grestore setfont moveto> + \makeatother +% + \psset{unit=0.5} + \psboxfill{\begin{pspicture}(1,1)\psframe[dimen=middle](1,1)\end{pspicture}} + \begin{pspicture}(3,3.3) + \psframe[fillstyle=boxfill](3,3) + \end{pspicture} + or + \begin{pspicture}(3,3.3) + \psframe[fillstyle=boxfill](3,3) + \end{pspicture} +} +as we can see that initial position is arbitrary and dependent of +the current point. + + It's clear that usage of filling is very restrictive comparing to tiling, +as desired effects required very often the possibility to control the starting +point. So, this mode was of limited interest, but unfortunately the +\emph{manual} one has the very big disadvantage to require very huge amounts +of ressources, mainly in disk space and consequently in printing time. +A small tiling can require sometimes several megabytes in \emph{manual} mode! +So, it was very often not really usable in practice. + +It is why I modified the code, to allow tilings in \emph{automatic} mode, +controlling in this mode too the starting point. And most of the time, that is +to say if some special options are not used, the tiling is done exactly in the +region described, which make it faster. So there is no more reason to use the +\emph{manual} mode, apart very special cases where \emph{automatic} one cannot +work, as explained later -- currently, I know only one case. + + To load this modified \emph{automatic} mode, with \LaTeX{} use +simply:\newline +\verb+\usepackage[tiling]{pst-fill}+\newline +and in plain \TeX{} after:\newline +\verb+\input{pst-fill}+\newline +add the following definition:\newline +\verb+\def\PstTiling{true}+ + + To obtain the original behaviour, just don't use the \emph{tiling} optional +keyword at loading. + + Take care than in \emph{tiling} mode, I introduce also some other changes. +First I define aliases on some parameter names for consistancy (all specific +parameters will begin by the \texttt{fill} prefix in this case) and I change +some default values, which were not well adapted for tilings (\texttt{fillsep} +is set to 0 and as explained \texttt{fillsize} set to \texttt{auto}). I rename +\texttt{fillcycle} to \texttt{fillcyclex}. I also restore normal way so that +the frame of the area is drawn and all line (\texttt{linestyle}, +\texttt{linecolor}, \texttt{doubleline}, etc.) parameters are now active (but +there are not in non \emph{tiling} mode). And I also introduce new parameters +to control the tilings (see below). + + \textbf{In all the following examples, we will consider only the +\emph{tiling} mode.} + +{\fvset{commandchars=JXY} + To do a tiling, we have just to define the pattern with the +\Verb+JHLReverseX\psboxfillY+ macro and to use the new \texttt{fillstyle} +\Verb+JHLReverseXboxfillY+. + + Note that tilings are drawn from left to right and top to bottom, which can +have an importance in some circonstances. + + PostScript programmers can be also interested to know that, even in the +\emph{automatic} mode, the iterations of the pattern are managed directly by +the PostScript code of the package which used only PostScript Level 1 +operators. The special ones introduced in Level 2 for drawing of patterns +\cite[section 4.9]{PostScript95} are not used. + + And first, for conveniance, we define a simple \cs{Tiling} macro, which +will simplify our examples: + +\begin{Verbatim} + \newcommand{\Tiling}[JHLEmphX2Y][]{% + \edef\Temp{JHLEmphX#1Y}% + \begin{pspicture}JHLEmphX#2Y + \ifx\Temp\empty + \psframe[fillstyle=JHLEmphXboxfillY]JHLEmphX#2Y + \else + \psframe[fillstyle=JHLEmphXboxfillY,JHLEmphX#1Y]JHLEmphX#2Y + \fi + \end{pspicture}} +\end{Verbatim} +} + +\newcommand{\Tiling}[2][]{% + \edef\Temp{#1}% + \begin{pspicture}#2 + \ifx\Temp\empty + \psframe[fillstyle=boxfill]#2 + \else + \psframe[fillstyle=boxfill,#1]#2 + \fi + \end{pspicture}} + +\subsection{Parameters} + + There are \textbf{14} specific parameters available to change the way the +filling/tiling is defined, and one debugging option. + +\begin{Description}{2cm} + \item [\HLTeletype{fillangle} (real)\hfill :] the value of the rotation + applied to the patterns (\emph{Default:~0}). +\end{Description} + + In this case, we must force the tiling area to be notably larger than the +area to cover, to be sure that the defined area will be covered after rotation. + +\begin{CenterExample} + \newcommand{\Square}{% + \begin{pspicture}(1,1) + \psframe[dimen=middle](1,1) + \end{pspicture}} + + \psset{unit=0.5} + \psboxfill{\Square} + \Tiling[JHLEmphXfillangleY=JHLReverseX45Y]{(3,3)}\hspace{3cm} + \Tiling[JHLEmphXfillangleY=JHLReverseX-60Y]{(3,3)} +\end{CenterExample} + +\newcommand{\Square}{% +\begin{pspicture}(1,1)\psframe[dimen=middle](1,1)\end{pspicture}} + +\begin{Description}{2cm} + \setcounter{footnote}{1} + \item [\HLTeletype{fillsepx} (real$|$dim)\hfill :] value of the horizontal + separation between consecutive patterns (\emph{Default:~0 for + tilings\footnotemark, 2pt otherwise}). \footnotetext{This option was added + by me, is not part of the original package and is available only if the + \texttt{tiling} keyword is used when loading the package.} + \setcounter{footnote}{1} + \item [\HLTeletype{fillsepy} (real$|$dim)\hfill :] value of the vertical + separation between consecutive patterns (\emph{Default:~0 for + ti\-lings\footnotemark, 2pt otherwise}). + \setcounter{footnote}{1} + \item [\HLTeletype{fillsep} (real$|$dim)\hfill :] value of horizontal and + vertical separations between consecutive patterns (\emph{Default:~0 for + tilings\footnotemark, 2pt otherwise}). +\end{Description} + + These values can be negative, which allow the tiles to overlap. + +\fvset{xrightmargin=0cm} +\begin{CenterExample} + \psset{unit=0.5} + \psboxfill{\Square} + \Tiling[JHLEmphXfillsepxY=JHLReverseX2mmY]{(3,3)}\hfill + \Tiling[JHLEmphXfillsepyY=JHLReverseX1mmY]{(3,3)}\hfill + \Tiling[JHLEmphXfillsepY=JHLReverseX0.5Y]{(3,3)}\hfill + \Tiling[JHLEmphXfillsepY=JHLReverseX-0.5Y]{(3,3)} +\end{CenterExample} + +\begin{Description}{2cm} + \item [\HLTeletype{fillcyclex}\footnotemark\ (integer)\hfill :] Shift + coefficient applied to each row (\emph{Default:~0}). + \footnotetext{It was \texttt{fillcycle} in the original version.} + \setcounter{footnote}{1} + \item [\HLTeletype{fillcycley}\footnotemark\ (integer)\hfill :] Same thing for + columns (\emph{Default:~0}). + \setcounter{footnote}{1} + \item [\HLTeletype{fillcycle}\footnotemark\ (integer)\hfill :] Allow to fix + both \texttt{fillcyclex} and \texttt{fillcycley} directly to the same value + (\emph{Default:~0}). +\end{Description} + + For instance, if \texttt{fillcyclex} is 2, the second row of patterns will +be horizontally shifted by a factor of $\frac{1}{2}=0.5$, and by a factor of +0.333 if \texttt{fillcyclex} is 3, etc.). These values can be negative. + +\begin{CenterExample} + \psset{unit=0.5} + \psboxfill{\Square} + \newcommand{\TilingA}[1]{\Tiling[JHLEmphXfillcyclexY=JHLReverseX#1Y]{(3,3)}} + + \TilingA{JHLReverseX0Y}\hfill\TilingA{JHLReverseX1Y}\hfill\TilingA{JHLReverseX2Y}\hfill\TilingA{JHLReverseX3Y} + + \vspace{3mm} + \TilingA{JHLReverseX4Y}\hfill\TilingA{JHLReverseX5Y}\hfill\TilingA{JHLReverseX6Y}\hfill\TilingA{JHLReverseX-3Y} + + \vspace{3mm} + \Tiling[JHLEmphXfillcycleyY=JHLReverseX2Y]{(3,3)}\hfill + \Tiling[JHLEmphXfillcycleyY=JHLReverseX3Y]{(3,3)}\hfill + \Tiling[JHLEmphXfillcycleyY=JHLReverseX-3Y]{(3,3)}\hfill + \Tiling[JHLEmphXfillcycleY=JHLReverseX2Y]{(3,3)}\hfill +\end{CenterExample} + +\begin{Description}{2cm} + \setcounter{footnote}{1} + \item [\HLTeletype{fillmovex}\footnotemark\ (real$|$dim)\hfill :] value of the + horizontal moves between consecutive patterns (\emph{Default:~0}). + \setcounter{footnote}{1} + \item [\HLTeletype{fillmovey}\footnotemark\ (real$|$dim)\hfill :] value of the + vertical moves between consecutive patterns (\emph{Default:~0}). + \setcounter{footnote}{1} + \item [\HLTeletype{fillmove}\footnotemark\ (real$|$dim)\hfill :] value of + horizontal and vertical moves between consecutive patterns + (\emph{Default:~0}). +\end{Description} + + These parameters allow the patterns to overlap and to draw some special +kinds of tilings. They are implemented only for the \emph{automatic} and +\emph{tiling} modes and their values can be negative. + + In some cases, the effect of these parameters will be the same that with the +\texttt{fillcycle?} ones, but you can see that it is not true for some other +values. + +\begin{CenterExample} + \psset{unit=0.5} + \psboxfill{\Square} + \Tiling[JHLEmphXfillmovexY=JHLReverseX0.5Y]{(3,3)}\hfill + \Tiling[JHLEmphXfillmoveyY=JHLReverseX0.5Y]{(3,3)}\hfill + \Tiling[JHLEmphXfillmoveY=JHLReverseX0.5Y]{(3,3)}\hfill + \Tiling[JHLEmphXfillmoveY=JHLReverseX-0.5Y]{(3,3)} +\end{CenterExample} + +\begin{Description}{2cm} + \item [\HLTeletype{fillsize} + (auto$|$\{(real$|$dim,real$|$dim)(real$|$dim,real$|$dim)\}) :] The + choice of \emph{automatic} mode or the size of the area in \emph{manual} + mode. If first pair values are not given, (0,0) is used. (\emph{Default: + auto when \emph{tiling} mode is used, {(-15cm,-15cm)(15cm,15cm)} + otherwise}). +\end{Description} + + As explained in the introduction, the \emph{manual} mode can require very +huge amount of computer ressources. So, it usage is to discourage in front off +the \emph{automatic} mode. It seems only useful in special circonstances, in +fact when the \emph{automatic} mode failed, which is known only in one case, +for some kinds of EPS files, as the ones produce by dump of portions of +screens (see \ref{sec:GraphicFiles}). + +\begin{Description}{2cm} + \setcounter{footnote}{1} + \item [\HLTeletype{fillloopaddx}\footnotemark\ (integer)\hfill :] number of + times the pattern is added on left and right positions (\emph{Default:~0}). + \setcounter{footnote}{1} + \item [\HLTeletype{fillloopaddy}\footnotemark\ (integer)\hfill :] number of + times the pattern is added on top and bottom positions (\emph{Default:~0}). + \setcounter{footnote}{1} + \item [\HLTeletype{fillloopadd}\footnotemark\ (integer)\hfill :] number of + times the pattern is added on left, right, top and bottom positions + (\emph{Default:~0}). +\end{Description} + + These parameters are only useful in special circonstances, as for complex +patterns when the size of the rectangular box used to tile the area doesn't +correspond to the pattern itself (see an example in Figure~\ref{fig:Sheeps}) +and also sometimes when the size of the pattern is not a divisor of the size +of the area to fill and that the number of loop repeats is not properly +computed, which can occur. + + They are implemented only for the \emph{tiling} mode. + +\begin{Description}{2cm} + \setcounter{footnote}{1} + \item [\HLTeletype{PstDebug}\footnotemark\ (integer, 0 or 1)\hfill :] to + require to see the exact tiling done, without clipping (\emph{Default:~0}). +\end{Description} + + It's mainly useful for debugging or to understand better how the tilings +are done. It is implemented only for the \emph{tiling} mode. + +\begin{CenterExample} + \psset{unit=0.3,JHLEmphXPstDebugY=JHLReverseX1Y} + \psboxfill{\Square} + \psset{linewidth=1mm} + \vspace{0.8cm} + \Tiling{(2,2)}\hspace{3cm} + \Tiling[fillcyclex=JHLEmphX2Y]{(2,2)}\hspace{4cm} + \Tiling[fillmove=JHLEmphX0.5Y]{(2,2)} +\end{CenterExample} + +\vspace{1cm} +\section{Examples} + + In fact this unique \cs{psboxfill} macro allow a lot a variations and +different usages. We will try here to demonstrate this. + +\subsection{Kind of tiles} +\label{sec:KindTiles} + + Of course, we can access to all the power of PSTricks macros to define the +\emph{tiles} (\emph{patterns}) used. So, we can define complicated ones. + + Here we give four other Archimedian tilings (those built with only some +regular polygons) among the twelve existing, first discovered completely by +Johanes \textsc{Kepler} at the beginning of 17th century \cite{GS87}, the two +other \emph{regular} ones with the tiling by squares, formed by a unique +regular polygon, and two other formed by two different regular polygons. + +\begin{CenterExample} + \newcommand{\Triangle}{% + \begin{pspicture}(1,1) + \pstriangle[dimen=middle](0.5,0)(1,1) + \end{pspicture}} + \newcommand{\Hexagon}{% + % JHLCommentXsin(60)=0.866Y + \begin{pspicture}(0.866,0.75) + \SpecialCoor + % JHLCommentXHexagonY + \pspolygon[dimen=middle] + (0.5;30)(0.5;90)(0.5;150)(0.5;210)(0.5;270)(0.5;330) + \end{pspicture}} + + \psset{unit=0.5} + \psboxfill{JHLReverseX\TriangleY} + \Tiling{(4,4)}\hfill + % JHLCommentXThe two other regular tilingsY + \Tiling[fillcyclex=JHLEmphX2Y]{(4,4)}\hfill + \psboxfill{JHLReverseX\HexagonY} + \Tiling[fillcyclex=JHLEmphX2Y,fillloopaddy=JHLEmphX1Y]{(5,5)} +\end{CenterExample} + +\begin{CenterExample} + \newcommand{\ArchimedianA}{% + % JHLCommentXArchimedian tiling 3^2.4.3.4Y + \psset{dimen=middle} + % JHLCommentXsin(60)=0.866Y + \begin{pspicture}(1.866,1.866) + \psframe(1,1) + \psline(1,0)(1.866,0.5)(1,1)(0.5,1.866)(0,1)(-0.866,0.5) + \psline(0,0)(0.5,-0.866) + \end{pspicture}} + \newcommand{\ArchimedianB}{% + % JHLCommentXArchimedian tiling 4.8^2Y + \psset{dimen=middle,unit=1.5} + % JHLCommentXsin(22.5)=0.3827 ; cos(22.5)=0.9239Y + \begin{pspicture}(1.3066,0.6533) + \SpecialCoor + % JHLCommentXOctogonY + \pspolygon(0.5;22.5)(0.5;67.5)(0.5;112.5)(0.5;157.5) + (0.5;202.5)(0.5;247.5)(0.5;292.5)(0.5;337.5) + \end{pspicture}} + + \psset{unit=0.5} + \psboxfill{JHLReverseX\ArchimedianAY} + \Tiling[fillmove=JHLEmphX0.5Y]{(7,7)}\hfill + \psboxfill{JHLReverseX\ArchimedianBY} + \Tiling[fillcyclex=JHLEmphX2Y,fillloopaddy=JHLEmphX1Y]{(7,7)} +\end{CenterExample} + + \setcounter{footnote}{3} + We can of course tile an area arbitrarily defined. And with the +\texttt{addfillstyle} parameter\footnote{Introduced in PSTricks 97.}, we can +easily mix the \texttt{boxfill} style with another one. + +\begin{CenterExample} + \psset{unit=0.5,dimen=middle} + \psboxfill{% + \begin{pspicture}(1,1) + \psframe(1,1) + \pscircle(0.5,0.5){0.25} + \end{pspicture}} + \begin{pspicture}(4,6) + \pspolygon[fillstyle=JHLEmphXboxfillY,fillsep=JHLEmphX0.25Y] + (0,1)(1,4)(4,6)(4,0)(2,1) + \end{pspicture} + \hspace{2cm} + \begin{pspicture}(4,4) + \pscircle[linestyle=none,fillstyle=solid,fillcolor=yellow, + JHLReverseXaddfillstyleY=JHLEmphXboxfillY,fillsep=JHLEmphX0.5Y](2,2){2} + \end{pspicture} +\end{CenterExample} + + Various effects can be obtained, sometimes complicated ones very easily, as +in this example reproduced from one shown by Slavik \textsc{Jablan} in the +field of \emph{OpTiles}, inspired by the \emph{Op-art}: + +\begin{CenterExample} + \newcommand{\ProtoTile}{% + \begin{pspicture}(1,1) + % JHLCommentX1/12=0.08333Y + \psset{linestyle=none,linewidth=0, + hatchwidth=0.08333\psunit,hatchsep=0.08333\psunit} + \psframe[fillstyle=solid,fillcolor=black, + addfillstyle=hlines,hatchcolor=white](1,1) + \pswedge[fillstyle=solid,fillcolor=white, + addfillstyle=hlines]{1}{0}{90} + \end{pspicture}} + + \newcommand{\BasicTile}{% + \begin{pspicture}(2,1) + \rput[lb](0,0){\ProtoTile} + \rput[lb](1,0){\rotateleft{\ProtoTile}} + \end{pspicture}} + + \ProtoTile\hfill\BasicTile\hfill + \psboxfill{\BasicTile} + \Tiling[fillcyclex=JHLEmphX2Y]{(4,4)} +\end{CenterExample} + + It is also directly possible to surimpose several different tilings. Here is +the splendid visual proof of the \textsc{Pytha\-gore} theorem done by the arab +mathematician \textsc{Annairizi} around the year 900, given by superposition +of two tilings by squares of different sizes. + +\fvset{xrightmargin=0cm} +\begin{CenterExample} + \psset{unit=1.5,dimen=middle} + \begin{pspicture*}(3,3) + \psboxfill{\begin{pspicture}(1,1) + \psframe(1,1) + \end{pspicture}} + \psframe[fillstyle=boxfill](3,3) + \psboxfill{\begin{pspicture}(1,1) + \rput{-37}{\psframe[linecolor=red](0.8,0.8)} + \end{pspicture}} + \psframe[fillstyle=boxfill](3,4) + \pspolygon[fillstyle=hlines,hatchangle=90](1,2)(1.64,1.53)(2,2) + \end{pspicture*} +\end{CenterExample} + + In a same way, it is possible to build tilings based on figurative patterns, +in the style of the famous \textsc{Escher} ones. Following an example of +Andr\'e \textsc{Deledicq} \cite{Deledicq97}, we first show a simple tiling of +the \emph{p1} category (according to the international classification of the +17~symmetry groups of the plane first discovered by the russian +crystalographer Jevgraf \textsc{Fedorov} at the end of the 19th century): + +\begin{CenterExample} + \newcommand{\SheepHead}[1]{% + \begin{pspicture}(3,1.5) + \pscustom[liftpen=2,fillstyle=solid,fillcolor=#1]{% + \pscurve(0.5,-0.2)(0.6,0.5)(0.2,1.3)(0,1.5)(0,1.5) + (0.4,1.3)(0.8,1.5)(2.2,1.9)(3,1.5)(3,1.5)(3.2,1.3) + (3.6,0.5)(3.4,-0.3)(3,0)(2.2,0.4)(0.5,-0.2)} + \pscircle*(2.65,1.25){0.12\psunit} % JHLCommentXEyeY + \psccurve*(3.5,0.3)(3.35,0.45)(3.5,0.6)(3.6,0.4)% JHLCommentXMuzzleY + % JHLCommentXMouthY + \pscurve(3,0.35)(3.3,0.1)(3.6,0.05) + % JHLCommentXEarY + \pscurve(2.3,1.3)(2.1,1.5)(2.15,1.7) + \pscurve(2.1,1.7)(2.35,1.6)(2.45,1.4) + \end{pspicture}} + + \psboxfill{\psset{unit=0.5}\SheepHead{yellow}\SheepHead{cyan}} + \Tiling[fillcyclex=JHLEmphX2Y,fillloopadd=JHLEmphX1Y]{(10,5)} +\end{CenterExample} +\label{fig:Sheeps} + + Now a tiling of the \emph{pg} category (the code for the kangaroo itself is +too long to be shown here, but has no difficulties ; the kangaroo is reproduce +from an original picture from Raoul \textsc{Raba} and here is a translation in +PSTricks from the one drawn by Emmanuel \textsc{Chailloux} and Guy +\textsc{Cousineau} for their MLgraph system \cite{MLgraphTSI}): + +\begin{CenterExample} + \psboxfill{% + \psset{unit=0.4} + \Kangaroo{yellow}\Kangaroo{red}% + \Kangaroo{cyan}\Kangaroo{green}% + \psscalebox{-1 1}{% + \rput(1.235,4.8){% + \Kangaroo{green}\Kangaroo{cyan}% + \Kangaroo{red}\Kangaroo{yellow}}}} + \Tiling[fillloopadd=JHLEmphX1Y]{(10,6)} +\end{CenterExample} + + And here a \textsc{Wang} tiling \cite{Wang65}, \cite[chapter +11]{GS87}, based on very simple tiles of the form of a square and composed +of four colored triangles. Such tilings are built with only a matching color +constraint. Despite of it simplicity, it is an important kind of tilings, as +\textsc{Wang} and others used them to study the special class of +\emph{aperiodic} tilings, and also because it was shown that surprisingly this +tiling is similar to a \textsc{Turing} machine. + +\begin{CenterExample} + \newcommand{\WangTile}[4]{% + \begin{pspicture}(1,1) + \pspolygon*[linecolor=#1](0,0)(0,1)(0.5,0.5) + \pspolygon*[linecolor=#2](0,1)(1,1)(0.5,0.5) + \pspolygon*[linecolor=#3](1,1)(1,0)(0.5,0.5) + \pspolygon*[linecolor=#4](1,0)(0,0)(0.5,0.5) + \end{pspicture}} + + \newcommand{\WangTileA}{\WangTile{cyan}{yellow}{cyan}{cyan}} + \newcommand{\WangTileB}{% + \WangTile{yellow}{cyan}{cyan}{red}} + \newcommand{\WangTileC}{% + \WangTile{cyan}{red}{yellow}{yellow}} + + \newcommand{\WangTiles}[1][]{% + \begin{pspicture}(3,3) + \psset{ref=lb} + \rput(0,2){\WangTileB}% + \rput(1,2){\WangTileA}% + \rput(2,2){\WangTileC} + \rput(0,1){\WangTileC}% + \rput(1,1){\WangTileB}% + \rput(2,1){\WangTileA} + \rput(0,0){\WangTileA}% + \rput(1,0){\WangTileC}% + \rput(2,0){\WangTileB} + #1 + \end{pspicture}} + + \WangTileA\hfill\WangTileB\hfill\WangTileC\hfill + \WangTiles[{\psgrid[subgriddiv=0,gridlabels=0](3,3)}]\hfill + \psset{unit=0.4} + \psboxfill{JHLReverseX\WangTilesY} + \Tiling{(12,12)} +\end{CenterExample} + +\subsection{External graphic files} +\label{sec:GraphicFiles} + + We can also fill an arbitrary area with an external image. We have only, +as usual, to matter of the \emph{BoundingBox} definition if there is no one +provided or if it is not the accurate one, as for the well known +\texttt{tiger} picture part of the \texttt{ghostscript} distribution. + +\begin{CenterExample} + \psboxfill{% JHLCommentXStrangely require x1=x2...Y + \begin{pspicture}(0,1)(0,4.1) + \includegraphics[bb=17 176 560 74,width=3cm]{images/JHLReverseXtigerY} + \end{pspicture}} + \Tiling{(6,6.2)} +\end{CenterExample} + + Nevertheless, there are some special files for which the \emph{automatic} +mode doesn't work, specially for some files obtained by a screen dump, as in +the next example, where a picture was reduced before it conversion in the +\emph{Encapsulated PostScript} format by a screen dump utility. In this case, +usage of the \emph{manual} mode is the only alternative, at the price of the +real multiple inclusion of the EPS file. We must take care to specify the +correct \texttt{fillsize} parameter, because otherwise the default values are +large and will load the file many times, perhaps just really using few +occurrences as the other ones would be clipped... + +\begin{CenterExample} + \psboxfill{\includegraphics{images/JHLReverseXflowersY}} + \begin{pspicture}(8,4) + \psellipse[fillstyle=JHLEmphXboxfillY,fillsize={(8,4)}](4,2)(4,2) + \end{pspicture} +\end{CenterExample} + +\subsection{Tiling of characters} + + We can also use the \cs{psboxfill} macro to fill the interior of characters +for special effects like these ones: + +\begin{CenterExample} + \DeclareFixedFont{\bigsf}{T1}{phv}{b}{n}{4.5cm} + \DeclareFixedFont{\smallrm}{T1}{ptm}{m}{n}{3mm} + \psboxfill{\smallrm JHLReverseXSince 182 days...Y} + \begin{pspicture*}(8,4) + \centerline{% + \pscharpath[fillstyle=gradient,gradangle=-45, + gradmidpoint=0.5,addfillstyle=JHLEmphXboxfillY, + fillangle=JHLEmphX45Y,fillsep=JHLEmphX0.7mmY] + {\rput[b](0,0.1){\bigsf JHLReverseX2000Y}}} + \end{pspicture*} +\end{CenterExample} + +\begin{CenterExample} + \DeclareFixedFont{\mediumrm}{T1}{ptm}{m}{n}{2cm} + \psboxfill{% + \psset{unit=0.1,linewidth=0.2pt} + \Kangaroo{PeachPuff}\Kangaroo{PaleGreen}% + \Kangaroo{LightBlue}\Kangaroo{LemonChiffon}% + \psscalebox{-1 1}{% + \rput(1.235,4.8){% + \Kangaroo{LemonChiffon}\Kangaroo{LightBlue}% + \Kangaroo{PaleGreen}\Kangaroo{PeachPuff}}}} + % JHLCommentXA kangaroo of kangaroos...Y + \begin{pspicture}(8,2) + \pscharpath[linestyle=none,fillstyle=JHLEmphXboxfillY,fillloopadd=JHLEmphX1Y] + {\rput[b](4,0){\mediumrm JHLReverseXKangarooY}} + \end{pspicture} +\end{CenterExample} + +\subsection{Other kinds of usage} + + Other kinds of usage can be imagined. For instance, we can use tilings in a +sort of degenerated way to draw some special lines made by a unique or +multiple repeating patterns. But it can be only a special dashed line, as here +with three different dashes: + +\begin{CenterExample} + \newcommand{\Dashes}{% + \psset{dimen=middle} + \begin{pspicture}(0,-0.5\pslinewidth)(1,0.5\pslinewidth) + \rput(0,0){\psline(0.4,0)}% + \rput(0.5,0){\psline(0.2,0)}% + \rput(0.8,0){\psline(0.1,0)} + \end{pspicture}} + + \newcommand{\SpecialDashedLine}[3]{% + \psboxfill{#3} + \Tiling[linestyle=none] + {(#1,-0.5\pslinewidth)(#2,0.5\pslinewidth)}} + + \SpecialDashedLine{0}{7}{\Dashes} + + \psset{unit=0.5,linewidth=1mm,linecolor=red} + \SpecialDashedLine{0}{10}{\Dashes} +\end{CenterExample} + + It allow also to use special patterns in business graphics, as in the +following example generated by \texttt{PstChart}\footnote{A personal +development to draw business charts with PSTricks, not distributed.}. + +\vspace{3mm} +\begin{figure}[!ht] +\centering +\psset{unit=0.75} +% Generated by pstchart.sh version 0.21 (11/28/97) +{\psset{dimen=middle} +\psset{xunit=2,yunit=0.005} +\begin{pspicture}(-0.6,-200)(6.6,2300) + % Title + \rput(3,2200){\shortstack{Fantaisist repartition of kangaroos\\ + in the world (in thousands)}} + % Frame background + \psframe[fillstyle=solid,fillcolor=LemonChiffon](0,0)(6,2000) + % Graduations + \multido{\n=0+500}{5}{\rput[r](-0.12,\n){\psscalebox{0.8}{\n}}} + % Minor ticks + \multips(0,100)(0,100){19}{\psline[unit=4.8pt](1,0)} + \multips(6,100)(0,100){19}{\psline[unit=4.8pt](-1,0)} + % Major ticks + \multips(0,500)(0,500){3}{\psline[unit=9.6pt](1,0)} + \multips(6,500)(0,500){3}{\psline[unit=9.6pt](-1,0)} + % Lines from major ticks marks + \multips(0,500)(0,500){3}{\psline[linestyle=dotted,linewidth=0.6pt](6,0)} + % Drawing for the data + \psboxfill{\psset{unit=0.78\psxunit}\KangarooPstChart{red}} + \psframe[linestyle=none,fillstyle=boxfill,fillloopaddy=1](0.61,0)(1.39,1800) + \psboxfill{\psset{unit=0.78\psxunit}\KangarooPstChart{yellow}} + \psframe[linestyle=none,fillstyle=boxfill,fillloopaddy=1](1.61,0)(2.39,800) + \psboxfill{\psset{unit=0.78\psxunit}\KangarooPstChart{cyan}} + \psframe[linestyle=none,fillstyle=boxfill,fillloopaddy=1](2.61,0)(3.39,550) + \psboxfill{\psset{unit=0.78\psxunit}\KangarooPstChart{magenta}} + \psframe[linestyle=none,fillstyle=boxfill,fillloopaddy=1](3.61,0)(4.39,500) + \psboxfill{\psset{unit=0.78\psxunit}\KangarooPstChart{green}} + \psframe[linestyle=none,fillstyle=boxfill,fillloopaddy=1](4.61,0)(5.39,200) + % Bottom labels + \uput{0.2}[270]{0}(1,0){\psscalebox{0.7}{Oceania}} + \uput{0.2}[270]{0}(2,0){\psscalebox{0.7}{Africa}} + \uput{0.2}[270]{0}(3,0){\psscalebox{0.7}{Asia}} + \uput{0.2}[270]{0}(4,0){\psscalebox{0.7}{America}} + \uput{0.2}[270]{0}(5,0){\psscalebox{0.7}{Europe}} + % Frame box around the chart + \psframe[linestyle=solid](0,0)(6,2000) +\end{pspicture}} + \caption{Bar chart generated by PstChart, with bars filled by patterns} + \label{fig:PstChart} +\end{figure} + +\section{``Dynamic'' tilings} + + In some cases, tilings used non \emph{static} tiles, that is to say that the +\emph{prototile(s)}, even if unique, can have several forms, by instance +specified by different colors or rotations, not fixed before generation or +varying each time. + +\subsection{Lewthwaite-Pickover-Truchet tiling} + + We give here for example the so-called \emph{Truchet} tiling, which much be +in fact better called \emph{Lewthwaite-Pick\-over-Truchet (LPT)} tiling% +\footnote{For description of the context, history and references about +S\'ebastien \textsc{Truchet} and this tiling, see \cite{EsperetGirou98}.}. + + The unique prototile is only a square with two opposite circle arcs. +This tile has obviously two positions, if we rotate it from 90 degrees (see +the two tiles on the next figure). A \emph{LPT tiling} is a tiling with +randomly oriented LPT tiles. We can see that even if it is very simple in it +principle, it draw sophisticated curves with strange properties. + + Nevertheless, in the straightforward way \FillPackage{} does not work, +because the \cs{psboxfill} macro store the content of the tile used in a +\TeX{} box, which is static. So the calling to the random function is done +only one time, which explain that only one rotation of the tile is used for +all the tiling. It's only the one of the two rotations which could differ from +one drawing to the next one... + +% Truchet (Lewthwaite-Pickover-Truchet) tiling +% -------------------------------------------- + +\begin{CenterExample} + % JHLCommentXLPT prototileY + \newcommand{\ProtoTileLPT}{% + \psset{dimen=middle} + \begin{pspicture}(1,1) + \psframe(1,1) + \psarc(0,0){0.5}{0}{90} + \psarc(1,1){0.5}{-180}{-90} + \end{pspicture}} + + % JHLCommentXLPT tileY + \newcount\Boolean + \newcommand{\BasicTileLPT}{% + % JHLCommentXFrom random.tex by Donald ArseneauY + \setrannum{\Boolean}{0}{1}% + \ifnum\Boolean=0 + \ProtoTileLPT% + \else + \rotateleft{\ProtoTileLPT}% + \fi} + + \ProtoTileLPT\hfill\rotateleft{\ProtoTileLPT}\hfill + \psset{unit=0.5} + \psboxfill{JHLReverseX\BasicTileLPTY} + \Tiling{(5,5)} +\end{CenterExample} + + But, for simple cases, there is a solution to this problem using a mixture +of PSTricks and PostScript programming. Here the PSTricks +construction \verb+\pscustom{\code{...}}+ allow to insert PostScript code +inside the \LaTeX{} + PSTricks one. + + Programmation is less straightforward, but it has also the advantage to be +notably faster, as all the tilings operations are done in PostScript, and +mainly to not be limited by \TeX{} memory (the \TeX{} + PSTricks solution +I wrote in 1995 for the colored problem was limited to small sizes for this +reason). Just note also that \cs{pslbrace} and \cs{psrbrace} are two +PSTricks macros to define and be able to insert the \verb+{+ and \verb+}+ +characters. + +\begin{CenterExample} + % JHLCommentXLPT prototileY + \newcommand{\ProtoTileLPT}{% + \psset{dimen=middle} + \psframe(1,1) + \psarc(0,0){0.5}{0}{90} + \psarc(1,1){0.5}{-180}{-90}} + + % JHLCommentXCounter to change the random seedY + \newcount\InitCounter + + % JHLCommentXLPT tileY + \newcommand{\BasicTileLPT}{% + \InitCounter=\the\time + \pscustom{\code{% + rand \the\InitCounter\space sub 2 mod 0 eq \pslbrace}} + \begin{pspicture}(1,1) + \ProtoTileLPT + \end{pspicture}% + \pscustom{\code{\psrbrace \pslbrace}} + \rotateleft{\ProtoTileLPT}% + \pscustom{\code{\psrbrace ifelse}}} + + \psset{unit=0.4,linewidth=0.4pt} + \psboxfill{JHLReverseX\BasicTileLPTY} + \Tiling{(15,15)} +\end{CenterExample} + + Using the very surprising fact (see \cite{EsperetGirou98}) that +coloration of these tiles do not depend of their neighbors (even if it is +difficult to believe as the opposite seems obvious!) but only of the parity of +the value of row and column positions, we can directly program in the same way +a colored version of the LPT tiling. + +\setcounter{footnote}{1} + We have also introduce in the \FillPackage{} code for \emph{tiling} mode two +new accessible Post\-Script variables, \texttt{row} and +\texttt{column}\footnotemark, which can be useful in some circonstances, like +this one. + +\begin{CenterExample} + % JHLCommentXLPT prototileY + \newcommand{\ProtoTileLPT}[2]{% + \psset{dimen=middle,linestyle=none,fillstyle=solid} + \psframe[fillcolor=#1](1,1) + \psset{fillcolor=#2} + \pswedge(0,0){0.5}{0}{90} + \pswedge(1,1){0.5}{-180}{-90}} + + % JHLCommentXCounter to change the random seedY + \newcount\InitCounter + + % JHLCommentXLPT tileY + \newcommand{\BasicTileLPT}[2]{% + \InitCounter=\the\time + \pscustom{\code{% + rand \the\InitCounter\space sub 2 mod 0 eq \pslbrace + JHLReverseXrowY JHLReverseXcolumnY add 2 mod 0 eq \pslbrace}} + \begin{pspicture}(1,1) + \ProtoTileLPT{#1}{#2} + \end{pspicture}% + \pscustom{\code{\psrbrace \pslbrace}} + \ProtoTileLPT{#2}{#1}% + \pscustom{\code{% + \psrbrace ifelse \psrbrace \pslbrace JHLReverseXrowY JHLReverseXcolumnY add 2 mod + 0 eq \pslbrace}} + \rotateleft{\ProtoTileLPT{#2}{#1}}% + \pscustom{\code{\psrbrace \pslbrace}} + \rotateleft{\ProtoTileLPT{#1}{#2}}% + \pscustom{\code{\psrbrace ifelse \psrbrace ifelse}}} + + \psboxfill{JHLReverseX\BasicTileLPT{red}{yellow}Y} + \Tiling{(4,4)}\hfill + \psset{unit=0.4} + \psboxfill{JHLReverseX\BasicTileLPT{blue}{cyan}Y} + \Tiling{(15,15)} +\end{CenterExample} + + Another classic example is to generate coordinates and numerotation for a +grid. Of course, it is possible to do it directly in PSTricks using nested +\cs{multido} commands. It would be clearly easy to program, but, nevertheless, +for users who have a little knowledge of PostScript programming, this offer +an alternative which is useful for large cases, because on this way it will +be notably faster and less computer ressources consuming. + + Remember here that the tiling is drawn from left to right, and top to +bottom, and note that the PostScript variable \texttt{x2} give the total +number of columns. + +\begin{CenterExample} + % JHLCommentX\Escape will be the \ characterY + {\catcode`\!=0\catcode`\\=11!gdef!Escape{\}} + + \newcommand{\ProtoTile}{% + JHLReverseX\SquareY% + \pscustom{% + \moveto(-0.9,0.75) % In PSTricks units + \code{% + /Times-Italic findfont 8 scalefont setfont + (\Escape() show JHLReverseXrowY 3 string cvs show (,) show + JHLReverseXcolumnY 3 string cvs show (\Escape)) show} + \moveto(-0.5,0.25) % In PSTricks units + \code{% + /Times-Bold findfont 18 scalefont setfont + 1 0 0 setrgbcolor % Red color + /center {dup stringwidth pop 2 div neg 0 rmoveto} def + JHLReverseXrowY 1 sub x2 mul JHLReverseXcolumnY add 3 string cvs center show}}} + + \psboxfill{JHLReverseX\ProtoTileY} + \Tiling{(6,4)} +\end{CenterExample} + +\subsection{A complete example: the Poisson equation} + + To finish, we will show a complete real example, a drawing to explain the +method used to solve the \textsc{Poisson} equation by a domain +decomposition method, adapted to distributed memory computers. The +objective is to show the communications required between processes and the +position of the data to exchange. This code also show some useful and powerful +technics for PSTricks programming (look specially at the way some higher level +macros are defined, and how the same object is used to draw the four +neighbors). + +\begin{CenterExample} + \newcommand{\Pattern}[1]{% + \begin{pspicture}(-0.25,-0.25)(0.25,0.25) + \rput{*0}{\psdot[dotstyle=#1]} + \end{pspicture}} + + \newcommand{\West}{\Pattern{o}} + \newcommand{\South}{\Pattern{x}} + \newcommand{\Central}{\Pattern{+}} + \newcommand{\North}{\Pattern{square}} + \newcommand{\East}{\Pattern{triangle}} + + \newcommand{\Cross}{% + \pspolygon[unit=0.5,linewidth=0.2,linecolor=red] + (0,0)(0,1)(1,1)(1,2)(2,2)(2,1) + (3,1)(3,0)(2,0)(2,-1)(1,-1)(1,0)} + + \newcommand{\StylePosition}[1]{% + \LARGE\textcolor{red}{\textbf{#1}}} + + \newcommand{\SubDomain}[4]{% + \psboxfill{#4} + \begin{psclip}{\psframe[linestyle=none]#1} + \psframe[linestyle=#3](5,5) + \psframe[fillstyle=boxfill]#2 + \end{psclip}} + + \newcommand{\SendArea}[1]{% + \psframe[fillstyle=solid,fillcolor=cyan]#1} + + \newcommand{\ReceiveData}[2]{% + \psboxfill{#2} + \psframe[fillstyle=solid,fillcolor=yellow, + addfillstyle=boxfill]#1} + + \newcommand{\Neighbor}[2]{% + \begin{pspicture}(5,5) + \rput{*0}(2.5,2.5){\StylePosition{#1}} + \ReceiveData{(0.5,0)(4.5,0.5)}{\Central} + \SendArea{(0.5,0.5)(4.5,1)} + \SubDomain{(5,2)}{(0.5,0.5)(4.5,3)}{dashed}{#2}% + % JHLCommentXReceive and send arrowsY + \pcarc[arcangle=45,arrows=->](0.5,-1.25)(0.5,0.25) + \pcarc[arcangle=45,arrows=->,linestyle=dotted,dotsep=2pt] + (4.5,0.75)(4.5,-0.75) + \end{pspicture}} + + \psset{dimen=middle,dotscale=2,fillloopadd=JHLEmphX2Y} + \begin{pspicture}(-5.7,-5.7)(5.7,5.7) + % JHLCommentXCentral domainY + \rput(0,0){% + \begin{pspicture}(5,5) + % JHLCommentXReceive from West, East, North and SouthY + \ReceiveData{(0,0.5)(0.5,4.5)}{\West} + \ReceiveData{(4.5,0.5)(5,4.5)}{\East} + \ReceiveData{(0.5,4.5)(4.5,5)}{\North} + \ReceiveData{(0.5,0)(4.5,0.5)}{\South} + % JHLCommentXSend area for West, East, North and SouthY + \SendArea{(0.5,0.5)(1,4.5)} + \SendArea{(4,0.5)(4.5,4.5)} + \SendArea{(0.5,0.5)(4.5,1)} + \SendArea{(0.5,4)(4.5,4.5)} + % JHLCommentXCentral domainY + \SubDomain{(5,5)}{(0.5,0.5)(4.5,4.5)}{solid}{\Central} + % JHLCommentXRedraw overlapped linesY + \psline(1,0.5)(1,4.5) + \psline(4,0.5)(4,4.5) + % JHLCommentXTwo crossesY + \rput(1.5,4){\Cross} + \rput(2,2){\Cross} + \end{pspicture}} + % JHLCommentXThe four neighborsY + \rput(0,5.5){\Neighbor{N}{\North}} + \rput{-90}(5.5,0){\Neighbor{E}{\East}} + \rput{90}(-5.5,0){\Neighbor{W}{\West}} + \rput{180}(0,-5.5){\Neighbor{S}{\South}} + \end{pspicture} +\end{CenterExample} + +% Bibliography +\begin{thebibliography}{99} +\bibitem{PostScript95} Adobe, Systems~Incorporated, \emph{PostScript Language +Reference Manual}, Addison-Wesley, 2~edition, 1995. + +\bibitem{Bolek98} Piotr Bolek, \MP{} and patterns, \emph{\TUB}, Volume~19, +Number~3, pages 276--283, September 1998, \CTANref{mpattern}. + +\bibitem{MLgraphTSI} Emmanuel Chailloux, Guy Cousineau and Asc\'ander +Su\'arez, Programmation fonctionnelle de graphismes pour la production +d'illustrations techniques, \emph{Technique et science informatique}, +Volume~15, Number~7, pages 977--1007, 1996 (in french). + +\bibitem{Deledicq97} Andr\'e Deledicq, \emph{Le monde des pavages}, ACL +\'Editions, 1997 (in french). + +\bibitem{EsperetGirou98} Philippe Esperet and Denis Girou, +Coloriage du pavage dit de Truchet, Cahiers GUTenberg, Number~31, +pages 5--18, December~1998 (in french). + +\bibitem{Girou94} Denis Girou, Pr\'esentation de PSTricks, \emph{Cahiers +GUTenberg}, Number~16, pages 21--70, February~1994 (in french). + +\bibitem{LGC97} Michel Goossens, Sebastian Rahtz and Frank Mittelbach, +\emph{The \LaTeX{} Graphics Companion}, Addison-Wesley, 1997. + +\bibitem{GS87} Branko Gr\"unbaum and Geoffrey Shephard, \emph{Tilings and +Patterns}, Freeman and Company, 1987. + +\bibitem{Hoenig97} Alan Hoenig, \emph{\TeX{} Unbound: \LaTeX{} \& \TeX{} +Strategies, Fonts, Graphics, and More}, Oxford University Press, 1997. + +\bibitem{XYpic} Kristoffer~H. Rose and Ross Moore, \XYpic. Pattern and Tile +extension, available from \CTAN, 1991-1998, \CTANref{xypic}. + +\bibitem{LAAN96} Kees van der Laan, Paradigms: Just a little bit of PostScript, +\emph{MAPS}, Volume~17, pages 137--150, 1996. + +\bibitem{LAAN97} Kees van der Laan, Tiling in PostScript and \MF{} -- Escher's +wink, \emph{MAPS}, Volume~19, Number~2, pages 39--67, 1997. + +\bibitem{vanZandt93} Timothy van Zandt, PSTricks. PostScript macros for +Generic \TeX, available from \CTAN, 1993, \CTANref{pstricks}. + +\bibitem{vanZandtGirou94} Timothy van Zandt and Denis Girou, Inside PSTricks, +\emph{\TUB}, Volume~15, Number~3, pages 239--246, September 1994. + +\bibitem{Wang65} Hao Wang, Games, Logic and Computers, \emph{Scientific +American}, pages 98--106, November 1965. +\end{thebibliography} + +\end{document} |