graphicstikz-pgf
I'd like to create a graphic of a set partitioned into subsets of various sizes/shapes/colors. (I'm trying to show a set partitioned by an equivalence relation into disjoint subsets, i.e., the equivalence classes).
I was hoping to find something on http://www.texample.net to give me an idea of a good method, but I'm having trouble finding any examples. Does anyone have any suggestions?
Update 2012-04-10: There's a preliminary package for this on the TeX-SX Launchpad site. You need to run tex on the file pgflibraryshapes.letters.dtx to produce the TikZ/PGF libraries. To generate the font files themselves, you need x2svg.pe font (uses fontforge) to convert to SVG format and svgtopgf.pl font.svg prefix > <fontname>-<fontshape>-paths.tex to convert the SVG to PDF paths (the prefix should be of the form letter@<fontname>@<fontshape>@). Take a look at letter-shapes-test.tex for a sample. The normal and italic shapes for the STIX fonts are already converted. Due to the licensing, they are called stikz!
Do you want something like this?
Here's the source code:
\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{%
svg.path,
decorations.text,
}
\begin{document}
\begin{tikzpicture}[scale=.3]
\draw[decorate,decoration={text along path,text={AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA}}] svg "M707 0h-255v19c36 0 43 2 55 9c8 4 14 15 14 24c0 15 -7 42 -19 70l-41 94h-262l-46 -114c-5 -13 -9 -30 -9 -42c0 -31 22 -41 70 -41v-19h-199v19c58 6 67 27 126 167l206 488h20l246 -563c28 -65 42 -86 94 -92v-19zM447 257l-116 275l-115 -275h231z";
\draw[xshift=25cm,decorate,decoration={text along path,text={aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa}}] svg "M442 66v-28c-30 -38 -56 -48 -90 -48c-37 0 -59 20 -64 73h-1c-53 -60 -102 -73 -145 -73c-62 0 -105 38 -105 104c0 52 31 91 70 117c30 20 67 39 180 81v54c0 62 -33 90 -78 90c-40 0 -70 -22 -70 -49c0 -18 6 -21 6 -42c0 -19 -20 -41 -46 -41c-21 0 -43 19 -43 46
c0 26 16 58 51 80c28 18 70 30 115 30c56 0 94 -16 118 -45s28 -50 28 -111v-191c0 -46 13 -66 31 -66c16 0 26 5 43 19zM287 127v141c-62 -22 -103 -43 -128 -66c-24 -22 -34 -46 -34 -77c0 -53 30 -77 69 -77c20 0 41 5 58 16c29 20 35 34 35 63z";
\end{tikzpicture}
\end{document}
The method of producing this was fairly straightforward. I loaded the font in fontforge and exported it as an SVG font. That then gave me the fonts as SVG paths. Since TikZ can accept SVG format, I could then cut and paste that in to a TikZ document. That lot could be done beforehand so that there was a file with the paths already specified.
Edit (2012-01-29): I had occasion to want to do this with fairly arbitrary letters so semi-automated it. It's not "production" ready, as there's still the odd bit needed to make it truly usable with no extra tweaking, but it's at the usable-if-you-know-what-you're-doing stage.
Convert the font to SVG. You need fontforge installed. Then the following script, made executable, will invoke fontforge and convert the font specified on the command line to SVG format (output saved in the current directory). Eg if it is saved as x2svg.pe (note the extension) then run as x2svg.pe /path/to/font/amazing-font.otf.
#! /usr/bin/fontforge -script
Open($1)
Generate($1:t:r + ".svg")
Extract the glyph paths from the resulting XML file. The following Perl script does a reasonable job: it should trim excess whitespace at the start and end as well. Also, one could do with a better naming scheme (I tried unicode, but that got confusing).
perl -MXML::Twig -e '
$xml = XML::Twig->new(
twig_handlers => {
glyph => sub { $n = $_->{att}{"glyph-name"}; $n =~ s/_//g; print %% "\\svgletter{" . $n . "}{" . $_->{att}{d} . "}\n";}
}
);
$xml->parsefile("amazing-font.svg");
' > amazing-font.letters.tex
Then in the TeX file, we just need to input this file and use the paths. Here's an example:
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{svg.path}
\newcommand\svgletter[2]{%
\expandafter\def\csname svgglyph#1\endcsname{svg "#2"}
}
\input{TeXGyreSchola-Bold.letters}
\def\STOP{stop}
\def\NOTHING{}
\def\empty{}
\newcommand\outline[1]{%
\outlinelet#1\STOP}
\let\thisis\newpage
\newcommand\vfillornewpage{%
\ifx\thisis\vfill
\let\thisis\newpage
\else
\let\thisis\vfill
\fi
\thisis}
\newcommand\outlinelet[1]{%
\let\next=\vfillornewpage
\ifx#1\STOP
\else
\tikz[baseline=0pt] \draw[scale=0.09,ultra thick] \csname svgglyph#1\endcsname;
\let\next=\outlinelet
\fi
\next}
\begin{document}
\outline{Outline}
\end{document}
With result:
Obviously, one could be more adventurous in the actual use of the path. Also, it would be good to have a more systematic way of getting the right scale factor (perhaps measuring the height of an "x"). Don't expect kerning!
I think you can do more simplifications both code-wise and presentation-wise. Once you start making it visual, in my opinion, you have to go all the way. In other words, they should have strong meaning, even though they don't have strong visual cues. Here as you complain, things are garbled and your row and column rectangles seem like a mistake due to the overlap since they don't have enough strong meaning. Also you don't need to use \ldots,\vdots since you are already using TikZ! I don't know what the G and H maps do but you shouldn't try to squeeze them in an extra row since you have already decided to color up the whole matrix. You shouldn't stop until it makes sense. So my suggestion is (possibly with the need of further tweaking) :
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix,positioning}
\begin{document}
What if the rest of the world was hopelessly drowning in vain? Where would our
self pity run? Suddenly everyone cares and we perform some row/column operations as the
following:
\[
\mathbf{U} = \begin{tikzpicture}[baseline=(U.center)]
\matrix [matrix of math nodes,left delimiter=[,right delimiter={]},nodes={outer sep=1pt}] (U) {
u_{1}^{\left(1\right)} &[1cm] u_{1}^{\left(j\right)} &[1cm] u_{1}^{\left(t\right)} \\[1cm]
u_{k}^{\left(1\right)} & u_{k}^{\left(j\right)} & u_{k}^{\left(t\right)} \\[1cm]
u_{r}^{\left(1\right)} & u_{r}^{\left(j\right)} & u_{r}^{\left(t\right)} \\
};
\foreach \x/\y/\z in {1/1/1,2/k/j,3/q/t}{
\draw[red] ([shift={(1pt,2pt)}]U-1-\x.north west) rectangle ([shift={(-1pt,-2pt)}]U-3-\x.south east);
\draw[blue,dashed] ([shift={(-2pt,-1pt)}]U-\x-1.north west) rectangle ([shift={(2pt,1pt)}]U-\x-3.south east);
\draw[thick,loosely dotted] (U-\x-1) -- (U-\x-2) -- (U-\x-3);
\draw[thick,loosely dotted] (U-1-\x) -- (U-2-\x) -- (U-3-\x);
\node[blue,right = 3 mm of U-\x-3] (U-\x-4) {$\mathbf{H}_{\y\y}$};
\node[red,below= 1 mm of U-3-\x] (U-4-\x) {$\mathbf{G}^{(\z,\z)}$};
};
\draw[thick,loosely dotted] (U-1-1) -- (U-2-2) -- (U-3-3) (U-1-2) -- (U-2-3) (U-2-1) -- (U-3-2);
\draw[thick,loosely dotted,red] (U-4-1) -- (U-4-2) -- (U-4-3);
\draw[thick,loosely dotted,blue] (U-1-4) -- (U-2-4) -- (U-3-4);
\draw[<->, thick, red, bend right=45] (U-4-1) to node[below, pos=0.5,sloped] {$\mathbf{G}^{\left(1, j\right)}$} (U-4-2);
\draw[<->, thick, red, bend right=45] (U-4-2) to node[below, pos=0.5,sloped] {$\mathbf{G}^{\left(j, t\right)}$} (U-4-3);
\draw[<->, thick, blue, bend left=60] (U-1-4) to node[right, pos=0.5] {$\mathbf{H}_{1k}$} (U-2-4);
\draw[<->, thick, blue, bend left=60] (U-2-4) to node[right, pos=0.5] {$\mathbf{H}_{jk}$} (U-3-4);
\end{tikzpicture}
\]
where we used colorful lines in the sand. People in prayer for me,everyone there for me. Sometimes I feel
I should face this alone. My soul exposed. It calms me to know that I won't.
\end{document}
G maps make smiley faces?
Best Answer
Some improvements to add colors are necessary.